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Analysis of a flight motion controller

Thanh Lan Vu & Russell Thamm Defence Science and Technology Organisation

Weapons Systems Division PO Box 1500

Edinburgh SA 5111 Australia

ABSTRACT

This study focuses on the performance analysis of a hydraulic based Flight Motion Simulator (FMS). Since the motion of each axis of the FMS is controlled independently from other axes by an individual motion controller, a nonlinear model of one axis of an FMS was developed in order to analyse and specify a new control system for the FMS. The paper presents a performance analysis of different control structures of an FMS motion controller, and the advantages and disadvantages of each control structure. In addition, the paper details the requirement specification of a new FMS motion controller in order to achieve the FMS’s optimum dynamic performance despite inherent nonlinearities, such as stiction and nonlinear orifice flow rate. Keywords: flight motion simulator, flight motion controller, flight motion table, HWIL.

1 INTRODUCTION Flight Motion Simulators play an important role for Hardware-In-The-Loop (HWIL) Simulation of air vehicles and missiles since they are used to simulate the rotational motion of the Unit Under Test (UUT). Hydraulic based FMS have a reasonably fast response, however, nonlinearities, such as stiction and nonlinear orifice flow rate, are often inherent in the hydraulic servo valves. The nonlinear effect should be considered when designing a control system for an FMS in order to minimise the impact of the nonlinearity on the dynamic performance of the FMS. Otherwise, the FMS can, in worst cases, start to oscillate if the nonlinearity becomes dominant. The first aim of this paper is to describe the characterisation of a FMS in order to identify the nonlinearities existing in the FMS. As part of the characterisation of an FMS, a nonlinear model of one axis of an FMS was developed in order to analyse and specify a new control system for the FMS. Secondly, the paper details the requirement specification for a new FMS motion controller in order to achieve the FMS’s optimum dynamic performance despite the nonlinearities existing in the system. Finally, the paper presents a performance analysis of different control structures of an FMS motion controller, and the advantages and disadvantages of each control structure. As the result of the analysis, the best control structure, in terms of stability, robustness and dynamic performance is proposed in the paper.

2 CHARACTERISATION OF THE FMS

2.1 Nonlinear behaviour of the FMS

2.1.1 Stiction Stiction or static friction is a well-known problem for hydraulic systems, and is mainly due to the friction between the spool and sleeve of a servo valve. Stiction increases greatly as the servo valves gradually clog over their life time due to oil contamination. Oscillations may occur in the control system if the stiction becomes severe. Since all the axes of the FMS are driven by hydraulic control valves, it is important to examine the severity of stiction existing in each axis of the FMS. As the motion of each axis of the FMS is controlled by an individual motion controller, the performance of each axis could therefore be characterised and analysed independently. Figure 1 shows a block

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diagram of the control system for one axis of the FMS which contains two feedback loops: an inner pressure loop and an outer displacement feedback loop.

Figure 1: Block diagram of the FMS control system for one axis.

During a HWIL simulation, the demanded displacement, velocity and acceleration for each axis generated from the airframe model of the UUT are fed to the motion controller. The motion controller then derives the command displacement, velocity and acceleration motion of each axis based on the demanded displacement, velocity and acceleration in order to ensure that the motion of the axis does not exceed the displacement, velocity or acceleration limits. The difference between the command displacement and estimated current displacement, and command velocity and estimated current velocity are fed to the displacement and velocity compensator. The compensator derives an output which is compared with the differential pressure signal measured across the valve orifice. The error between the compensator output and the measured differential pressure is then fed to a pressure compensator. The output of the pressure compensator is then used to drive the servo valves in such a way that the difference between the command displacement and estimated current displacement is minimised. In order to examine whether there is stiction existing in the control valves of the FMS, a low frequency sinusoidal signal with a small excitation amplitude was used to excite the inner pressure loop of one axis at a time, as shown Figure 2, while the outer displacement feedback loop was disconnected. Figure 3 shows the measured differential pressure against the demand pressure input to the control valves for a sinusoidal signal at 2 Hz with an excitation amplitude of 0.1 volts. As can be seen from the figure, the measured differential pressure was no longer coherent with the sinusoidal input. As the excitation amplitude increased, the measured differential pressure became coherent with the sinusoidal input as shown in Figure 4. The phenomenon is a typical characteristic of stiction. Without proper compensation, the axis will exhibit the nonlinear behaviour due to stiction.

