1 Smart Active Vibration Control System of a Wind Turbine Blade Using Piezoelectric Material 13 Fig. 1.6 Error percentage for each sensor under loading number 2 (30-degree attack angle) Fig. 1.7 The outcomes of applying controlling rule for the 45th sensor under loading number 2 (30-degree attack angle) 1.4 Conclusion In this paper, a smart active vibration control system including LQR control method and piezoelectric actuator is proposed to damp the transverse deflection of a wind turbine blade. In the first part, an effective semi-analytical solution based on a unique transfer function matrix for a wind turbine blade is presented. The energy technique was used to drive the governing equations of the Euler-Bernoulli beam with the attached piezoelectric actuator and sensor. The impact of changing mass, stiffness, and electromechanical coupling between the beam and the piezoelectric actuator and sensor is considered by integrating the characteristic vibration equations of the piezoelectric patches into the characteristic equations of the Euler-Bernoulli beam. The obtained governing equations are then solved using the assumed mode method. Rayleigh damping factors are used to develop the FE model of the wind turbine blade and piezoelectric patches. A pulse signal is applied to every actuator’s location in both systems to derive initial transfer function matrices and obtain the responses for the Euler-Bernoulli beam with PZT patches and the wind turbine blade with PZT patches. Concerning the linear feature of the whole system, the final transfer function matrix is derived by applying same external dynamic force to both systems. The Euler-Bernoulli beam and
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