From experiment design to closed-loop control

Abstract

The links between identification and control are examined. The main trends in this research area are summarized, with particular focus on the design of low complexity controllers from a statistical perspective. It is argued that a guiding principle should be to model as well as possible before any model or controller simplifications are made as this ensures the best statistical accuracy. This does not necessarily mean that a full-order model always is necessary as well designed experiments allow for restricted complexity models to be near-optimal. Experiment design can therefore be seen as the key to successful applications. For this reason, particular attention is given to the interaction between experimental constraints and performance specifications.

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

“…Iterative feedback tuning concepts, see e.g. [27][28][29][30], can possibly be used in this context, although it should be investigated whether these concepts apply to the nonlinear piecewise affine variable-gain control feedback configuration as considered in this paper. In this section, the data-based approach has been applied successfully to the performance-based tuning of a piecewise affine variable gain controller for a wafer stage of an industrial wafer scanner.…”

Data‐driven model reference control with asymptotically guaranteed stability

“…The approximation is good if the difference between K(ρ) and the ideal controller K * can be made small. This approximation has been used in model reduction and controller reduction, see [16] for an overview. A similar approximation in the H ∞ framework is for example used in [17], an H 2 example can be found in [18].…”

“…The discrete signals r(t), y(t), u 1 (t) and u 2 (t) of length N are available. The error ε(t, ρ) is given by (16). The error signal ε s (t, ρ) used in the stability constraints is given by (17).…”

Perspectives on system identification

“…Specific features for control applications are the problems and opportunities of using inputs, partly formed from output feedback, e.g. Hjalmarsson (2005). An important problem is to quantify the model error, and its contribution from the variance error and the bias error, cf.…”