Fuzzy Lyapunov synthesis control design for an underactuated 2-dimensional translational oscillator with rotational actuator

The underactuated 2-dimensional translational Oscillator with rotational actuator (2DTORA) system consisting of an rotational proof-mass and two unactuated translational carts is an extension version of the TORA system which is a well-known benchmark for nonlinear control design. In this paper, dynamics of 2DTORA system is normalized and written in general affine form. And we apply fuzzy Lyapunov synthesis to design a state feedback controller to stabilize the system with partial information on dynamics by using only a linguistic description. The designed state feedback controller is nonlinear which can be simplified as the classic linear state feedback controller. Simulation results demonstrate the effectiveness of the designed controller and its advantages in comparison with a previously designed linear controller for the 2DTORA system.