Control of MIMO mechanical systems interacting with actuators through viscoelastic linkages

Abstract

This paper proposes a new method for control of nonlinear multi input – multi output (MIMO) mechanical systems that incorporate viscoelastic dampers (VED) for reducing undesired vibrations of actuators. To this end, a control algorithm is proposed based on considering various characteristics of the described dynamical systems (namely mechanical dynamics, viscoelasticity and actuator dynamics) in generation of control inputs guaranteeing convergence of system response to desired reference signals. This procedure features three consecutive parts within the control loop which are conducted iteratively at each control sample. At each sample, initially necessary forces and moments exerted to mechanical system are calculated as virtual control inputs generated based on a MIMO discrete-time sliding mode control (DSMC) algorithm. As the aim of control model is obtaining a closed-loop system without resulting in notable vibrational effects, undesired chattering effects should be eliminated from inputs generated by DSMC. This objective is attained by calculation of appropriate input bounds. Next, an additional virtual input is assigned corresponding to viscoelastic strain such that virtual mechanical input from previous part of the control loop is generated. To this end, Maxwell model for viscoelastic material is considered. Finally, actual controller input is generated such that all virtual control objectives are satisfied. The effectiveness of control procedure is numerically illustrated for a 3-PRR manipulator.