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��Chapter 18�Compensator Design

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General Feedback Loop

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Ideal Loopshape

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Loopshaping Design Philosophy

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Controller Building Blocks

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Controller Building Blocks: Proportional Gain

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Controller Building Blocks: Integral Control

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Controller Building Blocks: Low-Pass Filter

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Controller Building Blocks: Phase Lag Filter

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Controller Building Blocks: Phase Lead Filter

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Controller Building Blocks: Phase Lead Filter

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Controller Building Blocks: Phase Lead Filter

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Example

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Loop-shaping Steps

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Loop-shaping Steps (part II)

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Controller Implementation

  • Two options provided in the example code:
    • State Space Implementation
    • Digital Filter

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State Space Implementation (Overview)

  • Turn C(s) into a state space representation (e.g. using controller canonical form)

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State Space Implementation (Overview)

  • Solve the state space equations

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Digital Filter

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  • The output of the compensator is a function of past outputs and errors:

 

  • Use the Tustin approximation to put into the Z-domain
  • Solve for the output at the current time step

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Digital Filter

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Pre-Filter

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  • With some phase margins, there will be a peak in the closed loop system, which can cause overshoot and ringing.
  • One way to reduce this is to add a prefilter.

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Pre-Filter

  • Can use a low pass filter or notch filter.

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  • Will flatten the peak in the Bode mag plot.

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Pre-Filter

  • In code, can implement it in the same way as we did the compensator.

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Pre-Filter

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Pre-Filter

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Successive Loop Closure Design

  • Design the outer loop taking into account the complete dynamics of the inner loop.

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  • Pre-filter is only applied to the outer loop

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Example

  • Python files:
    • loopshape_tools.py
    • loopshape_example.py
    • transferFunction.py
    • controller.py
    • exampleSim.py

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...more to come

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Design Study A

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Design Study B

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Design Study C

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