压电陶瓷叠堆执行器及其系统的迟滞现象模拟、线性化及控制方法的研究
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摘要
压电陶瓷执行器（Piezoelectric ceramic actuators, PCAs）是一种利用压电材料的逆压电效应制作而成的微位移执行器，具有体积小、能量密度高、分辨率高、频响快等优点，已经成为精密定位系统中重要定位及驱动元件。由于基于单片压电陶瓷晶片的压电陶瓷执行器的输出位移比较小，常常采用一定的工艺将多片压电陶瓷晶片和电极叠合而成压电陶瓷叠堆执行器（Piezoelectric ceramic stackactuators, PCSAs）以提高输出位移。然而这种通过一定的工艺叠合而成的压电陶瓷叠堆执行器存在的一些缺点限制了其在快速、高精密定位系统中的应用：首先压电陶瓷叠堆执行器会进一步加剧压电陶瓷晶片的输出位移与驱动电压之间存在多值对应的迟滞现象，如何实现对压电陶瓷叠堆执行器的有效控制成为精密定位控制研究中的重点和难点之一；其次叠合工艺会影响压电陶瓷叠堆执行器的动态性能，甚至缩短其使用寿命。因此，压电陶瓷叠堆执行器及其系统的迟滞线性化方法及压电陶瓷叠堆执行器的动态性能设计方法是压电陶瓷叠堆执行器在快速、高精密定位系统中应用时必须解决的问题，开展这方面的研究具有重要学术意义和工程应用前景。
为了解决上述问题，本文建立了能描述压电陶瓷叠堆执行器的迟滞现象的Bouc-Wen数学模型，提出了基于Bouc-Wen数学模型的线性化控制方法用于实现压电陶瓷叠堆执行器的迟滞线性化；建立了能够同时模拟压电陶瓷叠堆执行器的迟滞现象和动态特性的综合模型，提出了能够合理设计压电陶瓷叠堆执行器的动态性能的方法；建立了预压紧压电陶瓷执行器的现象模型；在此基础上，提出并实现了压电致动二维微位移扫描平台的基于现象模型的鲁棒模型参考自适应控制方法。
本文的主要研究工作和创新点可以归纳为以下六个方面：
1.提出并研究了能够模拟压电陶瓷叠堆执行器的迟滞现象的Bouc-Wen数学模型。相应地提出并实现了能够求取模型参数的解析解的参数辨识方法，并且在辨识过程中采用最小二乘法以降低外界随机干扰的影响。建立相应的实验系统对模型进行实验验证。实验结果表明，Bouc-Wen数学模型及相应的参数辨识方法能够有效地模拟压电陶瓷叠堆执行器的迟滞现象，其模拟误差在3%左右。
2.通过在Bouc-Wen迟滞算子中引入非对称因式用于模拟压电陶瓷叠堆执行器迟滞现象的非对称性，提出并研究了压电陶瓷叠堆执行器的非对称Bouc-Wen数学模型，建立了相应地能够求取模型参数的解析解的辨识方法。实验结果表明，非对称Bouc-Wen数学模型能够很好地模拟压电陶瓷叠堆执行器的迟滞现象，模拟误差与Bouc-Wen数学模型相比降低了30%左右。非对称Bouc-Wen数学模型以及相应的参数辨识方法也可以用于模拟其他具有非对称迟滞现象的材料或者系统。
3.提出了基于压电陶瓷叠堆执行器的Bouc-Wen模型的前馈线性化控制方法和前馈补偿与PI反馈相结合的复合线性化控制方法。采用基于dSPACE实时仿真控制系统的快速控制原型技术建立了前馈和复合线性化控制方法的快速原型系统并对其进行实验验证。实验结果表明，前馈和复合线性化控制都能将压电陶瓷叠堆执行器的迟滞现象线性化，而且复合控制的线性化误差比前馈控制有显著降低，经过线性化控制后压电陶瓷叠堆执行器可以当成线性执行器使用。分别采用本文提出的压电陶瓷叠堆执行器的前馈和复合线性化控制方法，建立了压电致动微夹钳的夹爪位移伺服控制的开环和闭环控制系统，并实验验证了提出的线性化方法可以简化了压电致动微夹钳的控制算法并提高其定位控制精度。
4.考虑粘结层为一个无源单自由度质量-阻尼-刚度系统，提出并建立了能够模拟压电陶瓷叠堆执行器的迟滞现象和动态特性的基于Bouc-Wen迟滞算子的综合模型。根据该综合模型，压电陶瓷叠堆执行器的叠合工艺可以看成通过改变粘结层的特性从而改变压电陶瓷叠堆执行器的动态特性但是不影响其迟滞特性，与实验测试结果相吻合。为了设计压电陶瓷叠堆执行器的动态特性，采用弹性变形元件对压电陶瓷叠堆执行器预压紧，提出了确定预压紧机构的参数的方法。仿真结果表明，该方法能够在一定程度上有效地设计压电陶瓷叠堆执行器的动态性能。
5.提出并建立了能够模拟预压紧压电陶瓷叠堆执行器的迟滞和动态特性的基于Bouc-Wen迟滞算子的现象模型以及相应的参数辨识方法。实验结果表明，该现象模型以及相应的参数辨识方法能很好的模拟预压紧压电陶瓷叠堆执行器的输入输出特性。
6.在上述工作的基础上建立了二维微位移扫描平台的现象模型，提出了基于二维微位移扫描平台的现象模型的鲁棒模型参考自适应控制方法，该方法在平台特性发生改变、存在着外界随机扰动和延时蠕变等情况下依然能够快速、精确地控制微位移扫描平台。在理论上证明了鲁棒模型参考自适应控制方法的稳定性。建立了相应的实验系统对鲁棒模型参考自适应控制进行实验验证，并将该控制方法的性能与基于现象模型的PID控制方法进行对比。实验结果显示鲁棒参考自适应控制系统能够显著地提高定位控制精度，并且具有较高的鲁棒性和学习能力。
本文对压电陶瓷叠堆执行器及其系统的迟滞现象模拟、线性化及控制方法的研究，为压电陶瓷叠堆执行器在快速、高精密定位系统中的应用奠定了理论基础。
