teaching process control in instrumentation and control...

TEACHING PROCESS CONTROL IN INSTRUMENTATION AND CONTROL LABORATORY

L. T. T. Vu, P. A. Bahri, G. R. Cole

School of Engineering and Energy, Murdoch University South Street Campus, Murdoch WA 6150

Email: [email protected]; [email protected]; [email protected]

ABSTRACT

The Instrumentation and Control Laboratory (IC-lab) was designed to provide separated modules of different types of heat exchangers, air-pressured vessels, water tanks, pumps, flow meters and control valves. These modules can be connected to provide various conventional pieces of process control equipment. Through the experiments designed for the IC-lab, students can obtain real hands-on experience. In the first two years of the IC course students learn to perform step-tests, develop linear and non-linear model, then design and implement P, PI and PID controllers in the real time systems. More sophisticated control schemes such as Cascade, Feedforward, Generic Model Control (GMC) or Fuzzy Logic Control can also be achieved in the lab. This paper demonstrated an example of generating a nonlinear system by connecting two pressured-air tanks and other modules. A step test is performed to determine an approximate model for the PI controller design. At the same time a mathematical model of the system is developed based on measurements and calibrations of the system. A GMC scheme is applied based on this model. Comparison of performances of the PI and GMC controllers to control the pressure in the vessel are finally presented and discussed.

INTRODUCTION

In 1997 Control and Thermal Engineering Pty Ltd in association with the School of Engineering at Murdoch University built the Instrumentation and Control Laboratory (IC-lab). This facility was designed to provide a physical process control environment for the purpose of training second-year and third-year Instrumentation and Control Engineering (ICE) students. The facility was composed of many separated modules such as different types of heat exchangers, air vessels, water tanks, pumps, flow meters and control valves. These modules can easily be connected to provide different process configurations. Each configuration is similar to a conventional piece of process control equipment. All switches, sensors, control valves and pneumatic actuators are operated through a networked computer based measurement and control system. The designed software support system for the IC-lab consists of a flexible interconnection network of analog and digital devices, which provides links from the modules to a Master I/O server. Students can independently design and implement their measurement and control programs on twelve individual workstations which in turn communicate with the Master I/O server over a TCP/IP network. LabVIEW, a graphical programming language is used in all server, measurement and control programs. LabVIEW can communicate with MATLAB to allow some desired computation and return of results to the control program.

In the first two years of the Instrumentation and Control course, engineering students have the opportunity of applying the control theories from the textbook to the laboratory replicating real processes. They can see and understand the actions of conventional

L.T.T. Vu, P.A. Bahri, G.R. Cole

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controllers on physical devices and processes. They can obtain hands-on experience from step-testing, model identification to designing and implementing the P, PI and PID controllers in real time. Design and implementation of more sophisticated control schemes such as GMC and fuzzy control schemes are also undertaken, providing an opportunity to gain further experience in the control area. To highlight the special nature of the IC-lab in training ICE students in the fields of intelligent control and real time systems, an example of the controller designing for the two pressured-air tanks will be discussed in the following sections.

PRESSURED-AIR TANK EXPERIMENT DESCRIPTION

Fig.1 shows a photo of five separated modules: (i) two modules containing two pressured-air tanks are mounted on the top rack; (ii) two modules containing two pneumatic control valves and two flow meters are on the middle one; and (iii) the fifth module on the bottom rack is the supply of water, steam, compressed air and low pressure instrument air particularly used for the pneumatic control valves.

Fig.1: Connection of five separated modules: (i) pressured-air tanks, (ii) pneumatic control valves, sensors and flowmeters, and (iii) supplies of steam, water and air

Each pressured-air tank is additionally equipped with a pressure gauge indicating the pressure in the vessel and two manual air valves. When connecting two or more tanks to create second or higher order, the manual valves can be adjusted to alter the steady state and dynamic characteristics of the overall system. The pressure in the tank can be controlled by manipulating the inlet or outlet valves, which in turn can alter the flowrate if the tank is connected to the pneumatic control valves and actuators on the second rack. In the same modules of the control valves there are two flow meters, which can be connected to the system to measure the actual inlet and outlet flowrates. These meters

Tank

Pressure gauge

Pneumatic actuator

Manual valve

Flow meter Sensor

Water, steam and air supply

Digital I/O

Analog I/O

Power supply


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measure the air flowrate, based on the same theory of a Pitot tube, by reading the difference in pressures between two points then converting to the mass or volumetric flowrate using the Bernoulli equation.

Sensors, control valves and pneumatic actuators on these modules can be connected to a panel of analog and digital inputs/outputs as shown on the left of Fig.1, providing links between modules and the Master I/O server. Measurements and control actions are implemented in one of the twelve workstations communicating with the Master I/O over a TCP/IP network. LabVIEW (National Instrument, 2009) is the graphical programming language used in the system. Fig.2 shows the front panel screen of the user developed LabVIEW program. It presents the flowsheet of the process, real-time measurements and graphs.

