Iterative Learning Control Algorithm Based On Orthogonal Polynomials And Its Application To Linear Motor

Iterative learning control (ILC) is a technique which is applicable to systems or processes operating repetitively over a fixed time interval. One attractive point in ILC is the utilization of the system repetitiveness to improve the control performance. The past control input signals and tracking errors are used to construct the present control input signals. Iterative learning control is early applied to output tracking control and lately applied to state steering control. But these two different control problems need to develop two different algorithms. Using the two-dimensional property of ILC and the approximation property of orthogonal polynomials, this dissertation presents an iterative learning control algorithm based on orthogonal polynomials to tackle the above-mentioned two different control problems. The key technique of the method is to represent the control input signal as a linear combination of orthogonal polynomials vector and then update the coefficient vector based on the error signal at the end of each trail. In this method, orthogonal polynomials vector denotes the time process of ILC, and orthogonal coefficient vector indicates the learning process of ILC. In this dissertation, we study systematically the iterative learning control algorithm based on orthogonal polynomials of continuous linear system, continuous T-S fuzzy system, discrete linear system and discrete T-S fuzzy system. The sufficient convergence condition of the algorithm for continuous linear system is analyzed by employing the operational matrices of integration and product of orthogonal polynomials. And the H∞control design method of uncertain discrete system is used to address the approximation error introduced by orthogonal polynomials. Then, combining the theory of continuous linear systems with fuzzy methodology, the algorithm for continuous T-S fuzzy system is researched. Under a few reasonable assumptions, the robust convergence condition is given. Parallel to continuous linear system, the algorithm is concerned for discrete linear system. The sufficient convergence condition for discrete linear system is obtained by employing orthogonal relations and boundary values of discrete Legendre orthogonal polynomials. Similar to continuous T-S fuzzy system, we study the algorithm for discrete T-S fuzzy system by combining the theory of discrete linear systems and fuzzy methodology. Finally, the algorithm is applied to the position and velocity control of linear motor. Simulation results show that satisfied performance is reached by using the proposed method. The main contributions of the algorithm presented are summarized as follows. (1) Only the error signal is used to update the control input for systems with arbitrary relative degree. (2) The convergence condition for the algorithm is derived based on the 2-norm instead of λ-norm. (3) The proposed learning strategy provides a feasible solution for nonlinear systems whose nonlinearities are not Lipschitz continuous.