Describing function matrix for multivariable systems and its use in multiloop PI design

Abstract

The describing function analysis for single-input single-output systems (SISO) is extended to multivariable plants under multiloop relay feedback control. Both necessary and sufficient conditions for limit cycle oscillations are given in terms of eigenvalues of the open loop system. The stability of such limit cycles is also established. Finally, the use of the describing function matrix in the design of multiloop PI controllers is demonstrated through some simulation examples. © 1994.