压电驱动器的迟滞非线性建模与控制
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摘要
迟滞现象是一种输入-输出关系呈多重分支的非线性，且分支的切换发生在输入达到极值的时刻，广泛地存在于压电材料、机械间隙系统、光学、电子束、经济等领域。由于这种现象十分普遍，而且涉及到多个学科，受到了许多研究者的关注。本课题研究了压电驱动器的建模方法，并基于模型设计了控制器。
压电陶瓷驱动器是一种高性能的功能器件，具有体积小、响应快、功耗低、位移分辨率高等优点，在智能结构、精密加工、纳米技术、微电子工程、精密光学、生物工程等领域有广泛地应用前景，如压电式微位移机构、扫描探针显微镜的探头定位、天文望远镜定位系统等。然而，压电陶瓷驱动器作为一种铁电材料，本身所固有的非线性迟滞特性是制约驱动精度的瓶颈。这种迟滞非线性不仅削弱闭环控制的反馈作用，而且有可能造成系统的不稳定。随着智能结构、精密加工以及微电子等技术的不断进步，对定位精度的要求也越来越高。本课题设计了一种前馈与反馈复合的控制策略，用于提高压电驱动器的定位精度。前馈控制器在Preisach迟滞模型理论的基础上，采用神经网络描述压电驱动器迟滞非线性的逆过程。与经典的Preisach迟滞模型相比，神经网络模型所需的参数更少，而且参数易于识别。反馈控制器根据传感器测量的位移信号，修正驱动电压，并补偿积累的误差。实验结果显示，这种控制方法能够有效的提高压电驱动系统跟踪控制的精度。
双曲函数模型能够用较少的参数描述压电叠堆驱动器的迟滞非线性，但是仅遵循记忆擦除性而不符合次环一致性。根据经典的Preisach模型理论，改进了双曲函数模型用来描述压电双晶片的迟滞过程。逆控制器采用改进的双曲函数模型描述迟滞的逆，与压电双晶片的迟滞过程相互抵消。通过分析压电双晶片与逆控制器构成的伪线性系统的幅频与相频特性，设计前馈控制器减小系统固有频率对定位精度的影响，同时设计了反馈控制器补偿压电双晶片的蠕变效应并进一步提高定位精度。实验结果显示，在单频率变幅值信号的驱动下，最大定位误差由控制前的0.0863mm减小到控制后的0.0095mm;在多频叠加信号的驱动下，最大定位误差由控制前的0.0825mm减小到控制后的0.0536mm。该系统能够有效的提高压电双晶片驱动器的定位精度，可用于宽频域的微定位系统中。
经典的Prandtl-Ishlinskii模型是不同阈值的线性Play算子或Stop算子的加权叠加。由于线性Play算子的迟滞环是关于中心对称的，经典Prandtl-Ishlinskii模型也只能描述关于中心对称的迟滞现象，而压电驱动器的迟滞非线性通常是一个非对称的过程。根据经典Prandtl-Ishlinskii迟滞模型的基本迟滞单元，设计了上升算子与下降算子，使改进后的模型能够模拟非对称的迟滞非线性过程。采用这种改进的Prandtl-Ishlinskii模型与逆系统控制理论，设计了用于压电驱动器的精密定位控制器。实验结果显示，采用这种控制器的跟踪定位的应用上是行之有效的。
为了提高压电式二维微定位平台的控制精度，本课题基于改进型Prandtl-Ishlinskii模型补偿平台的迟滞与耦合，设计了复合控制系统。在分析x与y方向输入电压与响应位移之间迟滞非线性关系的基础上，前馈控制器通过改进型Prandtl-Ishlinskii模型描述迟滞的逆过程，分别补偿了x与y方向的迟滞。解耦控制器通过改进型Prandtl-Ishlinskii模型估算出耦合位移值，然后修正驱动电压，抵消耦合位移。复合控制系统结合了前馈控制器与解耦控制器的优势，并加入PID反馈控制进一步提高定位精度。实验结果表明，复合控制方法能够补偿非线性的迟滞，减小耦合效应对定位的影响，有效的提高跟踪定位的精度。
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.
