A multiresolutional controller for sensitivity minimization of flexible structures

The control of flexible space structures presents many unique and challenging problems. For typical robust linear controllers the order of the controller tends to be the same as the order of the model used for the flexible structure. In addition, there tends to be no direct relationship between “optimal” linear controllers which were designed based on flexible structure models of different orders. This paper addresses, using wavelet theory, the multiresolutional control design for flexible structures. The main idea is to use a wavelet basis to model the plant and then determine the “optimal” controller using this same wavelet basis in an effort to obtain a nesting property between controllers of different order. The nesting property which wavelets possess is one of their primary strengths. The control problem addressed is that of minimizing the effect of disturbances on a SISO closed loop system, i.e., minimizing the sensitivity function, in terms of the H² norm