Estimated Dis/Vel

Filters Inductosyn

& Resolver

Dis/Vel Compensator

Servo amplifier _

Pressure Compensator

Valve &

Actuator &

Load

Differential Pressure

Transducer

_

Demanded Dis/Vel



Figure 2: Illustration of stiction testing for the inner pressure loop of one axis of the FMS.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time [s]

Pre

ssur

e [V

olts

]

Input to the current driverMeasured differential pressure

Figure 3: Measured differential pressure versus the current driver input for a sinusoidal signal at 2 Hz with an excitation

amplitude of 0.1 volts.

Estimated Dis/Vel

Filters Inductosyn

& Resolver

Demanded Pressure [volts]

Dis/Vel Compensator _


Valve &

Actuator &

Load


Transducer

Servo amplifier _



1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time [s]

Pre

ssur

e [V

olts

]

Input to the current driverMeasured differential pressure

Figure 4: Measured differential pressure versus the current driver input for a sinusoidal signal at 2 Hz with an excitation

amplitude of 0.3 volts. In order to illustrate the effect of stiction on the performance of the outer displacement feedback loop, a low frequency sinusoidal with low excitation amplitude was used to excite the outer displacement feedback loop as shown in Figure 1. Figure 5 shows the measured versus demanded displacement for one axis of the FMS for a sinusoidal input at 1 Hz with an excitation amplitude of 0.25◦. As can be seen from the figure, the measured displacement of the axis was no longer sinusoidal due to stiction existing in the system. The axis did not move when the demanded velocity is below the threshold, ±1◦/s as shown in Figure 6. However, both measured displacement and velocity of the axis were sinusoidal when the excitation amplitude increased to 30◦ for the same excitation frequency, at 1 Hz, as shown in Figures 7 and 8, respectively.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time [sec]

Dis

plac

emen

t [D

egre

es]

DemandedMeasured

Figure 5: Measured versus demanded displacement for a sinusoidal signal at 1 Hz with an excitation amplitude of 0.25◦.



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-5

-4

-3

-2

-1

0

1

2

3

4

5

Time [s]

Vel

ocity

[Deg

rees

/sec

]

DemandedMeasured

Figure 6: Measured versus demanded velocity for a sinusoidal signal at 1 Hz with an excitation amplitude of 0.25◦.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

-40

-30

-20

-10

0

10

20

30

40

50

Time [s]

Dis

plac

emen

t [D

egre

es]

DemandedMeasured

Figure 7: Measured versus demanded displacement for a sinusoidal signal at 1 Hz with an excitation amplitude of 30◦.



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-300

-200

-100

0

100

200

300

Time [s]

Vel

ocity

[Deg

rees

/sec

]

DemandedMeasured

Figure 8: Measured versus demanded velocity for a sinusoidal signal at 1 Hz with an excitation amplitude of 30◦. Figure 9 shows the effect of the stiction on the performance of the FMS during a typical HWIL simulation. The axis did not track the demand input well when the demand input was slowly varying.

6 6.5 7 7.5 8 8.5 9 9.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Time [s]

Dis

plac

emen

t [D

egre

es]

DemandedMeasured

Figure 9: Measured versus demanded displacement during a typical HWIL simulation.



2.1.2 Nonlinear servo valve flow rate Figure 10 shows the flow characteristic of a servo valve. As can be seen from the figure, the flow rate is nonlinear with the load pressure drop. In addition, the relationship between the flow rate and load pressure drop changes with the input current to the servo valve. Figure 11 shows the closed-loop frequency responses of one axis of the FMS for different excitation amplitudes. The gain of the closed-loop frequency response is the ratio of the measured displacement amplitude of the axis to a sinusoidal demanded displacement amplitude at a particular excitation frequency for a specified excitation amplitude. The phase shift of the closed-loop frequency response is the time separation between a sinusoidal demanded displacement input and the corresponding displacement output measured at a specified excitation frequency and amplitude. Both gain and phase shift are changing with excitation amplitude as well as excitation frequency. The larger the excitation amplitude, the larger the gain and the phase shift are. This is due to the nonlinear servo valve flow rate.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Normalised load pressure drop [%]

Ser

vo v

alve

flow

rate

[%]

25% Servo valve current




Figure 10: Servo valve flow characteristic.

