Design of Feedforward-Cascade Controllers for Multivariable Systems

The problems of disturbance decoupling and command matching in linear multivariable systems by means of feedforward and cascade controllers are formulated and solved in a transfer-function setting. It is shown that a necessary and sufficient condition for existence of the required controllers is that the plant zero polynomial is not identically zero and is stable. The required controllers are realized by parallel combination of a proportional-multiple-derivative term and a dynamic term, where the order of the dynamic term does not exceed the number of plant transmission zeros. The control scheme proposed in the paper is composed of a stabilizing feedback controller to enhance system stability, a feedforward controller to achieve disturbance decoupling and a cascade controller to ensure command matching. The three controllers have no effect on each other and can therefore be designed independently. A numerical example is given for illustration.