高精度永磁直线同步电动机的二自由度鲁棒跟踪控制研究
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摘要
本文以国家自然科学基金项目“永磁直线交流电机驱动的高精度微进给伺服系统的研究(59875061)”为背景,以现代高档数控机床用永磁直线同步电动机(PMLSM)伺服系统为研究对象,针对这种直线电机直接驱动的特点,以及数控机床对高精度的伺服系统鲁棒性和跟踪性能双重高要求,传统的单自由度控制器很难在抗扰性和跟踪性之间取得双赢,因此本文所用的方案是:在控制系统总体构建上,以反馈控制为基础,结合前馈控制,设计了一个新颖的二自由度控制器以确保控制系统的鲁棒性、高精度高速度的定位与轨迹跟踪性能。
二自由度控制系统是分别设计鲁棒反馈控制器和前馈控制器,鲁棒反馈控制器主要是确保系统的稳定性和强健的抗扰能力,鲁棒前馈控制器主要是解决系统输出的跟踪能力问题。二自由度控制设计,可以分别独立设计与调整控制器使系统的抗扰能力和跟踪性能都达到最佳状态。鲁棒反馈控制器结构包括:速度回路中的扰动观测器、速度P控制器(或PI控制器)、位置回路中的PD位置控制器与重复控制器。鲁棒前馈控制器是采用了零相位误差跟踪控制器(ZPETC)。设计各种控制器的出发点是根据被控对象与控制器的特点,外界对系统扰动形式以及数控机床进给系统对伺服驱动的要求。
针对PMLSM本身的参数不确定性以及包括摩擦在内的各种非线性扰动影响,本文提出了在速度回路中设计扰动观测器,目的是消除或削弱各种扰动的不良影响。为了确保系统实现渐近稳定过程,在位置回路中采用PD位置控制器的形式。PMLSM存在特有的端部效应而引起附加的周期性推力扰动,在扰动观测器已削弱了这种周期扰动的基础上,在此,有针对性地提出在位置回路中增设一个重复控制器来抑制这种周期性扰动,解决了端部效应所引起的推力周期性波动问题。为了提升高速反应、高精度的定位及对轨迹的跟踪性能,在整个的闭环反馈控制系统前面,采用ZPETC作为前馈控制器的控制方案。
ZPETC与反馈回路中的鲁棒控制器结构相结合,在控制总体框架下,构成了一个新颖的二自由度控制系统,这就很好地解决了扰动抑制能力与跟踪性能之间的矛盾,为控制器设计提供了很大的灵活性。为解决ZPETC的跟踪性能易受系统参数变化影响的缺点,提出了变增益ZPETC,以有效地克服建模误差与参数变化的影响,从而提高了ZPETC本身的参数鲁棒性。为克服ZPETC在补偿相位误差的同时所引起的自身增益损失,进一步改善跟踪性能,提出了L_2最优ZPETC,通过选取适当的目标函数,利用L_2范数优化设计数字前置滤波器,将此滤波器和ZPETC串联成新的前馈控制器来提高前馈增益,进一步提高了跟踪精度。
本文通过仿真和实验研究,验证了所采用的基本理论和提出的控制方法是行之有效的。
Taking the project supported by National Natural Science Foundation of China (The research of high precision micro-feed servo system driven permanent-magnet linear AC motor) as background, this dissertation researches on the permanent magnet synchronous linear motor(PMLSM) servo feeding system used in modern advanced NC machine tool. For the characteristic of direct drive and the double high requirements of robustness and tracking performance for high precision servo system in NC machine tool, it is very difficult to obtain dual gains between rejecting disturbance and tracking performance using traditional single degree of freedom controller, therefore in the dissertation the proposed scheme is to design a novel two-degree-of-freedom(2-DOF) controller to ensure the robustness and high precision and high speed positioning and tracking performance of the system, on the basis of the feedback control, combining with feedforward control.
