Study Of Robust Control And Filtering For LPV Repetitive Processes

Linear parameter-varying (LPV) systems are those systems that depend on unknown but measurable time-varying parameters, such that the measurement of the time-varying parameters provides real-time information on the variations of the plant's characteristics. In recent years, LPV systems become a hot sector in the field of control theory because it can describe the characteristic of nonlinear and time-varying of a class of physical systems in nature; moreover, its theory has applied successfully in engineering fields such as robot manipulators, automotive systems and aircraft.Recently, repetitive processes have received considerable research attention since repetitive processes are a distinct class of non-linear 2D systems (i.e., information propagation in two independent directions) of both theoretical importance and significant practice (include iterative learning control, long-wall coal cutting and metal rolling, et. al), a great deal of publications have been available in the literatures.In particular, the parameters of repetitive processes are some time-varying parameters that can be measured in real-time, and we concentrate on discrete LPV repetitive processes case. Inevitably, when repetitive processes is applied in modeling real-time plants such as manipulator control, the system would be naturally dependent on unknown but measurable time-varying parameters. Therefore, discrete LPV repetitive processes emerge as a more reasonable description to account for the parameter drifting phenomenon, and have a great potential in engineering applications. However, to the best of the authors'knowledge, robust H∞output feedback control problem has not been solved for discrete LPV repetitive processes.This thesis first proposes and proves H∞performance criterion for discrete LPV repetitive processes. The emphasis are focus on robust H∞filtering and H∞control for discrete LPV repetitive processes and robust H∞filtering and H∞control for continuous LPV repetitive processesApplying parameter-dependent Lyapunov functional approach and parameter linear matrix inequality (PLMI) technology, we propose and prove that discrete LPV repetitive processes that gurantees the system to be asymptotically stable and have H∞performance constraint. There exists the coupling between the parameter-dependent Lyapunov matrices and the system matrices in the above H∞performance criterion. Introducing a slack matrix, we can obtain decoupled H∞performance. We give the sufficient conditions for the existence of system that is asymptotically stable and satisfies H∞performance. According to decoupled H∞performance criterion, our attention is focused on the design of full-order H∞filtering. By approximating the function space with finite basis functions and gridding technology, Infinite dimensional PLMI are transformed into finite dimensional PLMI and further into feasible problems subject to a group of PLMI constraints.Finally, adopting the gain scheduling technology, we design the state feedback controller and output feedback controller. But there is the form of inverse constraints of PLMI in the state feedback controller. Because the obtained sufficient conditions are not described in the form of PLMI, the cone complementary linearization (CCL) method is used to cast them into minimization problems subject to PLMI constraints. Thus, we can solve the parameters of controller using standard mathematical software.