Stochastic Optional Control Of Beam Using Piezoelectric Actuator

In chapter 1, the present status of the stochastic control theory is briefly reviewed, thedevelopment and significance to study piezoelectric system are also introduced. The main of thethesis is to study control of piezoelectric beam using stochastic control theory. In chapter 2, theprinciples of the piezoelectric material and piezoelectric beam are expatiated, and the model ofpiezoelectric beam is founded. The position and the size of piezoelectric patch are discussed. Inchapter 3, the stochastic averaging method and stochastic optimal control strategy are introduced.In chapter 4, the piezoelectric system is used to actively control based on the principles describedin chapter 3. A partially averaged Ito stochastic differential equation of piezoelectric beam isderived by using the stochastic averaging method. For the ergodic control problem, a dynamicalprogramming equation is established based on the stochastic dynamical programming principleand solved to yield the optimal control law. The fully averaged Ito equation is obtained bysubstituting the optimal control force into partially averaged Ito equation and completing theaverage. Finally, the responses of the controlled system are obtained by solving the finaldynamical programming equation and the Fokker-Planck-Kolmogorov equation associated withthe fully averaged Ito equation. As an example the control strategy is used to first two modalequations. The numerical calculation is done compared with that of the LQG control. The resultindicates that both the effectiveness and efficiency of the proposed control strategy are better thanthose of the latter.