Adaptive Sliding Mode Control with Uncertainty Estimator for a 3-[P-2(US)] Translational Parallel Robot

In this paper, constraint equations are derived based on the kinematic model of the robot and Lagrange method is applied to derive the dynamic equations. In order to control the robot position on planned reference trajectories, in presence of uncertainties of the dynamic model, an adaptive robust controller with uncertainty estimator is designed which is robust against the uncertainties and induced noises. The proposed controller consists of an approximately known inverse dynamics model output as model-based part of the controller, an estimated uncertainty term to compensate for the un-modeled dynamics, external disturbances, and time-varying parameters, and also a decentralized PID controller as a feedback part to enhance closed-loop stability and account for the estimation error of uncertainties. Performance of the designed controller is simulated and evaluated in different conditions including the presence of noise and parameters variation. In this regard, a comparison has been made between the response of the proposed adaptive robust controller and response of a feedback linearization controller, indicating their capabilities in noise rejection and compensation of parameters variation. Also, the results show that the proposed sliding mode controller has a desirable performance in tracking the reference trajectories in presence of the model uncertainties and noises for this kind of parallel mechanism.