| In this thesis, we present a systematic design approach for high-gain compensation for a class of multivariable LTI systems which are minimum phase, based on the approach used in Miller and Davison (9) for SISO LTI systems. By performing a decomposition of the system on the input/output space via a spectral decomposition technique or singular value decomposition technique, a compensator can be designed to possess diagonal dynamics if the system is also decouplable and the high-frequency response can be measured experimentally; furthermore, a uniform high-gain compensator can also be developed by taking advantage of an "unmixing set". Based on these approaches we then pose a new model reference adaptive control problem in which the objective is not the usual one of forcing the error between the plant output and the reference model output asymptotically to be equal to zero, but instead, it is that of forcing the error to be less than an (arbitrarily small) prespecified constant after an (arbitrarily short) prespecified period of time, with an (arbitrarily small) prespecified upper bound on the amount of overshoot. To achieve this goal, various cases are discussed. The controller proposed consists of a LTI compensator together with a switching mechanism to adjust the compensator parameters, and is similar to that used in Miller and Davison (9) for SISO case. Finally, some experimental methods for obtaining certain a priori information required for the controllers are proposed. |
