Inverse control of discrete-time multivariable systems

The inverse control of discrete-time single-input/single-output linear systems is extended to multivariable systems. The extension considered is far from being trivial when a multivariable system possesses interactions and multiple delays, leading to ill-conditioning or even singularity of the problem. A feedback control algorithm suggested is based on decoupling and compensating the plant by preceding it with the inverse controller. The inverse controller is derived by using the regularization of the pseudoinverse of the plant convolution matrix. In this way a regularized multivariable control with a minimum norm is provided. A numerical example of the inverse control of a distillation column is presented.