Research On Active Vibration Suppression Of Varying Load Cantilever Beam Based On PZT

The flexible arm has been more and more widely used in aerospace and many otherfields because of its advantages such as light-weight, high load-weight ratio, goodflexibility and so on. However, the elastic vibration problems of the flexible arm canlead to a serious influence on its rapidity and precision, which has become a greatchallenge for vibration suppression research. In most practical applications, the loads ofthe flexible arm are not certain, but vary in a range, which deteriorates the control effectwhen it’s not a norm model. For the purpose of eliminate the residual vibration quicklyin load-varying cases, this work used Euler-Bernoulli beam as flexible arm model andresearched the vibration-suppression strategy based on the active vibration control(AVC) and how to adjust the parameters of the controller following the change of theload to optimize the control result.Firstly, the vibrational model of the cantilever under variable loads at the end of itare established and the natural frequency of the first4orders are calculated by theMATLAB and ANSYS software when the load-weight ratio is0,10%or20%respectively. On the other hand, the PZT are chosen as the actuator and modal equationof cantilever beam vibrational motion when PZT actuates. With the theoretical model, aprinciple of optimizing the position of the actuators are put forward and the calculationof the optimal position are done using the genetic algorithm.Secondly, in order to make the parameters of the controller follow the variation ofthe natural frequencies caused by the change of the loads so that realize the adaptivecontrol, it’s necessary to identify the natural frequencies with the inputs and the outputsof the system. This work designed the identification algorithm for the naturalfrequencies by the recursive least squares method (RLS), and explained the basic theoryof identification, and the calculation formula of the identification are derived.Then, based on modal equation of cantilever beam vibrational motion when PZTactuates, this work designed the integral resonant controller (IRC) and established theclosed-loop control model of the system, and optimized the control parameters, andexplained that this control strategy can increase the damping ratio. Also, the necessity ofadaptive control are proved by the robustness analysis of the closed-loop system and the adaptive controlling scheme of the closed-loop system.Finally, the real-time simulation control system is established with the software ofMATLAB/Simulink and the hardware of dSPACE. With the experiment platform, thiswork proved the accuracy of the natural frequency identification algorithm, theeffectiveness of the IRC control model and the optimization of the control parameters.The experiment result demonstrate that the natural frequency identification algorithm isof high accuracy and the error comparing with the analytical results can be controlledwithin5%; the IRC control model is able to suppress the vibrations of the cantileverunder the three different loading conditions, and the damping ratio can be increased byat least100%and the controller parameters designed are relatively optimal.