Modeling and control for single-link flexible-joint arm with random disturbances

Mechanical systems such as mobile robots, manipulators are usually vulnerable to the random noises in the movement process. For the mathematical modeling and control problems of single link flexible joint arm under random disturbances, there is no related research achievement up to now. For these systems, we adequately introduce some random noises to build a stochastic dynamic model with uncertain parameters. Then, by using the coordinate transformation, we transform this model to a fourth-order nonlinear system. On this basis, we employ the adaptive control theory, the dynamic surface method and Lyapunov method to build up a new controller. This controller effectively avoids the overparameterization and the explosion of complexity in routine controllers, and ensures the mean-square value of the tracking error to be arbitrarily small and all the signals in the closed-loop system to be bounded in probability. Finally, an example in the simulation is given to show the effectiveness of the presented theory.