Iterative learning control realized using an iteration-varying forgetting factor based on optimal gains

Abstract

Iterative learning control with forgetting factor (ILCFF) is widely used in control engineering. However, choosing the optimal parameters of ILCFF to improve system-output characteristics has been a challenging issue for controller designers. This paper proposes an iterative learning control (ILC) algorithm that involves a variable forgetting factor based on optimal gains for a class of discrete linear time-invariant systems with aperiodic disturbances. The convergence of the algorithm is analyzed, and the necessary and sufficient condition for its convergence is derived in terms of proportional–integral–derivative coefficients. A design method based on optimal gains is established to determine the algorithm coefficients and to accelerate system convergence. Furthermore, the influence of the forgetting factor on both the system-output error and the scope of the proposed algorithm is analyzed. Additionally, the most suitable system type for the application of the forgetting factor is determined. The effectiveness of the algorithm is verified by performing a theoretical analysis and a case-based simulation. The proposed iteration-varying optimal forgetting-factor-based ILC algorithm undergoes fast convergence with a small system-output error. The findings disrupt the conventional view that the use of the forgetting factor increases system-output error. In fact, in a system with small trajectory and increased disturbances, the error induced by the forgetting factor may be smaller than that of the traditional optimal ILC algorithm.

Model-Free Control for Doubly Salient Permanent Magnet-Generator-Based Tidal Stream Turbine Considering Flux-Weakening Operation

“…This algorithm can optimize the input error signal with an iterative method, and suppress the initial deviation of the system using the forgetting factor. The error will keep decreasing as the iteration times increase, which makes the system output as close as possible to the ideal value [38]. Therefore, the hybrid control ADRC-ILC in the speed loop can certainly improve the speed response, and suppress the speed ripple and steady-state error as well.…”

Optimization of servo accuracy of Y axis of dicing saw based on iterative learning control

“…Mandra et al(2019) incorporated a state feedback controller into the ILC, which improved the convergence speed of the iterative learning, enhancing the angular position tracking performance of the system. Dai et al (2021) proposed an ILC of the forgetting factor for optimal gain. The results show that the ILC algorithm based on iteratively varying optimal forgetting factors has fast convergence.…”