Design of Fractional-Order Iterative Learning Controller for Cross-Coupled Contour Motion Systems

For the contouring errors produced by repetitive tracking motion of single -axis linear motor on XY platform, a combined method of fractional iterative learning and cross coupled is proposed. Firstly, a positional controller of the fractional PD-type iterative learning is designed, and the integer differential operator is replaced by the differential operator defined by Grunwald-Letnikov fractional calculus to improve the traditional integer order iterative learning law. The convergence condition of the fractional iterative learning controller is given. Then, the cross-coupled control is adopted between two axes, and the contour error is estimated by using the real-time contour error estimation model to reduce the contour error. The compensation amount of X and Y axis is assigned according to the relationship of cross-coupled gain, and the real-time compensation. The simulation shows that compared with integral iterative learning, fractional iterative learning has faster convergent speed and higher accuracy of contouring process. Fractional iterative learning is an effective way to improve the contour error.