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In this paper, a rotating hub-blade system with a flexible support which represents a wide range of industrial applications is considered for modelling and control. The flexible blade is assumed as an Euler–Bernoulli beam. In addition, three piezoelectric layers are mounted on the blade as sensors and actuators to reduce vibrations of the blade attached to the hub. For modelling, the Lagrange’s method is utilized to obtain the equations of motion of the system. In order to simultaneously suppress vibrations of the system and track the desired angular position of the hub, designing an appropriate controller is carried out. In this regard, a fractional order sliding mode (FOSM) controller is proposed to fulfil these objectives and then the comparison between FOSM controller and the classical sliding mode controller is presented in order to investigate the effectiveness of the proposed controller. The simulation results indicate the superior performance of the fractional order controller in compare to the integer order sliding.

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In this article, modeling and control of a rotating hub-beam system are studied. The system consists of a solid rotating cylinder and an attached flexible arm with a payload at the end. The rotation is supposed to be in the presence of gravity and the flexible arm is assumed to be a Euler-Bernoulli beam. To derive the equations of motion of the system, Lagrange’s method is applied. Moreover, Galerkin’s technique is employed to discretize the equations of motion. Furthermore, designing an appropriate two-time (slow and fast) scale controller in the presence of uncertainties is considered in order to track the desired hub angular position and suppress vibrations of the arm simultaneously. For the so-called slow subsystem, a novel controller design is proposed as two different cases, with and without the presence of uncertainties in system dynamics are considered; and accordingly, a control law for tracking the desired path is introduced based on the idea of using the cross-term constructed Lyapunov function. For the fast subsystem, a pole placement technique is used to suppress vibration of the beam. The simulation results indicate notable effectiveness of the proposed controller.