超磁致伸缩致动器驱动系统关键技术研究
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摘要
超磁致伸缩材料具有应变大、输出力大、功率密度高、响应速度快和可靠性高等优点,基于超磁致伸缩材料研制的致动器在精密加工、精密定位、主动振动控制、机器人以及微型机电系统等领域显示出良好的应用前景。但是,超磁致伸缩材料本身所固有的磁滞回特性使得致动器存在强烈的非线性特性,这使得致动器难以精确控制,限制了超磁致伸缩致动器的发展和应用。如何解决超磁致伸缩致动器系统的非线性问题,进一步提高致动器系统的输出精度,已成为当前研究的热点。
超磁致伸缩致动器驱动系统既是驱动超磁致伸缩材料完成伸缩动作的功率源,又是实时控制伸缩量大小的控制器,是超磁致伸缩致动器系统的核心,驱动系统的性能对致动器的系统输出具有重要影响。基于此,本文深入分析了超磁致伸缩致动器驱动系统的研究现状,指出了驱动系统在功率驱动、系统建模和控制策略等方面存在的不足,在深入研究超磁致伸缩致动器功率驱动、系统建模及非线性控制的基础上,将功率驱动技术、非线性动态模型的建立及其线性化、高阶模型的降阶以及系统辨识应用于超磁致伸缩致动器驱动装置,研制了一套超磁致伸缩致动器驱动系统。并采用广义预测控制策略实现了对系统输出的精确跟踪,提高了致动器宽范围输入下的控制精度。主要研究内容如下：
1、分析了超磁致伸缩致动器的工作原理,在考虑超磁致伸缩致动器电-磁-机耦合特性的基础上基于分层建模原理建立了超磁致伸缩致动器非线性动态模型：
采用多项式拟合超磁致伸缩材料的磁化强度与电流的非线性关系,建立了磁滞模型,该模型区别于以往Preisach模型、Jile-AthetOn模型或自由能迟滞模型,使非线性曲线更加平滑、减少噪声影响、减小运算时间,以达到快速、实时控制的目的；对含有非线性弹性材料一—超磁致伸缩材料的致动器机构采用带耗散力的拉格朗日方程对该机构的Terfenol-D棒和广义负载进行动力学特性分析,建立超磁致伸缩致动器的结构动力学模型。
2、分析了磁致伸缩致动器非线性动态模型,获得了各个子模块间的关系,在此基础上对该非线性模型进行了线性化并采用平衡实现理论对该高阶线性模型进行降阶：
根据分层建模原理依据各子模块的特性将模块重新排序,采用纯时滞环节代替磁化滞回模块的非线性环节,结合功率驱动模块、线圈磁场模块、磁场驱动模块和结构动力学模块组成线性环节,实现磁致伸缩致动器非线性模型到线性模型的转换；利用平衡实现理论对磁致伸缩致动器系统线性模型进行降阶研究,提出了磁致伸缩致动器系统线性模型平衡实现算法,分析了平衡截断和平衡残差两种降阶方法的各降阶系统的误差,说明了磁致伸缩致动器系统模型降为二阶模型的合理性。
3、根据超磁致伸缩致动器驱动系统广义预测控制的需求,对超磁致伸缩致动器驱动系统模型的参数进行在线辨识研究：
确定了超磁致伸缩致动器驱动系统中功率驱动器、致动器机械结构以及致动器磁滞非线性等影响因素的参数作为辨识对象,提出了基于遗忘因子递推最小二乘法的超磁致伸缩致动器系统参数的在线辨识策略,建立了超磁致伸缩致动器系统的离散辨识参数模型,并依据遗忘因子递推最小二乘法理论对超磁致伸缩致动器系统进行在线参数辨识。
4、针对超磁致伸缩致动器驱动系统的精确控制问题,采用了广义预测控制策略对超磁致伸缩致动器系统进行跟踪控制：
研究了广义预测控制理论中多步预测、滚动优化和反馈校正的控制策略,应用Diophantine方程推导了广义预测控制的最优输出预测,通过求解其目标函数得到了广义预测控制的控制律,并分析了广义预测控制算法参数的选择策略；仿真分析了不同设定信号下,设定值与输出值的仿真曲线、误差曲线及控制电压曲线,验证了基于广义预测控制算法的超磁致伸缩致动器控制器设计的合理性。
5、研制了超磁致伸缩致动器驱动系统原型机,详细介绍超磁致伸缩致动器驱动系统的设计开发和性能测试过程,验证了本文提出的超磁致伸缩致动器驱动系统的可行性和有效性：
(1)利用傅里叶级数理论分析了半桥斩波逆变电路输出电压谐波的频谱分布,比较了LC滤波器和LCCR滤波器的特性,指出LC滤波器存在的不足,提出采用LCCR滤波器的方案,推导了带感性负载条件下的LCCR滤波器参数设计公式；
(2)基于半桥斩波逆变电路设计了超磁致伸缩致动器功率驱动器,采用I2控制方法,提高了系统的稳定性和响应速度；设计了超磁致伸缩致动器驱动系统的硬件平台,开发了超磁致伸缩致动器非线性系统广义预测控制算法库,并设计了控制器端图形化用户应用程序用于超磁致伸缩致动器驱动系统的控制和调试。实验验证了所设计的超磁致伸缩致动器驱动系统装置的可行性和有效性。
本研究的成功实施为超磁致伸缩致动器非线性控制提供了一条新的有效的途径,为解决超磁致伸缩致动器精密控制中存在的关键技术问题提供了一个解决方案。
Giant magnetostrictive material has unique characteristics of large strains, great output force, high power density, fast response and high reliability. Actuator based on giant magnetostrictive material show a good prospect in the areas of precision machining, precision positioning, active vibration control, robotics, and micro-electromechanical systems. However, there is a strong nonlinearity in actuator due to the inherent hysteresis characteristics of the giant magnetostrictive material, which makes it difficult to precisely control the actuator and thus hinders the development and applications of such actuator. How to solve the nonlinear problems in the giant magnetostrictive actuator system and to further improve the output accuracy of the actuator system has become a research of popularity.
