Model reference adaptive control of nonminimum phase discrete-time systems

This paper presents a new method for the model reference adaptive control of nonminimum phase discrete-time systems using approximate inverse systems obtained from the least-squares approximation. Utilizing this approximate inverse system, the gain response of the system can be made approximately unit and the phase response exactly zero. This approximate inverse system can be implemented as an FIR filter. This approximate inverse system can be designed in the same manner for both minimum and nonminimum phase systems. We incorporate an extra FIR filter to approximately cancel the effect of the numerator polynomial upon the output. Using this approximate inverse system the unstable pole-zero cancellation can be avoided, and so there will exist no unstable modes in the closed-loop system. Thus, it is possible to design a two degree of freedom controller such that the output of the plant tracks some arbitrarily chosen reference model output. Several simulation results are presented in the paper to illustrate the effectiveness of the proposed method.