Nonminimum-phase zeros - much to do about nothing - classical control - revisited part II

Abstract

The purpose of this article is to illuminate the critical role of system zeros in control-system performance for the benefit of a wide audience both inside and outside the control systems community. Zeros are a fundamental aspect of systems and control theory; however, the causes and effects of zeros are more subtle than those of poles. In particular, positive zeros can cause initial undershoot (initial error growth), zero crossings, and overshoot in the step response of a system, whereas nonminimum-phase zeros limit bandwidth. Both of these aspects have real-world implications in many applications. Nonminimum-phase zeros exacerbate the tradeoff between the robustness and achievable performance of a feedback control system. From a control-theoretic point of view, a nonminimum-phase zero in the loop transfer function L is arguably the worst feature a system can possess. Every feedback synthesis methodology must accept limitations due to the presence of open-right-half-plane zeros, and the mark of a good analysis tool is the ability to capture the performance limitations arising from nonminimum-phase zeros.