Smart materials and structures have a great appeal within the aerospace and automotive communities because they promise to enable better performance and functionality over existing structural and functional materials. The idea proposed in this work is part of this challenging and current scenario and can be applied to the study of morphing wings, helicopter blades, etc. Moreover, the mathematical modeling and velocity and shape control of a rotating flexible beam-like structure are investigated. The nonlinear partial differential governing equations of motion are derived using the extended Hamilton’s Principle and numerically integrated using a combination of finite difference and the fourth-order Runge–Kutta methods. In order to force the flexible structure to assume the desired shape and simultaneously control the velocity of the rotating axis, the optimal nonlinear control method named state-dependent Riccati equation (SDRE) is considered. This control technique is applied to piezoelectric actuators along the beam and an external torque coming from a DC motor and acting in the rotating axis. The numerical simulation results show that the proposed control technique is efficient when acting along the rotating beam to deform it into the desired shape while also acting on the motor axis to keep the rotation speed constant.
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