0 5 10 15 20 25 300

0.5

1

1.5

Frequency [Hz]

Gai

n

Excitation amplitude:1o



0 5 10 15 20 25 30-300

-200

-100

0

Frequency [Hz]

Pha

se [D

egre

es]




Figure 11: Frequency response of one axis of the FMS for different excitation amplitudes.



2.2 System performance analysis The following tests were performed in order to examine the performance of the FMS:

• Peak rate and acceleration • Step response • Frequency response

2.2.1 Peak rate and acceleration The maximum bandwidth of an axis is determined by the peak rate and acceleration of the axis. The higher the peak rate and acceleration of an axis is, the higher bandwidth the axis can achieve. Again, the higher bandwidth the axis has, the faster the axis can respond to the demand input. In order to measure peak rate and acceleration of an axis, a demand displacement step input of 90◦ was used to drive the axis. The controller was configured so that the axis response was not limited. The estimated rate of the axis was captured at a sample rate of 450 Hz which is much lower than the sample rate of the control loop and the sensors in order to avoid any spike due to sensor glitch in the estimated rate. The estimated rate was then used to estimate the peak acceleration.

2.2.2 Step response The step response of an axis provides the dynamic performance of the axis in terms of rise time, overshoot, settling time and steady state error. The rise time is defined as the time required for the response of the axis to rise from 10 % to 90% of it’s final value. The overshoot is the maximum peak value of the response of the axis. The settling time is defined as the time required for the response to decay within ±1% of it’s final value. The steady state error is the difference between the desired response and the actual response of the axis when the axis reaches a steady state. In order to ensure that the quality of a Hardware-In-the-Loop (HWIL) testing is not degraded by the performance of the FMS, the axis response is desired to have short rise time and settling time, small overshoot (an overshoot of less than 10% of it’s step input is desirable), and small steady state error (an error of less than 10% of it’s step input is desirable).The impact of the axis performance on the quality of the HWIL testing is dependent on the Unit-Under-Test (UUT). A highly agile UUT requires the response of the axis to have shorter rise time, smaller overshoot and steady state error than for the case of a less agile UUT.

7.5 7.55 7.6 7.65 7.7 7.75 7.80

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time [s]

Dis

plac

emen

t [D

egre

es]

1o

2o

3o

5o

Figure 12: Step responses of an axis for different positive excitation amplitudes.

Rise Time

Overshoot

Steady state error

Settling Time



2.2.3 Frequency response Figures 13 and 14 show the frequency response of the closed-loop of an axis of the FMS plotted in linear and logarithm scale, respectively. The closed-loop frequency response describes the relationship between the measured and demanded displacement in frequency when both differential pressure and measured displacement are fed back in order to determine the motion of the axis. The gain of the frequency response is the ratio between the magnitude of the sinusoidal input and the magnitude of the sinusoidal output. The time delay, Td, between the sinusoidal output and input at the excitation frequency ω of the axis can be derived based on the phase shift of the frequency response at the frequency ω [Hz] as follows:

°×−

=360ω

shiftPhaseTd Eq. (1)

The frequency response provides alternative information on the dynamic performance of the axis in terms of bandwidth, gain and phase shift. The bandwidth is defined to be the maximum frequency, ωb, at which the output of a system will track a sinusoidal input in a satisfactory manner [1]. By convention, for the system with a sinusoidal input at frequency ωb, the magnitude of the output is attenuated to a factor 0.707 times the magnitude of the input. The closed-loop bandwidth is inversely proportional to the rise time of the step response. In other words, a higher bandwidth means a shorter rise time in the step response of the axis. It is desirable to have the gain of the closed-loop frequency response close to 1 (or 0dB) for all the frequencies below half the bandwidth frequency. The closer the gain is to 1, the smaller tracking error the axis has. In fact, the low frequency gain of the closed-loop frequency response determines the steady state error of the step response. The overshoot of the step response of the axis is proportional with the resonance peak, which is defined as the maximum magnitude of the closed-loop frequency response.

