Iterative Learning Control Systems Design And Its Applications

Iterative learning control (ILC) is a technique for improving the transient response performance of systems or processes that operate repetitively over a fixed time interval. It refines the next control input using the information such as current control input and error signals after each trial until the specified desired trajectory is followed to a high precision. Although conventional ILC provides a good tracking performance through a few trials by the simple input update law, the absence of proper guidelines to design an ILC controller and the weak robustness to disturbances, noise and initialization errors put obstacles in the application of ILC in practical situations.In this dissertation, the optimality and robust convergence issues in ILC synthesis for the plant with uncertainties are studied mainly. We focus our attention on the ILC architecture of using feedback and feedforward actions in order to improve the robustness of the ILC scheme. This dissertation aims to develop new methodologies for robust ILC design that involves a tradeoff between rapid convergence and good tracking performance. These design methods are systematic to resolve the problem of choosing the parameters in learning law and enhancing the utilitarian of ILC. The problem to improving the rate of convergence and the accuracy of tracking of ILC for deterministic linear systems is considered, in the meanwhile, the effects of the plant characteristics, various types of disturbances, errors in initial conditions and the "slowly" varying desired trajectories on the convergence and performance of ILC for uncertain linear and nonlinear systems are also investigated. A series of robust ILC laws are proposed and the effectiveness of every law is guaranteed by the theory analysis and illustrated by the simulation studies. Furthermore, ILC technology is applied to wall thickness control during stretch reducing process of seamless pipe. The effectiveness of the scheme in practical application is demonstrated by extensive experimental results.The main contributions of this dissertation are summarized as follow: (1) An ILC approach combining feedforward with current feedback is developed based on optimal feedback control and the gradient method. A sufficient condition that guarantees the convergences is given for linear system. The procedures of designing the algorithm can employ LQR, H2 or H approaches to improve the convergence rate of learning in iterations. In particular, a simple iterative learning lawbased on infinite time optimal linear quadratic regulator is proposed and its convergence is analyzed in detail.(2) In order to overcome the difficulties caused by the non-minimum phase, an optimal ILC scheme with current feedback is presented for linear non-minimum phase plants based on noncausal stable inversion. The sufficient condition to ensure the convergence of this scheme is obtained and the utility mode of using the noncausal algorithm is given to fit the practical application.(3) An improved ILC based on optimality criterion is proposed for linear time-varying plants. The control signal in each trial is calculated as the solution of a minimum norm optimization problem with a reasonable performance index. The convergences of the tracking error sequence and the input sequence can be proved by the properties of optimality criterion immediately. The ILC algorithm assures that the input sequence will converge to the optimal control of linear quadratic tracking problem. The algorithm achieves an exponential rate of convergence.(4) An ILC framework based on two-degree-of-freedom control is presented for a linear plant with multiplicative perturbations and a sufficient condition in the frequency domain is obtained for robust convergence with the bounded asymptotic error in the case of that there are input disturbance, output disturbance and errors in initial states. Based on the sufficient condition, the problem of designing ILC can be converted to a robust performance problem and a robust ILC against dist...