Copyright © IF AC Identifi cation and System Parameter Estimation, Beijing, PRC 1988 COMPARATIVE STUDY OF ADAPTIVE CONTROL ALGORITHMS FOR MULTIPLE-INPUT -MULTIPLE-OUTPUT LINEAR SYSTEMS M. Kinnaert and R. Hanus Universite Libre de Bruxelks 50, av F. D. Roosevelt B-1050, Bruxelks, Belgium ABSTRACT suitable Three adapti ve c ontrol algorithms are compared. The y are for a large class of multiple-input-multiple-output (MIMO) linear sy stems, including in particular non minimum phase and / or unstable systems. The first algorithm is a generalization of Elliott 's direct arbitrary adaptive pole placement strategy [Elliott, 1984). An integrating action and a specific constant matrix are introduced in the controller in order to cancel an y steady state error. The second algorithm is an indirect adaptive pole placement control strategy achieving dynamic decoupling of the closed-loop system [Kinnaert, 1987a). The third algorithm is an extension of Clarke's generalized predictive control strategy [Clarke, 1987) to MIMO sy stems. The required prior knowledge for adaptive implementation of each scheme decreases from the first to the last algorithm. Prior knowledge of the system interactor matrix is never necessar y. It is shown that the major drawback of the first algorithm lies in the non-uniqueness of the closed-loop system obtained after convergence of the identification. Its main advantage is the small computational burden. The second algorithm is the onl y one which achieves closed-loop decoupling of the system. However it lacks robustness and might require heavy computations. The third algorithm avoids the drawbacks of the first two. However, the design parameters of this last scheme have a less transparent physical meaning than the desired closed-loop poles, which are the "tuning knobs" for the first two algorithms. KEYWORDS Adaptive control, Multivariable systems, Pole placement, Predictive control, Multivariable control systems. 1. INTRODUCTION When we developed and/or studied the alQorithms presented in this paper, we focused on three major points. First, we only considered algorithms which are suitable for non mimimum-phase plants. This requirement is justified by the fact that most continuous-time transfer functions tend to exhibit discrete-time zeros outside the unit circle when sampled at a fast enough rate [Clarke, 1984), Ou.- second objective was to try to reduce as much as possible the prior knowledge of the plant required for adaptive implementation of the control algorithms. Finally, in order to obtain offset-free performances, an integrating action was introduced in the three algorithms presented here. It can be seen as an extension of the minimum variance controller [Borison, 1979), of the generalized minimum variance controlle.- [Koivo, 1980), and of Ydstie's controller [Ydstie, 1984) which was translated to the multivariable case by Dugard (1984) . The algorithm is a natural continuation of the papers by Elliott (1984] on .. .-bitrary pole placement. The second one uses a decoupling compensator in order to reduce the prOblem of buildinQ a controller for a MIMO system into the design of several controllers for 5150 system. [Kinnaert, 1987a). The last algorithm is a predictive controller. 127 The paper is organized as follows. In the second part, we describe the class of systems we will deal with. The three algorithms mentioned above are presented in section 3, 4 and respectively. A comparative study of the three algorithms is performed in part 6. Some simulation results illustrate the properties of each controller in section 7. Finally, we end up with some concluding remarks. 2. PLANT MODELS We consider an m-input-m-output time invariant system described following minimal state representation : dxlt)/dt y( t) Ac xlt) + Bc ult) '" C xlt) I i near by the space (2.1) where x(t) ( Rn , yet) and ult) €