Abstract
Most methods used for designing model reference adaptive control systems are restricted to the case where all the parameters in the plant and control matrices are mutually independent. But, in many practical cases such an assumption is not necessarily valid. In this paper, new general design methods are presented via the method of Lyapunov which can be used in such cases as the same unknown parameters and adjustable parameters may appear in two or more elements of these matrices simultaneously. As these conditions are less restrictive compared with the other method, this design method is considered to have much applicability to a broad class of adaptive systems.
First, the relations among the parameters of the plant are classified into two cases and for the both cases the well known integral parameter adjustment rule is derived by applying the nonlinear equations previously suggested by Lüders and Narendra. After that, the “proportional plus integral” adjustment rule which is quite effective for the improvement of the transient response characteristics is also derived by choosing appropriate Lyapunov function.
Illustrative examples for these rules are given with their simulation results. In some cases, unrealizable adjustment rule may be derived. An example suggests how this situation can be overcome by constructing an approximate controller.