0 10 20 30 40 500.6

0.8

1

1.2

1.4

Frequency [Hz]

Gai

n

0 10 20 30 40 50

-80

-60

-40

-20

0

Frequency [Hz]

Pha

se [D

egre

es]

Figure 13: Frequency response of an axis plotted linear scale.



100 101

-2

0

2

Frequency [Hz]

Gai

n [d

B]

100 101

-80

-60

-40

-20

0

20

Frequency [Hz]

Pha

se [D

egre

es]

Figure 14: Frequency response of an axis plotted in logarithm scale.

3 MODELLING OF THE FMS Figure 15 shows a model of the control system for one axis of the FMS implemented in Simulink. As a main objective of this work is to analyse the performance of the FMS with different motion controllers, the development of the model of the servo valves, actuator and load for each axis of the FMS is, therefore, the main focus of modelling. The inputdata, dispdata and TP4 blocks shown in the figure are the demanded, measured displacement and differential pressure, respectively. The derived displacement and velocity of the axis are assumed to be noise free. In order to validate the model, the FMS control system for one axis is subdivided into subsystems for modelling and validation. The input and output of each subsystem were captured for validation, if possible, while the motion of each axis was controlled by a displacement feedback loop. Figure 16 illustrates the validation of the digital compensator for the motion controller as an example of the validation of a subsystem. The error between the demanded displacement, HardPos, and the measured displacement, disdata, and the demanded velocity, HardVel, are fed into the model of the digital compensator. The output of the model is compared with the captured output of the digital compensator while the axis was running in a digital closed displacement feedback loop. Figure 17 shows that the output of the model of the digital compensator agrees well with the captured output.



Figure 15: Simulink model of the control system for one axis of the FMS.

Figure 16: Illustration of the validation of the model for the digital compensator.

Scope4

-1

Gain

dispdata

FromWorkspace4

TP1

FromWorkspace3

HardVel

FromWorkspace1

HardPos

FromWorkspace

Digital compensator

Compensator1



0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time [s]

Out

put o

f the

dig

ital c

ompe

nsat

or [v

olts

]

Model outputMeasured output

Figure 17: Output of the digital compensator model versus the captured output.

Figure 18 shows a Simulink model of the servo valve, actuator and load.

Figure 18: Simulink model of the servo valve, actuator and load.

Figure 19 shows the measured differential pressure versus the differential pressure derived from the model. The high frequency component appearing in the measured differential pressure is believed to be due to electrical noise in the Analog-Digital converter used to capture the analog signal from the differential pressure transducer.



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.6

-0.4

-0.2

0

0.2

0.4

Time [s]

Diff

eren

tial P

ress

ure

[Vol

ts]

MeasuredEstimated

Figure 19: Measured versus estimated differential pressure.

Figures 20 to 23 show the measured displacement versus the displacement derived from the model for different excitation displacement inputs. As can be seen from the figures, the displacement derived from the model corresponded well with measured displacement for different excitation displacement inputs.

7.4 7.6 7.8 8 8.2 8.4 8.6-2

-1

0

1

2

3

4

Time [s]

Dis

plac

emen

t [D

egre

es]

DemandedMeasuredEstimated

Figure 20: Measured versus estimated displacement for a step input of ±2◦.



7.4 7.6 7.8 8 8.2 8.4 8.6 8.8

-20

-15

-10

-5

0

5

10

15

20

25

30

35

Time [s]

Dis

plac

emen

t [D

egre

es]


Figure 21: Measured versus estimated displacement for a step input of ±20◦.

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time [s]

Dis

plac

emen

t [D

egre

es]


Figure 22: Measured versus estimated displacement for a sinusoidal input at 10 Hz with excitation amplitude of 1◦.



0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

-10

-5

0

5

10

Time [s]

Dis

plac

emen

t [D

egre

es]


Figure 23: Measured versus estimated displacement for a sinusoidal input at 10 Hz with excitation amplitude of 7◦.

4 DETERMINE PERFORMANCE REQUIREMENT SPECIFICATIONS

4.1 Determine the closed-loop bandwidth of the FMS The maximum closed-loop bandwidth of an axis is defined to be the maximum bandwidth the closed-loop control system of the axis can achieve if the controller is optimally tuned. The closed-loop system, in this context, is the control system where the differential pressure and measured displacement are fed back in order to determine the motion of the axis. The bandwidth is as defined in Section 2.2.3.

