Development of Iterative Learning Control Method for Trajectory Tracking in Two-Dimensional Discrete-Time Systems

In this paper, an Iterative Learning Control (ILC) scheme is proposed to address the tracking problem of two-dimensional (2-D) discrete-time systems. To achieve the control objective, by using the model called Wave Advanced Model (WAM), the 2-D model of the system is converted to a one-dimensional (1-D) model while the system's describing matrices are rectangular with variable dimensions. This makes the stability analysis more complicated. By deriving the input-output transformation description and developing the ILC algorithm, a P-type ILC control law is proposed. The sufficient condition for the asymptotic convergence of the proposed controller is derived from the considered repetitive process. It is proved that under the proposed method, the norm of the tracking error is converged to zero and consequently the system output can track the desired trajectory with acceptable performance. Besides, the effectiveness of the proposed method is examined by providing the simulation results of a practical example.