Robust H<inf>2</inf>/H<inf>∞</inf> control for a robot manipulator fuzzy system

Abstract

In this article we investigate on robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control with regional Pole-Placement, for tool position control of a nonlinear uncertain flexible robot manipulator. First, to apply the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller, the uncertain nonlinear system is approximated by Takagi and Sugeno's (T-S) fuzzy model. Then, an extra state (error of tracking) is augmented to the T-S model in order to improve tracking control. Based on each local linear subsystem with augmented state, a regional pole-placement state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller by using linear matrix inequality (LMI) approach is employed. Parallel Distributed Compensation (PDC) is used to design the controller for the overall system and the total linear system is obtained by using the weighted sum of the local linear systems. A fuzzy weights online computation (FWOC) component is employed to update fuzzy weights in real time for different operating point of system. Simulation results are presented to validate the effectiveness of the proposed controller like robustness and good load disturbance attenuation and accurate tracking, even in the presence of parameter variations and load disturbances on motor and tool.