Optimal digital design of hybrid uncertain systems using genetic algorithms

Abstract

The paper presents a time-domain design methodology for optimal digital design of multivariable sampled-data parametric uncertain systems using genetic algorithms (GAs). A continuous-time parametric uncertain plant, cascaded with an analogue parametric uncertain prefilter is formulated by means of multiple linear cascaded continuous-time nominal models, generated from the perturbed system and prefilter parameters via the GAs. For each linear cascaded analogue nominal model, an optimal analogue controller with regional eigenvalue placement is designed. Then, a new digital redesign method, taking into account the closed-loop intersample behaviour, is developed to convert the optimal analogue controller into a PAM or PWM digital controller for digital control of the continuous-time plant cascaded with a digitised prefilter. The global optimisation searching technique provided in GAs is employed to determine the digital interval plant, prefilter and controller from the obtained respective multiple linear digital models for finding the ranges of their respective implementation errors. As a result, the obtained digital models and controller perfected by the design engineer can be practically implemented. Also, the searching technique is utilised to redetermine the practically implementable optimal PAM or PWM digital controller cascaded with a digital prefilter for optimal digital control of the multivariable sampled-data parametric uncertain system.