Fig.2: LabVIEW front panel screen presents the flowsheet of the two air-tank system, real-time pressure measurements and graphs of pressures in the tanks

The objects shown in the front panel screen of LabVIEW are wired together and the program graphical code is generated in the block diagram screen. With LabVIEW it is easy to measure and log data to a file, which can be later analysed in EXCEL or MATLAB for process model identification. Fig.3 shows a block diagram of this feature.


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Fig.3: LabVIEW block diagram shows the program graphical codes to measure and log data in an EXCEL file

PRESSURED-AIR TANK EXPERIMENT RESULTS AND DISCUSSION

All sensor measurements and actuator outputs are scaled from 0 to 100% of the normal range of operations, which represents from 0 to 140 psig in the flowmeter and 260 psig in the vessel. In this experiment, two air tanks were connected as shown in Fig.1; the manual valve between two tanks was 25% opened; the outlet valve was fixed at 25% and the inlet valve was stepped up from 25% to 75%. The dynamic responses of the pressures in the two vessels were displayed in Fig.1. Measured data were collected then sent to EXCEL and/or MATLAB for model identification as presented in the following sections.

Model identification, conventional controller design and implementation The dynamic response of the pressure in the second tank was slower than the pressure response of the first tank because the model of the overall system was second order, a combination of two first-order systems. The responses between the first order and second order systems were slightly different because the manual valve between two tanks was slightly opened resulting in a small valve resistance. These dynamic responses are presented in Fig.4, which shows the deviation of the new values from the steady state values of the two pressures in the first and second tanks, responding to a unit step point change in the inlet flow.


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Fig.4: Dynamic responses of pressures in the tanks to a unit step change in the inlet flowrate of air

To design a PI controller for controlling the air pressure in the second tank, a least square method was used in EXCEL to fit measured ∆P data to a first order model having gain K, time constant τ, and time delay α both in Laplace and time domain as shown in equation (1).

−=⇒

+=

−−−

ττ

αα )(

1)(1

)(ts

eKtgs

Kesg (1)

A second method involved with the MATLAB Identification Toolbox to estimate K, τ, and α. Both methods gave similar results.

The design of a PI controller was based on Ziegler-Nichols Approximate Model PID Tuning Rules (Ogunnaike and Ray, 1994). The controller gain Kc and integral time τi

were obtained from: ατατ

33.39.0 == ic K

K . The parameters of the model found for

both tanks and the PI controller parameters are shown in Tab.1; Fig.5 plots the approximate models compared with the pressures measured in both tanks.

LabVIEW has a built-in PID controller block for implementation, but for a better understanding of the control theories, students can design their own PI controller based on the approximate model. To control the pressure in the tank, the velocity form of a digital PI controller in equation (2) (Ogunnaike and Ray, 1994) was used in computing


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the position of the valve to adjust the air inlet flowrate, if a step change was introduced to the set-point of the pressure in the second tank.

)1()(1)1()( −−

∆++−= kKkt

Kkuku ci

c εετ

(2)

In equation (2) u(k) and u(k-1) are the current and previous control actions, respectively; ∆t stands for sample time selected by users; ε(k) and ε(k-1) are the current and previous errors defined by the deviation of the measured pressure from its set-point.

Tab.1: Approximate model and PI controller parameters

Tank 1

Tank 2

First order model

• Gain Kp (psi/%) 0.6 0.6

• Time constant τ (s) 11.1 11.8

• Time delay α (s) 3.5 4.6

PI controller design

• Gain Kc 4.8 3.8

• Integral time τi (s) 11.6 15.3

Fig.5: Dynamic responses of the pressures in the air tanks obtained from approximate models (curves) compared to measured data (data points)


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The discrete form of the controller in equation (2) could be easily coded in LabVIEW to read measured pressured from the tanks, compared with the desired set-point, calculated the control action and finally sent the signal back to the plant to adjust the position of the valve to increase or decrease the inlet flowrate, accordingly.

System model development and Generic Model Control design A mathematical model of the two air tank system was developed by a simple mass balance:

( )VM

RTww

dt

dP outin −=2 (3)

In these equations, P represents the pressure in psia, V is the volume of the tank in ft3, R is the gas constant (ft3.psi/lbmol°R), M is the molar weight of air (29 lbm/lbmol), T denotes the room temperature (68°F = 528°R), w is air mass flowrate (lb/s), and the subscript “in” and “out” stand for inlet and outlet flow rates, respectively.

Generic Model Control (GMC) strategy developed by Lee and Sullivan (1988) was implemented to maintain the pressure in the tank at a desired set-point by adjusting the

inlet flowrate. The GMC strategy is presented in equation (4), where ),(ˆ xyJ describes the approximate process model.

dtteKdtteKxyJt

∫+=0

21 )()(),(ˆ (4)

In equation (4), e is the difference between the desired output yd and the output y itself; x stands for the manipulated variable; K1 and K2 are tuning parameters. The procedure to select appropriate values of the tuning parameters was proposed by Lee et al. (1988). Equation (3) representing the mathematical model of the air tank could be substituted in equation (4) to solve for the manipulated variable win.

