Structure Design And Motion Control Of A2-DOF Precision Positioning Platform

The dissertation focuses on the development of a2-DOF piezo-driven precisionpositioning platform. The key technological issues arising during the structure design,modeling, and control of the platform have been fully investigated. Great efforts havebeen made in the static analysis, Finite Element Method (FEM) analysis, dynamicsmodeling, system identification, and rate-dependent hysteresis compensation. Thefollowing innovative work has been completed:The analytical linear and angular compliance models of a class of staticallyindeterminate symmetric (SIS) flexure structures have been established. Based on theFEM results, the modeling accuracy has been further improved. Theoretically, the SISflexure structures are free of parasitic motions. Thus, it can be utilized as the prismaticor revolute joint in precision positioning systems.A prototype of the2-DOF piezo-driven precision positioning platform has beenfabricated, where the difference of the SIS flexure structure’s linear stiffness betweenaxes is utilized to build the transmission mechanism. The platform has a maximumdisplacement range of8μm×8μm, and a first natural frequency of692Hz. For inputsignals below100Hz, the cross-axis coupling ratio is less than2.7%, indicating goodapplicability in fast planar positioning applications.The contact pair is utilized to build the Hertz contact of the platform. Therelation between the contact stiffness and the platform’s static and dynamicperformance has been investigated in FEM analyses. The contact stiffness is alsoincluded in the dynamics modeling process as an unknown parameter. Anidentification method for the contact stiffness has been proposed, which identifies thecontact stiffness through the measured first natural frequency of the platform.A novel dynamics modeling approach is proposed, where the piezoelectricactuator’s driving force is defined as the virtual input to the system. The actuator isfurther simplified as an elastic element with constant stiffness. By doing this, thepiezoelectric actuator’s nonlinearities have been totally separated out of the lineardynamics of the system. This helps to simplify the modeling and identificationprocesses. All the flexure hinges are simplified as massless springs and the dynamicsmodel of the platform is obtained in the state space formulation.Rate-dependent Prandtl-Ishlinskii (PI) model is powerful in describing thepiezoelectric actuator’s hysteresis. However, the valid inversion law for the rate-dependent PI model is not yet available. Simply extends the conventionalinversion law to the rate-dependent PI model will result in large theoretical modelingerror. A novel direct inverse hysteresis modeling approach is proposed herein, wherethe rate-dependent inverse PI model can be directly identified from the experimentaldata. As no inversion calculation is involved, this approach is time-efficient and themodeling accuracy can be greatly improved.On the basis of the hysteresis and creep compensations, a new decouplingcontroller is proposed to further eliminate the cross axis coupling of the platform infeedforward applications. Prefiltering can also be incorporated to filter out all the highfrequency components of the reference trajectory. The platform’s modal vibration canthen be suppressed. An all-pass filter can be employed to guarantee the platform’stransient performance in the very beginning of the movements. If feedback is alsointegrated as an error compensator, the platform’s tracking accuracy can be furtherimproved.