PERFORMANCE LIMITATIONS OF NONMINIMUM PHASE SYSTEMS IN THE SERVOMECHANISM PROBLEM

This paper studies the cheap regulator problem and the cheap servomechanism problem for systems which may be non-minimum phase. The study extends some well-known properties of ''perfect regulation'' and the ''perfect tracking and disturbance rejection'' of minimum phase systems to non-minimum phase systems. It is shown that perfect rejection to disturbances applied to the plant input can be achieved no matter whether the system is minimum phase or non-minimum phase, whereas a fundamental limitation exists in the achievable transient performance of tracking and rejection to disturbances applied to the plant output for a non-minimum phase system, and that this limitation can be simply and completely characterized by the number and locations of those zeros of the system which lie in the right half of the complex plane. Furthermore, this limitation provides a quantitative measure of the ''degree of difficulty'' which is inherent in the control of such non-minimum phase systems.