The giant Magnetostrictive actuator drive system is both the power source to drive the giant magnetostrictive material to complete the retractable action and the controller to achieve the real-time control of the expansion volume. Therefore, the giant Magnetostrictive actuator drive system is the core of the giant magnetostrictive actuator system and the performance of such drive system exerts an important impact on the output of the actuator system. This paper analyzes in depth the research status quo of the giant magnetostrictive actuator drive system, points out the shortcomings of such drive system in the areas of power drive, system modeling and control strategies, and applies the power drive technology, nonlinear dynamic model and its linearization, order reduction of the high-order model, and the system identification to the giant magnetostrictive actuator driver based on the in-depth study of the giant magnetostrictive actuator power driver technology, system modeling and nonlinear control. At the same time, a magnetostrictive actuator drive system is also developed, which achieves the accurate tracking of the system output using the generalized predictive control strategy, thus improving the control accuracy under the condition of a wide input range. The main contents of this paper are as follows:
1. Analyzing the operating principle of the giant magnetostrictive actuator, establishing the non-linear dynamic model for the giant magnetostrictive actuator based on the hierarchical modeling principle considering the electric-magnetic-mechanical coupling characteristics of the giant magnetostrictive actuator:
using polynomial fitting method of handling the relationship between the giant magnetostrictive material magnetization and current non-linear characteristic which is different from the past modeling theories of Preisach model, Jile-Atheton model or free-energy hysteresis model, thus smoothing the non-linear curve, reducing the noise impact, and reducing the operation time to achieve the purposes of fast, real-time control; analyzing the dynamic mechanism of Terfenol-D rods and generalized loads of the giant magnetostrictive actuator consisting of non-linear elastic materials using Lagrange equation with dissipative forces and establishing the dynamic model for the giant magnetostrictive actuator.
2. Analyzing the non-linear dynamic model for the giant magnetostrictive actuator, getting the relationship between sub-models, then linearizing such non-linear model and reducing the order of the high-order linear model using the balance-realizing theory:
Reordering the modules according to the characteristics of each sub-model based on the hierarchical modeling theory; using pure time delay unit instead of the nonlinear unit of the magnetization hysteresis module combining the power drive module, coil magnetic module, magnetic drive module and structural dynamics module to get the linear unit and thus achieving the transformation from the non-linear model to the linear model for the magnetostrictive actuator; carrying out order-reduction research on the linear model of the magnetostrictive actuator system using the balance-realizing theory, proposing the balance-realizing algorithm for the linear model of the magnetostrictive actuator system, analyzing the error of each order-reduction system using order-reduction methods of balance truncation and balance residual, indicating the reasonability of the magnetostrictive actuator system model reducing to second-order model.
