Robust Adaptive IMC Schemes

Abstract

In Chapter 5, we considered the design and analysis of adaptive internal model control (AIMC) schemes under ideal conditions, i.e. in the absence of modelling errors. The key idea was to combine an IMC control structure for the known parameter case, presented in Chapter 3, with a parameter estimator from Chapter 4 in a Certainty Equivalence fashion. Although in the absence of modelling errors, such schemes were proven to be stable, the instability examples presented in the last chapter clearly demonstrated that the adaptive laws of Chapter 4 could lead to totally unacceptable behaviour in the presence of modelling errors. The situation is likely to be even worse when such an adaptive law is used to implement a Certainty Equivalence adaptive control scheme, and modelling errors are present. In the last chapter, we also discussed several approaches for correcting this kind of erratic behaviour of the adaptive laws leading to the design of adaptive laws that are robust to the presence of a class of modelling errors. Since the IMC schemes of Chapter 3 were shown to be inherently robust to the presence of modelling errors, a natural question that comes to mind is whether robust adaptive IMC schemes can be designed by combining an IMC controller structure with a robust adaptive law. The objective of this chapter is to provide an affirmative answer to this question by showing that whenever any of the robust adaptive laws of the last chapter is combined with any of the IMC controller structures from Chapter 3 in a Certainty Equivalence fashion, the result is a robust adaptive IMC scheme.