Research On Control Methods Of2-DOF Micro-positional Stage Based On Parallel Structure

In order to eliminate the hysteresis non-linear of piezoelectric micro-position stage andincrease its speed of response, in this paper, the corresponding control systems were designedbased on the established dynamic model and hysteresis model, and the corresponding experimentalstudy were made. The specific study as follows:1) Based on the fact of that the slopes of the first half of the initial loading curve for thepiezoelectric micro-positional stage change much while the slopes of the second half change little,the PI hysteresis model of the stage is established by the non-equiinterval threshold value. theestablished model is identified by optimizing the minimumL22-norm of the model errors betweenmeasured initial load curve and the model output. The experimental results show that themaximum error and average error of the model are0.71μm and0.23μm in the displacementrange of22.75μm, respectively. The hysteresis model can guarantee precision and improve theoperation speed;2) The mathmatic models were established based on the analysis of the piezoelectric ceramicactuators’ mechanical and electrical properties and micro-position stage’s dynamic properties. thenthe dynamic model of piezoelectric micro-positional stage was established.The results show thatthe model is series of the first order inertia link on the electrical and the second-order oscillationlink on the mechanical; natural frequency ωnand damping ratio ξ were identified by the frequencyresponse of piezoelectric micro-positional stage, respectively ωn=1.35kHz, ξ=0.11, and thenthe dynamic model of piezoelectric micro-positional stage was obtained.3) The feedforward control system was designed based on the improved PI hysteresis modelof piezoelectric micro-positional stage,and its effectiveness was verified through experiments.The experimental results show that feedforward control can speed up its response speed,piezoelectric micro-positional stage reach the desired displacement of4μm with the time of0.01sunder the effect of feedforward control; feedforward control also can significantly reduced stage’shysteresis error,piezoelectric micro-positional stage’s hysteresis error reduced from4.0μm when ithad no control to1.4μm or so when it was under the feedforward control in22m targetdisplacement.4) Based on the improved integral term and derivative term of conventional PID control,thepiezoelectric micro-positional stage’s PID feedback control system with a trapezoidal integral anddifferential separation was designed.and experimental study also made.The result show that piezoelectric micro-positional stage reach8μm desired displacement with the time of0.08s, it hadno steady-state error although the displacement output have little overshoot.It is Visible that PIDfeedback control can completely eliminated the steady-state error that feedforward control don’talthough the response speed is longer than the feedforward control.Consist of the feedforward control based on the improved PI model and PID feedback controlwith trapezoidal integration and differential separation. Composite control system of piezoelectricmicro-positional stage was designed，and the effectiveness of complex control systems wasvalidated by the experience. The experimental results show that the complex control make thepiezoelectric micro-positional stage to obtain better static and dynamic performance than thefeedforward control and feedback control, this is means fast response speed and high steadyaccuracy.