Identification and control of delayed dynamical systems through pattern search methods

Resumen

The work developed in this thesis is aimed to improvement the behaviour of dynamical system with unknown delay. For it, we employ a delay identification scheme and a multi-model control scheme, which is able to estimate the delay with a high precision and then be used in the control law. Additionally, the controller design should be made over the rational part of the system, ignoring the delay, which is an advantage in comparison with the control schemes used commonly. The starting point is a multi-model control scheme with time-varying models. The basic idea consists in a battery of models running in parallel. Associated at each model there is a controller. The supervision logic allows switching between them, in function of the model that presents a better behaviour. In this way, any possible uncertainty of the plant delay is mitigated by the switching to a better model, making the system robust from variations of the delay. Multi-model schemes generally require a large number of fixed candidate models to obtain a good performance. This problem is circumvented in this work by using a relatively small set of candidate models evolving with time according to a so-called Pattern Search Method (PSM). PSM is an optimization method that has been used in Mathematics and Optimization Theory, but its use in Control Theory is rather limited, existing very few works using it. The approach is used on stable, unstable and integrating systems, where through a set of simulations it is corroborate the optimal performance of the proposed scheme. Additionally, an on-line estimation method is proposed which is able to identify the delay from a step response using a set of fixed models. In all cases convergence and stability results are presented.