Adaptive fuzzy control for 2D TORA systems with input dead zones

The two-dimensional translational oscillator with rotational actuator (2D TORA) system consists of two unactuated translational platforms and an actuated rotational eccentric ball, which is utilized for addressing translational vibrations. Nevertheless, the high degree of coupling and intricate dynamics present significant challenges for the control problem of 2D TORA. Moreover, practical actuators often fall short of ideal performance, meanwhile the presence of input dead zones introduces more challenges in controller designing phase. In this study, we introduce an adaptive fuzzy control strategy for 2D TORA systems to overcome these issues. Specifically, a fuzzy logic system is incorporated along with elaborately designed update laws to compensate the influence of uncertainties such as input dead zones. Additionally, combined with the energy based control idea, an effective controller is designed with the adaptive fuzzy technique. The accurate positioning and vibration suppression objectives are also achieved. Rigorous closed-loop stability analysis is provided based on Lyapunov stability theory. At last, simulation results show the satisfactory efficacy of the adaptive fuzzy method.