Controlador não-linear para servomecanismos de alto desempenho em tempo discreto

Abstract

This work addresses discrete time optimal controllers, in particular: the Proximate Time Optimal Servomecanism (PTOS) and the Dynamically Damped Proximate Time Optimal Servomecanism (DDPTOS). Lyapunov theory is used to ensure the stability of the controllers by casting the problem in terms of Linear Matrix Inequalities (LMI). Considering this, there are two main objectives of this work: shown the discrete formulation of the DDPTOS and; relaxed constraints of the classic proof of stability of these controllers, allowing an extension of these techniques to damped systems. Initially, the stability of the closed-loop system is assessed by casting the PTOS nonlinearities in a sector-bounded framework, leading to a set of LMI conditions to be satisfied by the controller parameters. Then, a similar formulation is applied to the discrete DDPTOS, where a linear parametric varying model is used to represent the nonlinearity that adds damping to the system. As a result, a polytopic approach is taken on the limits of the varying parameter given by this representation. The two proposed approaches are validated through experiments in a physical system consisting of a damped servomechanism.