FrequencyDomain Control Design for HighPerformance Systems
This book serves as a practical guide for the control engineer, and attempts to bridge the gap between industrial and academic control theory. Frequency domain techniques rooted in classical control theory are presented with new approaches in nonlinear compensation that result in robust, highperformance closedloop systems. Illustrative examples using data from actual control designs are included.
Inspec keywords: frequencydomain synthesis; nonlinear control systems; linear systems; stability; feedforward; feedback; control system synthesis
Other keywords: feedback control; nonlinear feedback design; plant descriptions; linear feedback design; feedforward; frequencydomain control design; stability; highperformance systems
Subjects: Control system analysis and synthesis methods; Nonlinear control systems; General and management topics; Stability in control theory
 Book DOI: 10.1049/PBCE078E
 Chapter DOI: 10.1049/PBCE078E
 ISBN: 9781849194815
 eISBN: 9781849194822
 Page count: 184
 Format: PDF

Front Matter
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1 Justification for feedback control
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If a PhD candidate in control theory is asked, 'in what applications should feedback be applied?', he will typically struggle to deliver a learned response. This usually is not a consequence of a lack of rigorous training in control theory. More often than not, it is the result of weaknesses in the training process itself. The academy has over the last few decades increasingly distanced itself from control applications in favor of strictly theoretical development. The result is a population of PhDs in control who is expert in elegant (if not always applicable) mathematics and crashingly ignorant in the engineering of control design. This has opened an ever widening rift between the academic and industrial control communities. The former largely disregards the latter as primitive; the latter disregards the former as purveyors of the useless.

2 Plant descriptions
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Typically, a mathematical model of the plant dynamics, consisting of a set of equations with time or frequency as the independent variable, is developed for control design purposes. Although useful from a mathematical perspective, the development of a plant model of sufficient fidelity for highperformance control can be an arduous, if not impossible, task. Simple systems with lumped parameters, such as a massspringdamper with a force input, are well suited for accurate model development. The three parameters of this secondorder system are usually easy to find. However, it is common in real applications for the plant to have additional dynamics beyond what is described in first principles models. Although the second order model of the massspringdamper captures the rigid body mode, it does not include the flexible body dynamics that the actual system might exhibit at higher frequencies, the presence of which can threaten the stability of a feedback con troller if not compensated for. To augment the secondorder model to include these dynamics is no longer the straightforward task of determining easily measured parameters, but a complicated modeling task, perhaps involving distributed para meters. Confidence in such highorder models is often low.

3 Feedback
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Consider the block diagram of a singleinput, singleoutput (SISO) feedback system shown in Figure 3.1. The plant and feedback compensators are modeled by the rational functions G(s) and C(s), respectively. Exogenous inputs r(s), d(s) and n(s) are the reference, disturbance and sensor noise signals, and y(s) is the plant response. T(s) 1/4 C(s)G(s) is the return ratio, sometimes referred to as the open loop gain or the loop transmission function. F(s) 1/4 1 þ T(s) is the return differ ence and its magnitude F(s) 1/4 1 þ T(s) is the feedback. Although they share the same name, this function should not be confused with the feedback signal from the plant output to the compensator input.

4 Feedforward
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In this chapter, methods that improve the performance of a feedback system by utilizing knowledge of system parameters are investigated. These are referred to as feedforward systems, although prefilters in series with a feedback system also belong to this category.

5 Stability
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In this chapter, the effect of feedback on system stability is developed. First, definitions of stability for linear systems must be developed both in the frequency and time domains. The Nyquist Stability Criterion, an extremely powerful analysis tool in determining not only the stability of a feedback system but also its relative stability, is presented. The generalized Nyquist Criterion is also discussed along with Gershgorin's Theorem for the stability analysis of multivariable systems. The deleterious effect of hidden unstable pole/zero cancellations that Nyquist analysis cannot detect is addressed in defining the important concept of internal stability. The Lyapunov method for stability analysis of nonlinear systems is presented so that a treatment of absolute stability can be included. The latter is of critical importance in the development of nonlinear compensators discussed in Chapter 7.

6 Feedback design  linear
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This chapter describes the design process, starting with the determination of the linear parts of the control system. After this design is complete, requisite nonlinear compensation is designed and implemented.

7 Feedback design  nonlinear
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Frequencydomain techniques for high performance control are introduced in the previous chapter for singleinput, singleoutput (SISO), singleinput, twooutput (SITO) and TISO architectures. Taking into consideration the bandwidth limitations presented by all practical control design problems, these techniques provide more feedback (thus performance) than commonly used controllers, like proportionalintegralderivative (PID). The principle tradeoff is increased com pensator order, which is very inexpensive and well worth the controller perfor mance improvement.

8 References
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Back Matter
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