Multivariable Adaptive Control Design Under Internal Model Control Structure.

Abstract

A new adaptive multivariate control scheme has been devised. The method combines the best characteristics of conventional adaptive systems and internal model control (IMC) structure. The control scheme builds by itself the required models and avoids the ambiguities in the definition of performance specifications. The problem of plant inversion associated with the IMC structure has been solved. The method introduced in this work is based on the properties of the Smith-McMillan form. However, the method does not require the explicit determination of the form. Furthermore, the computation of a stable plant inverse requires only matrix inversion and scalar polynomial factorization. The resulting algorithm is suitable for on-line operation. The control schemed is implemented through the following stages: (1) Identification. The parameters of a multivariable ARX model are estimated using a recursive least square algorithm with variable forgetting factor. The input and output orders can be used as additional degrees of freedom. The algorithm developed shows good numerical characteristics with fast convergence even for a large number of parameters. (2) Computation of the manipulated variables. The model is used to determine a controller following the IMC approach. The resulting equations are solved to compute the required manipulated variables. The algorithm for system inversion allows computations to be executed on-line. (3) Filtering. The usual filters of the IMC approach are also used in the adaptive scheme. The objective is to reduce the sensitivity of the controller. Only non-adaptive non-interactive filters have been considered. The results with first order low pass filters are satisfactory. The bandwidth of the filter is used as an additional tuning parameter. The adaptive control strategy has been extensively tested using computer simulation. The tests include extensions to non-linear plants. Comparisons with non-adaptive IMC control show the advantage of the new scheme developed in this work.