Model reference adaptive control of nonminimum‐phase discrete‐time systems using approximate inverse systems

Abstract

AbstractThe model reference adaptive control is well known in the deterministic system, as a method of adaptive control for the linear discrete‐time system. In the model reference adaptive control, the plant is controlled to follow the output of the given reference model while estimating the unknown parameters of the plant. One of the important problems in this system is the control of the nonminimum‐phase system. Often even if the plant as the continuous‐time system is minimum‐phase, the representation of the plant as the discrete‐time system is nonminimum‐phase.From such a viewpoint, the control of the nonminimum‐phase system is very important from the practical standpoint. This paper proposes a new method of model reference adaptive control which can effectively control the nonminimum‐phase discrete‐time system using the approximate inverse system by division method. In this method, the approximate inverse system with any accuracy can be constructed by appropriately defining the threshold. The method is very useful in practice since the approximate inverse system of the nonminimum‐phase system can be determined only by iterating simple divisions.To examine in detail the result of application of the proposed method, various computer simulations were made and the results are discussed.