Investigação experimental de controle robusto aplicado ao problema de rastreamento de pêndulo invertido considerando incertezas politópicas

Abstract

This work aims to investigate a new robust control methodology that takes into account polytopic uncertainties to carry out a case study applied to the tracking problem of an inverted pendulum (IP) system. For the proposed technique, firstly, a state feedback project based on linear matrix inequalities (LMI) is carried out, through the controller 𝐻2 norm, as well as the mixed 𝐻2/𝐻∞ control, aiming to provide a solution feasible for the controller’s gains, in the presence of parametric uncertainties, resulting from the system variation mass, which causes a deterioration of its dynamic response, as well as causing instability to the system. Then, adopted the state feedback gains obtained previously calculate to develop a controller’s project in an external loop, having the Proportional-Integral (PI) controller such as control structure, using Kharitonov’s theorem. Finally, the proposed methodology configuration is a cascade control structure that intertwines the internal control loop via a state-feedback LMI approach and an external loop via LP in a PI controller structure project, ensuring robustness and robust performance the presence of parametric variations in the IP system. Several tests in a simulation and experimental environment were carried out to demonstrate the proposed methodology’s effectiveness and robustness. The results show that the proposed methodology provided the system with robust stability given a family of uncertainties and better dynamic performance than other methodologies.