Improved data-driven high-order model-free adaptive iterative learning control with fast convergence for trajectory tracking systems

The data-driven high-order pseudo-partial derivative-based model-free adaptive iterative learning control (HOPPD-MFAILC) is always slow to converge and difficult to have excellent tracking results. To address the problem, an improved high-order pseudo-partial derivative-based model-free adaptive iterative learning control (iHOPPD-MFAILC) with fast convergence is proposed. First, to reduce the impact of the initial value of the pseudo-partial derivative (PPD) on the convergence speed of the algorithm, the initial PPD is corrected by introducing the high-order model estimation error. Second, to reduce the influence of system noise on the control performance, the original HOPPD-MFAILC control law is improved by introducing time-varying iterative proportional and time-varying iterative integral terms. Then, the convergence of the proposed improved control algorithm is demonstrated by theoretical analysis. Finally, simulations and experiments on the ball screw motion system show that the proposed iHOPPD-MFAILC can track the desired trajectory better. In addition, iHOPPD-MFAILC has better robustness in the noisy environment and achieves better convergence as well as trajectory tracking performance under different initial PPD conditions. The proposed control scheme has excellent application potential in precision motion control.