The maximum closed-loop bandwidth of an axis for a particular excitation amplitude is determined by the peak acceleration of the axis as follows:

2/1

maxb 2

1⎟⎠⎞

⎜⎝⎛≤

aA

πω Eq.(2)

where Amax is the peak acceleration of the axis, and a is the excitation amplitude of the sinusoidal input.

The higher the peak acceleration, the larger the closed-loop bandwidth will be. The closed-loop bandwidth decreases with increasing excitation amplitude.

In order to reduce excessive wear of the actuator, the closed-loop bandwidth should be lower than the bandwidth of the hydraulic servo valves installed in the axis.

The peak accelerations and rates of the axes of the FMS should be greater than the body accelerations and rates of the airframe of the UUT. Generally, a tolerance of at least 10% should be taken into account in the system performance specification. In other words, if the maximum demand body rate and acceleration of an axis of the UUT are φ (◦/s) and ω (◦/s2), the peak rates and accelerations of the FMS should be Vmax ≥ 1.1φ and Amax ≥ 1.1ω, respectively.



Ideally, the FMS should be designed so that the structural resonances are well above the closed-loop bandwidth. However, if structural resonances do occur below the closed-loop bandwidth, notch filters can be introduced in the control loops in order to reduce the instability caused by such resonances.

4.2 Determine the closed-loop frequency response In order to ensure that the performance of the FMS does not degrade the HWIL testing, the axes are required to have good tracking capability. In other words, the measured displacement of axis follows the demanded displacement with the minimum difference possible. The difference between the measured and demanded displacement of the axis in this paper is defined as an orientation error of the axis. The impact of orientation errors of the FMS axes on the HWIL testing will increase with the increasing speed of the UUT. The orientation error of an axis is determined by the rise time, overshoot and steady state error characteristics of the axis. The shorter the rise time, and the smaller steady state error and overshoot of the step response, the smaller the orientation error of the axis will be. The rise time is inversely proportional to the closed-loop bandwidth. The higher the closed-loop bandwidth, the shorter the rise time. The steady state error is determined by the low frequency gain of the closed-loop frequency response, and the overshoot is determined by the resonance peak of the closed-loop frequency response. Let ε and ∆ε be the maximum orientation error and the error margin of an axis, respectively. The maximum orientation error is, in this context, defined as the most acceptable orientation error an axis can have without compromising the HWIL testing of the particular UUT. The error margin is the gap between the maximum and the actual orientation error, α. In order to ensure that the orientation error of an axis never exceeds the maximum orientation error, the gain of the closed-loop frequency response of the axis for all frequencies well below half the bandwidth frequency should be equal or less than 1± α or 1± (ε -∆ε), where ∆ε could be between 60% and 80% of the maximum acceptable orientation error, ε. In other words, αω ±≤− 1)(loopclosedH for all bωω 5.0<< , where )(ωloopclosedH − is the gain of the closed-loop

frequency response, and bω is the closed-loop bandwidth. The phase shift or time lag between the demanded and measured displacement also contributes to the orientation. It is therefore desirable that the phase shift of the closed-loop frequency response is less than 90◦ for all frequencies below the closed-loop bandwidth. Figure 26 illustrates the specification of the closed-loop frequency response of an axis in terms of gain and phase in order to ensure that the orientation error is within the maximum orientation error of the axis.

100 101

-4

-2

0

2

Frequency [Hz]

Gai

n [d

B]

100 101-100

-50

0

Frequency [Hz]

Pha

se [D

egre

es]

Figure 24: Specification for the closed-loop frequency response.

Closed-loop bandwidth, ωb

1±α

obloopclosedH 90)( −≤<∠ − ωω



4.3 Determine controller structure In order to ensure that the measured displacement of an axis follows the demanded displacement input, the controller should have a displacement feedback loop as a minimum requirement for a control structure. In addition to the displacement feedback loop, there are differential pressure and rate feedback loops which can be introduced as internal loops. In this paper, the performance of the following controller structures will be investigated:

• Displacement feedback loop only • Displacement and differential pressure feedback loops • Displacement, differential pressure and rate feedback loops • Displacement, differential pressure and rate feedback loops and rate feedforward loop.

