Limitations of non-minimum-phase feedback systems†

Abstract This paper is devoted to the stable linear time-invariant plant whose transfer function P{s) has right half-plane (RHP) zeros, denoted as a non-minimum-phase (NMP) plant. We can always write P(s) = Pm(s)A(s), | A(jw)| = 1, arg A(jm) raonotonically decreasing from zero at W = 0, and Pm minimum-phase (MP). In the traditional design, the plant loop transmission L(s) has |L(jw) | > 1 for w in [0, wc), wc, the cross-over frequency. The benefits of feedback are then restricted to [0, wc) with wc, < wc. If P(s) is MP, wc may theoretically be arbitrarily large but in the NMP ease wc < Wa, given approximately by arg A(JW )= — 60°. It is shown that other options are available in NMP systems, by having several cross-over frequencies. If A (s) has finite degree, it is even theoretically possible to achieve arbitrarily large | L(jw) | over an arbitrarily large-frequency range (w1, w2). However, the price is paid with one or more ‘holes’ (finite-frequency ranges) in [0, w1, ]in which |L(jw)<1. The ...