The Pennsylvania State UniversityThe Graduate School

College of Engineering

HOIST MOTION CONTROL: HYDRAULIC SOLENOID VALVE CURRENT

REGULATION AND IDENTIFICATION OF MINIMUM CURRENT FOR MOTION

A Thesis inElectrical Engineering

byDaphny Oviya Devadoss

© 2019 Daphny Oviya Devadoss

Submitted in Partial Fulfillmentof the Requirements

for the Degree of

Master of Science

August 2019

The thesis of Daphny Oviya Devadoss was reviewed and approved∗ by the following:

Jeffrey L. SchianoAssociate Professor of Electrical EngineeringThesis Advisor

Minghui ZhuDorothy Quiggle Assistant Professor of Electrical Engineering

Victor PaskoProfessor of Electrical EngineeringGraduate Program Professor in Charge of Electrical Engineering

∗Signatures are on file in the Graduate School.

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AbstractThis thesis addresses two challenges in optimizing the operation of hydraulic systems on a boomcrane. The first challenge is to develop an algorithm for choosing control gains for the proportional-integral controllers that regulate the average current in hydraulic solenoid cartridge valves. Thesecond challenge is to develop an algorithm that determines the minimum average current Imin

through a solenoid cartridge valve that produces motion in a hydraulic actuator. The proposedcontrol algorithm achieves an overdamped response with a rise-time of about a second in responseto a step change in the commanded average current. In addition, the algorithm places the polesso that Imin is reached early during the one second rise-time. The minimum average currentImin required through the solenoid valve for hydraulic motion is affected by the solenoid valveparameters and the hydraulic motor coupling to the load. A binary search algorithm is proposed asit has a maximum complexity of O(log n), for the determination of Imin across different hydraulicmechanisms. The algorithms for determining control gains and Imin are validated using hardware-in-the-loop simulation and on a Grove Rough Terrain crane at the Manitowoc Product Verificationcentre located in Shady Grove, Pennsylvania. As the cranes are operated across various geographicallocations with temperatures ranging from -40 deg F to 120 deg F, the effect of the temperaturevariation on the solenoid parameters and on the controller design is also studied.

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Table of Contents

List of Figures vi

List of Tables viii

Acknowledgments ix

Chapter 1Challenges in Crane Control 11.1 Basic Mechanisms of a Grove Rough Terrain Crane . . . . . . . . . . . . . . . . 11.2 Hydraulic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Solenoid Cartridge Valve . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Operation of the Hydraulic System . . . . . . . . . . . . . . . . . . . . . 7

1.3 Current Regulation in Solenoid Cartridge Valves . . . . . . . . . . . . . . . . . . 111.4 Embedded Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5 Determination of Minimum Current for Crane Motion . . . . . . . . . . . . . . . 121.6 Approach and Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . 12

Chapter 2Solenoid Cartridge Valve Model 142.1 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Averaging State-Space Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Small-Signal Linearized Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.4 Model Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Chapter 3Controller Design and Verification 283.1 Controller Design Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Closed-Loop Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3 Calculation of Controller Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4 Controller Design Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4.1 Simulation and experimental verification . . . . . . . . . . . . . . . . . . 36

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3.4.2 Crane Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.5 Temperature Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Chapter 4Determination of Minimum Current for Hydraulic Motion 454.1 Search Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2 Algorithm Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Chapter 5Conclusions and Future Work 52

Appendix AGraphical User Interface 54A.1 Send PCAN Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55A.2 Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57A.3 Calculate Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59A.4 Controller Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60A.5 Imin Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Appendix BHIL and MATLAB Simulation 63B.1 HIL Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63B.2 MATLAB Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Bibliography 68

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List of Figures

1.1 Hydraulic mechanisms of a GRT crane . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Hydraulic schematic symbol for a 3-way, 2-position, single-acting, electro-proportional,pressure reducing-relieving valve . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Photograph (top) and body diagram (bottom) of solenoid cartridge valve . . . . . 6

1.4 Pressure versus current graph of solenoid cartridge valve . . . . . . . . . . . . . 6

1.5 Basic hydraulic components (A) lines, (B) reservoir, (C) pump, and (D) motor . . 7

1.6 Hydraulic schematic of a directional control valve . . . . . . . . . . . . . . . . . 7

1.7 Schematic diagram of the hydraulic system [1] . . . . . . . . . . . . . . . . . . 10

2.1 Solenoid cartridge valve model . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Electrical circuit schematic of a solenoid cartridge valve . . . . . . . . . . . . . . 16

2.3 Waveform of the control voltage vc(t) applied to the FET . . . . . . . . . . . . . 17

2.4 Simplified circuit model for the interval 0 ≤ t ≤ DT s . . . . . . . . . . . . . . . 19

2.5 Simplified circuit model for the interval DT s ≤ t ≤ T s . . . . . . . . . . . . . . 20

2.6 Plot of average current from simulations and experimental test setup . . . . . . . 27

3.1 General block diagram of the closed-loop system . . . . . . . . . . . . . . . . . 28

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3.2 Simplified block diagram of the closed-loop system . . . . . . . . . . . . . . . . 30

3.3 Controller validation through simulations and experimental test setup . . . . . . . 37

3.4 Graphical user interface for controller validation . . . . . . . . . . . . . . . . . . 38

3.5 Controller validation on hoist mechanism of a GRT crane . . . . . . . . . . . . . 39

3.6 Controller validation on boom mechanism of a GRT crane . . . . . . . . . . . . 40

3.7 Effect of temperature on closed-loop response from experiments . . . . . . . . . 42

3.8 Effect of temperature on closed-loop response from HIL simulation . . . . . . . . 43

4.1 User interface for determination of minimum average current . . . . . . . . . . . 49

A.1 PCAN Control GUI - Send PCAN Data . . . . . . . . . . . . . . . . . . . . . . 56

A.2 PCAN Control GUI - Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

A.3 PCAN Control GUI - Calculate Resistance . . . . . . . . . . . . . . . . . . . . . 59

A.4 PCAN Control GUI - Controller Tuning . . . . . . . . . . . . . . . . . . . . . . 60

A.5 PCAN Control GUI - Imin calculation . . . . . . . . . . . . . . . . . . . . . . . 62

B.1 HIL simulation - plant and controller loop . . . . . . . . . . . . . . . . . . . . . 64

B.2 HIL simulation - hoist dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 64

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List of Tables

2.1 Solenoid valve electrical circuit parameter description . . . . . . . . . . . . . . . 16

2.2 Sensitivity of linearized plant model . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1 Effect of temperature on rise-time from HIL simulation and experiments . . . . . 44

4.1 Binary search algorithm parameter description . . . . . . . . . . . . . . . . . . . 47

4.2 Outline of the binary search algorithm for determining Imin . . . . . . . . . . . . 48

4.3 Minimum average current for hoist up mechanism on a GRT crane . . . . . . . . 49

4.4 Minimum average current for hoist down mechanism on a GRT crane . . . . . . 50

4.5 Minimum average current for boom up mechanism on a GRT crane . . . . . . . . 50

4.6 Minimum average current for boom down mechanism on a GRT crane . . . . . . 51

A.1 PDO data format for hoist mechanism . . . . . . . . . . . . . . . . . . . . . . . 54

A.2 PDO data format for boom mechanism . . . . . . . . . . . . . . . . . . . . . . . 55

A.3 An example PDO format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

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Acknowledgments

My words are not enough to describe how much it means to be a part of Penn State. My deepestgratitude to my research advisor Dr. Jeffrey L. Schiano, for the tremendous encouragement andsupport. He has been an inspiration to me. My sincere thanks to the team at Manitowoc Cranes,Shady Grove, Pennsylvania for their extended support during the entire time of research.

I am extremely grateful for my mom Delight Mary Soosai, for the unconditional love andsupport, without whom none of this would be possible. She is my best critic and yet my strongestsupporter. I thank my aunt Josephine Selvi Soosai, for giving me the courage to pursue my dreamand for believing in me, which made all the difference. I am appreciative of my family for wishingme well and for always being there for me. I also thank my friends for the unforgettable momentsand for making the hardships easier.

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A tribute to my mom, Delight Mary Soosai, who has sacrificed so much of her life for me!

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Chapter 1 |Challenges in Crane Control

Manitowoc Cranes, a division of The Manitowoc Company, Inc has five product lines of cranes,Grove Mobile Telescoping Cranes, Manitowoc Lattice Boom Crawler Cranes, National Crane BoomTrucks, Potain Tower Cranes and Shuttlelift Carrydeck Cranes, each serving different applications.The facility of Manitowoc Cranes located at Shady Grove, PA is collaborating with Penn State todevelop feedback algorithms for improving the performance of Grove Mobile Telescoping Cranes.These cranes range in capacity from 8 t to 450 t, comprising all terrain, rough terrain, truck mountedand industrial cranes. In particular, this thesis considers the following two challenges on GroveRough Terrain cranes. The first challenge is to regulate the average current through solenoidcartridge valve in the hydraulic system, which is described in detail in Section 1.3. The secondchallenge is to determine the minimum average current required through the solenoid cartridgevalve for motion in the hydraulic systems, as described in Section 1.5.

1.1 Basic Mechanisms of a Grove Rough Terrain Crane

The Grove Rough Terrain (GRT) crane is a hydraulic crane, which is a heavy-duty equipment tolift and move heavy loads. Unlike smaller cranes, which rely on electric or diesel-powered motors,a hydraulic crane includes internal hydraulic systems that allow the crane to lift heavier loads.The Grove Rough Terrain crane consists of five hydraulic mechanisms that include the main hoist,auxiliary hoist, telescope, lift and swing. The description of the hydraulic mechanisms and thecomponents of Grove Rough Terrain crane is provided in order to facilitate the understanding of thebasic mechanisms and the significance of addressing the challenges. The picture of a Grove Rough

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Terrain crane, GRT8100 with the five hydraulic mechanisms marked is shown in Figure 1.1.

Figure 1.1. Hydraulic mechanisms of a GRT crane

1. Main Hoist - The primary hoist mechanism provided for lifting and lowering the rated loadof the crane. The hoist mechanism operates by means of a drum or lift-wheel around which arope wraps and couple to loads using a lifting hook. The hook is suspended from the hoistrope through sheaves, to connect the load to the crane. Sheaves are pulley assemblies witha grooved wheel inside of a frame. They allow the wire rope (or cable) to move freely andminimize abrasion when the rope is redirected or used to lift loads.

2. Auxiliary Hoist - The supplemental hoist mechanism provided in addition to the main hoist,

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which is usually of lighter capacity (lower load rating) and higher speed than provided for themain hoist.

3. Telescope - The telescoping mechanism provides the extension and retraction of the boom.The boom is essentially the arm of the crane that supports hoist mechanism to lift and lowerheavy materials. The telescopic boom consists of two or more symmetrically shaped, tubulartelescopic sections fitted one inside the other. The boom base section is the largest segmentwhile the boom tip is the smallest. The telescoping mechanism extends or retracts thesetubular sections in order to increase or decrease the total length of the boom.

4. Lift - The boom hoist mechanism which raises and lowers the boom in order to change theboom angle - the angle between the base section of the boom and the horizontal plane.

5. Swing - The swing mechanism provides a full rotation of the superstructure over the carrier.The superstructure is the revolving frame of equipment on which the operating machineryis mounted along with the operator cab. The operator cab houses the various controlsused to drive the crane such as steering and as well as the controls used to operate theboom. The carrier is the under carriage of crane designed for transporting the rotating cranesuperstructure.