Piezoelectric ceramic actuators (PCAs) based on inverse piezoelectric effect havebeen widely used in precision positioning systems due to their apparent advantages,such as the small size, high energy density, high resolution, and quick frequencyresponse. The output displacement of single-wafer PCAs is relatively small, so thatpiezoelectric ceramic stack actuators (PCSAs), which are realized by assemblingmulti-chip piezoelectric ceramic wafers and electrodes, are the best choice to achievelarge output displacement with high resolution. However, some of the shortcomings ofPCSAs fabricated by layering/stacking processes greatly limit their applications in fastand high-precision positioning systems. Firstly, the hysteretic behavior of PCSAs isfurther worsened because of the accumulation of the hysteretic behavior of piezoelectricceramic wafers, so how to effectively control PCSAs is difficult and emphasized inprecise positioning systems; secondly, the different layering/stacking processes greatlyaffect the dynamic performances of PCSAs, even possibly shorten the life of PCSAs. Inthese cases, in order to let PCSAs be used in fast and high-precision positioning systems,it is urgent to study the linearization control method, which can linearize the hysteresisbehavior of PCSAs and PCSAs’ based systems, and the method to design dynamicperformance of PCSAs. Carrying out these methods has an important academicsignificance and prospect of engineering application.
In this dissertation, in order to solve the above problems, a Bouc-Wenmathematical model for PCSAs to characterize the hysteresis behavior of PCSAs is putforward. Based on the proposed Bouc-Wen mathematical model for PCSAs, twolinearization control methods to linearize the hysteresis behavior of PCSAs areproposed and realized. In order to design dynamic performance of PCSAs, acomprehensive model that can accurately simulate the hysteresis behavior and thedynamic performance of PCSAs is put forward and a method to design dynamicperformance of PCSAs is established based on the proposed comprehensive model forPCSAs. In these cases, a phenomenon model for pre-stressed PCSAs is established andinvestigated and a robust model reference adaptive control method for atwo-dimensional piezo-driven micro-displacement scanning platform (2D-PDMDSP)based on the proposed phenomenon model is put forward.
