Adaptive Output Feedback Control for 2D TORA System Based on Velocity Observer

The typical underactuated system two-dimensional translational oscillator with rotational actuator (2D TORA) that consist of two unactuated translational carts and an actuated rotational eccentric ball which acts as its control input. As an extension of TORA system, the 2D TORA system is more general, meanwhile, the dynamic characteristics of this system makes it challenging to design a proper control scheme. It is very important to realize the accurate positioning of payloads in special application environment. In this paper, an adaptive output feedback controller is proposed to realize all state variables positioning. Specifically, in order to solve the matter of uncertain friction and unknown disturbance, an adaptive method for unknown friction coefficient is designed. Moreover, we come up with a velocity observer to calculate the angular velocity instead of differentiating the output signals. Based on Lyapunov stability theory, the state convergence and stability of the 2D TORA system are analysed. Finally, simulation test results exhibit that the presented control method is effective.