1.2 Hydraulic System

The basis of a hydraulic system of the crane is the transmission of forces from one point to anotherthrough a fluid. The principle of operation is based on Pascal’s law, which states that a pressurechange occurring anywhere in a confined incompressible fluid (a fluid whose density does notchange when the pressure changes) is transmitted throughout the fluid such that the same changeoccurs everywhere with no loss. The pressure acts with equal force on all equal areas of theconfining walls and perpendicular to the walls. Typically, oil is used as the incompressible fluid. Ahydraulic drive system, in general, consists of three parts: (1) the generator (e.g. a hydraulic pump)to provide the hydraulic flow needed to transmit power; (2) valves, filters and piping to guide andcontrol the system; (3) the actuator (e.g. a hydraulic motor) to drive the machinery. The hydraulicfluid drawn from reservoir is deposited back into the reservoir in an open loop system, whereas it isdeposited directly back to the hydraulic pump through a hydraulic filter in a closed-loop system.

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The five hydraulic systems of interest to this thesis are responsible for actuating motion onthe main hoist, auxiliary hoist, telescope, lift and swing systems. Common to each of these fivehydraulic systems are solenoid cartridge valves that allow an electric signal to actuate crane motion.In general, each hydraulic system use two solenoid cartridge valves that individually commandmotion in opposing directions. For example, in the hoist system, one solenoid cartridge valve isactuated to raise the load, while the other is actuated to lower the load. In general, only one ofthe two solenoid cartridge valves associated with a given hydraulic system is actuated at a given time.

1.2.1 Solenoid Cartridge Valve

The solenoid cartridge valve is an electromechanical device, which consists of a movable ferromag-netic core (plunger/poppet) placed co-axially inside a hollow cylindrical metallic tube containingan electromagnetic coil (solenoid). It is a 3-way, 2-position, single-acting, electro-proportional,

pressure reducing-relieving valve. The term 3-way describes that the valve has three connectionports - two inputs (Port T - Tank and Port P - Pump) and one output (Port A - Actuator). The term2-position describes that the valve has two operating states - normally closed when the valve is notenergized and normally open when the valve is completely energized. It is a single acting valvewith solenoid actuated in one direction and spring return to the default position when not actuated.The term electro-proportional means that the actuator output of the valve is proportional to theelectrical energization of the solenoid coil. It is a pressure reducing-relieving valve which reduces ahigh primary pressure at the input port P to a proportional reduced pressure at the output port A,with a full-flow relief function from the output port A to input port T.

Figure 1.2 shows the symbol used for a 3-way, 2-position, single-acting, electro-proportional,pressure reducing-relieving valve in a hydraulic schematic. The two rectangular boxes in Figure1.2 indicate the extreme valve positions. The leftmost box indicates the position, maintained bythe spring (a), when the average current is zero. In this position, the input port (P) is not connectedto the output port (A). The parallel lines (b) and symbol (c) indicate a proportional valve that iscontrolled by a solenoid. When the applied current reaches the maximum value, the position of thevalve is shown by the rightmost box in Figure 1.2, where the line (d) shows that the input port (P)is directly connected to the output port (A). Symbol (e) indicates a pressure reducing-relieving valve.

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A

P T(a)

(b)

(b)

(c)(d)

(e)

(e)

Figure 1.2. Hydraulic schematic symbol for a 3-way, 2-position, single-acting, electro-proportional, pressurereducing-relieving valve

Under normal operating conditions, a spring holds the plunger in position in such a way that thevalve is normally closed. This means that the inlet port (P) is completely sealed and there is no flowto the outlet port (A). When the solenoid is electrically energized, the current flowing through thecoil generates a magnetic field, creating a difference in magnetic potential across the air gap betweenthe plunger and the solenoid enclosure. As the current through the coil increases, the strength ofgenerated magnetic field increases, which in turn increases the force exerted by the armature on theplunger. The plunger starts moving when the force exerted is strong enough to move it against thespring force. The path between the inlet port (P) and the outlet port (A) is opened, establishing fluidflow. The photograph and body diagram of the solenoid cartridge valve is shown in Figure 1.3.

The valve is constructed in such a way that the fluid flow at the outlet port (A) is proportional tothe movement of the plunger. The electromagnetic force exerted on the plunger directly relates to theelectric current flowing through the solenoid coil. The armature of the solenoid and the plunger aredesigned to produce a more linear force and displacement characteristic. Thus, the control pressureat the outlet is proportional to the average current flowing through the solenoid coil. Increasing theaverage current through the solenoid coil will increase the control (reduced) pressure proportionally.The proportional nature of the output characteristic of the solenoid cartridge valve is shown inFigure 1.4. The x-axis represents the current flowing through the solenoid coil and the y-axisrepresents the pressure output of the valve. The two lines Max Pressure and Min Pressure shows theproportional variation of pressure output with respect to the current flowing through the solenoid coil.

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Figure 1.3. Photograph (top) and body diagram (bottom) of solenoid cartridge valve

Current (A)

Pre

ssure

(bar

)

Max Pressure Min Pressure

Figure 1.4. Pressure versus current graph of solenoid cartridge valve

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1.2.2 Operation of the Hydraulic System

Before discussing the operation of one of the five hydraulic systems, it is first necessary to introducethe elementary hydraulic symbols in 1.5. Paths for hydraulic flow are indicated by solid lines formain flow lines, and dashed lines for pilot and drain lines, as indicated in Figure 1.5(A).

PumpReservoir Hydraulic MotorPilot/Drain Line

Main Flow Line

Figure 1.5. Basic hydraulic components (A) lines, (B) reservoir, (C) pump, and (D) motor

Figures 1.5 (B),(C) and (D) show the symbols for the hydraulic fluid reservoir, pump andhydraulic motor respectively. Unlike the hydraulic pump which has a single outward pointing arrowindicating fluid flow direction, the hydraulic motor has two inward pointing arrows, indicating thatthe direction of fluid flow through the motor determines the direction of the output shaft rotation. Ahydraulic motor is typically driven by a directional control valve whose symbol appears in Figure 1.6.

A B

T P

(b)(a)

(c) (d)(e)

(e)

Figure 1.6. Hydraulic schematic of a directional control valve

This example valve has four ports indicated by A, B, P and T. The A and B ports connect acrossthe hydraulic motor, while the input port (P) connects to the hydraulic pump and the port T is thereturn to the reservoir. The valve has three extreme positions, indicated by the three rectangular

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boxes. The valve position is controlled by two hydraulic control lines (a) and (b). When there is noflow on either control line (a) and (b), the springs (c) and (d) hold the valve in the position indicatedby the middle rectangular box, where output ports A and B are connected to the tank port (T) and ina float neutral condition. The parallel lines (e) indicate that the hydraulic flow at the output port Aand B is proportional to the control flow (a) and (b) respectively. When there is a flow on controlline (a), the valve takes the leftmost rectangular position, where input line (a) connects port P to Aand Port T to B. The hydraulic fluid flowing out of A is proportional to flow (a). Similarly, whenthere is a flow on control line (b), the rightmost rectangular box shows that the port P is connectedto B, while port T is connected to A. In this case, hydraulic fluid flows out of B at a rate proportionalto flow (b).

The simplified schematic diagram of one of the five hydraulic system is shown in Figure 1.7.The hydraulic circuit consists of a reservoir, a hydraulic pump, two solenoid cartridge valves, adirectional control valve and a hydraulic motor. The reservoir stores non-pressurized hydraulicfluid, typically hydraulic oil in a convenient location for the pump inlet. The reservoir also holdsexcess fluid needed when the hydraulic system is in operation. In addition, it provides for heat dissi-pation (cooling the hydraulic fluid) and fluid conditioning (dissipation of contaminants and aeration).

The hydraulic pump converts mechanical energy into hydraulic energy and produces the flownecessary for the development of pressure which is a function of resistance to fluid flow in thesystem. When a hydraulic pump operates, it performs two functions. The first function is to createvacuum at the pump inlet which allows atmospheric pressure to force liquid from the reservoir intothe inlet line to the pump. The second function is to deliver this liquid to the pump outlet and forceit into the hydraulic system. A variable displacement pump is used in this case and it delivers thehydraulic flow as and when required by the system. The displacement, or amount of fluid pumpedper revolution of the pump input shaft can be varied while the pump is running. The output ofa variable displacement pump can be changed by altering the geometry of the displacement chamber.

The two electro-proportional solenoid valves control the proportional, hydraulic operated direc-tional control valve, which in turn operates the hydraulic motor. The hydraulic motor is bidirectionaland converts hydraulic pressure and flow into torque and angular displacement (rotation). Thedirectional control valve has a float neutral, in which the pressure port is blocked and both the outletsare connected to the tank. When the valve is in neutral position, the motor will be at standstill. The

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fluid pressure at the outlet port of the solenoid valve is proportional to the current flowing throughthe solenoid coil. The directional control valve that drives the hydraulic motor is also proportionalin nature. As a result, the speed of the hydraulic motor is proportional to the output pressure at thedirectional valve, which in turn is proportional to the output pressure at the solenoid valve. Hence,the speed of the hydraulic motor is controlled by the current flowing through the solenoid valve.This emphasizes the importance of current regulation in the solenoid valve.

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Pump

Motor

Reservoir

A

P T

A

PT

A

PT

Tank

Pump

A

B

Figure 1.7. Schematic diagram of the hydraulic system [1]

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1.3 Current Regulation in Solenoid Cartridge Valves

In the hydraulic system, as mentioned in Section 1.2, the speed of the hydraulic motor variesproportionally with the electric current flowing through the solenoid cartridge valve. As detailed inSection 2.3, with no current regulation, the rise-time (the time required for a signal to rise from 10percent to 90 percent of its steady value) of the average current through the solenoid valve is abouta hundredth of a second. It means that the hydraulic motor goes to full speed quickly, dependingon the hydraulic and mechanical time constant of the system. The rapid speed change is highlyundesirable, especially when lifting heavy loads, as it could cause the entire superstructure to fail.This necessitates the regulation of average current through the solenoid valve in order to achieve amuch slower rise-time of about a second. A proportional-integral controller design is carried outwith the specified rise-time being the design specification. The controller gains depend largely onthe solenoid electrical parameters, namely the solenoid coil resistance and inductance.

The cranes are operated across various geographical locations with temperatures ranging from-40 deg F to 120 deg F. The effect of the change in temperature on the solenoid electrical parameters,namely the solenoid coil resistance and inductance is studied. As the controller design is based onthese solenoid electrical parameters, the gains can be re-tuned for the change in these parameters.For the change in solenoid coil resistance and inductance, and without changing the controllerdesign, the effect of temperature on rise-time is investigated.

1.4 Embedded Control System

The electrical system of the crane consists of multiple Manitowoc crane control modules (MWCCM)to control the operation of crane functions and realize the user interface for the crane operator. Thisthesis is concerned with a single MWCCM that realizes a feedback control system for regulating theaverage current through solenoid cartridge valves. The MWCCM provides digital input/output ports,analog inputs and pulse width modulated (PWM) output channels that can directly drive solenoidcartridge valves. The MWCCM also uses a controller area network (CAN) to communicate withother modules, sensors and displays. The CANopen protocol is used for communication on theCAN bus.

