Decentralized LPV Gain-Scheduled PD Control of a Robotic Manipulator

Abstract

In this paper, low-complexity linear parameter-varying (LPV) modeling and control of a two-degrees-of-freedom robotic manipulator is considered. A quasi-LPV model is derived and simplified in order to facilitate LPV controller synthesis. An LPV gain-scheduled, decentralized PD controller in linear fractional transformation form is designed, using mixed sensitivity loop shaping to take — in addition to high tracking performance — noise and disturbance rejection into account, which are not considered in model-based inverse dynamics or computed torque control schemes. The controller design is based on the existence of a parameter-dependent Lyapunov function — employing the concept of quadratic separators — thus reducing the conservatism of design. The resulting bilinear matrix inequality (BMI) problem is solved using a hybrid gradient-LMI technique. Experimental results illustrate that the LPV controller clearly outperforms a decentralized LTI-PD controller and achieves almost the same accuracy as a model-based inverse dynamics and a full-order LPV controllers in terms of tracking performance while being of significantly lower complexity.