Fixed-order H<inf>∞</inf> loop-shaping synthesis: A time domain approach

Abstract

This work deals with a new approach of loop-shaping H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synthesis based on the Particle Swarm Optimization (PSO) algorithm. Indeed, such stochastic algorithms are interesting to solve problems based on complex industrial specifications and so seem to be particularly well suited to optimal robust controller synthesis. In this work we investigate the optimal weight tuning along a fixed order controller computation without any structural assumption on the searched filters except of course their order. The absence of any structural assumption is important to avoid affecting the quality of the solution towards a complex specification and allows us to reduce the synthesis problem to a simple time domain one with static scalings in place of frequency weights. Using a version of PSO well adapted for high dimensional problems, we succeed in computing a fixed-order controller for complex industrial specifications toward a generic non constraint fitness with quite reasonable computing time.