ZERO PHASE ERROR TRACKING SYSTEM WITH ARBITRARILY SPECIFIED GAIN CHARACTERISTICS

This paper considers a design problem of discrete-time preview feedfor ward controllers such that the gain characteristics of the overall sys tem is within an arbitrarily specified bound subject to the zero phase error condition for a plant having nonminimum phase zeros. In order t o solve this problem, a feedforward controller termed Optimal-Feedforw ard Controller with Zero Phase Error Tracking Controller (Optimal-FCZP ETC) is introduced. With this controller, the phase characteristics of the overall system is zero for all frequencies and the maximum value of the gap between the gain of the overall system and unity, which is ideal gain characteristics, is minimized under given preview steps. Th e choice of the preview steps is an unsolved problem. In this paper, w e investigate the Optimal-FCZPETC from the viewpoint of the preview st eps. The contribution is to give explicitly the minimum value of the m aximum gap between the gain of the overall system and unity for given preview steps and to show that the minimum value can be made arbitrari ly small as the preview steps increase. As a result, a simple algorith m is proposed to find the minimum preview steps such that the gain cha racteristics of the overall system is within an arbitrarily specified bound. The effectiveness is shown by simulation results.