Self-tuning of a switching controller for scanning motion systems

Abstract

a b s t r a c tFor a class of switching motion control systems, in particular scanning stage systems, a self-tuning method is proposed to find the optimal switching control parameters. In this method, a combined model/data-based approach is used to derive the gradients with respect to these parameters. The gradients are used in an update scheme which subsequently renders an updated set of parameters. Each set is applied to the machine while operating under closed-loop conditions. By repeating the process, the switching control parameters show convergence to an optimized set of values that induce servo performance inaccessible to linear control. This is because high-gain feedback is incidentally switched on to suppress large amplitude oscillations and is otherwise switched off to avoid amplification of small amplitude noises. In time-domain this gives improved low-frequency disturbance rejection properties with minimal deterioration of the sensitivity to high-frequency noises. Stability and convergence of the switching control system and optimization scheme in the face of perturbations is proved using Lyapunov analysis. Servo performance is demonstrated on a commercial and nano-positioning scanning motion system.

Variable Gain Motion Control of Wafer Scanners

“…Here, a sketch of the proof is given, see Heertjes & Nijmeijer (22) for the details. Satisfying conditions ii), iii), and iv) implies the existence of a positive definite P = P T 0, P ∈ R m×m , that satisfies the strictly positive real condition:…”

Performance optimization of piecewise affine variable-gain controllers for linear motion systems

“…In particular, any gradient-based optimization routine, such as e.g. Gauss-Newton [15], can directly be employed in combination with the estimated gradients in (19). Remark 3.2.…”

“…This problem has, to a certain http://dx.doi.org/10.1016/j.mechatronics.2014.02.011 0957-4158/Ó 2014 Elsevier Ltd. All rights reserved. extent, also been addressed in [15], where a more constructive tuning method has been used to tune the parameters of an a priori fixed dead-zone characteristic. However, an a priori selection of a fixed nonlinear structure, e.g.…”

“…In this paper, we develop a synthesis approach for a more general class of piecewise affine variable-gain controllers, as opposed to the tuning procedure for a particular variable-gain controller in [15]. This means that the controller design and tuning tailors the shape of the variable-gain element to the particular disturbance situation at hand.…”

“…The data-based method will adopt the iterative approach from [15], where measured closed-loop error-signals are used in combination with model knowledge in order to compute the gradients of the closed-loop error signals with respect to the variable-gain controller parameters, using a single experiment. The model knowledge, employed in this approach, consists of a controller model (which is exactly known) and a plant model of the system.…”