Two-degree-of-freedom design method of LQI servo systems: use of frequency-dependent weighting matrices for sensitivity reduction

The authors previously (1996) proposed a new method to design two-degree-of-freedom robust servo systems for step references and step disturbances. In this method, the tracking characteristics for step references are determined optimally with respect to a quadratic-integral performance index, while the feedback characteristics for step disturbances are determined also optimally with respect to another quadratic-integral performance index. The paper extends these results by introducing frequency-dependent weighting matrices into the latter performance index. By employing appropriate frequency-dependent weighting matrices, some sort of loop-shaping can be achieved for the sensitivity characteristics, and thus more design freedom is obtained. In particular, loop-shaping ability and tuning ability can be separated in some sense. A numerical example is also studied to illustrate the results