4.3.1 Displacement feedback Figure 25 shows the control loop of one axis of the FMS where only displacement feedback was employed.

Figure 25: The control structure with displacement feedback loop only.

The advantage of this control structure is its simplicity. Only a displacement transducer is required. Since it is only a single loop, it is easy to tune. A Proportional or Proportional-Derivative (PD) controller is recommended. A Proportional-Integral-Derivative (PID) is not desirable since there is sufficient lag in the system. Care should be taken when tuning the Derivative of the PD controller. The disadvantage of this control structure is that the performance of the axis is sensitive to any change in the system such as load change or oil temperature change. Figure 26 shows the step responses of an axis for different loads. The heavier the load is, the larger the overshoot and rise time of the step response.

Estimated Displacement Filters

Inductosyn &

Resolver

Displacement Compensator

Servo amplifier

Demanded Displacement

Valve &

Actuator &

Load _ +

Dither



5 5.5 6 6.5 7 7.5 80

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time [s]

Dis

plac

emen

t [de

gree

s]

Step inputStep response with a ligher loadStep response with a heavier load

Figure 26: Step responses for different loads.

In addition, the control structure with displacement feedback only is not capable of compensating for the nonlinear orifice flow rate and stiction existing in the hydraulic servo valves as mentioned in Section 2. Figure 27 shows the step responses of an axis for different excitation amplitudes. As can be seen from the figure, the step response has higher overshoot with increasing excitation amplitudes.

5 5.5 6 6.5 7 7.5 80

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Time [s]

Dis

plac

emen

t [de

gree

s]

17% overshoot

12% overshoot

10% overshoot

Response for a step input of 10



Figure 27: Step responses for different excitation amplitudes.

There are two alternatives to compensate for the nonlinear orifice flow rate. The first option is to introduce gain scheduling in the displacement feedback loop as shown in Figure 28. The gain scheduling should be an inverse of the



nonlinear characteristic of the servo valves. The gain scheduling is only recommended if the nonlinear characteristic of the servo valves can be determined. Another alternative is to introduce differential pressure and rate feedback loops. In addition to the compensation of the nonlinearity, a combination of differential pressure and rate feedback compensates any change in the plant as well as yields better stability performance in terms of improving the bandwidth, steady state error and better damping. Further details on the performance of a combination of the displacement, differential pressure and rate feedback loops will be presented in Section 4.3.3.

Figure 28: The control structure with displacement feedback loop only and gain scheduling. Stiction can be reduced by superimposing the control signal with a dither signal at a frequency well above the bandwidth (varied from 300Hz to 400 Hz). The amplitude of the dither should be reasonably low in order to reduce excessive wear of the servo valves, but large enough to move the actuator. Figure 29 shows the response with versus without the implementation of the dither signal for a sinusoidal displacement input at 1 Hz with an excitation amplitude of 0.1◦. As can be seen clearly from the figure, the impact of the stiction can be significantly reduced by introducing the dither signal. The measured displacement with the implementation of the dither signal becomes more sinusoidal than for the case without the dither.

4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2

-0.1

-0.05

0

0.05

0.1

0.15

Time [s]

Dis

plac

emen

t [de

gree

s]

Demanded displacementResponse without ditherResponse with dither

Figure 29: Response with versus without dither for a sinusoidal input at 1 Hz with an excitation amplitude of 0.1◦.

Estimated Displacement Filters

Inductosyn &

Resolver


Servo amplifier

Valve &

Actuator &

Load _

+


Gain Scheduling

Dither



4.3.2 Displacement and differential feedback loops Figure 30 shows the controller structure with a combination of displacement and differential feedback loops. The differential pressure feedback is an internal loop whereas the displacement feedback is an outer loop. A Proportional – Integral (PI) controller is recommended for the differential pressure feedback loop whereas a PD controller is implemented in the displacement feedback loop.

Figure 30: A control structure with a combination of displacement and differential feedback loops.