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1.5 Determination of Minimum Current for Crane Motion

The hydraulic motor that controls the hoist and boom mechanisms require a minimum startingtorque to turn the load, which depends on the pressure input. As mentioned in Section 1.2, thispressure is controlled by the directional control valve, which in turn is controlled by the solenoidvalve. Thus, to have a minimum required pressure at the hydraulic motor input, there should be aminimum value of current flowing through the solenoid valve. This current is called as the minimumaverage current for crane motion. Presently, the value of the minimum average current required formotion is determined by a crane operator/technician manually. The operator physically moves thejoystick until they could see any motion and records the value of current at which the motion started.The procedure has to be repeated for the hydraulic mechanisms such as hoist up, hoist down, boomup and boom down. This method is time-consuming, inaccurate and imprecise. A binary searchalgorithm is proposed to determine the minimum average current required through the solenoidcartridge valve for motion in the hydraulic system. The algorithm is verified by determining theminimum average current required for motion on the hydraulic mechanisms such as hoist up, hoistdown, boom up and boom down.

1.6 Approach and Thesis Organization

The MWCCM module discussed in Section 1.4 along with several solenoid cartridge valves andCAN interface is available at the Magnetic Resonance and Applied Control laboratory, Penn Statefor test and validation purposes. Since it is impractical to perform all the necessary tests on theactual crane while developing the system model and control algorithm, a more efficient methodfor testing the embedded control systems called hardware-in-the-loop (HIL) simulation is used.Also, by thoroughly testing the embedded control device in a virtual environment before proceedingto real-world tests on a crane, we can maintain safety and reliability in a cost-effective manner.LabVIEW, a data-flow, graphical programming environment from National Instruments is used for(1) the development of simulation models and deployment to real-time hardware HIL simulatorand (2) the development of graphical user interface (GUI) to carry out the essential validationand collection of data. The GUI runs on a personal computer/laptop and communicates with theMWCCM module/HIL simulator through a CAN bus. The GUI and the HIL simulator are detailedin Appendix A and Appendix B respectively. There are three software programs - GUI, MWCCMC code and HIL simulator.

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In Chapter 2, the mathematical model of the solenoid cartridge valve is described and the elec-trical model is considered. The electrical circuit schematic of the solenoid valve and the regulationof average current of the solenoid valve through pulse-width modulation (PWM) by MWCCMmodule is discussed. The electrical system model is obtained by applying the averaging state-spaceapproach [2], which results in a nonlinear system model. The model is then linearized about aquiescent operating point using perturbation technique and a small signal model is derived. Thederived electrical model is simulated in MATLAB and HIL. The results are compared with theactual current waveform obtained from the test setup described in Section 2.1.

Chapter 3 describes the controller design requirements and the development of proportional -integral controller to meet those requirements. The proportional-integral controller applied with thesystem model derived in Chapter 2, results in a second order system. The controller design detailsthe calculation of controller gains by using the two time constants of the system, the slow timeconstant to achieve the desired rise-time and the fast time constant to reach the minimum averagecurrent through the solenoid valve for crane motion. The closed-loop system model is simulated inMATLAB and HIL. The controller design is further validated on a GRT crane at the ManitowocProduct Verification Center in Shady Grove, Pennsylvania and the results are discussed. The effectof temperature on the controlled system response and the solenoid electrical parameters, namelyresistance and inductance of the solenoid coil is also studied.

In Chapter 4, the requirement of the minimum average current through the solenoid valve forcrane motion is discussed. It also details the binary search algorithm developed for the determinationof minimum average current through the solenoid valve for motion. The algorithm is validated withHIL and on a GRT crane for the hydraulic mechanisms such as hoist up, hoist down, boom up andboom down and the results are discussed.

In Chapter 5, the contributions of this thesis are summarized. It also includes a discussion onrecommended future work.

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Chapter 2 |Solenoid Cartridge Valve Model

The mathematical model of a solenoid cartridge valve can be divided into two subsystems, theelectromagnetic and mechanical subsystems [3, 4], as shown in Figure 2.1. The input signal isa voltage applied to the electromagnetic subsystem, which causes the flow of electric current inthe solenoid coil and in turn produces an electromagnetic force. The force generated then causesa linear movement of the plunger in the mechanical subsystem. The model is derived based onthe assumption that the valve is working in the linear region of the magnetization curve given byB = µ0H , where B is the magnetic flux density, µ0 is the permeability of free space and H isthe magnetic field intensity. It is also assumed that the flux leakage, eddy current losses and thephenomenon of hysteresis are considered to be negligibly small.

Electromagnetic

Subsystem

Mechanical

Subsystem

ForceApplied

Voltage

Plunger

Position

Figure 2.1. Solenoid cartridge valve model

The electrical part of the electromagnetic subsystem is represented as a series combination ofinductance and resistance, associated with the solenoid coil. According to Kirchhoff's voltage law

14

(KVL), the voltage, vsol(t), applied across the solenoid coil is equal to the algebraic sum of thevoltages across the resistance and inductance of the solenoid coil, which is represented by Equation2.1.

vsol(t) = Rsol i(t) +dψ

dt, (2.1)

where Rsol is the resistance of the solenoid coil, i(t) is the current flowing through the coil, and ψ isthe magnetic flux linkage.

According to classical electromagnetic theory, the magnetic flux linkage ψ is related to theinductance of the solenoid coil Lsol and the current through the coil i as,

ψ = Lsol i(t). (2.2)

Substituting Equation 2.2 in Equation 2.1 and simplifying yields

vsol(t) = Rsol i(t) + Lsoldi

dt+ i(t)

dLsol

dt. (2.3)

The third term in Equation 2.3 accounts for the fact that the solenoid inductance depends on themechanical position of the plunger. For simplicity, this term is neglected as it has a small effect onthe average current. This assumption is later justified by comparing the simulation and experimentalmeasurement of average current. And hence, Equation 2.3 is approximated as

vsol(t) = Rsol i(t) + Lsoldi

dt, (2.4)

where Lsol is a constant.

2.1 Network Model

The average current flowing through the solenoid cartridge valve is regulated through pulse-widthmodulation (PWM) by the crane control module (MWCCM) mentioned in Section 1.4. The sim-plified circuit schematic of the solenoid valve with the crane control module and the test setup isshown in Figure 2.2. The circuit parameter description and the nominal values are tabulated in Table2.1.

15

Rsol

Cout

Vs

Lsol

Rds

Rfbd,Vfbd Rm_int Rm_ext

IN+

IN-

INA 149

Vout

REFa

Rout

NI USB

6211

AI 3

AI GND

Host

Computer

4

19

MWCCM

Figure 2.2. Electrical circuit schematic of a solenoid cartridge valve

Parameter Nominal Value Unit DescriptionVs 24 V Voltage of DC power supply

Rfbd 0.02 Ω Resistance of the flyback diodeVfbd 0.7 V Forward Voltage of the flyback diodeRds 0.028 Ω ON Resistance of the FETRsol 5.3 Ω Resistance of the solenoid coil [5]Lsol 80 mH Inductance of the solenoid coil [5]

Rm_int 0.047 Ω Internal measurement resistanceRm_ext 0.1 Ω External measurement resistanceRout 1 MΩ Output resistanceCout 0.1 µ F Output capacitance

Table 2.1. Solenoid valve electrical circuit parameter description

16

In Figure 2.2, the dashed line denote the components internal to the crane control module(MWCCM). The voltage to the solenoid cartridge valve is applied by connecting the electricalinput of the valve between a digital high side output (Pin 4 on KS2 connector) and a PWM lowside output of the crane control module (Pin 19 on KS2 connector) of MWCCM. As the circuitschematic is simplified, the transistor to switch on the voltage between digital high side output andthe power supply is not shown. The PWM low side output is operated by a HITFET (HeterojunctionInterband Tunneling Field Effect Transistor) that switches on and off depending on the gate signal.The gate signal is a PWM signal which has two significant characteristics, namely duty cycle andfrequency associated with it. Figure 2.3 shows the control voltage, vc(t), applied to the FET, whereD represents the duty cycle and T s represents the total period of a cycle.

DTs Ts time

v c(t

)

ON OFF

Figure 2.3. Waveform of the control voltage vc(t) applied to the FET

The duty cycle D defines the ratio of amount of time during which the signal is high to thetotal period of a complete cycle. It is expressed as a fractional value between 0 and 1 and referredas fractional duty cycle. The frequency f defines the rate at which the signal switches betweenhigh and low states. It is the reciprocal of the total period of a cycle T s. For a proportionalcurrent controlled solenoid valve, the frequency of PWM is typically in the range of 200 to 1000Hz. Such high frequency is required to prevent the valve from responding instantaneously as ina digital on-off control and to respond to time averaged current. The PWM frequency used is 500 Hz.

17

Internal to the crane control module, the internal measurement resistance Rm_int is connected onthe PWM low side output for measuring the average current through the solenoid coil as a feedbackto the crane control module. The external measurement resistance Rm_ext is added in series with thesolenoid valve on the PWM low side output in order to measure the average current through thesolenoid coil for test and validation purposes.

The circuit also allows measurement of the solenoid current using an external data acquisitiondevice. The current is estimated by observing the voltage across the external measurement resistanceRm_ext. As the flyback diode is not connected in parallel with the solenoid inductance, the voltagebetween ground on either side of the measurement exhibits a large voltage spike when the switchis opened (FET is off). For this reason, it is necessary to select an instrumentation amplifier thatcan tolerate a large common-mode voltage. The Texas Instruments INA 149 is selected as it ratedfor common-mode voltages up to ±275 VDC. The output from the difference amplifier is passedthrough a passive low pass filter and further connected to an analog input channel (AI 3) of NIUSB-6211. The National Instruments multifunction data acquisition device NI USBâAS6211 offersanalog and digital I/O with the facility of data capture on a computer. The measurement of averagecurrent through the solenoid coil with this test setup is further discussed in Section 2.4.

2.2 Averaging State-Space Model

The linear switched circuit model is obtained for each switching state of the PWM over oneswitching cycle. The state-space equations for each switching state is derived based on circuittheory and it is time averaged using duty cycle as a weighting factor over one switching period [2] .The desired output variable y(t) is the current through the solenoid coil i(t), which is also the statevariable x(t).

18

During the interval 0 ≤ t ≤ DT s, the gate signal is high and the switch is closed (FET is on).The circuit schematic in Figure 2.2 reduces to the circuit model shown in Figure 2.4.

Rsol

Vs

Lsol

Rm_ext

i(t)

Rds

Rm_int

Figure 2.4. Simplified circuit model for the interval 0 ≤ t ≤ DT s

The supply voltage V s is applied to the solenoid valve and the current through the circuitincreases until reaching a steady state value. The flyback diode is reverse-biased by the DC voltageand it appears open. Applying Kirchhoff's voltage law (KVL) across the loop,

V s = Lsoldi

dt+ (Rsol +Rm_ext +Rm_int +Rds) i(t). (2.5)

Rearranging the last equation with the derivative term to the left-hand side of the equation anddividing both sides of the equation by Lsol,

di

dt=

−(Rsol +Rm_ext +Rm_int +Rds)

Lsoli(t) +

V s

Lsol. (2.6)

The state-space representation for the time period 0 ≤ t ≤ DT s is obtained as,

x(t) = a1 x(t) + b1

y(t) = c1 x(t)(2.7)

where

a1 =−(Rsol +Rm_ext +Rm_int +Rds)

Lsol(2.8)

b1 =V s

Lsol(2.9)

c1 = 1. (2.10)

19

During the interval DT s ≤ t ≤ T s, the gate signal is low and the switch is open (FET is off).The circuit schematic in Figure 2.2 reduces to the circuit model shown in Figure 2.5.