The major research works and the innovations in this dissertation are summarized as follows
1. A Bouc-Wen mathematical model for PCSAs which can model the hysteresisbehavior of PCSAs is proposed, and a corresponding parameter identification method,which can identify the parameters by obtaining analytical solutions, is established. Inthe parameter identification, the least-squares method is used to reduce external randomdisturbances. The performance of the Bouc-Wen mathematical model with thecorresponding parameter identification method is experimentally verified by theestablished experimental setup. The experimental results show that the Bouc-Wenmathematical model can simulate PCSAs and the modeling errors are about3%.
2. A non-symmetrical Bouc-Wen hysteresis operator for modeling thenon-symmetrical hysteresis of PCSAs is established by introducing a non-symmetricalformula into the Bouc-Wen hysteresis operator. Accordingly, a non-symmetricalBouc-Wen mathematical model for PCSAs is put forward by modeling thenon-symmetrical hysteresis component of PCSAs with the non-symmetrical Bouc-Wenhysteresis operator, and a corresponding parameter identification method, which canidentify the parameters by obtaining analytical solutions, is established. Theperformance of the non-symmetrical Bouc-Wen mathematical model with thecorresponding parameter identification method is experimentally verified by theestablished experimental setup. The experimental results show that the non-symmetricalBouc-Wen mathematical model can simulate PCSAs with the non-symmetricalhysteresis more accurately than the Bouc-Wen mathematical model, and the modelingerrors are decreased by about30%. The proposed non-symmetrical Bouc-Wenmathematical model with the corresponding parameter identification method can also beused to model other materials and systems with the non-symmetrical hysteresis.
3. In order to linearize the hysteresis behavior of PCSAs, the feedforwardlinearization method based on the proposed Bouc-Wen mathematical model and thehybrid linearization method combining the feedforward and PI feedback loop tolinearize the hysteresis behavior of PCSAs are proposed and explored. The rapid controlprototypes of the linearization controllers for PCSAs using the proposed feedforwardand hybrid linearization methods with rapid control prototyping technique based on thereal-time simulation system are established and experimentally tested. The experimentalresults show that both the feedforward and hybrid linearization methods for PCSAs canlinearize the hysteresis behavior of PCSAs, and the proposed hybrid linearizationmethod can reach higher linearization accuracy than the feedforward linearization method. Utilizing the proposed linearization methods, the open-loop and closed-loopcontrols for the tip displacement of a piezoelectric-driven microgripper are realized,which indicates that the proposed linearization methods can simplify the control for thepiezoelectric-driven microgripper with high accuracy.
4. Considering the bonding layers as passive single-DOF mass-damping-stiffnesssystems, a comprehensive model for PCSAs based on the Bouc-Wen hysteresis operator,which can simulate both the hysteresis behavior and the dynamic performance ofPCSAs, is proposed. According to the proposed comprehensive model, thelayering/stacking processes of PCSAs change the dynamic performance of PCSAs bychanging the parameters of the bonding layers but can’t affect the hysteresis behavior ofPCSAs, which is consistent with the experimental results. Letting PCSAs bepre-stressed with elastic deformation mechanisms, a method to determine themechanical parameters of pre-stressed mechanisms of PCSAs is proposed. Thesimulation results show that the proposed method can effectively design the dynamicperformance of PCSAs to some extent.
5. A phenomenological model for modeling the hysteresis behavior and thedynamic performance of pre-stressed PCSAs by using the Bouc-Wen hysteresis operator,as well as the corresponding parameter identification method, is proposed. Theperformance of the phenomenological model with the corresponding parameteridentification method is experimentally verified by the established experimental setup.The experimental results show that the proposed phenomenological model forpre-stressed PCSAs with the corresponding parameter identification method canaccurately model the hysteresis behavior and the dynamic performance of pre-stressedPCSAs.
