Research On An Active Control Of Precision Smart Flexible Paraboloidal Shell Systems

With the rapid development of space technologies, the requirement for integrated and intelligent structures applied to various space vehicles, structures and their payloads has been continuously raised. Therefore, the structronic system and active control, based on smart materials and intelligent control systems, have been becoming one of the mainstream research and development activities. Although the research on active control of piezoelectric laminated smart shell structures has been carried out in the last two decades precision control of smart flexible paraboloidal shells of revolution, especially applied to space structures, has just begun and needs to strive to make a technological breakthrough. Supported by the National Science Fund of China projects"Research on Dynamic Modeling and Smart Shape Control of Thin Structure of Revolution"and"Research on Non-contact Precise Control of Flexible Photostrictive Coupled Shells of Revolution,"with the background of vibration control of thin shell components in the precision optical apparatus and space antenna systems, this research focuses on developing precision smart flexible paraboloidal shell and its active vibration control system, by way of theoretical analysis, numerical simulation, and laboratory demonstration. This research provides theoretical fundamentals, practical implementation, for design applications of this class of smart paraboloidal shell structures.This paper begins with the theories of differential geometry and elastic plate and shell, and analyzes component mechanical model of elastic paraboloidal shell of revolution, based on Love-Kirchhoff's shell assumption and the theory of first order shear deformation; According to the theory of multifunctional hybrid shells and piezoelectric constitutive equation, the switch between force and electricity field and their coupling relations in the piezo-elastic laminated shell structure are fully discussed, thus coming to a basic resultant force and moment expression of piezoelectric laminated shell component; Based on the Hamilton's principle, the linear piezoelectric theory and basic assumption of thin shell theory, the systemematic dynamic equations of generic piezoelectric laminated smart double curvature shell structure is deduced.In consideration of the difficulty in finding a solution to the vibration feature of double curvature elastic shell in the filed of mathematics, the systematic dynamic equations of the piezoelectric laminated shell smart structure and the strain expressions are simplified by Membrane approximation in this paper, after the analysis of the three common vibration approximation theories. Meanwhile, concerning the free boundary condition of the paraboloidal shell of revolution in space antenna, a series of vibration mode shape functions of free flexible paraboloidal shell is proposed based on the membrane approximation theory. By comparing the results among the theoretical modal shape simulation and experiment modal test of the elastic shell model, the characteristics of the low modal shapes of membrane paraboloidal shell continuum with free boundary condition are investigated.Based on positive piezoelectric effect, Gauss theory, open loop assumption and Maxwell equation, the distributed sensing signal equation of the general laminated shell is derived; using the mode shape function of paraboloidal shell with free boundary condition, the modal sensing signal is formulated, and distributed sensing signal components consist of different membrane strains in the meridianal and circumferential direction are defined. In combination with the typical parameters of paraboloidal shell of revolution, the effects of various sensing signal components and their mode sensitivity are analyzed; the magnitude of the sensing signal influenced by the layout of sensors is evaluated.On the basis of piezoelectric laminated shell mechanical-electrical coupling modeling, this paper raises the system governing equations of membrane paraboloidal shell of revolution smart structure, and transfers the equations to modal domain by applying modal orthogonality and modal expansion method. By introducing Love control operator and unit step function, the modal control force expression of distributed actuator is deduced, and mainly grounded on transverse vibration, the membrane and bending control components in meridianal and circumferential direction are discussed. Through the numerical simulation, this paper has respectively analyzed the micro-control action, effective area and normalized control action of distributed piezoelectric actuator laminated on the flexible paraboloidal shells, thereby making a guidelines to distributed actuator layout and configuration design.According to the basic function and characteristics of PVDF film sensor/actuator, the circuit modules are devised to be applied to the adjustment of microscopic sensing signal and to the high voltage actuation. In consequence of the system software that is developed by VC and aims at collection, analysis and processing of the multiplex signals, as well as the active control, the system experiment platform of piezoelectric laminated flexible paraboloidal shell smart structure is built. Through the open loop test on the distributed sensing and actuation of the experimental model, the availability and reliability of the system are verified, and the experimental data also prove the regular conclusions in the theoretical analysis of sensing and actuation signal. Through the parameter identification on the hardware system, the transfer functions of all links are established, and in terms of the pole placement and positive position feedback method, two kinds of controllers were designed, which have been put into use to the vibration control experiments, focusing on the low independent mode and coupled modes in piezoelectric laminated paraboloidal shell respectively. The experiment data show that these control methods enlarge the system damping and restrain the amplitude of vibration, making the active control come true. Finally, in accordance with random of the environment excitation of the space paraboloidal shell structure system and the limitation of the control energy, this paper proposes a self-adaptive modal control method. The experiment proves that, in the case of random excitation, the method can accurately judge the prefect actuator position, and effectively exert the active control on the smart structure.