Rsol Lsol

Rm_ext

i(t)

Rfbd

Rm_intVfbd

Figure 2.5. Simplified circuit model for the interval DT s ≤ t ≤ T s

The flyback diode is modeled as a series combination of a voltage source V fbd that representsthe forward voltage of the diode and a resistance Rfbd that represents resistance of the diode. Thesupply voltage V s is disconnected from the solenoid coil and the current flowing through the circuitdecreases rapidly. The inductance of the solenoid coil opposes the change in current by generating alarge induced voltage with polarity opposite to that of the DC supply polarity. The induced voltage,thus forward biases the flyback diode. Applying Kirchhoff's voltage law (KVL) across the loop,

−V fbd = Lsoldi

dt+ (Rsol +Rm_ext +Rm_int +Rfbd) i(t). (2.11)

Rearranging the last equation with the derivative term to the left-hand side of the equation anddividing both sides of the equation by Lsol yields

di

dt=

−(Rsol +Rm_ext +Rm_int +Rfbd)

Lsoli(t) − V fbd

Lsol. (2.12)

20

The state-space representation for the time period DT s ≤ t ≤ T s is obtained in the general formas,

x(t) = a2 x(t) + b2

y(t) = c2 x(t)(2.13)

where

a2 =−(Rsol +Rm_ext +Rm_int +Rfbd)

Lsol(2.14)

b2 =−V fbd

Lsol(2.15)

c2 = 1. (2.16)

The state variable x(t) in Equations 2.7 and 2.13 represents the instantaneous current through thecircuit, x(t) = i(t).

The averaging state-space model is obtained by multiplying the state-space Equations 2.7 and2.13 with the switching periods DT s (duration for which the switch is on) and T s −DT s (durationfor which the switch is off) respectively, then adding them together and dividing by one PWMperiod T s [2],

x(t) =

(a1(DT s) + a2(T s −DT s)

T s

)x(t) +

b1(DT s) + b2(T s −DT s)

T s

y(t) =

(c1(DT s) + c2(T s −DT s)

T s

)x(t).

(2.17)

The last equation is further simplified by canceling out the common factor T s and setting c1 = c2 = 1to obtain

x(t) = (a1D + a2(1 −D))x(t) + (b1D + b2(1 −D))

y(t) = x(t).(2.18)

Equation 2.18 represents the time averaged state-space model for one switching period T s. Thestate variable x(t) in Equation 2.18 represents the average current through the solenoid valve,x(t) = iavg(t).

21

The averaging state-space model described by the Equation 2.18 is obtained by assuming that theduty cycle does not change with time and is constant across every cycle of PWM. In general, the dutycycle changes through cycles of PWM and varies as a function of time, which is represented hereas d(t). This makes the state-space model nonlinear and time-variant. The nonlinear time-variantaveraged state-space model for the system is,

x(t) = (a1 d(t) + a2(1 − d(t)))x(t) + b1 d(t) + b2(1 − d(t))

y(t) = x(t).(2.19)

The derived open-loop state-space model is expressed in the general form as,

x(t) = a(t)x(t) + b(t)

y(t) = c(t)x(t)(2.20)

where

a(t) = a1 d(t) + a2(1 − d(t))

b(t) = b1 d(t) + b2(1 − d(t))

c(t) = 1,

(2.21)

where the duty cycle d(t) represents the system input.

2.3 Small-Signal Linearized Model

In order to simplify the process of system analysis and controller design, the nonlinear systemdescribed by the Equation 2.19 is linearized about a quiescent operating point. The sensitivityof the linearized model about the quiescent operating point is discussed. The linearization iscarried out using small-signal approximation [6] with the perturbation technique, in which small acperturbations are superimposed on the steady state quantities.

22

Each variable p is expressed as p = P e + δp where P e is the variable value at the quiescentoperating point around which the linearization will be carried out, and δp is the small deviation ofthe considered variable from the quiescent operating point. For a system, operating with a quiescentoutput current of Ieavg , a variation in duty cycle δd about the quiescent operating duty cycle De,will produce variations δi in the output current. If the magnitude of the change in duty cycle δd issufficiently small, then the resulting output current variation can be approximated using a linearmodel. Thus, the linearized and nonlinear system representations, will exhibit approximately samecharacteristics provided that the duty cycle variations are sufficiently small.

Re-writing the state equation from Equation 2.18 by substituting the state variable x(t) as iavg(t),

diavg(t)

dt= a iavg(t) + b (2.22)

diavg(t)

dt= (a1 d(t) + a2(1 − d(t))) iavg(t) + b1 d(t) + b2(1 − d(t)). (2.23)

The perturbation technique is applied by superimposing small ac perturbations on the steady statequantities by assuming d(t) = De + δd and iavg(t) = Ieavg + δi and Equation 2.23 reduces to

dδi

dt= (a1(D

e + δd) + a2(1 −De − δd))(Ieavg + δi) + b1(De + δd) + b2(1 −De − δd). (2.24)

Expanding the product terms, retaining only the first order terms and neglecting the higher orderterms,

dδi

dt= (a1 D

e + a2 (1 −De))Ieavg + (a1 De + a2 (1 −De))δi+ b1 D

e + b2 (1 −De)

+ ((a1 − a2)Ieavg + b1 − b2)δd.

(2.25)

By replacing the terms a1 De + a2 (1 − De) and b1 D

e + b2 (1 − De) as ae and be respectively,Equation 2.25 reduces to

dδi

dt= ae Ieavg + ae δi+ be + ((a1 − a2)I

eavg + b1 − b2)δd. (2.26)

Equating the steady state component on both sides of the Equation 2.26 and solving for the steadystate value of average current,

Ieavg =−be

ae. (2.27)

23

Equating the dynamic component on both sides of the Equation 2.26,

dδi

dt= ae δi+ ((a1 − a2)I

eavg + b1 − b2)δd. (2.28)

Equation 2.28 describes the plant model representation in time-domain.The transfer function of the system is obtained by transforming the time-domain Equation

2.28 into the frequency domain by using the Laplace transform. Applying Laplace transform,re-arranging, and equating it to the general form of transfer function yields

∆I(s)

∆D(s)=

(a1 − a2)Ieavg + b1 − b2

s− ae=

b

s+ a, (2.29)

where the values of a and b are obtained in terms of the circuit parameters in Table 2.1. Substitutinga1, b1, a2 and b2 as given by Equations 2.8, 2.9, 2.14, and 2.15 respectively yields

a = −ae = −(a1 De + a2 (1 −De))

=

(Rds −Rfbd

Lsol

)De +

Rsol +Rm_ext +Rm_int +Rfbd

Lsol

(2.30)

b = (a1 − a2) Ieavg + b1 − b2 =

(Rfbd −Rds

Lsol

)Ieavg +

V s + V fbd

Lsol, (2.31)

In addition, using Equation 2.27 yields

Ieavg =−be

ae=

−(b1 De + b2 (1 −De))

(a1 De + a2 (1 −De))

=De(V s + V fbd) − V fbd

De(Rds −Rfbd) +Rsol +Rm_ext +Rm_int +Rfbd,

(2.32)

an expression for the quiescent operating current.

24

The small-signal linearized model derived in Equation 2.29 depends on the quiescent operatingcurrent Ieavg, which in turn depends on the quiescent operating duty cycle De. The operating rangeof the solenoid current is between the minimum current required for crane motion Imin, discussedin Chapter 4 and the maximum rated current of solenoid cartridge valve Imax. The sensitivity ofthe parameters a and b is expressed in terms of the percentage of change in the parameters over theoperating range of solenoid current [Imin, Imax] and it is documented in Table 2.2. The values of aand b are calculated with the parameter values mentioned in Table 2.1.

Parameter Imin (Ieavg = 750 mA) Imax (Ieavg = 1300 mA) Sensitivitya 68.3569 68.3691 ∼ 0.02%b 308.6750 308.6200 ∼ 0.02%

Table 2.2. Sensitivity of linearized plant model

From Table 2.2, it could be seen that over the entire operating range of the average currentthrough the solenoid valve, the parameters of the open-loop transfer function a and b change onlyby 0.02%. Thus, the small-signal linearized model can be used as the plant model for the controllerdesign in order to regulate the average current.

25

2.4 Model Verification

The open loop system model derived in Section 2.3 is simulated in MATLAB and the HIL systemwith the circuit parameter values described in Table 2.1. The average current obtained from thesimulation is compared with the actual average current data obtained from the solenoid cartridgevalve in Figure 2.33. The average current through the solenoid cartridge valve is measured throughthe test setup mentioned in Figure 2.2. As mentioned in Section 2.1, the voltage vm_ext(t) across theexternal measurement resistance Rm_ext is measured through the data acquisition device NI USB6211 at a sampling rate of 100kS/s (kilo samples per second). The current through the externalmeasurement resistance Rm_ext, which is same as the current through the solenoid coil is obtainedby applying ohm's law.

iavg(t) = vm_ext(t)/Rm_ext = 10 vm_ext(t). (2.33)

The acquired voltage data is scaled by a factor of 10 to get the current data. The acquired currentdata, on the software level, is then passed through two stage low pass filter with cut off frequenciesas 33.86 Hz and 72.4 Hz respectively. This is done in order to replicate the current sense circuitinside the MWCCM.

The ability of the model to predict average current is tested under the following condition. Theinput duty cycle is stepped from 0 to 0.25. For experimental data, the plunger of the solenoidcartridge valve is unpinned and average current is measured. In MATLAB, the average current issimulated by obtaining the system response of the model derived in Equation 2.29. The m-file isincluded in Appendix B. The system model is also simulated in real-time through HIL, which isalso detailed in Appendix B. Figure 2.6 shows the average current obtained from simulations andtest setup, as a function of time. The vertical axis represents average current in milliamperes andthe horizontal axis represents time in seconds. At time 0, the duty cycle is changed from 0 to 0.25.The red solid curve Iavg exp, blue dashed curve Iavg HIL and black dotted curve Iavg sim denotes theaverage current obtained from experiment, HIL and MATLAB simulation respectively.

A comparison of the curves in Figure 2.6 shows that the derived plant model predicts the averagecurrent close to the average current obtained from the experimental setup. As the experimental datais obtained with the plunger of the solenoid valve unpinned and the simulation data closely matchesthe experimental data, it justifies neglecting the effect of plunger position in Equation 2.3.

26

Figure 2.6. Plot of average current from simulations and experimental test setup

27

Chapter 3 |Controller Design and Verification

The significance of regulating the average current through the solenoid valve is discussed in Sec-tion 1.3 and hence, it is important to obtain the desired system response. The controller designrequirements and the desired key characteristics of the system response are discussed in Section 3.1.The block diagram of the closed-loop system is shown in Figure 3.1. The closed-loop system is asampled-data system in which the continuous-time plant is controlled by a discrete-time controlsystem by sample and hold operations.

Figure 3.1. General block diagram of the closed-loop system

The ADC and PWM blocks represent analog-to-digital converter and pulse-width-modulationsystem respectively. The output of the ADC is passed through two low-pass filters LPF 1 andLPF 2 with cutoff frequencies 33.86 Hz and 72.4 Hz respectively. The output of the plant andthe system parameter that needs to be controlled is the average current iavg(t) flowing through thesolenoid coil. The input to the controller is the error term, e(k) represented in discrete-time, whichis the difference between the set point average current and the average current flowing through the

28

solenoid coil. The output of the controller and the input to the plant is the duty cycle of PWM signal.The average current is sensed by low-pass filtering the voltage drop across the internal measurementresistance Rm_int inside MWCCM shown in Figure 2.2. The controller design is carried out in thecontinuous-time domain and converted to discrete-time domain.

3.1 Controller Design Specification

The most critical requirement of the controller design is that the system should be stable for alloperating conditions at all times. The key characteristics desired from the closed-loop responseare desired rise-time of about a second, zero percent overshoot and zero steady-state error. Thedefinition of the characteristics desired is given as follows. The rise-time is the amount of time thesystem takes to go from 10% to 90% of the steady-state value. The percent overshoot is the amountby which the parameter under control (average current) overshoots the final value, expressed as apercentage of the final value. The steady-state error is the final difference between the set pointaverage current and the actual average current through the solenoid coil.

