Iterative Learning Control for High Relative Degree Discrete-Time Systems with Random Initial Shifts

In this paper, an iterative learning control (ILC) strategy under compression mapping framework is presented for high relative degree discrete-time systems with random initial shifts. Firstly, utilizing the high relative degree of the system and difference term, a control law is designed and a p-order non-homogeneous linear difference equation is established. The appropriate control gain is selected according to the characteristics of solution of the difference equation and the initial shifts, so as to ensure that the high relative degree discrete-time system can reach a steady-state deviation output at a fixed time. Subsequently, a PD-type control law is employed to correct the fixed deviation of the system. Theoretical analysis indicates that this ILC strategy can ensure that the high relative degree systems achieve accurate tracking after the predefined time. Finally, the simulation experiments are conducted on a linear discretetime Multiple-Input Multiple-Output(MIMO) system with relative degree 1 and a Multiple-Input Single-Output(MISO) system with relative degree 2, respectively, and the results verify the effectiveness of the algorithm.