Multi-Objective Optimization of Tip Tracking Control Using LMI

Abstract

This paper presented multi-objective optimization of tip tracking control for non-collocated flexible beam. The desired trajectory is specified at the tip displacement of the flexible structure, which undergoes translation base motion actuated by a linear motor. The system model is first formulated from modal truncation approach for the flexible structure representing a single Cartesian robot manipulator. The linear system model of the flexible structure always has structural uncertainties. Robust stability and robust performance on tip tracking can be expressed as H2/H∞ norm constraints, which are converted into the Linear Matrix Inequality (LMI). The multi-objective controller design is solved by the convex minimization. In order to reduce the conservatism generated when the same Lyapunov matrix is selected, the Lyapunov matrix is scaled for different norm constraints. Simulation results have demonstrated favorable tip tracking of the proposed robust controller.