Constraints in Servo System Design for Non-Minimum Phase System

This paper is concerned with the analysis of constraints of poles and zeros for servo system design of plants which are non-minimum phase. It is a known fact that when a closed-loop system has a non-minimum phase zero, the output displays an inverse response before tracking the desired trajectory. This imposes limitations to the transient performance. In this paper, we consider a servo system for a SISO plant having only one non-minimum phase zero. We first characterize the achievable closed-loop system. Based on the characterization and the tracking condition, we show for some combinations of degree and relative degree of the closed-loop system that the admissible location of poles is restricted. For these cases, we provide a quantitative measure for the limitation of the constrained poles. Besides poles, we also show that zeros are constrained and that the number of NMP zeros must be increased in some cases. The latter suggests that it is necessary to worsen the transient performance by introducing additional non-minimum phase zeros into the system