PRECISION TRACKING CONTROL OF NONMINIMUM-PHASE SYSTEMS WITH ZERO PHASE ERROR

In this paper, a method is proposed for designing the command feedforw ard controller for zero phase error tracking control of systems having unacceptable zeros. The unacceptable zeros include both non-minimum p hase zeros and lightly damped zeros. In the proposed approach, a digit al preview filter along with the acceptable part of the system's inver se model is designed to form the command feedforward controller. Using preview information of the input trajectory, the designed tracking co ntroller guarantees zero phase error and high precision tracking perfo rmance. In the proposed design, the best tracking performance can be a chieved by minimizing a weighted penalty function, which controls the gain error between the desired output and the actual output. Two desig n cases were examined. The first is the design based on a uniform weig hting function. In this study, the optimal solution of the design can be analytically obtained and three prior approaches were shown to be t he special cases of the proposed solution. The second case is the desi gn based on input trajectory. It was shown that in the trajectory-base d design, the proposed penalty function in the frequency domain is, in fact, the total squared tracking errors in the time domain. Therefore , the proposed digital preview filter based on input trajectory is the optimal solution in achieving the best tracking performance.