])()([0

21 dtteKdtteKRT

VMww

t

outin ∫++= (5)

Equation (5) is a simplified model. A complex model that more accurately takes into account the flow pressure characteristics of the valves and disturbances would result in a better control. The calibration of the flow meters to convert from flowrate to pressure then to the valve position was calculated based on the information given by the manufacturer Pcw ∆= α , where c and α were a known constant and position of the valve, respectively. Hence in terms of the valve position, equation (5) becomes


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])()([0

21 dtteKdtteKRT

VMPcPc

t

outoutoutininin ∫++∆=∆ αα (6)

inin

t

outoutout

inPc

dtteKdtteKRT

VMPc

∆

++∆=

∫ ])()([0

21αα (7)

To implement GMC control in LabVIEW, equation (7) must be in a discrete form. There are various ways of obtaining digital approximation of the integral term. The simplest method is the rectangular rule for numerical integration (Ogunnaike and Ray,

1994). Hence the integration ∫t

dtteK0

2 )( is replaced by the summation ∑=

∆k

t

ketK1

2 )( .

Equation (8) is obtained from discretising equation (7) and then taking the inverse z-transform.

inin

outoutout

inPc

ekekekeKkeKRT

tVMPc

∆

+−+−++∆+∆=

)]}1(....)2()1()([)({ 21αα (8)

Similar to a conventional controller, the discrete form of the GMC controller can be coded in LabVIEW to read measured values of pressures in the tanks, compare the measurements with the desired set-point, calculate the control action and finally send the signal back to the plant to adjust the position of the valve to increase or decrease the inlet flowrate, accordingly.

The control performances of the PI and GMC controllers responding to a set-point change in pressure from 20 to 60 psi are shown in Fig.6. The response of the PI controller is more sluggish compared to the GMC controller because only 90% of the tuned values of the gain and time constant were implemented. The values shown in Tab.1 made the control valve respond faster but as a result the control action was too aggressive. The GMC performance seems better but as a trade-off the overshoot is higher. The computation and coding in LabVIEW for a GMC controller are more complicated than for a PID controller. More importantly the GMC scheme requires a mathematical model, which can only be developed for a simple system like the system in this experiment. However for educational purposes this simplified model is more than adequate to demonstrate the principles of GMC to students. For a more complex system or when information required for developing a mathematical model is not available, step tests and PID controllers are more favourable.


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Fig.6: Comparison of control performances of PI and GMC controllers responding to a set-point change of pressure in Tank 2, from 20 psi to 60 psi

The experiment shown in the paper is a simple example to demonstrate two different ways of designing and implementing a conventional and more sophisticated control scheme. In a similar fashion other combinations of the modules generate different systems, for example different types of heat exchangers and conical-shape water tanks for model identification in the time domain or in the frequency-response domain. More creative combinations of these modules form more complex control systems. Another example is the connection of two water tanks with two inlet flows, which can be used to demonstrate the cascade control and feedforward control schemes. Finally for difficult dynamic systems or processes, which do not exist in the IC-lab, in particular an inverse response system or an unstable system, it is necessary to generate a hybrid system, a combination of a real time simulation and physical devices. Then the design of the compensation or pole cancellation control can be performed on this hybrid model.

CONCLUSION

To narrow the gaps between control theories and practice, the IC-lab was designed and built at the School of Engineering and Energy, Murdoch University to provide a real, practical environment for ICE students. The paper has demonstrated one example of how to realise the control theories in textbooks to control a physical system in real time. From such experience students can gain more knowledge of process and control engineering through learning to create both higher order and non-linear systems by connecting vessels, manual and control valves, sensors and actuators; perform a step test to find an approximate model and at the same time develop a mathematical model for the system. In doing so design and implementation of conventional and advanced controllers can be achieved based on the developed models. Controller tuning guidelines


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in textbooks are sometimes based on rules-of-thumbs. The IC-lab with computerised measurement and control capability and graphical display of results and performance offers students practical hands-on experiences in controlling different industrial-like processes. The facility plays an important role in teaching undergraduate process control engineering at Murdoch University.

REFERENCES

LabVIEW Software, National Instrument (2009) Lee, P.L. and Sullivan, G.R. (1988). Generic Model Control. Computer & Chemical Engineering, 12, 573 – 580. Lee, P.L., Newell R.B. and Cameron, I.T. (1988). Process Control and Management. Blackie Academic & Professonal, London. Ogunnaike, B.A. and Ray, W.H. (1994). Process dynamics, modelling and control. New York Oxford, Oxford University Press.

teaching process control in instrumentation and control...

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