In this work, the control of Translational Oscillations with a Rotational Actuator (TORA) system is presented in this paper. The optimal sliding mode controller is proposed to control the two DOF underactuated mechanical system. The nonlinear coupling from the rotational to the translational motion is the main problem that faces the controller design. The H2 sliding mode controller is designed to give a better performance if only sliding mode control is used. The results illustrate that the proposed H2 sliding mode controller can achieve the stabilization of the system with the variation in system parameters and disturbance.

The design of an H2 sliding mode controller for a mobile inverted pendulum system is proposed in this paper. This controller is conducted to stabilize the mobile inverted pendulum in the upright position and drive the system to a desired position. Lagrangian approach is used to develop the mathematical model of the system. The H2 controller is combined with the sliding mode control to give a better performance compared to the case of using each of the above controllers alone. The results show that the proposed controller can stabilize the system and drive the output to a given desired input. Furthermore, variations in system parameters and disturbance are considered to illustrate the robustness of the proposed controller.

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