6. Based on the afore-mentioned works, a phenomenological model for the2D-PDMDSP is established. Accordingly, a robust model reference adaptive controlmethod for the2D-PDMDSP is proposed and established and the stability istheoretically proved. The proposed control method is experimentally verified by theestablished experimental setup and the corresponding controlled results are comparedwith those by the PID control method based on the proposed phenomenon model. Theexperimental results show that robust model reference adaptive control method cansignificantly improve the accuracy of the positioning with high robustness and learningability.
The research results on the hysteretic modeling, linearization, and control method for PCSAs and PCSAs’ based systems has established the theoretical foundation forapplying PCSAs in fast and high-precision positioning systems.
为了解决上述问题，本文建立了能描述压电陶瓷叠堆执行器的迟滞现象的Bouc-Wen数学模型，提出了基于Bouc-Wen数学模型的线性化控制方法用于实现压电陶瓷叠堆执行器的迟滞线性化；建立了能够同时模拟压电陶瓷叠堆执行器的迟滞现象和动态特性的综合模型，提出了能够合理设计压电陶瓷叠堆执行器的动态性能的方法；建立了预压紧压电陶瓷执行器的现象模型；在此基础上，提出并实现了压电致动二维微位移扫描平台的基于现象模型的鲁棒模型参考自适应控制方法。
本文的主要研究工作和创新点可以归纳为以下六个方面：
1.提出并研究了能够模拟压电陶瓷叠堆执行器的迟滞现象的Bouc-Wen数学模型。相应地提出并实现了能够求取模型参数的解析解的参数辨识方法，并且在辨识过程中采用最小二乘法以降低外界随机干扰的影响。建立相应的实验系统对模型进行实验验证。实验结果表明，Bouc-Wen数学模型及相应的参数辨识方法能够有效地模拟压电陶瓷叠堆执行器的迟滞现象，其模拟误差在3%左右。
2.通过在Bouc-Wen迟滞算子中引入非对称因式用于模拟压电陶瓷叠堆执行器迟滞现象的非对称性，提出并研究了压电陶瓷叠堆执行器的非对称Bouc-Wen数学模型，建立了相应地能够求取模型参数的解析解的辨识方法。实验结果表明，非对称Bouc-Wen数学模型能够很好地模拟压电陶瓷叠堆执行器的迟滞现象，模拟误差与Bouc-Wen数学模型相比降低了30%左右。非对称Bouc-Wen数学模型以及相应的参数辨识方法也可以用于模拟其他具有非对称迟滞现象的材料或者系统。
3.提出了基于压电陶瓷叠堆执行器的Bouc-Wen模型的前馈线性化控制方法和前馈补偿与PI反馈相结合的复合线性化控制方法。采用基于dSPACE实时仿真控制系统的快速控制原型技术建立了前馈和复合线性化控制方法的快速原型系统并对其进行实验验证。实验结果表明，前馈和复合线性化控制都能将压电陶瓷叠堆执行器的迟滞现象线性化，而且复合控制的线性化误差比前馈控制有显著降低，经过线性化控制后压电陶瓷叠堆执行器可以当成线性执行器使用。分别采用本文提出的压电陶瓷叠堆执行器的前馈和复合线性化控制方法，建立了压电致动微夹钳的夹爪位移伺服控制的开环和闭环控制系统，并实验验证了提出的线性化方法可以简化了压电致动微夹钳的控制算法并提高其定位控制精度。
4.考虑粘结层为一个无源单自由度质量-阻尼-刚度系统，提出并建立了能够模拟压电陶瓷叠堆执行器的迟滞现象和动态特性的基于Bouc-Wen迟滞算子的综合模型。根据该综合模型，压电陶瓷叠堆执行器的叠合工艺可以看成通过改变粘结层的特性从而改变压电陶瓷叠堆执行器的动态特性但是不影响其迟滞特性，与实验测试结果相吻合。为了设计压电陶瓷叠堆执行器的动态特性，采用弹性变形元件对压电陶瓷叠堆执行器预压紧，提出了确定预压紧机构的参数的方法。仿真结果表明，该方法能够在一定程度上有效地设计压电陶瓷叠堆执行器的动态性能。
5.提出并建立了能够模拟预压紧压电陶瓷叠堆执行器的迟滞和动态特性的基于Bouc-Wen迟滞算子的现象模型以及相应的参数辨识方法。实验结果表明，该现象模型以及相应的参数辨识方法能很好的模拟预压紧压电陶瓷叠堆执行器的输入输出特性。
6.在上述工作的基础上建立了二维微位移扫描平台的现象模型，提出了基于二维微位移扫描平台的现象模型的鲁棒模型参考自适应控制方法，该方法在平台特性发生改变、存在着外界随机扰动和延时蠕变等情况下依然能够快速、精确地控制微位移扫描平台。在理论上证明了鲁棒模型参考自适应控制方法的稳定性。建立了相应的实验系统对鲁棒模型参考自适应控制进行实验验证，并将该控制方法的性能与基于现象模型的PID控制方法进行对比。实验结果显示鲁棒参考自适应控制系统能够显著地提高定位控制精度，并且具有较高的鲁棒性和学习能力。
本文对压电陶瓷叠堆执行器及其系统的迟滞现象模拟、线性化及控制方法的研究，为压电陶瓷叠堆执行器在快速、高精密定位系统中的应用奠定了理论基础。
