An Infinite Dimensional Distributed Base Controller for Regulation of Flexible Robot Arms

An exponentially stable variable structure controller is presented for regulation of the angular displacement of a one-link flexible robot arm, while simultaneously stabilizing vibration transient in the arm. By properly selecting the sliding hyperplane, the governing equations which form a nonhomogenous boundary value problem 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 measurements, an on-line perturbation estimation routine is introduced to overcome the measurement imperfections and ever-present unmodeled dynamics. Depending on the composition of the controller, some favorable features appear such as elimination of control spillovers, controller convergence at finite time, suppression of residual oscillations and simplicity of the control implementation. Numerical simulations along with experimental results are provided to demonstrate and validate the effectiveness of the proposed controller.