Design of cascade compensators using generalized singular values

When active control is used to improve plant dynamics, cascade compensators (or loop shaping filters) are often used to help direct the available cont rol energy to the 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 bandpass filters. There are applications in which this is not the case, A method is describe d to obtain cascade compensators that achieve the stated goal when frequenc y selective filters do not suffice to obtain a solution, The computations r equired to implement the results an? rather simple and involve the calculat ion of the generalized singular value decomposition of a matrix: pair const ructed with frequency response data. When combined with robust methods for controller design, the results yield a simple and effective method for desi gning controllers that modify. the dynamics associated with a specified sub set of plant poles, A detailed numerical example is included to illustrate ideas and computations.