Optimal Control of Piezoelectric Laminated Parabolic Cylindrical Panels Available to Purchase

Vibration control of parabolic cylindrical shell panels by piezoelectric patches using optimal control algorithm is presented in this study. Laminated piezoelectric patches serve as distributed sensors and actuators. Dynamic behaviors and mode shape functions in three directions are obtained by the Rayleith-Ritz method. The sensing sensitivity of the piezoelectric sensor and the actuation force of the piezoelectric actuator are obtained. Feedback control gain between sensing and control signals is solved using the LQ optimal control algorithm. LQ controllers for independent modes are designed, and relative optimal control gains and control voltages are presented. Control results with respect to independent mode and optimal design parameters are evaluated in case studies. Numerical results show that the LQ optimal controller with optimal feedback control gain is effective for the vibration control of parabolic cylindrical shell panels. The damping ratio can be greatly enhanced; the maximal damping ratio reach 7.79% for mode (1,3). Studies on parametric designs suggest that relatively larger Q₂₂ and/or smaller R results in rapider reduction of mechanical motion with more control energy cost, and vice versa. These results would provide a design reference in practical engineering.