Low-order SISO controller tuning methods for the H₂, H_∞ and μ objective functions

A methodology for synthesizing low-order compensators is outlined that explicitly accounts for model uncertainty, allows on-line controller adjustment, and is computationally simple. The method consists of applying the Internal Model Control (IMC) design procedure to a control-relevant reduced-order model; that is, a model obtained by incorporating features of the closed-loop problem as weights in the reduction procedure. As a consequence, lower-order yet better performing controllers, as compared to those resulting from equivalent methods, are obtained. The computational algorithm is outlined, and it is shown that the model reduction problem can be solved efficiently through standard linear or quadratic programming algorithms, while only the IMC filter parameters and process deadtime need to be obtained through more elaborate search techniques. The benefits of the proposed algorithm are shown through examples.