With this control structure, the axis has slightly better damping. In other words, the step response will have smaller overshoot compared to the step response for the control structure with displacement feedback only as can be seen in Figure 31. Another advantage of this control structure is that the performance of the axis is less sensitive to any change in the system such as load change or oil temperature change. Figure 32 shows the step responses of an axis for different loads. As can be seen from the figure, the step responses of an axis are very similar for different loads. The disadvantage of this control structure compared to the control structure with displacement feedback only is the added complexity since there are two feedback loops. It, therefore, requires more time for tuning. Furthermore, additional transducers such as pressure transducers are required for the pressure feedback loop. Similar to the control structure with displacement feedback only, this control structure does not compensate for the nonlinear orifice flow rate. Figure 33 shows the step responses of the control structure combining the displacement and differential pressure feedbacks for different excitation amplitudes. As can be seen from the figure, the overshoot of the step response increases with increasing excitation amplitude.

Estimated Displacement

Filters Inductosyn

& Resolver



Transducer

_ Pressure

Compensator +

Dither

Servo amplifier


_

Valve &

Actuator &

Load



5 5.05 5.1 5.15 5.2 5.25 5.3 5.35 5.40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time [s]

Dis

plac

emen

t [de

gree

s]

Step inputStep response with disp & diff pressure fbacksStep response with displacement feedback only

Figure 31: Step response with displacement feedback only versus with a combination of displacement and differential

pressure feedbacks.

5 5.05 5.1 5.15 5.2 5.25 5.3 5.35 5.40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time [s]

Dis

plac

emen

t [de

gree

s]

Step inputStep response with a ligher loadStep response with a heavier load

Figure 32: Step responses for different loads.



5 5.1 5.2 5.3 5.4 5.5 5.60

1

2

3

4

5

Time [s]

Dis

plac

emen

t [de

gree

s]

16% overshoot

12% overshoot

10% overshoot





4.3.3 Displacement, differential pressure and rate feedback loops Figure 34 shows the control structure with a combination of the displacement, differential pressure and rate feedback loops. There are two internal loops: the first internal loop is the differential pressure feedback, and the second is the rate feedback; and one outer displacement feedback. A Proportional controller is recommended for the differential pressure feedback loop since the rate feedback loop substitutes the benefits of the Integral part of the PI controller in the differential pressure feedback. A Proportional controller is also recommended for both rate and displacement feedbacks.

Figure 34: The control structure with a combination of the displacement, differential pressure and rate feedback loops.


Filters

Displacement Compensator _


Demanded Displ

_ Rate

Compensator

Estimated Rate

_ Servo

amplifier

Valve &

Actuator &

Load

+

Dither


Transducer

Inductosyn &

Resolver



Figure 35 shows the step responses of an axis for three different control structures: a) a combination of displacement, differential pressure and rate feedbacks, b) a combination of displacement and differential pressure feedbacks and c) displacement feedback only. As can be seen from the figure, the control structure with a combination of displacement, differential pressure and rate feedbacks yields superior step response performance compared to the other two control structures in terms of rise time, overshoot and settling time.

5 5.05 5.1 5.15 5.2 5.25 5.3 5.35 5.40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time [s]

Dis

plac

emen

t [de

gree

s]

Step response with disp, diff pressure & rate fbacksStep response with disp & diff pressure fbacksStep response with displacement feedback only

Figure 35: Step responses for three different control structures.

Another advantage of this control structure is that it is capable of compensating for the nonlinear orifice flow rate. Figure 36 shows the step responses of an axis for different excitation amplitudes for the control structure with a combination of displacement, differential pressure and rate feedbacks. It is clear in this case that the variation of the step response overshoot with increasing excitation amplitude is not as prominent as that obtained by using the other two control structures (as shown in Figures 27 and 33).

5 5.05 5.1 5.15 5.2 5.25 5.30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time [s]

Dis

plac

emen

t [de

gree

s]

10% overshoot

11% overshoot

12% overshoot







Although this control structure is more complex than the other two due to the number of feedback loops, it is easier to tune as all the feedback loops require only Proportional control. The control structure requires the same number of transducers as for the control structure with a combination of displacement and differential pressure feedbacks. Rate of an axis can be estimated using the information provided by the displacement transducers.

