Design of Multi-Loop Modal Control Systems for Plants Having Complex Eigenvalues

Abstract

In this paper a design procedure is developed which makes it possible to alter both the real and imaginary parts of any number of pairs of conjugate complex plant eigenvalues: this procedure alters one pair of conjugate eigenvalues at a time by the provision of a suitable pair of control loops. In this way, multi-variable linear plants can be designed so as to possess oscillatory response modes having any desired decrement and frequency. The procedure is illustrated by designing control loops for second- and fourth-order plants having matrices with conjugate complex eigenvalues.