Model Reference Adaptive Control for MIMO Nonminimum Phase Discrete-Time Systems Using Approximate Inverse Systems

Usually the model reference adaptive control tech niques cannot be applied to nonminimum phase systems, because the boundedness of all signals is not assured due to the unstable pole-zero cancellation in the model reference adaptive control systems[1,2]. To avoid un stable pole-zero cancellation, pole-assignment schemes have been proposed[3]. However, these methods assign only the poles in the close-loop system, and also the re sponse characteristic of these techniques is not as good as that obtained from the reference model type. Thus, these pole-assignment schemes cannot be used for model reference adaptive control systems. For solving this problem, we proposed a method for the model reference adaptive control of SISO ( single-input single-output) nonminimum phase discrete-time systems based on approximate inverse systems[4]. It is important to note that the zero locations of an MIMO system are in no way related to the zero location of the individual SISO transfer functions constituting the MIMO system. Thus, MIMO system may be nonminimum phase even if all the SISO transfer function are minimum phase and vice versa[5]. In this paper, We show, however, how un stable pole-zero cancellations can be avoided for MIMO nonminimum phase systems. One of the main points in our method is the use of least-squares approximation to determine an approximate inverse system in an easy way, that is suitable for practical applications in control systems. 2. Problem Statement