Design of static cascade compensators using generalized singular values

Cascade compensators are often used to direct the available control energy to a particular subset of plant modes whose dynamics is to be modified. In certain applications the cascade compensators can be taken to be simple frequency selective filters such as low-pass or band-pass filters. There are applications in which such simple solutions do not work. This paper describes a method to obtain cascade compensators when frequency selective filters do not suffice. The computations required to implement the results are rather simple and involve the calculation of the generalized singular value decomposition of a matrix pair constructed with frequency response data. When combined with robust methods for controller design, the results in this paper yield a simple and effective method for designing controllers that modify the dynamics associated with a specified subset of plant poles.