Direct Adaptive Dynamic Compensation For MIMO Minimum Phase Systems With Unknown Relative Degree

The thesis focuses on the investigation of direct adaptive control for MIMO systems. We design adaptive stabilization controller for the MIMO minimum phase systems with unknown relative dgeree, at the same time, extend the adaptive stabilization controller to address the adaptive command following and disturbance rejection. For command following and disturbance rejection, we firstly design adaptive controller to realize it, where the command signal is measurable, but the disturbance signal is unmeasurable. Then, we study adaptive state feedback stabilization of MIMO linear systems, and the poles placement of systems have adaptability and a certain extent randomicity. The main contents of this thesis are composed of the following three parts:(I) Direct adaptive dynamic compensation for MIMO minimum phase systems with unknown relative degreeIn this part, we study the design problem of MIMO minimum phase systems, analyze and define MIMO minimum phase systems based on the SISO minimum phase systems, and design parameter-monotonic adaptive controller for MIMO minimum phase systems. Firstly, comparing with others controllers, the upper bound of relative degree of each transfer function matrix element, the sign of high frequency gain and the upper bound of magnitude of the high frequency gain are known. Secondly, performance analysis and rigorous proof of Systems stability are given.(II) Direct adaptive command following and disturbance rejection for MIMO minimum phase systems with unknown relative degreeIn this part, we consider command following and disturbance rejection of MIMO minimum phase systems with unknown relative degree, and design adaptive compensator based on the controller of SISO systems to realize command following and disturbance rejection. Firstly, the characteristic polynomial of command signal and disturbance signal are known. Secondly, the command signal is measurable, but the disturbance signal is unmeasurable.(III) Adaptive state feedback stabilization for uncertain MIMO linear systems In this part, we study the problem of state feedback of MIMO linear systems, use a simple method to design state feedback law. Firstly, we use adaptive output to design state feedback law. Secondly, the poles are chosen to be in approximate proportion with each other, while the parameter is monotonically increasing and reach a limit in a short time, then the systems are stable.The above-mentioned three parts give the corresponding simulation examples, respectively, to illustrate the correctness and effectiveness of the compensator design methods.