A proportional-plus-integral (PI) controller design is proposed where the proportional termdetermines the desired dynamic response of the system and the integral term drives the steady-state error to zero. A derivative term is not included in the controller to avoid accentuating theeffect of measurement noise on the controlled average current. The PI control algorithm consistsof two basic coefficients - proportional and integral, which are varied to get the desired systemresponse. The proportional component depends only on the present error term and the propor-tional gain Kp determines the ratio of output response to the error signal. In general, increasingthe proportional gain will result in a faster system response with reduced rise-time. However, ifthe proportional gain is too large, the process variable will begin to oscillate. If Kp is increasedfurther, the oscillations will become larger and the system will become unstable. The integralcomponent sums the error term over time. The result is that even a small error term will cause theintegral component to increase slowly. The integral response will continually increase over timeunless the error is zero, and hence, the effect of this term is to drive the steady-state error to zero.However, large values of integral gain are undesirable as they increase the settling time of the system.

29

The closed-loop system of the PI controller with the plant results in a second-order system,which consists of two poles. The controller is designed in such a way that (1) the poles are placed inthe left-half of s-plane far apart from one another, (2) one pole is placed closer to the origin, whichis the dominant pole and it determines the overall rise-time of the system and (3) the other pole isplaced far away from the origin to get the response of the system iavg(t) to reach minimum currentfor crane motion Imin rapidly.

3.2 Closed-Loop Model

The overall controller function in time domain based on the definitions provided is

d(t) = Kp e(t) +K i

∫ t

0

e(τ)dτ, (3.1)

where d(t) is the controller signal and e(t) is the error signal. The transfer function of the controlleris obtained by taking Laplace transform as

D(s)

E(s)=sKp +K i

s. (3.2)

This represents the proportional-integral controller model.

The small-signal model derived in Section 2.3 is the plant under control. The block diagram ofthe closed-loop system shown in Figure 3.1 is reduced to the block diagram shown in Figure 3.2by substituting the transfer function of the controller and the plant derived in Equations 2.29 and3.2 respectively. In Figure 3.2, R(s) represents the set point average current and Y (s) representsthe process variable under control, which is the average current through the solenoid coil. The

Figure 3.2. Simplified block diagram of the closed-loop system

30

closed-loop transfer function of the system is,

Y (s)

R(s)=

b Kp

(s+

K i

Kp

)s2 + s(a+Kp b) +K i b

. (3.3)

The poles of the transfer function are the roots of the characteristic equation. The most criticalcontroller requirement is that the system should be stable at all time. For a system to be asymptoti-cally stable, the poles of the transfer function should be real, distinct and located in the left-halfof s-plane. Satisfying this condition, one pole is assumed to be at s = −λ and the other pole isassumed to be at s = −αλ, where α is positive and very large. The reason for choosing α this wayis discussed in detail in Section 3.3. The general characteristic equation of the closed-loop systemis given by,

(s+ λ)(s+ αλ) = s2 + sλ(α + 1) + αλ2 = 0. (3.4)

The controller gains Kp and K i are computed in terms of α and λ by comparing the characteristicequation of the closed-loop system described in Equation 3.3 with the general characteristic equationdescribed in 3.4 and equating the coefficients of like terms. This analysis leads to

Kp =λ (α + 1) − a

b

K i =αλ2

b.

(3.5)

Replacing the controller gains Kp and K i in terms of α and λ, Equation 3.3 yields,

Y (s)

R(s)=

(λ(α + 1) − a)

(s+

αλ2

λ(α + 1) − a

)(s+ λ)(s+ αλ)

. (3.6)

This equation describes the transfer function of the closed-loop system in terms of the system poles.

31

3.3 Calculation of Controller Gains

As mentioned in the controller design requirements, the controller gains Kp and K i are determinedfor the system to be stable and in order to achieve the specified rise-time with no overshoot and nosteady-state error. The controller gains are expressed in terms of λ and α. The unit step responseis obtained in order to compute the control gains by analysing the exponential components of theresponse. For a unit step input r(t) = u(t), the Laplace transform of the output of the closed-loopsystem is given by,

Y (s) =

(λ(α + 1) − a)

(s+

αλ2

λ(α + 1) − a

)(s+ λ)(s+ αλ)

(1

s

). (3.7)

In order to find the unit step response in time domain, partial fraction expansion with Heavisidecover-up method is employed. Using partial fraction expansion,

Y (s) =A

s+

B

s+ λ+

C

s+ αλ. (3.8)

where the coefficients A, B and C are computed with Heaviside cover-up method as

A =

(λ(α + 1) − a)

(s+

αλ2

λ(α + 1) − a

)(s+ λ)(s+ αλ)

∣∣∣∣∣s=0

= 1, (3.9)

B =

(λ(α + 1) − a)

(s+

αλ2

λ(α + 1) − a

)s(s+ αλ)

∣∣∣∣∣s=−λ

=λ− a

λ(α− 1), (3.10)

C =

(λ(α + 1) − a)

(s+

αλ2

λ(α + 1) − a

)s(s+ λ)

∣∣∣∣∣s=−αλ

=a− αλ

λ(α− 1). (3.11)

32

The computation of the partial fraction expansion coefficients A, B and C is verified by computingthe output response of the system y(t) at t = 0, as

y(0) = A+B + C = 1 +λ− a

λ(α− 1)+

a− αλ

λ(α− 1)=λ(α− 1) + λ− a+ a− αλ

λ(α− 1)= 0. (3.12)

This is a necessary, but not a sufficient method to verify the validity of Equation 3.13. Substitutingthe partial fraction expansion coefficients A, B and C in Equation 3.8 and taking inverse Laplacetransform, the unit step response of the closed-loop system is obtained as,

y(t) =

(1 +

λ− a

λ(α− 1)e−λt +

a− αλ

λ(α− 1)e−αλt

)u(t). (3.13)

The output response of the system consists of two exponential components as given in Equation3.13.

Because αλ >> λ, the time constant 1/αλ is far lesser than the time constant 1/λ and hence,the exponential component with a time constant of 1/αλ is considered as a fast exponential and theexponential component with a time constant of 1/λ is considered as a slow exponential. Because ofthe short time constant, the fast exponential component reaches the equilibrium state much morequickly than the slow exponential component. From the perspective of the overall response, thefaster exponential comes to equilibrium (i.e., has decayed to zero) almost instantaneously comparedto the slower exponential. Therefore, the slower exponential component determines the overallrise-time of the closed-loop system and the corresponding pole at s = −λ is considered as thedominant pole.

Considering the dominant pole at s = −λ, the rise-time tr of the system is given by,

tr =ln(9)

λ, (3.14)

λ =ln(9)

tr. (3.15)

Equation 3.15 shows that the value of λ is determined directly from the specified rise-time.

33

From the transfer function of the closed-loop system represented in Equation 3.6, the zero, z, ofthe system is given by,

z = − αλ2

(λ(α + 1) − a). (3.16)

The zero is placed in the left-half of s-plane to avoid the unit step response from initially moving inthe wrong direction. Using this constraint,

− αλ2

λ(α + 1) − a< 0. (3.17)

Since α and λ are both positive, the term on the numerator αλ2 is also positive. Hence, to satisfythe condition imposed in Equation 3.17, the term on the denominator term must also be positive.

λ(α + 1) − a > 0. (3.18)

Solving Equation 3.18 for the value of α,

α >a

λ− 1. (3.19)

This gives the lower limit on the value of α.

As mentioned in Section 1.5, the crane mechanism requires a minimum average current Imin

through the solenoid coil for motion. The controller is designed to take advantage of the fastexponential component to increase the average current rapidly (with the time constant of 1/αλ)from zero to the minimum value required. As the fast exponential component reaches the equilibriumstate, the slow exponential component determines the system response and the rise-time of thesystem. This is added as a feature in the computation of the controller gains.

After the fast exponential component reaches the equilibrium state, the output response of thesystem given by Equation 3.13 can be approximated as,

1 +λ− a

λ(α− 1)= Imin. (3.20)

Solving Equation 3.20 yields,

α = 1 +λ− a

λ(Imin − 1). (3.21)

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This gives an approximation for the maximum value of α.

Thus, the controller gains Kp and K i are determined using Equation 3.5, in which the value ofλ and α are computed as,

λ =ln(9)

tr(3.22)

a

λ− 1 < α ≤ 1 +

λ− a

λ(Imin − 1). (3.23)

The controller gains are computed based on the values of rise-time (s), solenoid resistance, solenoidinductance and the minimum current required for motion.

The controller designed in continuous-time domain is converted into discrete-time domain.When converting from continuous-time domain to discrete-time domain, the approximation erroris less than 3% and the discrete-time controller behaves similar to a continuous-time controllerwhen [7]

T ≤Kp

20K i. (3.24)

The discrete-time controller realized in the MWCCM has a sampling period T of about 0.03 s.For the given sampling period and the chosen values of Kp and Ki, the discrete-time controllerwill always satisfy the condition in Equation 3.24 and will behave similar to the continuous-timecontroller. The transfer function of the controller in discrete domain is obtained by applyingthe backward finite difference approximation technique, as this approximation method is usedby Manitowoc Cranes in realizing the PI controller on the MWCCM module. According to thebackward difference, the term 1

sin continuous frequency domain corresponds to the term T z

z−1in

discrete frequency domain, where T represents the sampling period. The transfer function of thecontroller in discrete domain is given by,

D(z)

E(z)= Kp +

K i T z

z − 1. (3.25)

The controller difference equation in discrete-time domain is obtained by taking the inverse ztransform of Equation 3.25,

d(k) = d(k − 1) +Kp (e(k) − e(k − 1)) +K i T e(k). (3.26)

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The controller Equation 3.26 is implemented on the MWCCM as a part of the C code. The controllergains are calculated in continuous-time and the controller is simulated in discrete-time to validatethe system response.

3.4 Controller Design Validation

The proportional-integral controller designed to regulate the average current is validated to verifythe desired system response characteristics, by observing the average current as a function of time.Section 3.4.1 describes the controller validation through simulations on MATLAB and HIL. Italso describes the controller validation on a solenoid valve with the test setup shown in Figure 2.2.In section 3.4.2, the controller validation on a GRT crane with a set of experiments conducted isdescribed.

3.4.1 Simulation and experimental verification

The derived plant model and controller model in Equations 2.29 and 3.26 respectively are simulatedin MATLAB and HIL. These simulations are detailed in Appendix B. The controller gains arecalculated for a rise-time of about a second and minimum average current of about 420 mA. Theaverage current set point is changed from 0 mA to 1000 mA. For experimental data with test setup,the plunger of the solenoid cartridge valve is unpinned and average current is measured. Theproportional-integral control algorithm is implemented in embedded C, as a part of the base codeon the crane control module.

Figure 3.3 shows the plot of average current obtained from simulations and test setup, as afunction of time. The vertical axis represents average current in milliamperes and the horizontalaxis represents time in seconds. At time 0, the average current set point is changed from 0 mA to1000 mA. In Figure 3.3, the red dotted line Iavg MATLAB, blue dashed line Iavg HIL and black solidline Iavg exp and denotes the average current obtained from MATLAB simulation, HIL simulationand experiment respectively. The average current reaches the minimum average current requiredImin rapidly, as denoted with a brown dash-dotted line.