压电陶瓷驱动器是一种高性能的功能器件，具有体积小、响应快、功耗低、位移分辨率高等优点，在智能结构、精密加工、纳米技术、微电子工程、精密光学、生物工程等领域有广泛地应用前景，如压电式微位移机构、扫描探针显微镜的探头定位、天文望远镜定位系统等。然而，压电陶瓷驱动器作为一种铁电材料，本身所固有的非线性迟滞特性是制约驱动精度的瓶颈。这种迟滞非线性不仅削弱闭环控制的反馈作用，而且有可能造成系统的不稳定。随着智能结构、精密加工以及微电子等技术的不断进步，对定位精度的要求也越来越高。本课题设计了一种前馈与反馈复合的控制策略，用于提高压电驱动器的定位精度。前馈控制器在Preisach迟滞模型理论的基础上，采用神经网络描述压电驱动器迟滞非线性的逆过程。与经典的Preisach迟滞模型相比，神经网络模型所需的参数更少，而且参数易于识别。反馈控制器根据传感器测量的位移信号，修正驱动电压，并补偿积累的误差。实验结果显示，这种控制方法能够有效的提高压电驱动系统跟踪控制的精度。
双曲函数模型能够用较少的参数描述压电叠堆驱动器的迟滞非线性，但是仅遵循记忆擦除性而不符合次环一致性。根据经典的Preisach模型理论，改进了双曲函数模型用来描述压电双晶片的迟滞过程。逆控制器采用改进的双曲函数模型描述迟滞的逆，与压电双晶片的迟滞过程相互抵消。通过分析压电双晶片与逆控制器构成的伪线性系统的幅频与相频特性，设计前馈控制器减小系统固有频率对定位精度的影响，同时设计了反馈控制器补偿压电双晶片的蠕变效应并进一步提高定位精度。实验结果显示，在单频率变幅值信号的驱动下，最大定位误差由控制前的0.0863mm减小到控制后的0.0095mm;在多频叠加信号的驱动下，最大定位误差由控制前的0.0825mm减小到控制后的0.0536mm。该系统能够有效的提高压电双晶片驱动器的定位精度，可用于宽频域的微定位系统中。
经典的Prandtl-Ishlinskii模型是不同阈值的线性Play算子或Stop算子的加权叠加。由于线性Play算子的迟滞环是关于中心对称的，经典Prandtl-Ishlinskii模型也只能描述关于中心对称的迟滞现象，而压电驱动器的迟滞非线性通常是一个非对称的过程。根据经典Prandtl-Ishlinskii迟滞模型的基本迟滞单元，设计了上升算子与下降算子，使改进后的模型能够模拟非对称的迟滞非线性过程。采用这种改进的Prandtl-Ishlinskii模型与逆系统控制理论，设计了用于压电驱动器的精密定位控制器。实验结果显示，采用这种控制器的跟踪定位的应用上是行之有效的。
为了提高压电式二维微定位平台的控制精度，本课题基于改进型Prandtl-Ishlinskii模型补偿平台的迟滞与耦合，设计了复合控制系统。在分析x与y方向输入电压与响应位移之间迟滞非线性关系的基础上，前馈控制器通过改进型Prandtl-Ishlinskii模型描述迟滞的逆过程，分别补偿了x与y方向的迟滞。解耦控制器通过改进型Prandtl-Ishlinskii模型估算出耦合位移值，然后修正驱动电压，抵消耦合位移。复合控制系统结合了前馈控制器与解耦控制器的优势，并加入PID反馈控制进一步提高定位精度。实验结果表明，复合控制方法能够补偿非线性的迟滞，减小耦合效应对定位的影响，有效的提高跟踪定位的精度。
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.
引文
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