Robust Model Predictive Control for Two-DOF Flexible-Joint Manipulator System

Abstract

This paper presents a practical study on how to improve the ℋ∞ performance and meet the input–output constraints of the two-degrees-of-freedom (DOF) flexible-joint manipulator system (FJMS) with parameter uncertainties and external disturbances. For this reason, a robust constrained moving-horizon ℋ∞ controller is designed to improve the system ℋ∞ performance while still satisfying the input–output constraints of the uncertain system. First, the uncertain controlled system model of the two-DOF FJMS is established via the Lagrange equation method, Spong’s assumption, and the linear fractional transformation (LFT) technique. Then, the control requirements and input–output constraints of the uncertain system are transformed into the linear matrix inequality (LMI) via the theory of ℋ∞ control and the full-block multiplier technique. Next, the LMI optimization problem refreshed by the current state is addressed at each sample moment with the idea of the moving-horizon control of the model predictive control (MPC), and the calculated gain is implemented to the nonlinear closed-loop system under the state feedback structure. The validity and feasibility of the designed control scheme is finally verified via the results of simulation experiments.

Keywords

• two-DOF FJMS
• LFT
• LMI
• moving-horizon control
• robust ℋ_∞ control