Piezoelectric Flexible Manipulator Dynamics Modelmodifiedand Optimizedallocation

Compared with traditional rigid mechanical manipulator, flexible manipulator has beenwidely used in aerospace, advanced manufacturing, precision machining and positioning, etc,as the advantages of light weight, low power consumption, high precision, high efficiency,payload mass ratio, soft touch with the environment. Therefore the study on flexiblemanipulator has become a frontier research and hot spot in recent years. The structure’s elasticvibration is the main obstacle which effects its practical application. Especially flexiblemanipulator was required more and more strictly on space precision and time indexes.Therefore, this paper presented an effective reasonable and economical method that couldcontrol the elastic vibration which was produced on the operation of flexible manipulator.Taking two-link flexible manipulator as the research object, after the flexible manipulatorvibration as well as the input and output characteristics of piezoelectric ceramic wereanalyzed, general coupling dynamics equation which contains a plurality of piezoelectricceramics sheets is deduced by integrating assumed mode method and Lagrange equation. Asthe equation derived process and result were simplified, the influence of flexiblemanipulator’s structure change, joint friction, structure damping and wire factors were ignored.An elastic vibration modified method of dynamic model was presented, which modified thesystem’s stiffness and damping appropriately, and the characteristics of modified model wereanalyzed by using MATLAB software.A multi-objective optimization criterion (control effect and control energy consumption)was presented to optimize the parameter of actuators/sensors which were pasted on flexiblemanipulator. Its optimized parameters were determined by using PSO, as well as PID controlparameters, Ki, Kp, Kd. The optimization results are checked after the system simulationmodel was established. The simulation results show that the vibration can be effectivelysuppressed when the flexible manipulator system works under PID control with optimizedparameters sensors/actuators pasted.The optimal allocation experiments of flexible manipulator system were carried out,which took computer control system as the core to implement active control. By comparingdifferent experimental scheme, elastic vibration can be restrained when the experimentalsystem took PID control as the active control algorithm and pasted optimized parameterssensors/actuators. It also found that whether pasted optimized size sensors/actuators in theposition out of optimized, or in the optimized position pasted the sensors/actuators that is notoptimized parameters, the vibration suppression effect was much less than the system pastedoptimized size sensors/actuators in the optimized position. And the experimental results are basically consistent with the simulation results, which show the PSO optimized results ofsensor/actuator number, location position and size are feasible and correct.