Hysteresis Modeling And Nonlinear Control Of Piezoelectric Actuators

The hysteresis system is characterized by its input-output relationship that is a multibranchnonlinearity for which branch-to-branch transitions occur after input extrema. The phenomenon ofhysteresis is ubiquitous and has been attracting the attention of many investigators for a long time.It is encountered in many different areas of science. Examples include magnetic hysteresis,piezoelectric actuator, mechanical hysteresis, optical hysteresis, electron beam hysteresis,economic hysteresis, etc. In this research, the hysteresis of piezoelectric actuators was investigatedwith different mathematical models, and the controllers were designed to compensate thehysteresis.Due to their characteristics of high displacement resolution, high stiffness, and highfrequency response, piezoelectric actuators have been widely used in high-precision positioningdevices and tracking systems, such as scanning tunneling microscopy, and diamond turningmachines. However, the piezoelectric actuators have the drawback of hysteretic behavior, whichseverely limits system precision and may cause the control system instability. In order to mitigatethe hysteresis influence to system, the inverse control schemes have been proposed, which is alsothe popular method used in controller design. The idea of inverse control is to construct an inversemodel to cancel out the hysteresis nonlinearity. There surely exist several models to describehysteresis nonlinearity such as Preisach model, but they are all difficult to identify parameters. Aninverse control method which is a combination of a feedforward loop and a feedback loop isdeveloped to compensate the hysteresis of piezoelectric actuator. In the feedforward loop,hysteresis nonlinearity is compensated by inverse neural network model. Feedback loop is used toreduce the static error and possible creep in the piezoelectric actuator. Experiment results showthat the neural networks can precisely model the hysteresis of piezoelectric actuator, and issuitable for controller design.A precision positioning control system for the piezoelectric bimorph actuator was designedwith inverse hysteresis model. Based on the wiping-out and congruency property of classicPreisach hysteresis model, a hyperbola model is developed to describe the hysteresis ofpiezoelectric bimorph actuator. Since the inverse controller and the piezoelectric hysteresiscanceled each other out, the combination can be considered as a pseudo linear system. With theamplitude-frequency and Phase-frequency characteristic analysis, a feedforward and a feedbackcontroller were designed to reduce the tracking control error and compensate the creep of thepiezoelectric bimorph. For single frequency tracking control, the maximum error is0.0863mmwithout control, and reduced to0.0095mm with control; for multi-frequency tracking control, the maximum error is0.0825mm, and reduced to0.0536mm with control. The experimental resultshows that the precision control system have potential applications for wide-bandmicro-positioning devices.Classical Prandtl-Ishlinskii model is a linearly weighted superposition of many play operatorswith different threshold and weight values, which inherits the symmetric property of the backlashoperator at about the center point of the loop formed by the operators. To describe the asymmetrichysteresis of piezoelectric stack actuators, two modified operators were developed, one forascending branches and another for descending branches. Based on this modified model, afeedforward controller was designed to compensate the hysteresis. Since the modified modeldescribes the inverse of hysteresis, the feedforward controller and the hysteresis of piezoelectricstack actuator canceled each other. To attenuate the creep effect and reduce tracking error, afeedback controller was proposed to work with the feedforward controller. Experimental resultsshow that this control scheme that combines feedforward and feedback controllers greatlyimproves the tracking of the piezoelectric actuator and the error is less than0.15mm.To improve the accuracy of piezoelectrically driven micro positioning stage, a compoundcontrol system was developed to compensate for the hysteresis of piezoelectric actuator andattenuate the coupling effect between different actuating directions. With modifiedPrandtl-Ishlinskii hysteresis models, two feedforward controllers were designed to compensate forthe hysteresis respectively in X and Y direction. To attenuate the coupling effect, the decouplingcontroller estimated the coupling shift, and then manipulated the voltage to cancel this shift. Thecompound control system incorporated feedforward, decoupling and PID feedback controllers toreduce the tracking error. Experimental result shows that the compound control system can wellcompensate for the hysteresis and coupling effect.