Study On Active Vibration Control Techniques For Flexible Structrue Using Piezoelectric Actuators

Aiming at the active vibration control of space flexible structures and combined with the National Natural Science Foudation Project, the torsional vibration of a space flexible bar and the bending-torsional-coupled vibration of a two-link flexible structure were investigated theoretically and experimentally.In chapter one, the background information and significance of the dissertation were presented. And then the up-to-date research status of the flexible structures was given in the following aspects which are the system modeling of the flexible structures, studies on the typically flexible structures, application of smart materials, optimization placement of the actuators/sensors and conventional control algorithms in active vibration control. At last, the main research content of this dissertation was presented.In chapter two, the piezoelectric constitutive equations and the application of piezoelectric materials were presented. A piezoelectric torisonal actuator was designed using axial poling method, and the output torque of the actuator was derived. The torisonal resonant frequency of the piezoelectric torsional actuator was analyzed and its fabrication method was discussed. The fundamental of the strain gauge in testing torsional vibration was investigated and the relationship between the torsional angle and output voltage of the electric bridge was founded.In chapter three, the torsional vibration of the flexible bar was analyzed. A space flexible structure consiting of a flexible bar, a piezoelectric torsional actuator and strain gauges was proposed. Aiming at the optimization placement of the actuator/sensor, the dynamic governing equation of the system was derived, and the state-space expression of the dynamic system was developed. A hybrid optimization algorithm combined with minimum input energy, maximum energy transferring and maximum of minmum singular value of controllability Grammian was proposed. The optimization process was carried out using genetic algorithm. And optimal placement position of the actuator/sensor was obtained. Also a comparable research was implemented compared with other positions.In chapter four, linear quadratic optimal control theory was summarized. Choosing method of the weight matrix was investigated. A method based on genetic algorithm combined with constraints was proposed. Simulations were implemented using the model founded in chapter three. The results show the proposed choosing method of the weighting matrix is effective and feasible. Also an active control was implemented when the actuator/sensor was placed in other position. Results validate the optimization conclusions made in chapter three. In chapter five, a two-link space flexible structure system consisting of a flexible beam and a flexible bar was proposed. Two piezoelectric actuators with different poling methods were used to suppress the bending-torsional-coupled vibration of the system. The dynamic governing equation of the system was derived using Lagrange equation and assumed mode method. Piezoelectric torsional actuators were bonded on the flexible bar to suppress the torsional vibraition of the bar, and piezoelectric bending actuators were bonded on the flexible beam to suppress the bending vibration of the beam. Two control strategies were proposed, the first was a modal velocity control strategy based on the Lyapunov stability. The second was a variable structure control method combined with a saturation element and a low-pass filter. Simulations were carried out. At last, the proposed two control methods were compared.In chapter six, experimental system of the flexible structure was founded, and the corresponding soft ware and hard ware of the experimental system were summarized. Active vibration control research of the flexible bar system and the two-link flexible structure system were carried out respectively.In chapter seven, some conclusions were made, and the future work was proposed.