Study Of Robust Control Approach For LPV Repetitive Processes

Repetitive processes are a distinct class of non-linear2D systems that has strongengineering background, and they have important application in coal mining, metal forgingand iterative learning control, which are widely concerned by scholars at home and abroad.But the current research of repetitive processes is mainly for linear repetitive processes andthe uncertain repetitive processes have to be further study. Linear parameter varying （LPV）systems are a kind of special nonlinear system, its parameters are variable and real-timemeasurement, and many nonlinear systems can be converted to LPV system, which has mademany achievements in the stability analysis and controller design of the one-dimensionalsystems, but in the two-dimensional system especially the analysis and synthesis of repetitiveprocesses is still a challenging problem. Therefore, the study for LPV repetitive processes hasvery important theoretical and engineering significance.This paper using the technology of LMI, Lyapunov function, Shur complement lemmaand other mathematical tools to analyze the stability andl2l performance criterion of thelinear repetitive processes. The sufficient conditions were given that can make theclosed-loop repetitive processes are asymptotically stable along the channel and have acertain disturbance rejection level.Based on the research for the linear repetitive processes, we further expand studiedl₂-l_∞state feedback and dynamic output feedback control problems of the discrete LPVrepetitive processes. LPV repetitive processes are a kind of complicated time-varing2Dsystems. Traditionally, based on the quadratic stability framework, a comment controllerwhich has usually large conservatism is designed for whole paremeter variation space. In thispaper, the controller was designed by using parameter-dependent Lyapunov can effectivelyreduce the conservatism and improve the control precision. But this designed method has aproduct term between the parameter dependent Lyapunov function and the system matrices, itis a nonlinear problem by introducing a relaxation matrix decoupling purpose.The existence condition of l₂-l_∞robust filter is given by using the design method ofthe condition for discrete LPV repetitive processes. And based on the PLMI condition, thefilter design problem was converted to a convex optimization problem subject to the PLMIconstraints. It is an infinite dimensional problem, using the approximate basis function andthe grid technology to obtain the desired filter. The designed filter can ensure the filteringerror repetitive processes are asymptotically stable along the channel and have a certainl₂-l_∞disturbance rejection level. Finally, the l₂-l_∞state feedback control and filtering problem for the continuous LPVrepetitive processes was investigated. Because of the performance criterion along the channelasymptotically stable for the discrete LPV repetitive processes and the continuous LPVrepetitive are different, so the decoupling methods are also different, here using the projectionlemma to realized decouping purpose. And the simulation results can prove the effectivenessof the designs.