3. Researching online identification of parameters of the giant magnetostrictive actuator drive system model according to the needs for the generalized predictive control of the giant magnetostrictive actuator system:
Identifying the influencing factors of the power drivers, mechanical structures of the actuator and hysteresis nonlinearity as the identification objects, proposing the controlled-object online parameter identification strategy of the giant magnetostrictive actuator system based on the forgetting-factor recursive least squares method and establishing the discrete parameter identification model of the giant magnetostrictive actuator system with online identification of the giant magnetostrictive actuator system based on the forgetting-factor recursive least squares method.
4. As for the precise control of the giant magnetostrictive actuator drive system, using a generalized predictive control strategy for tracking control of the giant magnetostrictive actuator system:
Studying multi-step prediction, rolling optimization and feedback correction strategies of the generalized predictive control theory, deriving the optimum output prediction of the generalized predictive control by application of the Diophantine equations and acquiring the control law of the generalized predictive control by solving its objective function, analyzing the parameter selection strategy of the generalized predictive control algorithm; Analyzing by simulation the setting values and output simulation curve, the error curve and the control voltage curve under different setting signals, verifying the reasonability of giant magnetostrictive actuator controller design based on the generalized predictive control algorithm.
5. Having developed the giant magnetostrictive actuator drive system prototype, detailing the process of design and development and performance testing for the giant magnetostrictive actuator drive system, verifying the feasibility and effectiveness of the giant magnetostrictive actuator drive system proposed in this paper:
Analyzing theoretically the spectral distribution of the output voltage harmonics of the half-bridge chopper inverter circuit using the Fourier series, comparing the LC filter and the LCCR filter characteristics, and pointing out the shortcomings of the LC filter, thus proposing using the LCCR filter instead of the LC filter with the derivation of parameters design formulas for the LCCR filter with inductive load conditions.Designing the power driver of the giant magnetostrictive actuator based on the half-bridge chopper inverter circuit, improving the stability and response speed of the system by using the12control method; designing the hardware platform for the giant magnetostrictive actuator drive system, developing the algorithm library for the generalized predictive control of the giant magnetostrictive actuator non-linear system, designing a graphical user application at the controller for controlling and debugging the giant magnetostrictive actuator driving system. Verifying experimentally the feasibility and effectiveness of the giant magnetostrictive actuator drive system designed in this paper.
