Stability margin based design of multivariable controllers

In this paper we describe a new approach to the design of Multi-Input Multi-Output (MIMO) controllers which attain predesigned gain and phase margins. This is achieved by considering the Smith-McMillan form of the n×n plant transfer function with diagonal elements P
_i
(s), designing Single-Input Single-Output (SISO) controllers Ci(s) for the Smith-McMillan plants with corresponding loop gain margins g
_i
and phase margins φ
_i
, i = 1, 2, ...., n. Then it is shown that the MIMO controller can be recovered in such a way that the MIMO system achieves gain and phase margins that are the minimum of gain margins and the minimum of phase margins of the scalar unity feedback Smith-McMillan loops. These results are then applied to the design of Proportional-Integral (PI) controllers where achievable gain and phase margins can be exactly quantified. The result is illustrated by examples.