G. Pipeleers, Optimal Linear Controller Design for Periodic Inputs and Extended LMI Characterizations for Linear Stability and Performance, 2009

Abstract

Periodic reference and disturbance signals are widespread in engineering practice, as every rotating machinery and repeated process involves periodicity. Exploiting the periodic input characteristics in the controller design is indispensable to meet tight performance demands in spite of measurement noise, model inaccuracies, ...
This thesis develops a general design methodology for linear controllers facing periodic inputs, which applies to all controller types reported in the literature. The proposed design methodology is able to reproduce and outperform the major current design approaches, where this superior performance stems from the following properties: (i) uncertainty on the input period is explicitly accounted for, (ii) periodic performance is traded-off against conflicting design objectives, and (iii) the controller design is translated into a convex optimization problem, guaranteeing the efficient computation of its global optimum. Apart from extensive numerical evaluation, the potential of the design methodology is experimentally illustrated on an active air bearing setup.

In an independent second part, this thesis develops a general methodology for deriving so-called extended LMI characterizations for stability and performance of linear systems. These LMIs constitute a valuable tool for reducing conservatism in hard problems like multi-objective control and robust stability and performance analysis. Relying on the projection lemma, the proposed methodology provides a straightforward and unified proof for the majority of literature results as well as some currently missing extended LMIs.

Handle

Online version
Access might be restricted.

Order Code

Code: 09D09