This successful study in this paper provides a new and effective way of implementing the giant magnetostrictive actuator nonlinear control and presents a solution to solving the key technological problems in the precise control in the giant magnetostrictive actuators.
超磁致伸缩致动器驱动系统既是驱动超磁致伸缩材料完成伸缩动作的功率源,又是实时控制伸缩量大小的控制器,是超磁致伸缩致动器系统的核心,驱动系统的性能对致动器的系统输出具有重要影响。基于此,本文深入分析了超磁致伸缩致动器驱动系统的研究现状,指出了驱动系统在功率驱动、系统建模和控制策略等方面存在的不足,在深入研究超磁致伸缩致动器功率驱动、系统建模及非线性控制的基础上,将功率驱动技术、非线性动态模型的建立及其线性化、高阶模型的降阶以及系统辨识应用于超磁致伸缩致动器驱动装置,研制了一套超磁致伸缩致动器驱动系统。并采用广义预测控制策略实现了对系统输出的精确跟踪,提高了致动器宽范围输入下的控制精度。主要研究内容如下：
1、分析了超磁致伸缩致动器的工作原理,在考虑超磁致伸缩致动器电-磁-机耦合特性的基础上基于分层建模原理建立了超磁致伸缩致动器非线性动态模型：
采用多项式拟合超磁致伸缩材料的磁化强度与电流的非线性关系,建立了磁滞模型,该模型区别于以往Preisach模型、Jile-AthetOn模型或自由能迟滞模型,使非线性曲线更加平滑、减少噪声影响、减小运算时间,以达到快速、实时控制的目的；对含有非线性弹性材料一—超磁致伸缩材料的致动器机构采用带耗散力的拉格朗日方程对该机构的Terfenol-D棒和广义负载进行动力学特性分析,建立超磁致伸缩致动器的结构动力学模型。
2、分析了磁致伸缩致动器非线性动态模型,获得了各个子模块间的关系,在此基础上对该非线性模型进行了线性化并采用平衡实现理论对该高阶线性模型进行降阶：
根据分层建模原理依据各子模块的特性将模块重新排序,采用纯时滞环节代替磁化滞回模块的非线性环节,结合功率驱动模块、线圈磁场模块、磁场驱动模块和结构动力学模块组成线性环节,实现磁致伸缩致动器非线性模型到线性模型的转换；利用平衡实现理论对磁致伸缩致动器系统线性模型进行降阶研究,提出了磁致伸缩致动器系统线性模型平衡实现算法,分析了平衡截断和平衡残差两种降阶方法的各降阶系统的误差,说明了磁致伸缩致动器系统模型降为二阶模型的合理性。
3、根据超磁致伸缩致动器驱动系统广义预测控制的需求,对超磁致伸缩致动器驱动系统模型的参数进行在线辨识研究：
确定了超磁致伸缩致动器驱动系统中功率驱动器、致动器机械结构以及致动器磁滞非线性等影响因素的参数作为辨识对象,提出了基于遗忘因子递推最小二乘法的超磁致伸缩致动器系统参数的在线辨识策略,建立了超磁致伸缩致动器系统的离散辨识参数模型,并依据遗忘因子递推最小二乘法理论对超磁致伸缩致动器系统进行在线参数辨识。
4、针对超磁致伸缩致动器驱动系统的精确控制问题,采用了广义预测控制策略对超磁致伸缩致动器系统进行跟踪控制：
研究了广义预测控制理论中多步预测、滚动优化和反馈校正的控制策略,应用Diophantine方程推导了广义预测控制的最优输出预测,通过求解其目标函数得到了广义预测控制的控制律,并分析了广义预测控制算法参数的选择策略；仿真分析了不同设定信号下,设定值与输出值的仿真曲线、误差曲线及控制电压曲线,验证了基于广义预测控制算法的超磁致伸缩致动器控制器设计的合理性。
5、研制了超磁致伸缩致动器驱动系统原型机,详细介绍超磁致伸缩致动器驱动系统的设计开发和性能测试过程,验证了本文提出的超磁致伸缩致动器驱动系统的可行性和有效性：
(1)利用傅里叶级数理论分析了半桥斩波逆变电路输出电压谐波的频谱分布,比较了LC滤波器和LCCR滤波器的特性,指出LC滤波器存在的不足,提出采用LCCR滤波器的方案,推导了带感性负载条件下的LCCR滤波器参数设计公式；
(2)基于半桥斩波逆变电路设计了超磁致伸缩致动器功率驱动器,采用I2控制方法,提高了系统的稳定性和响应速度；设计了超磁致伸缩致动器驱动系统的硬件平台,开发了超磁致伸缩致动器非线性系统广义预测控制算法库,并设计了控制器端图形化用户应用程序用于超磁致伸缩致动器驱动系统的控制和调试。实验验证了所设计的超磁致伸缩致动器驱动系统装置的可行性和有效性。
本研究的成功实施为超磁致伸缩致动器非线性控制提供了一条新的有效的途径,为解决超磁致伸缩致动器精密控制中存在的关键技术问题提供了一个解决方案。
Giant magnetostrictive material has unique characteristics of large strains, great output force, high power density, fast response and high reliability. Actuator based on giant magnetostrictive material show a good prospect in the areas of precision machining, precision positioning, active vibration control, robotics, and micro-electromechanical systems. However, there is a strong nonlinearity in actuator due to the inherent hysteresis characteristics of the giant magnetostrictive material, which makes it difficult to precisely control the actuator and thus hinders the development and applications of such actuator. How to solve the nonlinear problems in the giant magnetostrictive actuator system and to further improve the output accuracy of the actuator system has become a research of popularity.
