Motivation: The nonlinearities in sensors and actuators lead to performance degradation in LPNI systems as compared with linear ones. In this situation, two questions arise: (1) How can nonlinear instrumentation be selected so that the degradation is no more than a given bound? (2) Is it possible to modify the controller so that for a given nonlinear instrumentation, the linear performance is recovered? These questions motivate the subject matter of this chapter. Specifically, the first question leads to a method of partial performance recovery and the second to a complete performance recovery technique.

Overview: We develop techniques for both partial and complete performance recovery. Specifically, we show that the solution of the former is given by a Nyquist stability criterion-type technique (Section 7.1), while the latter is provided by the so-called controller boosting approach (Section 7.2).

Partial Performance Recovery

Scenario

In practice, control systems are often designed using linear techniques. In reality, control systems often (or, perhaps, always) include saturating actuators. The question arises: How large should the level of saturation be so that the performance predicted by linear design does not degrade too much? In this section, this question is addressed in the framework of the disturbance rejection problem.