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Figure 3.3. Controller validation through simulations and experimental test setup

3.4.2 Crane Experiments

The controller is validated for a set of experiments on a GRT crane at the Manitowoc ProductVerification Center in Shady Grove, Pennsylvania. The proportional-integral control algorithm isimplemented in embedded C, as a part of the base code on the crane control module. A graphicaluser interface (GUI) is developed in LabVIEW, detailed in Appendix A, communicates with thecrane control module over CAN bus. The controller gainsKp andK i are computed on the LabVIEWGUI, based on the parametric values and deployed to the crane control module via CAN messages.A screenshot of the user interface is shown in Figure 3.4. On the GUI, under Controller Design, theparametric values of the solenoid circuit along with the desired rise-time and the minimum averagecurrent is configured and the controller gains are computed. The controller gains are calculated fora rise-time of about a second and minimum average current of about 300 mA. The average current

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set point is changed from 0 mA to 1000 mA. Under Controller Verification, when the button Deploy

Gains and Meas tr is pressed, the specified setpoint current and the controller gains are sent viaCAN messages.

Figure 3.4. Graphical user interface for controller validation

The average current through the solenoid coil is measured by the crane control module and itstreams the data via CAN messages. The GUI reads the average current data from the CAN busand measures the rise-time. The controller design is validated on a GRT crane with the hydraulicmechanisms such as hoist up, hoist down, boom up and boom down.

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Figure 3.5 shows the plot of average current obtained from the hoist hydraulic mechanism ofGRT crane, as a function of time. The vertical axis represents average current in milliamperes andthe horizontal axis represents time in seconds. At time 0, the average current set point is changedfrom 0 mA to 1000 mA. The red solid line Hoist Up and black dashed line Hoist Down denotes theaverage current obtained from hoist up and hoist down mechanism respectively. In Figure 3.5, theaverage current reaches the minimum average current required Imin rapidly, as denoted with a bluedash-dotted line. The rise-time of the average current for the hoist up and hoist down mechanismsare measured as 940 ms and 950 ms respectively.

Figure 3.5. Controller validation on hoist mechanism of a GRT crane

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Figure 3.6 shows the plot of average current obtained from the boom hydraulic mechanism ofGRT crane, as a function of time. The vertical axis represents average current in milliamperes andthe horizontal axis represents time in seconds. At time 0, the average current set point is changedfrom 0 mA to 1000 mA. The red solid line Boom Up and black dashed line Boom Down denotesthe average current obtained from boom up and boom down mechanism respectively. The averagecurrent reaches the minimum average current required Imin rapidly, as denoted with blue dash-dottedline. The rise-time of the average current for the hoist up and hoist down mechanisms are measuredas 980 ms and 940 ms respectively. The two curves do not begin at the same point of time, markedby a dotted box in Figure 3.6. This is due to a delay in the data transmitted every 100 ms over theCAN bus.

Figure 3.6. Controller validation on boom mechanism of a GRT crane

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3.5 Temperature Dependence

As mentioned in Section 1.3, the cranes are operated across various geographical locations withtemperatures ranging from -40 deg F to 120 deg F. The variations in temperature affect the solenoidelectrical parameters, namely the solenoid coil resistance and inductance. As the controller design isbased on the solenoid parameters, the variation of these parameters with temperature is characterized.The performance of the controller designed with the solenoid parameters at ambient temperature ischaracterized across the entire working range of temperatures. The controller gains Kp and K i arecalculated with the solenoid parameters at ambient temperature for a rise-time of about a second andminimum average current of about 300 mA. For the same controller gains, the effect of temperatureon the rise-time of the average current is characterized through HIL simulation and experimentalvalidation.

In experimental validation, as a part of a senior design project [5], a team of students measuredthe resistance and inductance of 30 solenoid cartridge valves as a function of temperature rangingfrom -40 deg F to 120 deg F. These extreme temperatures are achieved with dry ice and incandescentlight bulbs respectively. The solenoid resistance is measured with a Hewlett Packard 34401A DigitalMultimeter. The solenoid inductance is calculated using phasor analysis, where sinusoidal voltageof various frequencies are applied and the phase difference between the voltage and current of thesolenoid is measured through the data acquisition device discussed in Section 2.1. The controllergains are calculated for the solenoid parameters at ambient temperature. For the same controllergains, the average current is measured by subjecting the solenoid valve to extreme temperatures.

In HIL simulation, the solenoid valve parameters resistance and inductance, measured fromexperiments are used. For the same controller gains computed at ambient temperature, the averagecurrent is obtained for different solenoid resistance and inductance values, as measured from theexperiments.

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Figure 3.7 shows the plot of average current obtained from experimental setup, as a function oftime for three different temperatures -40 deg F, 73 deg F and 120 deg F. The vertical axis representsaverage current in milliamperes and the horizontal axis represents time in seconds. At time 0, theaverage current set point is changed from 0 mA to 1000 mA. The blue dotted line, black solid lineand red dashed line denotes the average current obtained for temperatures -40 deg F, 73 deg F and120 deg F respectively. The rise-time of the average current for temperatures -40 deg F, 73 deg Fand 120 deg F are measured as 770 ms, 1040 ms and 1140 ms respectively.

Figure 3.7. Effect of temperature on closed-loop response from experiments

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Figure 3.7 shows the plot of average current obtained from HIL simulation, as a function oftime for three different temperatures -40 deg F, 73 deg F and 120 deg F. The vertical axis representsaverage current in milliamperes and the horizontal axis represents time in seconds. At time 0, theaverage current set point is changed from 0 mA to 1000 mA. The blue dotted line, black solid lineand red dashed line denotes the average current obtained for temperatures -40 deg F, 73 deg F and120 deg F respectively. The rise-time of the average current for temperatures -40 deg F, 73 deg Fand 120 deg F are measured as 730 ms, 990 ms and 1090 ms respectively.

Figure 3.8. Effect of temperature on closed-loop response from HIL simulation

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The effect of temperature on the solenoid valve parameters and on the controller responseis documented in Table 3.1. It shows the solenoid resistance and inductance measured fromexperiments for temperatures of about -40.4 deg F, 73.4 deg F and 120 deg F. It also shows themeasured rise-time of the controller response from HIL simulation and experiments. The desiredrise-time is about 1000 ms and the observed rise-time through HIL and actual experiment is withinthe permissible range of about 250 ms.

Temperature [F] Resistance [Ω] Inductance [mH] Rise Time [msec]Simulation Experiment

-40.4 4.308 26.7 730 77073.4 5.543 32.4 990 1040120 6.093 34.1 1090 1140

Table 3.1. Effect of temperature on rise-time from HIL simulation and experiments

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Chapter 4 |Determination of Minimum Currentfor Hydraulic Motion

The average current required through the solenoid valve to achieve motion in the hydraulic systemof a crane is referred as Imin, the minimum average current for hydraulic motion. The value of Imin isdetermined by the properties of solenoid valve and the hydraulic pressure at the input port. In thehydraulic system of a crane described in Section 1.2, the solenoid valve has a spring to hold thevalve in normally closed position when it is not energized. The solenoid valve also has a certainamount of poppet overlap in order to reduce leakage in the null position and to provide a greaterdegree of safety in power failure or emergency stop situations. This spring force and poppet overlapcauses a phenomenon called deadband, which is defined as the range of operation during whichthere is no flow or pressure output from the solenoid valve for some specified range of commandinput. In this case, the command input is the average current flowing through the solenoid coil. Thedeadband has to be traversed before the valve physically starts moving and it requires a certainminimum average current to be present at the solenoid coil before any noticeable result occurs inthe system. The overlap and hence, the deadband is also caused by packing friction, unbalancedforces operating on the valve and other factors in the solenoid valve assembly. For pressure andflow control, the deadband generally occurs at the start of poppet movement.

The other factor that affects the minimum average current is the hydraulic motor coupled to theload, which requires a minimum starting torque to get it moving from standstill. The torque outputof the motor depends on the pressure input. As mentioned in Sections 1.2 and 1.2.1, this pressureis controlled by the directional control valve, which in turn is controlled by the solenoid valve. In

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order to have a minimum required pressure at the hydraulic motor input, there should be a minimumvalue of current flowing through the solenoid coil.

4.1 Search Algorithm

The minimum average current for hydraulic motion Imin is determined systematically by applyinga particular value of average current and checking for any motion. The default interval for theminimum average current is between any value above 0 mA to the maximum rated current of thesolenoid valve. The search interval is defined as a closed interval with endpoints [I low, Ihigh], whereI low and Ihigh are the lowest and highest value of average current to search respectively. The termaccuracy refers to the closeness of the determined minimum average current to it’s true value and isdenoted as ∆. For example, if the accuracy is 10 mA, the determined value of minimum currentis within 10 mA deviation from the actual value of minimum current that will cause motion. Thenumber of data points in the search interval is given by

n =Ihigh − I low

∆+ 1. (4.1)

Search algorithms can be generally classified into sequential search and interval search. Insequential search, also referred as linear search, each value of the average current in the searchinterval is applied sequentially starting from the lowest value until there is any motion. The linearsearch algorithm performs utmost n iterations and has a maximum complexity of O(n). It meansthat it is time intensive and hence, not desirable. In interval search, also referred as binary search,the algorithm is performed by repeatedly dividing the search interval in half. Hence, a binary searchalgorithm is proposed as it has a maximum complexity of O(log n). This means that the maximumnumber of iterations needed to find the target minimum average current is a logarithmic function ofthe size of the search space.

In the binary search algorithm, the target value of average current is computed as the averagevalue of the endpoints of the search interval. The computed value of average current is regulatedthrough the solenoid valve and checked for any motion in the hydraulic system. If there is nomotion, it means that a higher value of average current is required and the lower half of the searchinterval in which the minimum average current cannot lie is eliminated. If there is motion, it means

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that a lower value of average current could possibly cause motion and the upper half of the searchinterval is eliminated. This iterative procedure essentially keeps record of the search boundarieswith the two variables I low and Ihigh. The search process continues on the remaining half, againtaking the average of the endpoints to check for motion, and repeating this until the target value ofaverage current is found with the required accuracy. Assuming the search interval has n elements,this algorithm basically eliminates half of the elements in the search interval after one iteration andthere are only n/2 elements left in the search interval. After second iteration, there are only n/4elements left and so on. After i th iteration, there will be n/2i elements left. If the search elementis found on the i th iteration, then the number of elements left in the search interval n/2i equals 1,and hence, solving for i will result in i = log n. Thus, the binary search algorithm has a maximumcomplexity of O(log n). The description of the parameters used in the algorithm and it’s nominalvalue is given in Table 4.1.

Parameter Nominal Value Unit DescriptionIlow 250 mA Lowest value of average current to start searchingIhigh 1000 mA Highest value of average current to stop searching

Wait Time 3000 ms Time to wait and look for motion∆ 10 mA Accuracy of determining the minimum average current

Table 4.1. Binary search algorithm parameter description

The parameter I low is any non-zero value of average current to begin searching, Ihigh depends onthe maximum rated average current for the solenoid valve, Wait Time is chosen to be significantlylarger than the mechanical time constant of the hydraulic system and ∆ depends on how accurate Imin

should be calculated. The detailed procedure of the binary search algorithm for the determinationof minimum value of average current for motion is described. The input to the function are theparameters described in Table 4.1 and the output of the function is the minimum average currentdetermined.

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1. The input parameters I low, Ihigh, ∆ and Wait Time are initialized with the desired values.

2. The target or the setpoint average current is calculated as the average value of the endpointsof the search interval as given by,

Iavg =I low + Ihigh

2(4.2)

The calculated average current is applied through the solenoid valve to check for any motionin the hydraulic system.

