Optimal control of clamped-free conical shell using diagonal piezoelectric sensor and actuator

In this paper, optimal vibration control of a clamped-free conical shell is presented. A diagonal piezoelectric sensor/actuator (S/A) pair is proposed to control the axial, bending and transverse vibrations of the conical shell. The modal functions are adapted to satisfy the clamped-free boundary condition. Based on the independent modal control method, the response of conical shell to external excitations can be represented by the summation of all participating natural modes and their respective modal participation factors and each mode can be controlled independently. The modal equation is transformed into the linear state space form. The modal participation factor and its time derivative are chosen to be the state variables. The sensing signals are chosen to be the output vector. The modal force is chosen to be the control input vector. The linear quadratic (LQ) controllers are designed for each independent mode. The optimal gain matrix is related to the ratio between control voltage and sensing signal by the modal control force per unit voltage and the sensing signal. Numerical examples show that, the proposed optimal control method can achieve significant active control effects and the optimal gains are mainly related to the modal velocity. This effect varies with the locations of S/A pair and the mode of the shell. The results indicate that, to achieve the best control effects for all wanted modes, the optimal controller and the optimization of the S/A location should be taken into account in the design of the optimal controller.