Adaptive Zero Phase Error Tracking Controller with Extended Gain Characteristics

Abstract

This paper deals with a tracking control problem for a discrete-time non-minimum phase system in the framework of frequency domain. The contributions are as follows. First, the proposed feedforward controller can provide the overall system with the following frequency characteristics; (i) The phase shift is equal to zero for all frequencies. (ii) The gain at any given frequency is equal to unity. (iii) The maximum deviation of the gain from unity over a given frequency range is less than an arbitrarily given positive number. Especially, the frequency at which the gain is made equal to unity can be chosen arbitrarily, while in the previous schemes, the frequency is restricted to zero. Secondly, the class of desired outputs for which the deadbeat tracking can be achieved is generalized, while in the previous results the class is restricted to only steps and ramps. Thirdly, the proposed controller is given in an explicit form and the design method is simple and straightforward. Finally, an adaptive control system based on the proposed feedforward controller is presented and its effectiveness is demonstrated by simulations.