Adaptive second-order sliding mode controller for a twin rotor multi-input–multi-output system

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Abstract
In this study, an adaptive second-order sliding mode (SOSM) controller is proposed to control a laboratory helicopter called the twin-rotor multi-input–multi-output system (TRMS). The design objectives of the controller are to stabilise the TRMS in significant cross couplings, reach a desired position and accurately track a specified trajectory. The TRMS model is divided into a horizontal and a vertical subsystem (VS). The cross coupling existing between the two subsystems is considered as the system uncertainty. A simple adaptive tuning law is developed for the SOSM controller to deal with the bounded system uncertainty. The major advantage offered by this adaptive SOSM controller is that advance knowledge about the upper bound of system uncertainty is not a necessary requirement. The adaptive SOSM controller for the VS uses a proportional plus integral sliding surface to counter the offset present in the pitch angle. System robustness and the stability of the controller are proved by using the Lyapunov criterion. Apart from imparting robustness, the proposed adaptive SOSM controller reduces undesired chattering in the control input and thus is suitable for application in practical motion control applications. The proposed control scheme is validated by simulation results and is compared against the existing proportional-integral-derivative controllers to show that the overall performance of the proposed adaptive SOSM controller is better in the aspects of error and control indices.