3. For the duration of Wait Time specified, the algorithm continuously checks for any motion. Ifany motion is detected, stop checking, end the Wait Time, assign I low = Iavg and proceed tothe next step. If no motion is detected during the entire period of Wait Time, assign Ihigh = Iavg

and proceed to the next step.

4. Check if the average current determined from the previous step is within the specified accuracyby computing the difference between the present iteration’s average current with the averagecurrent to be computed in the next iteration as given by,∣∣∣∣Iavg −

I low + Ihigh

2

∣∣∣∣ ≤ ∆ (4.3)

If the determined average current is not within the specified accuracy, repeat steps 2 through4 until the average current is found with specified accuracy.

Table 4.2. Outline of the binary search algorithm for determining Imin

4.2 Algorithm Validation

The binary search algorithm is validated on the HIL system and on a GRT crane. The HIL systemis detailed in Appendix B. The search algorithm is coded as a part of the graphical user interface(GUI) developed in LabVIEW, which is further detailed in Appendix A. The GUI communicateswith the MWCCM/HIL over the CAN bus. The setpoint average current is sent over the CAN bus tothe MWCCM/HIL. On HIL system, a mechanical model is included to account for the dynamics ofthe crane and it simulates the hoist/boom rotation. On a crane, the hoist/boom rotation is measuredin degrees by means of a sensor and this information is available on the CAN bus. The algorithm isvalidated for different Wait Time of 1500 and 3000 milliseconds for the hoist and boom hydraulicsystems.

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Figure 4.1. User interface for determination of minimum average current

The binary search algorithm is validated on the hoist up hydraulic mechanism of a GRT crane.The parameters of the algorithm Ilow, Ihigh and Resolution are configured as 0 mA, 1200 mA and10 mA respectively. The experiment is conducted for a Wait Time of 1500 ms and 3000 ms. Theminimum average current determined for 3 trials is documented in Table 4.3. The minimum averagecurrent determined for Wait Time of 1500 ms and 3000 ms is determined as 758 mA and 742 mArespectively.

Hoist Up 1500 ms 3000 msTrial 1 758 742Trial 2 758 742Trial 3 758 742

Table 4.3. Minimum average current for hoist up mechanism on a GRT crane

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The binary search algorithm is validated on the hoist down hydraulic mechanism of a GRTcrane. The parameters of the algorithm Ilow, Ihigh and Resolution are configured as 0 mA, 1200 mAand 10 mA respectively. The experiment is conducted for a Wait Time of 1500 ms and 3000 ms.The minimum average current determined for 3 trials is documented in Table 4.4. The minimumaverage current determined for Wait Time of 1500 ms and 3000 ms is about 758 mA.

Hoist Down 1500 ms 3000 msTrial 1 758 758Trial 2 758 758Trial 3 758 758

Table 4.4. Minimum average current for hoist down mechanism on a GRT crane

The binary search algorithm is validated on the boom up hydraulic mechanism of a GRT crane.The parameters of the algorithm Ilow, Ihigh and Resolution are configured as 0 mA, 1200 mA and10 mA respectively. The experiment is conducted for a Wait Time of 1500 ms and 3000 ms. Theminimum average current determined for 3 trials is documented in Table 4.5. The minimum averagecurrent determined for Wait Time of 1500 ms and 3000 ms, as an average of 3 trials is about 711mA and 685 mA respectively.

Boom Up 1500 ms 3000 msTrial 1 758 696Trial 2 618 632Trial 3 758 726

Table 4.5. Minimum average current for boom up mechanism on a GRT crane

The binary search algorithm is validated on the boom down hydraulic mechanism of a GRTcrane. The parameters of the algorithm Ilow, Ihigh and Resolution are configured as 0 mA, 1200 mAand 10 mA respectively. The experiment is conducted for a Wait Time of 1500 ms and 3000 ms.The minimum average current determined for 3 trials is documented in Table 4.6. The minimumaverage current determined for Wait Time of 1500 ms and 3000 ms is about 774 mA and 758 mArespectively.

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Boom Down 1500 ms 3000 msTrial 1 774 758Trial 2 774 758Trial 3 774 758

Table 4.6. Minimum average current for boom down mechanism on a GRT crane

The minimum average current determined across the hoist and boom hydraulic systems differby about 30 mA. There is a trade-off between selecting the Wait Time and the calibration time ittakes to determine the minimum average current. It is desirable to choose a small value of Wait

Time to reduce the calibration time in determining Imin. However, given the limited resolution of theposition encoders on the hydraulic systems, a small value of Wait Time may not be able to identifythe presence of motion.

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Chapter 5 |Conclusions and Future Work

This thesis presents solution to two challenges on Grove Rough Terrain cranes. The first challengeis to regulate the average current through solenoid cartridge valve in the hydraulic system. Aproportional-integral controller design is provided to regulate the average current. The secondchallenge is to determine the minimum average current required through the solenoid cartridgevalve for motion in the hydraulic systems. A binary search algorithm is proposed to determine theminimum average current required.

The average current through the solenoid valve is controlled by pulse-width-modulation throughthe crane control module MWCCM. The solenoid valve is electrically modeled as a series com-bination of resistance and inductance. The open-loop plant model is obtained by applying theaveraging state-space approach and assuming the duty cycle to be a constant. The duty cyclevaries as a function of time and results in a non-linear model. The non-linear model is linearizedabout a quiescent operating duty cycle using the perturbation technique and a small-signal model isobtained. The open-loop plant model is validated through simulation and experimental setup. Aproportional-integral (PI) controller is designed to regulate the average current through solenoidvalve. The desired characteristics of the closed-loop system response - a rise-time of about a second,zero percent overshoot and zero steady-state error. The PI controller along with the plant modelresults in a second-order system, with two poles and one zero. The two poles correspond to twotime constants, a slow and fast time constant. The fast time constant takes the average current to Imin

and the slow time constant gradually reaches steady state depending on the rise-time specified. Thecontroller design is validated through simulation and it is also validated on a Grove Rough Terraincrane at Manitowoc Cranes, for the hydraulic mechanisms hoist up, hoist down, boom up and boom

52

down. The cranes are operated across various geographical locations with temperatures rangingfrom -40 deg F to 120 deg F. The effect of the temperature changes on the solenoid parameters andon the controller design is studied.

The minimum average current Imin required through the solenoid valve for hydraulic motion isaffected by the solenoid valve parameters and the hydraulic motor coupling to the load. A binarysearch algorithm is proposed for the determination of Imin across different hydraulic mechanisms.The algorithm is validated through hardware-in-loop simulation and on a Grove Rough Terrain crane.

The scope for future work would include the binary search algorithm to be integrated as apart of the embedded code on MWCCM module. This will enable a crane operator to determineminimum average current systematically. The calculation of the controller gains for proportional-integral controller can also be integrated as a part of the embedded code on MWCCM module.This functionality is restricted for use only by a certified crane technician to tune the controller gains.

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Appendix A|Graphical User Interface

The graphical user interface (GUI) is developed in LabVIEW, which communicates with theMWCCM module through CAN bus. The CANopen protocol is used as the communication proto-col over the CAN bus. The GUI application runs on the host computer and a PCAN-USB interface isused between the MWCCM and the computer for communication. The CANopen protocol consistsof process data objects (PDOs), for broadcasting high-priority control and status information. APDO consists of a single CAN frame and communicates up to 8 byte of pure application data. ThePDO data format used in the CAN communication between the MWCCM and the computer isshown in Table A.2. Each parameter is a 16-bit number. If x is a parameter, lo(x) represents thelower 8-bits and hi(x) represents the higher 8-bits of the parameter.

Function CAN-ID 0 1 2 3 4 5 6 7Transmit x216 lo(I) hi(I) lo(Im) hi(Im) lo(Kp) hi(Kp) lo(Ki) hi(Ki)Receive x296 lo(V) hi(V) lo(D) hi(D) lo(I) hi(I) lo(C) hi(C)Receive x396 lo(H) hi(H) – – – – lo(C) hi(C)

Table A.1. PDO data format for hoist mechanism

PDO x216 is used to transmit data to the MWCCM, where I represents the average currentin mA, Im represents the minimum average current in mA, Kp represents the controller gain andKi represents the integral controller gain. PDOs x296 and x396 are used to receive data from theMWCCM, where V represents the bus voltage applied to the solenoid valve in V, D represents theduty cycle in percentage, I represents the average current in mA, H represents the drum rotation ofthe hoist in degrees and C represents the count.

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The PDO data format for the boom mechanism follows the same format as that of a hoistmechanism, but with different CAN-ID to transmit and receive.

Function CAN-ID 0 1 2 3 4 5 6 7Transmit x217 lo(I) hi(I) lo(Im) hi(Im) lo(Kp) hi(Kp) lo(Ki) hi(Ki)Receive x297 lo(V) hi(V) lo(D) hi(D) lo(I) hi(I) lo(C) hi(C)Receive x397 lo(H) hi(H) – – – – lo(C) hi(C)

Table A.2. PDO data format for boom mechanism

As an example, the PDO data to transmit I = 500mA, Im = 300mA, Kp = 3000 and Ki = 1800,in the hoist mechanism is given in Table A.3. The data in the table is represented in hexadecimalformat.

Function CAN-ID 0 1 2 3 4 5 6 7Transmit x216 F4 01 2C 01 B8 0B 08 07

Table A.3. An example PDO format

The GUI has the functionality to send and receive PCAN data, graphing PCAN data, computationof controller gains and controller verification, determination of minimum average current for motionand to perform system identification experiments. The screenshot of the different tabs of the GUIand the details of the controls/indicators are included.

A.1 Send PCAN Data

1. Iavg Setpoint [mA] - The set point average current in milliamperes sent to the MWCCMmodule through a PDO on the CAN bus. The positive value of current correspond to onedirection of hydraulic mechanism (hoist down) and the negative value of current correspondto the opposite direction of hydraulic mechanism (hoist up).

2. Settings

(a) PCAN Channel - The PCAN-USB channel connected to the computer.

(b) Sample Time [ms] - The sampling period of the discrete-time proportional-integral (PI)controller in milliseconds.

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Figure A.1. PCAN Control GUI - Send PCAN Data

(c) Time delay between direction change [ms] - The time delay required between direc-tion change of the hydraulic mechanism i.e, the time delay required between sendingthe positive and negative value of average current.

3. Data Write - It has the data to be sent to the MWCCM module over the CAN bus, for thetwo hydraulic mechanisms hoist up and hoist down.

(a) Imin - A numeric control to configure the minimum average current in milliamperes.

(b) Kp - A numeric control to configure the proportional controller gain.

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(c) Ki - A numeric control to configure the integral controller gain.

(d) Send PCAN Data - A button which sends the data (Imin, Kp, Ki) to the MWCCMthrough a PDO on the CAN bus, when pressed.

(e) Data Sent - An indicator which turns green when data is sent to MWCCM and turnsblue when any data is changed, but not sent yet.

4. Data Read - It indicates the data read back from the MWCCM over the CAN bus and includesthe duty cycle in percentage, average current in milliamperers, drum rotation of the hoist indegrees and the bus voltage applied to the solenoid valve in volts.

(a) Duty Cycle[%] - A numeric indicator displaying the duty cycle of the PWM signal inpercentage.

(b) Iavg[mA] - A numeric indicator displaying the average current flowing through thesolenoid valve in milliamperes.

(c) Hoist Drum Rotation[deg] - A numeric indicator displaying the drum rotation of thehoist in degrees.

(d) UB Voltage[V] - A numeric indicator displaying the bus voltage applied to the solenoidvalve in volts.

