Optimal Trajectory Tracking Control of a Nonlinear under actuated Ball and Beam system by Applying Hybrid Adaptive Robust Controller

This paper concentrates on implementation of a hybrid adaptive control structure for four-order nonlinear under-actuated systems. The first challenge for these systems is linearization and use of a suitable controller in confronting parametric uncertainties. For this purpose, combination of feedback linearization with an adaptive sliding mode controller by using update mechanism is considered. The update mechanism is obtained based on gradient descend method and chain role of derivation for sliding mode parameters. In the following, to eliminate the tedious trial-and-error process of determining the proposed control coefficients, an evolutionary algorithm (MOPSO) is used to extract the optimal parameters by minimizing the tracking error and control input. To prove the capability of the proposed controller, the stability of a ball on the beam has been investigated. The results of the proposed controller despite an external disturbance in comparison with adaptive sliding mode and feedback linearization demonstrate the system robustness and stability in the shortest possible time.