Regulation of a lightweight one-link flexible robot arm using an exponentially stable variable structure controller

Abstract

An exponentially stable variable structure controller is presented for regulation of the angular velocity of a lightweight one-link flexible robot arm, while simultaneously stabilizing vibration transient in the arm. By properly selecting a sliding hyperplane, the non-homogenous governing equations are converted to homogenous ones, and hence, analytically solvable. The controller is then designed based on the original infinite dimensional distributed system which, in turn, removes some disadvantages associated with the truncated-model-base controllers. Utilizing only the arm base angular position and tip deflection for the controller, an on-line perturbation estimation routine is introduced to overcome the measurement imperfections and the ever-present unmodeled dynamics. Depending on the composition of the controller, some favorable features appear such as elimination of control spillovers, suppression of residual oscillations and simplicity of the control implementation. Numerical simulations along with an experimental setup are provided to verify the theoretical concept and validate the effectiveness of the proposed controller.