12 - Frequency-domain analysis and design methods

Abstract

Analysis of a system frequency response is a powerful tool to predict the behavior of a control system. In fact, frequency-domain analysis allows us to conclude the closed-loop stability from the open-loop frequency response. When the input to a linear system is a sinusoid, its output is a sinusoid of the same frequency but with different amplitude and phase. The amplitude and phase as functions of the frequency can be plotted in Nyquist- and Bode-diagrams. Particularly in Bode-diagrams, the concept of gain- and phase-margins gives rise to the notion of relative stability, that is, how much variation of process parameters is allowable before a feedback control system turns unstable. Similar insights are gained from the Nyquist criterion, which allows us to conclude from the loop gain to the presence of closed-loop poles in the right half-plane.