Study Of Robust Control And Filtering For Linear Repetitive Processes

Repetitive processes are a distinct class of 2D linear systems with extensive existing in the practical industry. The essential unique characteristic of a repetitive process is a series of sweeps, termed passes, through a set of dynamic defined over a finite and fixed duration known as the pass length. On each pass an output termed the pass profile. Repetitive processes have had essential application in coal mining, metal rolling and iterative learning control. In the course of the practice, stochastic factors exit objectively, and the system described by certain method may lose some properties that lead to errors. Therefore, the stochastic factor must be taken into account in the description of the system. In addition, time-delay is commonly encountered in real systems, and often result in instability or performance degradation of systems. The problem of stability analysis and controller synthesis for time-delay systems is an important topic in automatic control. In practical industrial process control systems, it is usually difficult to characterize the dynamics of the controlled object exactly by a mathematical model, which renders inevitable error to exist between the derived mathematical model and the practical object. This error can be described as the uncertainties in the model arguments. Therefore, it has important theory and engineering significance to study repetitive processes with the effects of the stochastic factor, uncertainty and time-delay.This thesis, based on previous works of others, mainly investigates the following problems which around repetitive processes on the basis of Lyapunov stability theory, linear matrix inequality.1) Robust H_∞filtering for linear differential repetitive processes, a method is proposed for designing robust H_∞filter, which converts the existence condition of admissible filter into the feasibility of convex problems subject to LMI. The design problem of robust H_∞filter is solved for linear differential repetitive processes.2) Robust L₂ - L_∞filtering of stochastic linear repetitive processes, and the obtained results are further to more general cases whose process matrices contain parameter uncertainties represented by both norm-bounded and polytopic form.3) Robust l₂ - l_∞dynamic output feedback control for discrete linear repetitive processes, the robust stability and l₂ - l_∞performance conditions are proposed, the cone complementary linearization (CCL) method is exploited to case them into sequential minimization problems subject to LMI constraints. The design problem of l₂ - l_∞dynamic output feedback controller is solved for discrete linear repetitive processes.4) Robust H_∞control of uncertain stochastic time-delay linear repetitive processes. The design problem of robust H_∞controller is solved for linear differential repetitive processes with stochastic and time-delay.5) The design of output feedback controller for discrete linear repetitive processes and illustrated them by application to a simple practical material rolling process, which makes the theory has strong background in practical applications.