Data-driven rational feedforward tuning: With application to an ultraprecision wafer stage

Abstract

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.

Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

“…With the parameter updating law in (34), it is obvious that the θopt obtained in Section 4 is 𝜃 1 when the initial parameter 𝜃 0 is zero. The estimation accuracy of 𝜃 1 has been analysed in Section 4.…”

“…Remark 8. Different from the iterations in Section 4.4, the iterations in (34) is not offline, and one reference-tracking trial is required in every iteration to update η(𝜃 k−1 ).…”

“…By contrast, significant reference-induced error still exists in the worst-case tracking errors of Q 1 and Q 2 after the first iteration. In the subsequent iterations, with the parameter updated using (34), the reference-induced error in the worst-case tracking error of Q 2 is reduced iteration by iteration, as shown in Figure 5. It can be observed from Figure 6 that Compare the above results with Figure 4 and Table 3, it can be concluded that the magnitude of worst-case tracking error is highly correlated with the parameter estimation accuracy.…”

“…In the experiments, the reference-tracking performance and extrapolation properties of the following three methods are compared. M 1 : standard ILC in [12]; M 2 : the pre-existing approach associated with RBFs in [34]; M 3 : the proposed approach mentioned here.…”

Iterative Tuning of Feedforward Controller with Precise Time-Delay Compensation for Precision Motion System

“…For the non-minimum phase system, the stability problem of model inversion is solved by the input shaping method [16,17]. e unbiased parameter estimation with optimal accuracy in terms of variance is obtained for feedforward controllers with a rational basis [18], and the feedforward control with rational basis functions can enable higher performance and more enhanced extrapolation capabilities than polynomial basis functions [18,19]. A high-order IFT algorithm is proposed by introducing the iterative domain into the IFT, and IV is also employed to tolerate the noise data [6].…”