On hierarchical sliding mode control of underactuated TORA system

Two different hierarchical sliding mode controllers are designed for an underactuated TORA (Translational Oscillator with Rotational Actuator) system. Firstly, the dynamics of TORA system is separated into two subsystems according to the motion degrees of freedom. Each subsystem contains two state variables, which are chosen to construct a sub-sliding mode surface. And the total sliding mode surface is defined as a function of the two sub-sliding mode surfaces. For the two methods of hierarchical sliding mode control, the first method is to define the total sliding mode surface as a piecewise linear function of the two sub-sliding surfaces. The coefficient of the function needs to be frequently switched to guarantee the system stability. The second method is to define the total sliding mode surface as a continuous liner function of the two sub-sliding mode surfaces. The coefficient sign of the continuous liner function is determined by analyzing the model. Finally, simulation results demonstrate the feasibility of the two controllers, and show that the second controller has better performance.