Robust control and data‐driven tuning of a hybrid integrator‐gain system with applications to wafer scanners

Abstract

A hybrid integrator-gain system is discussed that aims for improved low-frequency disturbance rejection, while, at the same time, does not deteriorate overshoot and settling times when compared with a linear integrator. The hybrid integrator has similar phase advantages as the well-known Clegg integrator but without inducing the discontinuous behavior resulting from resetting system state values. Optimal tuning of the controller parameters of the hybrid integrator is strongly influenced by machine-specific properties and therefore favors a data-driven optimization approach. However, as a time-domain optimization algorithm can easily lead to nonrobust solutions in the sense of large peaking of the closed-loop frequency response functions, frequency-domain robustness constraints will be imposed. By means of an adaptive weighting filter design, the parameter updates are penalized upon violation of said robustness constraints. Posed in an unconstrained problem formulation, this is subsequently solved by applying a Gauss-Newton-based parameter update scheme.Closed-loop stability of the linear time-invariant plant and controller in feedback connection with a hybrid integrator-gain system element follows from a circle-criterion-like analysis, which is based on evaluating (measured) frequency response data. Measurement results obtained from an industrial wafer scanner demonstrate the effectiveness of the approach.

Hybrid Integrator-Gain Systems: A Remedy for Overshoot Limitations in Linear Control?

“…For a formal introduction of HIGS, inspired by projected dynamical systems, along with a proof for global existence of solutions, the reader is referred to [13]. Specific control applications with HIGS can be found in [3], [4], [10].…”

“…The step-response of the plant (7) in feedback with the HIGS-based controller, the latter being the series interconnection of the filters Ĉ1 (s), and Ĉ2 (s) with τ = 5 • 10 −3 see Remark 1, and the HIGS in (4) with ω h = 0.8 rad/s, is shown in Fig. 4 (in red), along with the generated control output u.…”

“…Although the performance-enhancing potential of HIGSbased control was already shown by the (experimental) results in [3], [4], and [10], an open question that remains is whether HIGS-based controllers can indeed go beyond performance achievable by LTI controllers. In this letter, one of the objectives is to answer this question positively.…”

“…O VERSHOOT performance limitations inherent to linear time-invariant (LTI) feedback control [1], [2], motivate the use of so-called hybrid integrator-gain systems, further abbreviated as HIGS [3], [4]. To reduce overshoot, the main philosophy underlying HIGS is to keep the sign of the integrator's output the same as that of its input, thereby constantly forcing the system in the direction toward zero error.…”

Editorial for the Special Issue on Learning‐based Adaptive Control: Theory and Applications

“…communication delays, and uncertainties in the dynamics of the human drivers and the autonomous vehicles. Heertjes et al present a solution to the problem of adaptive optimal feedback autotuning of an industrial wafer stage system. A hybrid integrator‐proportional controller is used together with data‐driven optimal gains autotuning to improved low‐frequency disturbance rejection properties without deteriorating overshoot and settling‐time performances.…”