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

In order to improve the control precision of piezoelectric micro-positional stage, this thesisinvestigated the control method based on mathematical model to reduce the hysteresis nonlinearity.The main works are listed as follows:1) The hysteresis model with only7backlash operators was established. The slopes of theinitial loading curve in the adjoining threshold are equal. When the range of the micro-positionalstage is16.115μm, the maximum error and the average error between the model curve and theactual displacement curve are0.4284μm and0.1175μm, respectively. The mechanical propertiesand dynamic characteristics of the micro-positional stage were analyzed. Then the transfer functionand CARMAX model were established.2) The feedforward control system based on the hysteresis model was designed and verifiedby experiments. The experimental results show that the feedforward control does not reduce thespeed of the system response. The step response time is0.01s for feedforward control.Feedforward control can effectively reduce the hysteresis error. With the help of feedforwardcontrol, the maximum error between the actual displacement and reference was reduced from1.5749μm to0.6968μm in the range of17μm. And the average error was reduced from0.6214μm to0.1718μm.3) The incremental PID feedback controller based on the transfer function was designed. Theeffect of the feedback controller was verified by simulation and experiments. The experimentalresults show that the step response time with feedforward control is0.01s, which is slower thanthat without feedforward control. Hysteresis error of piezoelectric micro motion platform waseliminated by PID feedback control completely in the range of17μm. The maximum error and theaverage error were reduced by0.1093μm and0.0278μm respectively.4) The complex control system combining the feedforward control with the PID feedbackcontrol was set up and tested. The experimental results show that the step response with compoundcontrol is0.18s. It is slower than that with feedforward control, but much faster than PID feedbackcontrol. When peak to valley of the reference triangular wave displacement is17μm, themaximum error and the average error are0.3973μm and0.1167μm, respectively. It is less thanthat with the feedforward control or the PID feedback control.5) The adaptive control system base on the CARMAX model was build for the piezoelectricmicro-positional platform. The affectivity was verified by simulation and experiments. Theexperimental results show that the step response with adaptive control is0.23s that is slower thanthat with compound control. When peak to valley of the reference triangular wave displacement is17μm, the maximum error and the average error are0.3196μm and0.0796μm, respectively. It isless than that with compound control.