Low order tracking controller synthesis for two classes of MIMO plants

A unified direct synthesis method is derived to harness the established capabilities in the control industry for the control of high order unstable plants using low order controllers. The method uses properties of coprime factorization, polynomials and H-infinity norm to synthesize n-th order controllers for two classes of unstable proper Multi-Input-Multi-Output plants with n factorable zeros or poles in the unstable region. For the class with n factorable zeros in the unstable region with no restriction on the number of unstable plant poles and for the class with n factorable unstable poles with no restriction on the number of plant zeros in the unstable region. For n less than three, conditions to obtain Proportional-Integral-Derivative tracking controllers are presented. For higher values of n, two algorithms for solving the sufficient conditions for strong stabilization are provided. Illustrative examples using plants from the literature are provided to show the reduction of controller complexity compared to the conventional design method. Observations on properties that could extend the results, as well as a list of unstable systems are documented for further investigation.