Estudo de técnica de controle robusto de um sistema sujeito a uma falha operacional tratado como incerteza politópica

Abstract

This paper proposes the study of a robust control technique for dynamic linear systems subject to operational failures treated as parametric uncertainties of polytopic type. The technique approached for the control of the systems proposed in the literature is portrayed as: robust design technique subject to decay rate with optimization of the controller’s norm. The systems are, mass-spring-damper system and physical system DC Servo mechanism, in which are matched the mathematical models that characterize the dynamic behavior of the system. The representation is described in the quadratic form of Linear Matrix Inequalities (LMIs) based on the Lyapunov theory for the stability of dynamic systems. It is applied the robust control technique with decay rate in both systems, with and without optimization, for later comparison of the performances. The estimated models of each system are calculated through MATLAB. For the mass-spring-damper system, which is only subject to simulation, the results for the robust controller are obtained for a given initial condition and the relevant graphical responses analyzed. The Servo-mechanism DC is modeled in state space and the technique implemented in the laboratory practice using control by tracking. Robust controllers are tested in pre-determined study scenarios, analyzing the response curves and influences of the parameters involved, such as gains, decay rate, and optimization. We conclude with qualitative and quantitative approaches the robust control with decay rate with and without the optimization for the proposed uncertain systems, arriving at significant reductions in the magnitudes of the controllers, from 94.45% for the mass-spring-damper system, 99.99 % and 90.39% for the DC Servo mechanism.