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

To circumvent performance-limiting trade-offs encountered in the control of linear motion systems, we introduce a method for designing performance-optimal piecewise affine variable-gain feedback controllers. Variable-gain controllers are known to improve upon the performance trade-off between low-frequency tracking on the one hand and sensitivity to high-frequency disturbances on the other hand. However, the performance-based tuning of such variable-gain controllers is far from trivial. In this paper, we consider a class of variable gain controllers comprising a loop-shaped linear controller and a generic add-on piecewise affine variable gain element. This structure warrants both an intuitive design procedure of the linear part of the control design and a high level of versatility in the design of the nonlinear control part. The add-on piecewise affine control structure introduced in this paper allows for synthesizing the shape of the variable-gain controller by means of either a full model-based optimization approach of a certain L2L2 performance indicator or by extending this approach with data-based elements. As a result, the controller design can be tuned for the disturbance situation at hand while optimizing performance. To illustrate the effectiveness of the approach, the proposed performance-based controller synthesis strategy is demonstrated on an industrial wafer scanner.