Basis Function Based Iterative Learning Control For Non-minimum Phase System

Flexible link manipulator(FLM) has wide applications in areas of aerospace and manufacturing due to their lightweight, energy saving and high payload-weight ratio. However, the FLM is generally a typical non-minimum phase system, which makes endpoint perfect tracking unachievable under conventional control strategies in actual operation. Non-causal stable inversion is the unique energy-bounded input to achieve endpoint perfect tracking. However the stable inversion method requires an exact system model, which makes it hardly applicable to FLM. This paper proceeds from the endpoint trajectory tracking of FLM and summarizes this issue as a non-minimum phase system trajectory tracking problem. Combining stable inversion theory with iterative learning control, a data driven basis function based iterative learning control method is proposed. Compared with the traditional "modeling first, then control" routine, the proposed method need not the model information, but chooses appropriate basis functions to approximate the stable inversion. By using input output data from several trials, the basis function space model can be identified and the iterative control task can be completed with robustness ensured.The main work of the paper is detailed as follows:(1) Combined with stable inversion, a new basis function based adaptive iterative learning control (BFAILC) algorithm is proposed to track the desired output trajectory for repetitive non-minimum phase SISO systems. In this method, an adaptive iterative identification algorithm is designed to estimate the basis function space model of the system. Based on the computational formula of stable inversion, a sufficient condition for the approximation of stable inversion using basis function is derived. And a pseudo inverse type learning law is used to approximate the stable inversion of the non-minimum phase system, which guarantees the convergence and robustness of the control system. Using extended time-domain Fourier basis function as an example, the performance and effectiveness of the proposed algorithm is verified through numerical simulations for non-minimum phase system.(2) A basis vector-valued function based iterative learning control (BVFILC) algorithm is proposed for repetitive non-minimum phase MIMO systems. The vector-valued function space is constructed by grouping the basis functions, and then the basis vector-valued function space model is derived through realignment of the matrix coefficients. Based on the computational formula of stable inversion, a sufficient condition for the approximation of stable inversion is obtained. By converting the optimal control problem to the basis space, an optimal learning law is designed, which ensures the convergence of the algorithm. Numerical simulations are carried out for non-minimum phase systems and the effectiveness of the proposed algorithm is verified.(3) An Experiment set-up of modular flexible manipulator is developed using the maxon series motors. Motion control software platform for the FLM set-up is designed, which has a good human-machine interface and a fine extensibility. Test experiments and endpoint trajectory tracking experiments are carried out on the set-up, the BFAlLC algorithm is implemented and its effectiveness is verified.