Mixed Sensitivity Control of Euler-Lagrange Models

Abstract

Fully actuated Euler-Lagrange (E-L) and Hamilton models are considered. A linearized E-L model is obtained, assuming that the positions of the centers of mass (CM) do not depend explicitly on time. A non-iterative mixed sensitivity control (MSC) and a calculated torque control law guaranteeing stability and assigning a desired output stationary state for the closed-loop system are proposed. A mixed sensitivity control (MSC) is designed for a linearized E-L model, and additive uncertainty model is proposed based on the state difference between linear and nonlinear E-L models. Stability is guaranteed by the small-gain theorem when the MSC is applied to the nonlinear model, and for the additive uncertainty level, an approximated optimal pole placement minimizes simultaneously the infinity norms of the output sensitivity function at low frequency and at high frequencies the transfer function from the output additive disturbance to the controller output, so assuring a desired output stationary state at low frequency and maximizing the set of admissible uncertainties at high frequencies. Also, Hamilton’s equations of motion and a calculated torque control are gotten based on quadratic forms. The MSC is compared with the proposed calculated torque designed for Hamilton equations and the calculated torque designed for the E-L model. The results are applied to a double pendulum on a plane and a Robot Maker 110.