Piezoelectric ceramic actuators (PCAs) based on inverse piezoelectric effect havebeen widely used in precision positioning systems due to their apparent advantages,such as the small size, high energy density, high resolution, and quick frequencyresponse. The output displacement of single-wafer PCAs is relatively small, so thatpiezoelectric ceramic stack actuators (PCSAs), which are realized by assemblingmulti-chip piezoelectric ceramic wafers and electrodes, are the best choice to achievelarge output displacement with high resolution. However, some of the shortcomings ofPCSAs fabricated by layering/stacking processes greatly limit their applications in fastand high-precision positioning systems. Firstly, the hysteretic behavior of PCSAs isfurther worsened because of the accumulation of the hysteretic behavior of piezoelectricceramic wafers, so how to effectively control PCSAs is difficult and emphasized inprecise positioning systems; secondly, the different layering/stacking processes greatlyaffect the dynamic performances of PCSAs, even possibly shorten the life of PCSAs. Inthese cases, in order to let PCSAs be used in fast and high-precision positioning systems,it is urgent to study the linearization control method, which can linearize the hysteresisbehavior of PCSAs and PCSAs’ based systems, and the method to design dynamicperformance of PCSAs. Carrying out these methods has an important academicsignificance and prospect of engineering application.
In this dissertation, in order to solve the above problems, a Bouc-Wenmathematical model for PCSAs to characterize the hysteresis behavior of PCSAs is putforward. Based on the proposed Bouc-Wen mathematical model for PCSAs, twolinearization control methods to linearize the hysteresis behavior of PCSAs areproposed and realized. In order to design dynamic performance of PCSAs, acomprehensive model that can accurately simulate the hysteresis behavior and thedynamic performance of PCSAs is put forward and a method to design dynamicperformance of PCSAs is established based on the proposed comprehensive model forPCSAs. In these cases, a phenomenon model for pre-stressed PCSAs is established andinvestigated and a robust model reference adaptive control method for atwo-dimensional piezo-driven micro-displacement scanning platform (2D-PDMDSP)based on the proposed phenomenon model is put forward.
The major research works and the innovations in this dissertation are summarized as follows
1. A Bouc-Wen mathematical model for PCSAs which can model the hysteresisbehavior of PCSAs is proposed, and a corresponding parameter identification method,which can identify the parameters by obtaining analytical solutions, is established. Inthe parameter identification, the least-squares method is used to reduce external randomdisturbances. The performance of the Bouc-Wen mathematical model with thecorresponding parameter identification method is experimentally verified by theestablished experimental setup. The experimental results show that the Bouc-Wenmathematical model can simulate PCSAs and the modeling errors are about3%.
