This paper presents a new control strategy based on Fourier transformation and intelligent optimization for a planar Pendubot with a passive second link, which can be treated as a second-order nonholonomic system whose control has been an open and challenging issue. A controller acting within a time corresponding to the frequency of its fundamental harmonic term is designed to realize the system control objective, which is to move the system from its initial position to the target position. By employing Fourier transformation, a general expression of the controller composed of a constant term and harmonic terms is obtained.Next, the constant term is obtained by the angular momentum theorem, and the particle swarm optimization algorithm is employed to obtain the harmonic terms of the controller. A feedback control strategy based on a nonlinear disturbance observer is then applied to overcome the uncertainties/disturbances in the system. Finally, simulation results prove the validity of this control method.

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