Combined vibration control of flexible cantilever beam driven by MFC actuators and rotary motor

This paper proposed a novel combined vibration control method, designed to rapidly stabilize the flexible cantilever beam driven by MFC actuators and rotary motor. Firstly, the dynamic model of the flexible cantilever beam system, incorporating MFC actuators and a rotary motor, was established based on the Euler–Bernoulli beam theory and Hamilton’s principle, using orthogonal polynomials as mode shapes. Then, the voltage applied to the MFC actuators and the rotation angle of the rotary motor, both serving as inputs, have a phase delay relative to the elastic deformation deflection of the flexible cantilever beam to achieve combined control. Moreover, convergence analysis and model effectiveness verification were conducted. Finally, the effects of the phase delay coefficient, voltage control gain, and rotation angle control gain on vibration control effectiveness and system energy were studied. The results show that compared to the individual action of either the MFC actuators or the rotary motor alone, the combined action of the MFC actuators and the rotary motor can achieve superior vibration control effectiveness. These results confirm the feasibility of applying the combined vibration control to suppress the vibration of the flexible cantilever beam and provide a new approach to vibration control for flexible cantilever structures.