Gain Scheduled LPV <i>H</i>_∞ Control Based on LMI Approach for a Robotic Manipulator

Abstract

Abstract A new approach to the design of a gain scheduled linear parameter‐varying (LPV) H ∞ controller, which places the closed‐loop poles in the region that satisfies the specified dynamic response, for an n ‐joint rigid robotic manipulator, is presented. The nonlinear time‐varying robotic manipulator is modeled to be a LPV system with a convex polytopic structure with the use of the LPV convex decomposition technique in a filter introduced. State feedback controllers, which satisfy the H ∞ performance and the closed‐loop pole‐placement requirements, for each vertex of the convex polyhedron parameter space, are designed with the use of the linear matrix inequality (LMI) approach. Based on these designed feedback controllers for each vertex, a LPV controller with a smaller on‐line computation load and a convex polytopic structure is synthesized. Simulation and experiment results verify that the robotic manipulator with the LPV controller always has a good dynamic performance along with the variations of the joint positions. © 2002 Wiley Periodicals, Inc.