Precision Tracking Control of Discrete Time Nonminimum-Phase Systems

In this paper, a precision tracking control scheme for linear discrete time non-minimum phase systems is proposed. This control scheme consists of a preview filter, a tracking-performance filter, a command feedforward controller, and a feedback controller. The use of the command feedforward controller, whose design is based on the minimal order inverse model of the plant being controlled, will result in a completely decoupled system. The preview filter is introduced to compensate the phase and gain errors induced by the non-minimum phase zeros or lightly damped zeros of the system. Using the command feedforward controller along with the proposed preview filter, the tracking performance of the proposed control scheme can be characterized by the frequency response of the the tracking-performance filter. For the design of the preview filter, a generalized Nth order preview filter and its associated penalty function that quantifies the tracking error of a design are defined. It is shown that, given the desired bandwidth and the order of the preview filter, the optimal solution for the design of the preview filter can be obtained explicitly. The proposed control scheme together with the optimal preview filter is shown to be very effective in achieving precision tracking control of discrete time MIMO non-minimum phase systems. It is also shown that the tracking performance is improved as the order of the the preview filter is increased.