Global Stabilization of Underactuated TORA based on Equivalent-Input-Disturbance Approach

A. Zhang (PR China, Japan), T. Liu, J. She (Japan), X. Lai, and M. Wu (PR China)


Equivalent-input disturbance (EID), translational oscillator with rotational actuator (TORA), underactuated mechanical system.


This paper concerns the benchmark problem of the global stabilization control of a nonlinear translational oscillator with a rotational actuator (TORA), which is composed of a cart moving in a line and an eccentric rotational proof mass. To solve it, we develop a new control strategy that requires only the positions, not the velocities, of the cart and proof mass: First, a coordinate transformation transforms the TORA into a simple nonlinear system. The new system is then divided into linear and nonlinear parts; and taking the nonlinear part to be an artiļ¬cial disturbance enables use of the equivalent-input-disturbance (EID) approach to globally and asymptotically stabilize the new system. Since the transformation is homeomorphous, the stability of the original TORA is guaranteed. Simulation results demonstrate the validity of this control strategy.

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