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7.9 Proportional+Integral+Derivative (PID) control
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The following points arise:
• with acceleration feedback the maximum pressure differential is around 20 bar compared with around 110bar without acceleration feedback
• the introduction of acceleration feedback has removed the high frequency oscillation in pressure differential
• the position transient behaviour might be considered as improved in an overall sense but the response cannot be made initially faster by the use of additional acceleration feedback
• increasing the accelerometer gain +D
will create a larger over-shoot and the response at the beginning will be more sluggish189
In electrohydraulic control systems PID control is useful if a free integrator does not exist in the system forward loop transfer function, for example speed control, since by definition the integral component in PID control adds this effect. It does seem in practice that for the case of steady-state error removal it is usual to just consider PI control by adding an integral term.
The Derivative element of PID control does not seem to be popular for many electrohydraulic control systems, particularly servodrives, one exception perhaps being for materials dynamic test machines where the load dynamics includes material stiffness. The machine manufacturer will provide design rules for setting up the controller.
In some control systems such as with a servovalve directly moving a pilot valve poppet, which then controls flow into the drive actuator, then a double intergrator term dominates the OLTF. the addition of Derivative control in the forward loop, or in the feedback loop, can be considered. If derivative action is generated via a digital controller then again the signal will require bandwidth limitation to avoid higher noise frequencies being amplified.
For conventional servodrives the use of Derivative control in the forward loop has the same effect as adding it into the feedback loop. It also seems that wherever it is added it may not have any significant effect on reducing pressure oscillations.
Example 7.5
Consider the motor speed control system investigated as Example 6.3 where stability was ensured using frequency response, and an open-loop gain .= 0.76 was selected for proportional control only. The system is again shown.
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Servovalve damping ratio ȗVY§ undamped natural frequency ȦQVY UDGV§+]
Motor damping ratio ȗ undamped natural frequency ȦQ UDGV§+]
Demanded motor speed ωd = 100rpm
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PID control is now investigated to both reduce the speed fluctuations still existing in the original design and also to remove the steady-state error in achieved motor speed. The new block diagram is next shown.
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• the existing gain . = 0.76 was retained
• derivative action was first introduced using the computer simulation and a time constant was found by trial and error, a suitable value being IJG = 0.01s to give an acceptable transient response overshoot
• integral action was then added and a time constant selected, coincidentally, to be the same as that for derivative action and therefore IJL = 0.01s
The PID tuning then produced an acceptable transient response. Further tuning could be pursued, particularly with regard to gain selection and the tracking error in response to a ramp demand speed.
This is not pursued here and the new design performance is now shown.
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It can be seen that the addition of derivative control has adequately reduced the oscillation and the further addition of integral control has resulted in the desired steady-state speed.