2. A non-symmetrical Bouc-Wen hysteresis operator for modeling thenon-symmetrical hysteresis of PCSAs is established by introducing a non-symmetricalformula into the Bouc-Wen hysteresis operator. Accordingly, a non-symmetricalBouc-Wen mathematical model for PCSAs is put forward by modeling thenon-symmetrical hysteresis component of PCSAs with the non-symmetrical Bouc-Wenhysteresis operator, and a corresponding parameter identification method, which canidentify the parameters by obtaining analytical solutions, is established. Theperformance of the non-symmetrical Bouc-Wen mathematical model with thecorresponding parameter identification method is experimentally verified by theestablished experimental setup. The experimental results show that the non-symmetricalBouc-Wen mathematical model can simulate PCSAs with the non-symmetricalhysteresis more accurately than the Bouc-Wen mathematical model, and the modelingerrors are decreased by about30%. The proposed non-symmetrical Bouc-Wenmathematical model with the corresponding parameter identification method can also beused to model other materials and systems with the non-symmetrical hysteresis.
3. In order to linearize the hysteresis behavior of PCSAs, the feedforwardlinearization method based on the proposed Bouc-Wen mathematical model and thehybrid linearization method combining the feedforward and PI feedback loop tolinearize the hysteresis behavior of PCSAs are proposed and explored. The rapid controlprototypes of the linearization controllers for PCSAs using the proposed feedforwardand hybrid linearization methods with rapid control prototyping technique based on thereal-time simulation system are established and experimentally tested. The experimentalresults show that both the feedforward and hybrid linearization methods for PCSAs canlinearize the hysteresis behavior of PCSAs, and the proposed hybrid linearizationmethod can reach higher linearization accuracy than the feedforward linearization method. Utilizing the proposed linearization methods, the open-loop and closed-loopcontrols for the tip displacement of a piezoelectric-driven microgripper are realized,which indicates that the proposed linearization methods can simplify the control for thepiezoelectric-driven microgripper with high accuracy.
4. Considering the bonding layers as passive single-DOF mass-damping-stiffnesssystems, a comprehensive model for PCSAs based on the Bouc-Wen hysteresis operator,which can simulate both the hysteresis behavior and the dynamic performance ofPCSAs, is proposed. According to the proposed comprehensive model, thelayering/stacking processes of PCSAs change the dynamic performance of PCSAs bychanging the parameters of the bonding layers but can’t affect the hysteresis behavior ofPCSAs, which is consistent with the experimental results. Letting PCSAs bepre-stressed with elastic deformation mechanisms, a method to determine themechanical parameters of pre-stressed mechanisms of PCSAs is proposed. Thesimulation results show that the proposed method can effectively design the dynamicperformance of PCSAs to some extent.
5. A phenomenological model for modeling the hysteresis behavior and thedynamic performance of pre-stressed PCSAs by using the Bouc-Wen hysteresis operator,as well as the corresponding parameter identification method, is proposed. Theperformance of the phenomenological model with the corresponding parameteridentification method is experimentally verified by the established experimental setup.The experimental results show that the proposed phenomenological model forpre-stressed PCSAs with the corresponding parameter identification method canaccurately model the hysteresis behavior and the dynamic performance of pre-stressedPCSAs.
6. Based on the afore-mentioned works, a phenomenological model for the2D-PDMDSP is established. Accordingly, a robust model reference adaptive controlmethod for the2D-PDMDSP is proposed and established and the stability istheoretically proved. The proposed control method is experimentally verified by theestablished experimental setup and the corresponding controlled results are comparedwith those by the PID control method based on the proposed phenomenon model. Theexperimental results show that robust model reference adaptive control method cansignificantly improve the accuracy of the positioning with high robustness and learningability.
The research results on the hysteretic modeling, linearization, and control method for PCSAs and PCSAs’ based systems has established the theoretical foundation forapplying PCSAs in fast and high-precision positioning systems.
引文
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