Controller parameters
The last step is the computation of controller parameters for your process model and design specifications. The PID controller in PIDlab applets has a 2DOF ISA form.
A priori selected parameters
Before you define design specifications, it is necessary to choose the derivate filter part N and the ratio between integral and derivative time constant f=Ti/Td. You can start with predefined values that are recommended. These parameters have a strong influence at the robustness regions shape.
Choice of parameters K, Ki
These parameters should be chosen in intersection of admissible regions that are generated by design specifications. Typical is the intersection of two regions generated by gain and phase margin shaping points - see the left picture. We have always to choose the point with maximum Ki coordinate in the admissible area (the fastest and most aggressive controller).
Contradictory design specifications
Several admissible areas lie outside the region painted. One example is the region for low frequency disturbance dumping which is the contradictory design specification to the phase margin. Therefore, the intersection of admissible areas looks like the one depicted in the right picture.
How to fulfill the design specifications for the whole model set?
To ensure the fulfillment of design specifications while taken into account the uncertainty given by value sets you have to do the following: Firstly, choose the extremal processes creating the boundary of the band of frequency responses. Then select the controller parameters in the intersection of all admissible areas for all extremal processes. It will ensure that the complete open loop band of frequency responses will be well shaped as shown in the picture bellow.
Tuning of feedforward parameters
Once the frequency domain design specification are fulfilled, we have to tune the two feedforward parameters b, c
- b - decreasing of proportional weight leads to the overshot reduction (default b=1)
- c - decreasing of the derivative weight moves the derivative part to the feedback and reduces high frequency noises gaining (default c=0)
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