The giant Magnetostrictive actuator drive system is both the power source to drive the giant magnetostrictive material to complete the retractable action and the controller to achieve the real-time control of the expansion volume. Therefore, the giant Magnetostrictive actuator drive system is the core of the giant magnetostrictive actuator system and the performance of such drive system exerts an important impact on the output of the actuator system. This paper analyzes in depth the research status quo of the giant magnetostrictive actuator drive system, points out the shortcomings of such drive system in the areas of power drive, system modeling and control strategies, and applies the power drive technology, nonlinear dynamic model and its linearization, order reduction of the high-order model, and the system identification to the giant magnetostrictive actuator driver based on the in-depth study of the giant magnetostrictive actuator power driver technology, system modeling and nonlinear control. At the same time, a magnetostrictive actuator drive system is also developed, which achieves the accurate tracking of the system output using the generalized predictive control strategy, thus improving the control accuracy under the condition of a wide input range. The main contents of this paper are as follows:
1. Analyzing the operating principle of the giant magnetostrictive actuator, establishing the non-linear dynamic model for the giant magnetostrictive actuator based on the hierarchical modeling principle considering the electric-magnetic-mechanical coupling characteristics of the giant magnetostrictive actuator:
using polynomial fitting method of handling the relationship between the giant magnetostrictive material magnetization and current non-linear characteristic which is different from the past modeling theories of Preisach model, Jile-Atheton model or free-energy hysteresis model, thus smoothing the non-linear curve, reducing the noise impact, and reducing the operation time to achieve the purposes of fast, real-time control; analyzing the dynamic mechanism of Terfenol-D rods and generalized loads of the giant magnetostrictive actuator consisting of non-linear elastic materials using Lagrange equation with dissipative forces and establishing the dynamic model for the giant magnetostrictive actuator.
2. Analyzing the non-linear dynamic model for the giant magnetostrictive actuator, getting the relationship between sub-models, then linearizing such non-linear model and reducing the order of the high-order linear model using the balance-realizing theory:
Reordering the modules according to the characteristics of each sub-model based on the hierarchical modeling theory; using pure time delay unit instead of the nonlinear unit of the magnetization hysteresis module combining the power drive module, coil magnetic module, magnetic drive module and structural dynamics module to get the linear unit and thus achieving the transformation from the non-linear model to the linear model for the magnetostrictive actuator; carrying out order-reduction research on the linear model of the magnetostrictive actuator system using the balance-realizing theory, proposing the balance-realizing algorithm for the linear model of the magnetostrictive actuator system, analyzing the error of each order-reduction system using order-reduction methods of balance truncation and balance residual, indicating the reasonability of the magnetostrictive actuator system model reducing to second-order model.
3. Researching online identification of parameters of the giant magnetostrictive actuator drive system model according to the needs for the generalized predictive control of the giant magnetostrictive actuator system:
Identifying the influencing factors of the power drivers, mechanical structures of the actuator and hysteresis nonlinearity as the identification objects, proposing the controlled-object online parameter identification strategy of the giant magnetostrictive actuator system based on the forgetting-factor recursive least squares method and establishing the discrete parameter identification model of the giant magnetostrictive actuator system with online identification of the giant magnetostrictive actuator system based on the forgetting-factor recursive least squares method.
4. As for the precise control of the giant magnetostrictive actuator drive system, using a generalized predictive control strategy for tracking control of the giant magnetostrictive actuator system:
Studying multi-step prediction, rolling optimization and feedback correction strategies of the generalized predictive control theory, deriving the optimum output prediction of the generalized predictive control by application of the Diophantine equations and acquiring the control law of the generalized predictive control by solving its objective function, analyzing the parameter selection strategy of the generalized predictive control algorithm; Analyzing by simulation the setting values and output simulation curve, the error curve and the control voltage curve under different setting signals, verifying the reasonability of giant magnetostrictive actuator controller design based on the generalized predictive control algorithm.
5. Having developed the giant magnetostrictive actuator drive system prototype, detailing the process of design and development and performance testing for the giant magnetostrictive actuator drive system, verifying the feasibility and effectiveness of the giant magnetostrictive actuator drive system proposed in this paper:
Analyzing theoretically the spectral distribution of the output voltage harmonics of the half-bridge chopper inverter circuit using the Fourier series, comparing the LC filter and the LCCR filter characteristics, and pointing out the shortcomings of the LC filter, thus proposing using the LCCR filter instead of the LC filter with the derivation of parameters design formulas for the LCCR filter with inductive load conditions.Designing the power driver of the giant magnetostrictive actuator based on the half-bridge chopper inverter circuit, improving the stability and response speed of the system by using the12control method; designing the hardware platform for the giant magnetostrictive actuator drive system, developing the algorithm library for the generalized predictive control of the giant magnetostrictive actuator non-linear system, designing a graphical user application at the controller for controlling and debugging the giant magnetostrictive actuator driving system. Verifying experimentally the feasibility and effectiveness of the giant magnetostrictive actuator drive system designed in this paper.
This successful study in this paper provides a new and effective way of implementing the giant magnetostrictive actuator nonlinear control and presents a solution to solving the key technological problems in the precise control in the giant magnetostrictive actuators.
引文
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