Flexible Joints Robotic Manipulator Control By Adaptive Gain Smooth Sliding Observer-Controller

An adaptive gain sliding observer for uncertain parameter nonlinear systems together with an adaptive gain sliding controller is proposed in this paper. It considered nonlinear, SISO affine systems, with uncertainties in steady-state functions and parameters. A further parameter term, adaptively updated, has been introduced in steady state space model of the controlled system, in order to obtain useful information despite fault detection and isolation. By using of the sliding observer with adaptive gain, the robustness to uncertainties is increased and the parameters adaptively updated can provide useful information in fault detection. Also, the state estimation error is bounded accordingly with bound limits of the uncertainties. The both of them, the sliding adaptive observer and sliding controller are designed to fulfill the attractiveness condition of its corresponding switching surface. An application to a single arm with flexible joint robot is presented. In order to alleviate chattering, a parameterized tangent hyperbolic has been used as switching function, instead of pure relay one, to the observer and the controller. Also, the gains of the switching functions, to the sliding observer and sliding controller are adaptively updated depending of estimation error and tracking error, respectively. By the using adaptive gains, the transient and tracking response can be improved. The state and parameter uncertainties in the model of the rigid joints-rigid links robotic manipulators, as SISO non-linear systems and the deviations of the parameters from their nominal values lead to the difficulties of parameter identification and state estimation. All of these, do absolutely necessary the designing of the controller and/or the observer such as the closed loop to be robust. That means stability with small tracking and estimation errors. It is well known the robustness to model and parameter uncertainties and external disturbances of the closed loop with variable structure controller. Maintaining the system on sliding surface, the influence of the uncertainties into the closed loop performances is alleviated and the evolution is quickly to an equilibrium point. In [2] is used adaptive variable structure control with parameterized sigmoid as switching function (denoted k-sigmoid) with adaptive modifications of its amplitude (denoted λ-modification), instead of a pure relay one with constant gain. In this paper is used a parameterized