Síntese de controladores robustos aplicados em sistemas com atrasos temporais

Abstract

This work aims the study, development and application of the synthesis of a robust control technique for time-delayed systems. The synthesis is modeled by a LMI approach in the formulation of a convex optimization problem, incorporating LQR, so that the guaranteed cost associated with the control system is minimized. The development is based on a synthesis technique already presented in the literature that considers delays in the states of an uncertain system, being the greatest contribution of this work the extension of the synthesis to the case of delayed inputs. The resolution of the optimization problem is performed on the MATLAB platform, and provides stabilizing state feedback gains with an optimized guaranteed cost. A physical implementation of the controller on an embedded system is also presented, composed of a microcontroller of the PIC18 series, responsible for controlling the speed of a servomotor, while intentional delays are inserted in the communication between the devices in order to test and validate the developed synthesis technique.