Multivariable controller synthesis using SISO design methods

This paper proposes a new method to design multivariable controllers for linear Multi-Input Multi-Output (MIMO) control systems using the Smith-McMillan form. The Smith-McMillan form of the transfer function matrix of a MIMO plant is an equivalent diagonal transfer function matrix using which the problem of multivariable controller synthesis can be reduced to multiple Single-Input Single-Output (SISO) controller designs. If the designed SISO controllers satisfy certain relative degree conditions, then the corresponding multivariable controller, to be connected to the MIMO plant, will be proper. In this paper we show how such multivariable controllers can be designed to satisfy closed loop stability and reference tracking. We also provide some illustrative examples.