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4.2  Feedback maximization

4.2.1  Structural design

We already mentioned the advantages of structural design in Section 2.9 (and will further discuss them in Section 7.2.1). The structural design flowchart for the basic feedback control system is shown in Fig. 4.1.

Fig. 4.1  Feedback system design flowchart

The performance specifications comprise the desired responses of

  A

the disturbance rejection and the sensitivity, i.e., the loop gain, and

  B

the nominal command-to-output transfer function.

The preliminary design addresses specification A first, by loop response shaping. This can be subdivided into

  A1

achieving maximum feedback bandwidth by appropriate loop shaping at higher frequencies, and

  A2

distributing of the achieved feedback over the functional frequency range so as to exceed the worst-case specifications.

Since the first subproblem is to a large extent independent from the second one, it makes sense to solve them sequentially. At this stage, the responses need not be expressed by rational functions. They can be expressed by rational or transcendental functions, by plots, or by tables.

After the loop is shaped, the command-to-output response is modified (if required) by adding an appropriate prefilter or command feedforward to meet specifications B.

During the conceptual design of complex engineering systems, only the steps A1 and A2 (and sometimes B1) need to be performed to provide the system engineers with the accurate data on the available control performance. The system engineers evaluate different versions of the hardware/software configurations iteratively, using the preliminary design results on the available control performance. Inclusion of only the stages A1, A2, B in the iteration loop makes the loop fast.

After the system engineers finally decide which hardware configuration is the best, the compensator and prefilter are designed. The compensator response is found by subtracting the plant response from the loop response. Then

  C

the compensator and prefilter responses are approximated by m.p. rational functions and implemented as algorithms or as analog circuits, and

  D

the compensator is augmented with nonlinear elements and the system is simulated.

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