Polytopic gain scheduled H ∞ control for robotic manipulators

Abstract

A new approach to the design of a polytopic gain scheduled H∞ controller with pole placement for n-joint rigid robotic manipulators is presented. With linearization around the equilibrium manifold, the robotic system is transformed into a continuous linear parameter-varying (LPV) system with respect to the equilibrium manifold. A filter is introduced to obtain an augmented system, which is apt to have the polytopic gain scheduled controller designed. This system is put into a polytopic expression by a convex decomposition. Based on the concepts of quadratic D-stability and quadratic H∞ performance, the polytopic features are used to simplify the controller design to be a vertices' controller design for the polytope. A state feedback gain, which satisfies H∞ performance and dynamic characteristics for each vertex of the polytope, is designed with a Linear Matrix Inequality (LMI) approach. A global continuous gain scheduled controller is then obtained by a synthesis of the vertex gains. Experiments demonstrate the feasibility of the designed controller.