Multi-phase iterative learning control for high-order systems with arbitrary initial shifts

Aiming at the second-order tracking system with arbitrary initial shifts, this paper presents a multi-phase iterative learning control strategy. Firstly, utilizing the form of solution of the second-order non-homogeneous linear differential equation with constant coefficients and the initial shifts, we can select the appropriate control gain to ensure that the second-order systems are stable and reach the stable output after a fixed time. Secondly, on the premise that the second-order systems have reached the fixed output, two methods are proposed for rectifying the fixed shift, namely, shifts rectifying control and varied trajectory control. Theoretical analysis shows that the multi-stage iterative learning control strategy proposed in this paper can ensure that the second-order systems achieve complete tracking in the specified interval. Finally, the simulation examples affirm the validation of the designed algorithms.