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This paper is concerned with the issue of nonlinear dynamic surface control for an underactuated translational oscillator with a rotating actuator (TORA). The nonlinear feedback cascade model of the underactuated TORA is obtained through a collocated partial feedback linearization and a global change of coordinates. A nonlinear controller is designed to treat the state variables as virtual control inputs to design the virtual controller step by step. Dynamic surface control is used to avoid the “explosion of complexity” in the backstepping design process. Considering that there is no affine appearance of the variables to be used as virtual controls for the second state, the first step is designed for a one-input and two-state system. It is proved that the proposed design method can guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system with arbitrary small tracking error by appropriately choosing design constants. The simulation results demonstrate the effectiveness of the proposed approach.

Nonlinear Dynamic Surface Control for the Underactuated Translational Oscillator With Rotating Actuator System