A.2 Graph

The second tab of the GUI has the functionality of a scope to graphically display the varying data,by means of a two-dimensional plot of the data as a function of time. The plot legend is shown inthe bottom right corner of the graphic display. The data displayed are the duty cycle(%), averageset point current (mA), average current measured (mA) by MWCCM, drum rotaion of the hoist (deg).

1. Scale - The y-axis scale that defines the unit per division of y-scale.

2. Vertical Position - The y-axis offset added to the plot.

3. Duty Cycle - The y-axis scale is defined in % per division.

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Figure A.2. PCAN Control GUI - Graph

4. Iavg Command - The average set point current sent to the MWCCM module diaplyed inmilliamperes. The y-axis scale is defined in milliamperes per division.

5. Iavg Read - The average current measured by the MWCCM module displayed in mil-liamperes. The y-axis scale is defined in milliamperes per division.

6. Hoist Position - The drum rotation of the hoist displayed in degrees. The y-axis scale isdefined in degrees per division.

7. Time/Div - The x-axis scale that defines the unit per division of x-scale.

8. Pause - It pauses the graphic display.

9. Clear Buffer - It clears the graphic display.

10. Save Data - It saves the displayed data into an excel sheet.

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A.3 Calculate Resistance

The Calculate Resistance tab computes the resistance of the solenoid valve of the correspondinghydraulic mechanism. When Find Resistance is pressed, the set point average current is sent to theMWCCM, the GUI waits for the specified time and then computes the resistance according to theformula given by,

Rtotal =V s D

Iavg(A.1)

where Rtotal is the total resistance of the solenoid coil and the internal measurement resistance insidethe MWCCM in ohms, Vs is the voltage applied to the solenoid coil in volts, D is the duty cycle infraction and Iavg is the average current in amperes.

Figure A.3. PCAN Control GUI - Calculate Resistance

1. Hoist Up/Down - Selection of the hydraulic mechanism between hoist up or hoist downmechanism to send the average current command to.

2. Setpoint Current[mA] - A numeric control to configure the average current command to be

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sent to MWCCM.

3. Wait Time[ms] -A numeric control to configure the time to wait after sending the set pointcurrent command and before computing the resistance.

4. Resistance(Ohm) - A numeric indicator displaying the computed resistance value.

A.4 Controller Tuning

The Controller Tuning tab consists of two parts - controller design and controller verification. Incontroller design, the controller gains Kp and Ki are computed based on the equations derived inSection 3.3.

Figure A.4. PCAN Control GUI - Controller Tuning

1. R_total - A numeric control to configure the total resistance of the solenoid coil and theinternal measurement resistance inside the MWCCM in ohms.

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2. Lsol - A numeric control to configure the inductance of the solenoid coil in henrys.

3. Rds - A numeric control to configure the ON Resistance of the FET in ohms.

4. Rfbd - A numeric control to configure the resistance of the flyback diode in ohms.

5. Vs - A numeric control to configure the voltage of DC power supply in volts.

6. Vfbd - A numeric control to configure the forward voltage of the flyback diode in volts.

7. Imin[mA] - A numeric control to configure the minimum average current for crane motionin milliamperes.

8. Rise time[ms] - A numeric control to configure the desired rise-time in milliseconds.

9. Kp - A numeric indicator to display the computed proportional gain.

10. Ki - A numeric indicator to display the computed integral gain.

In controller verification, the computed controller gains are deployed to the MWCCM. A zerocurrent command is sent initially and the GUI waits for the specified time, then sends the set pointcurrent command along with the controller gains. The GUI collects the average current data sent byMWCCM over the CAN bus and displays the data. It also measures the rise-time of the data.

1. Setpoint current[mA] - A numeric control to configure the set point average current sent tothe MWCCM.

2. Wait Time[ms] - A numeric control to configure the time to wait after sending a zero currentcommand and before sending the set point current command.

3. Hoist Up/Down - A numeric control to configure the ON Resistance of the FET in ohms.

4. Deploy Gains and Meas tr - Sends the controller gains along with the set point averagecurrent to MWCCM, collects the average current data from MWCCM, plots the data andcomputes the rise-time.

5. Save Data - Saves the average current data displayed.

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A.5 Imin Calculation

The Imin Calculation tab determines the minimum average current required for crane motion basedon the binary search algorithm proposed in Section 4. The graph displays the average current setpoint, average current measured and the drum rotation of the hoist.

Figure A.5. PCAN Control GUI - Imin calculation

1. Wait Time[ms] - A numeric control to configure the time to wait and look for motion.

2. I_low[mA] - A numeric control to configure the lowest value of average current to startsearching.

3. I_high[mA] -A numeric control to configure the highest value of average current to stopsearching.

4. Resolution[mA] - A numeric control to configure the accuracy of determining the minimumaverage current.

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Appendix B|HIL and MATLAB Simulation

B.1 HIL Simulation

The hardware-in-the-loop simulation is carried out using NI cRIO-9024, an embedded real-timecontroller. The real-time simulation is done through FPGA in order to achieve a simulation period ofabout 1µs. There are two programs (VI - Virtual Instrument) created - one is the FPGA VI and oneis the host VI that communicates with the FPGA VI. The FPGA VI consists of three loops runningin parallel. The solenoid valve dynamics obtained in Section 2 forms the plant model loop. Theproportional-integral controller designed in Section 3 forms the controller loop. The mechanicalmodel of the hydraulic system forms the hoist dynamics loop.

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Figure B.1. HIL simulation - plant and controller loop

Figure B.2. HIL simulation - hoist dynamics

B.2 MATLAB Simulation

The plant model obtained in Section 2 and the proportional-integral controller designed in Section 3are simulated in MATLAB using m-file. The MATLAB code used in the simulations are described.

1 S c a l i n g = 1 . 3 * 1 0 0 0 0 / ( 6 5 5 3 6 * 3 2 7 6 8 ) ;2

3

4 Kp = 3000*2* S c a l i n g ;

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5 Ki = 1800*2* S c a l i n g / 0 . 0 3 ;6 Kd = 0 ;7

8 %D ef in e C i r c u i t E lemen t s9 Rsol = 5 . 3 6 5 ;

10 %Rsol = 1 9 . 9 7 ;11 Lso l = 0 . 1 ;12 Rds = 0 . 0 3 ; %From pure r e s i s t i v e c i r c u i t R t o t a l was 16 ohm13 Rdiode = 0 . 0 5 ;14 Rmeas = 0 . 7 9 5 ;15

16 %When FET i s ON17 A1 = (−( Rso l +Rmeas+Rds ) / Lso l ) ;18 B1 = 2 4 . 1 5 / Lso l ;19 C1 = 1 ;20 D1 = 0 ;21

22 %When FET i s o f f23 A2 = (−( Rso l +Rmeas+Rdiode ) / Lso l ) ;24 B2 = −0.7/ Lso l ;25 C2 = 1 ;26 D2 = 0 ;27 dc1 = 0 . 1 5 ;28 dc2 = 1−dc1 ;29

30 A = ( A1* dc1 ) +(A2* dc2 ) ;31 B = ( B1* dc1 ) +(B2* dc2 ) ;32 X = −B /A;33

34 K = ( ( A1− A2 ) *X) + ( ( B1 − B2 ) ) /(−A)35 Tau = −1/A36

37 %C o n t i n o u s Time

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38 Gp_s = t f (K , [ Tau , 1 ] ) ;39 Gc_s = t f ( [ Kp , Ki ] , [ 1 , 0 ] ) ;40 H_ct = f e e d b a c k ( Gp_s*Gc_s , 1 ) ;41 %D i s c r e t e Time42 Gp_z = c2d ( Gp_s , 0 . 0 3 , ’ zoh ’ )43 Gc_z = p i d ( Kp , Ki , ’ Ts ’ , 0 . 0 3 , ’ IFormula ’ , ’ Backward ’ ) ;44 H_dt = f e e d b a c k ( Gp_z*Gc_z , 1 ) ;45

46 t = l i n s p a c e ( 0 , 1 4 , 1 0 0 0 0 0 ) ;47 f i g u r e ( 1 )48 s t e p ( H_ct , ’ r ’ , t )49 ho ld on50 s t e p ( H_dt , ’−k ’ )51 l e g e n d ( ’ C o n t i n o u s Time ’ , ’ D i s c r e t e Time ’ )52 %s q r t ( Ki*b ) * ( ( a+Kp*b ) / ( 2 * s q r t ( Ki*b ) ) + s q r t ( ( ( a+Kp*b ) ^ 2 / ( 4 * Ki*b ) )

−1) )

1 %2 c l o s e a l l3 Tsim = 10e−06; % time−s t e p f o r f i x e d−s t e p s i z e

ODE s o l v e r4 T f i n a l = 2 ;5 Tres = 1 / Tsim ;6 t = ( 0 : 1 : 1 9 5 )7

8 %D ef in e C i r c u i t E lemen t s9 Rsol = 5 . 3 ;

10 Lso l = 0 . 0 8 ;11 Rds = 0 . 0 3 ; %From pure r e s i s t i v e c i r c u i t R t o t a l was 16 ohm12 Rdiode = 0 . 0 5 ;13 Rmeas = 0 . 7 9 5 ;14

15 %When FET i s ON

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16 A1 = (−( Rso l +Rmeas+Rds ) / Lso l ) ;17 B1 = 2 4 . 1 5 / Lso l ;18 C1 = 1 ;19 D1 = 0 ;20

21 %When FET i s o f f22 A2 = (−( Rso l +Rmeas+Rdiode ) / Lso l ) ;23 B2 = −0.7/ Lso l ;24 C2 = 1 ;25 D2 = 0 ;26 s = t f ( ’ s ’ ) ;27 %D ef in e du ty c y c l e28 dc1 = 0 . 1 5 ;29 f i g u r e ( )30

31

32 dc2= 1−dc1 ;33

34 A = A1* dc1+A2* dc2 ;35 B = B1* dc1+B2* dc2 ;36

37 H = B / ( s−A) ;38 ho ld on39 [Y, t ime ] = s t e p (H) ;40

41

42 I avg = i m p o r t d a t a ( ’ OpenLoop_data . x l s x ’ )43 f i g u r e ( 1 )44 p l o t ( I avg . d a t a ( : , 1 ) , I avg . d a t a ( : , 2 ) , ’−r ’ , I avg . d a t a ( : , 5 ) , I avg . d a t a

( : , 6 ) , ’−−b ’ , I avg . d a t a ( : , 3 ) , I avg . d a t a ( : , 4 ) , ’ : k ’ )45 y l a b e l ( ’ I avg (A) ’ )46 x l a b e l ( ’ Time ( s e c ) ’ )47 l e g e n d ( ’ I_ avg exp ’ , ’ I_ avg HIL ’ , ’ I_ avg sim ’ )

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[3] MANU BALAKRISHNAN, N. K. N. (2015) “Detection of Plunger Movement in DC Solenoids,”A White Paper by Texas Instruments.

[4] BADR, M. F. (2018) “Modelling and Simulation of a Controlled Solenoid,” IOP ConferenceSeries: Materials Science and Engineering, 433 012082.

[5] KRAMER, A. and A. PHILLIPS (2018) “Hydraulic Solenoid Valve System Identification forCrane Hoist Control System,” An undergraduate project report, Department of ElectricalEngineering, The Pennsylvania State University.

[6] ALI ASGHAR GHADIMI, A. K., HASSAN RASTEGAR (2007) “Development of Average Modelfor Control of a Full Bridge PWM DC-DC Converter,” Journal of Iranian Association ofElectrical and Electronics Engineers, 3(2).

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