4.3.4 Displacement, differential pressure and rate feedback loops and rate feedforward loop Figure 37 shows the control structure with a combination of the differential pressure, rate and displacement feedback loops and rate feed-forward loop. In addition to the demanded displacement, demanded rate was used to determine the movement of an axis. A Proportional controller is recommended for all the loops. Rate feedforward can increase the bandwidth of an axis further, but care should be taken when tuning the rate feedforward compensator since it can easily destabilise the behaviour of the axis. Figure 38 shows the step responses for the cases with and without rate feedforward loop. The step response for the control structure with rate feedforward loop has slightly shorter rise time than the step response for control structure without rate feedforward loop. The higher the gain of the rate feedforward loop, the faster the step response becomes. However, there is a trade-off between the rise time and overshoot. The overshoot increases with increasing gain value. The axis can even become unstable if the gain is too high.

Figure 37: Control structure with a combination of displacement, differential pressure and rate feedbacks and rate

feedforward.


Filters

Displacement Compensator _


Demanded Displ

_ Rate

Compensator

Estimated Rate

_

dtxd&

+

Estimated Demand Rate

Rate feedforward

Servo amplifier

Valve &

Actuator &

Load

+

Dither


Transducer

Inductosyn &

Resolver



5 5.02 5.04 5.06 5.08 5.1 5.12 5.14 5.16 5.18 5.2

0.2

0.4

0.6

0.8

1

1.2

Time [s]

Dis

plac

emen

t [de

gree

s]

With rate feedforwardWithout rate feedforward

Figure 38: Step responses for the control structure with and without rate feedforward loop.

In summary, Sections 4.3.1 to 4.3.4 describe the advantages and disadvantages of four different control structures:

1. Displacement feedback loop only, 2. A combination of displacement and differential pressure feedback loops, 3. A combination of displacement, differential pressure and rate feedback loops, and 4. A combination of displacement, differential pressure and rate feedback loops, and rate feedforward.

The first control structure is simple, but is not capable of compensating for any changes to the system or nonlinear orifice flow rate existing in the hydraulic FMS. Adding the differential pressure feedback, but without rate feedback, the step response is very slightly improved in terms of overshoot. In addition, the step response is less sensitive to any change such as load change in the FMS compared to the step response for the first control structure. However, the second control structure is unable to compensate for the nonlinear flow rate. The step response improves significantly in terms of overshoot, rise time and steady state error with the third control structure where the rate feedback is added. This control structure is also capable of compensating for any system change or nonlinear orifice flow rate. The step response for the fourth control structure is slightly faster than the one for the third control structure, but extreme care must be taken when tuning the gain of the rate feedforward loop. The FMS can easily destabilise if the gain is too high. In addition, in a long run there is a higher risk for mechanical wear and tear with the fourth control structure since the demand on the physical systems such as servo valves and actuators is higher. Therefore, the third control structure appears to be the best control structure in terms of stability, robustness, and dynamic performance such as overshoot, rise time and steady state error. Although the control structure with a combination of displacement, differential pressure and rate feedbacks contains three feedback loops, it is easy to tune since Proportional control can be implemented for all the loops. This control structure is highly recommended for any hydraulic based FMS.

5 CONCLUSIONS The paper has described the method used for the characterisation of a hydraulic based FMS and for determining the performance and controller requirements for the FMS.



A nonlinear model of one axis of the FMS has been proposed in the paper. The performance of this model correlates well with that of the actual response of the FMS axis. The model exhibits the nonlinear behaviours of the axis observed during the characterisation of the FMS. This developed nonlinear model has been useful for the performance analysis of different controller structures. The controller structure with a combination of displacement, differential pressure and rate feedbacks appears to be the best control structure for a hydraulic based FMS. It is capable of compensating for the nonlinearity as well as any change in the hydraulic FMS system. However, rate feedback should never be implemented without differential pressure feedback loop[2].

6 ACKNOWLEDGEMENTS The authors would like to acknowledge Mr Mark Warner for his contribution in operating the FMS, and Dr Domenic Bucco for his valuable comments on this paper.

7 REFERENCES [1] Franklin, G.F., Powell, J. D. and Emami-Naeini, A., [FEEDBACK CONTROL OF DYNAMIC SYSTEMS],

Addison-Wesley Publishing Company, New York, p.343, Third Edition, 1994. [2] Haugen, F., [Anvendt regulerings teknikk], Tapir forlag, Norway, p.467, 1990.



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