Rational basis functions are introduced into iterative learning control to enhance the flexibility towards nonrepeating tasks. At present, the application of rational basis functions either suffers from nonconvex optimization problem or requires the predefinition of poles, which restricts the achievable performance. In this article, a new data-driven rational feedforward tuning approach is developed, in which convex optimization is realized without predefining the poles. Specifically, the optimal parameter which eliminates the reference-induced error is directly solved using the least square method. No parametric model is involved in the parameter tuning process and the optimal parameter is estimated using the measured data. In the noisy condition, it is proved that the estimated optimal parameter is unbiased and the estimation accuracy in terms of variance is analysed. The performance of the proposed approach is tested on an ultraprecision wafer stage. The experimental results confirm that high performance is achieved using the proposed approach.

Feedforward control has been widely used to improve the tracking performance of precision motion systems. This paper develops a new data-driven feedforward tuning approach associated with rational basis functions. The aim is to obtain the global optimum with optimal estimation accuracy. First, the instrumental variable is employed to ensure the unbiased estimation of the global optimum. Then, the optimal instrumental variable which leads to the highest estimation accuracy is derived, and a new refined instrumental variable method is exploited to estimate the optimal instrumental variable. Moreover, the estimation accuracy of the optimal parameter is further improved through the proposed parameter updating law. Simulations are conducted to test the parameter estimation accuracy of the proposed approach, and it is demonstrated that the global optimum is unbiasedly estimated with optimal parameter estimation accuracy in terms of variance with the proposed approach. Experiments are performed and the results validate the excellent performance of the proposed approach for varying tasks. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

No abstract

It is necessary to keep the closed-loop system stable in data-driven feedback tuning. A widely-used strategy is using stability criterions as the constraint while parameter updating. In this strategy, the conservatism of the stability constraint has great influence on the achievable convergence performance. In this paper, a less conservative stability constraint is proposed to improve the convergence rate of data-driven feedback tuning methods. Specifically, the proposed stability constraint is developed based on small gain theorem (SGT). The conservatism is reduced through extension of SGT and further reduced using the properties of H∞ norm. Besides, an unbiased data-driven estimation method of H∞ norm is employed to estimate the proposed stability constraint accurately. Simulations are conducted to test the performance of the proposed stability constraint. The results demonstrate that the proposed stability constraint is less conservative and contributes to higher convergence rate.

This paper aims to develop a new data-driven feedforward tuning approach to achieve high performance for linear parameter varying (LPV) motion systems. In the proposed approach, the feedforward controller is linearly parameterized with polynomial basis functions and parameter varying coefficients. Gauss-Newton Method is exploited to solve the corresponding parameter optimization problem. Parameter perturbing experiments are employed to estimate the gradient. The truncated singular value decomposition (SVD) method is adopted to deal with the ill-conditioned matrix inversion problem. No parametric model is required throughout the tuning process. Simulations are conducted to test the performance of the proposed approach. And the results indicate that the parameter varying dynamics of the plant are well compensated by the proposed approach.