Application of regularized instrumental variable method in iterative motion feedforward tuning

Abstract The feedforward controller ensures the high performance and high‐precision performance of the motion control system. In the two‐degree‐of‐freedom motion control system, the method of using iterative learning and optimization estimator to tune parameters to construct the feedforward controller is very popular. On the basis of constant iterative learning control (ILC), the system parameters identified by different optimization estimators in the same noise environment will affect the trajectory tracking performance of the constructed feedforward controller. In the existing optimization estimators, such as the least square (LS) estimator and the instrumental variable(IV) estimator, the parameters estimated in the process of iterative learning will have deviation or excessive variance, which will gradually reduce the trajectory tracking performance of the feedforward controller with the increase of noise variance or make the trajectory tracking performance of the feedforward controller unstable in each iteration. The contribution of this paper is to propose a new estimator application, which introduces regularization on the basis of IV estimator under the framework of feedforward ILC. The proposed estimator minimizes the mean square error (MSE) by trade‐off between deviation and variance of estimated parameters, leading to further improvement in the trajectory tracking performance of the feedforward controller. Simulation and experimental results show that the proposed estimator is effective and theoretical in a noisy environment.