Time scale separation in control of a single-link flexible-joint robot manipulator

In this article, an adaptive tracking control is presented for a class of flexible-joint robotic manipulators in the presence of parametric uncertainties. For this purpose, the parameter separation technique and the idea of positive function of linearly connected parameters are coupled effectively with combination of backstepping and time scale separation. Subsequently, the virtual/actual control inputs are derived from the solutions of a series of fast dynamical equations. Furthermore, the adaptation law of unknown parameters can be derived based on Lyapunov theory in the backstepping technique. Stability proof of the overall closed-loop system is given via the theorem in singular perturbation theory. In this paper, the problem of 'explosion of complexity' existing in the conventional backstepping control method is avoided. The detailed simulation results are provided to demonstrate the effectiveness of the proposed controller.