Adaptive Internal Model Control Schemes

Abstract

In the last two chapters, we have studied internal model control schemes and parameter estimators as two separate entities. Chapter 3 dealt with the internal model control of stable plants with known parameters while in Chapter 4 we developed on-line parameter estimation techniques for estimating the unknown parameters of a given plant. In this chapter, our main objective is to design internal model controllers for stable plants with unknown parameters. The intuitively obvious way of achieving such an objective is to design an on-line parameter estimator for estimating the unknown plant parameters as in Chapter 4, and then to use the techniques of Chapter 3 to design an internal model controller based on these parameter estimates. This approach of treating the estimated parameters as the true ones, and basing the control design on them is referred to in the adaptive literature as Certainty Equivalence. Although the estimated parameters in a certainty equivalence scheme rarely converge to the true values, nevertheless research in adaptive control theory over the last two decades has shown that many designs based on the certainty equivalence approach can be proven to be stable [19, 31, 32], Unfortunately, adaptive internal model control (AIMC) schemes were not included in this category, presumably because they arose in the context of industrial applications and consequently did not attract much attention from the theoreticians. Indeed, the literature on Adaptive Internal Model Control is replete with simulations and empirical studies showing the efficacy of certainty equivalence based adaptive internal model control schemes but hardly any instance exists where theoretical guarantees of stability and/or performance were obtained [40, 39]. Thus an important aspect of our treatment in this chapter will be the provable guarantees of stability, performance, etc. provided by the AIMC schemes to be designed.