Robust feedback controller and feedforward controller are designed respectively in 2-DOF control system. Robust feedback controller ensures the stability and the robust restraining disturbance ability of the system, and robust feedforward controller solves mainly the problem of the tracking ability of the system output. 2-DOF control can design and adjust controllers independently to obtain the best state of the restraining disturbance ability and tracking performance. Robust feedback controller consists of the following elements: a disturbance observer in the velocity loop, a velocity P controller( PI controller), a PD feedback controller and a repetitive controller in the position loop. Robust feedforward controller adopts zero phase error tracking controller (ZPETC). According to the characteristic of the controlled plant and controllers, the external disturbance modes and the requirement of servo drive, the controllers are designed.
For the parameters uncertainties for PMLSM servo system and nonlinear disturbances including the friction, a disturbance observer is utilized in the velocity loop to eliminate and attenuate the bad influences of the factors. A PD controller is used in the position loop to construct an asymptotically stable system. However, the periodic force disturbance is generated by specially existing end effect of PMLSM, which can not be rejected effectively by the disturbance observer. For it, a repetitive controller is designed in the position loop to restrain the periodic disturbances. The performance of restraining disturbance is improved. To enhance high-speed response and high accuracy positioning and tracking performance, a ZPETC is added to the closed-loop feedback control system as feedforward controller.
Combining ZPETC with robust feedback controller, a novel 2-DOF control system is designed to solve the conflict between the fast tracking performance and the interference rejection in the linear servo system. ZPETC depends on the model of the system and is sensitive to the parameters changes of the system. For it, the variable gain ZPETC is presented to overcome the influences modeling error and the parameters changes. Thus the robustness of ZPETC is greatly enhanced. ZPETC is used to compensate for the phase error, but this will also cause gain error. To improve the tracking performance of the ZPETC, the optimal design scheme of feedforward controller based on L_2-norm is proposed. The optimal digital pre-filter (DPF) is designed by selecting proper objective function and cascaded to ZPETC. The scheme can ensure the phase error of the system to be zero, at the same time, the gain performance of the system is greatly improved. The tracking precision is enhanced.
Finally, for the proposed methods, the simulations and experiments are conducted, which verify the feasibility of the theory studies and simulation results of the proposed control methods.
二自由度控制系统是分别设计鲁棒反馈控制器和前馈控制器,鲁棒反馈控制器主要是确保系统的稳定性和强健的抗扰能力,鲁棒前馈控制器主要是解决系统输出的跟踪能力问题。二自由度控制设计,可以分别独立设计与调整控制器使系统的抗扰能力和跟踪性能都达到最佳状态。鲁棒反馈控制器结构包括:速度回路中的扰动观测器、速度P控制器(或PI控制器)、位置回路中的PD位置控制器与重复控制器。鲁棒前馈控制器是采用了零相位误差跟踪控制器(ZPETC)。设计各种控制器的出发点是根据被控对象与控制器的特点,外界对系统扰动形式以及数控机床进给系统对伺服驱动的要求。
针对PMLSM本身的参数不确定性以及包括摩擦在内的各种非线性扰动影响,本文提出了在速度回路中设计扰动观测器,目的是消除或削弱各种扰动的不良影响。为了确保系统实现渐近稳定过程,在位置回路中采用PD位置控制器的形式。PMLSM存在特有的端部效应而引起附加的周期性推力扰动,在扰动观测器已削弱了这种周期扰动的基础上,在此,有针对性地提出在位置回路中增设一个重复控制器来抑制这种周期性扰动,解决了端部效应所引起的推力周期性波动问题。为了提升高速反应、高精度的定位及对轨迹的跟踪性能,在整个的闭环反馈控制系统前面,采用ZPETC作为前馈控制器的控制方案。
ZPETC与反馈回路中的鲁棒控制器结构相结合,在控制总体框架下,构成了一个新颖的二自由度控制系统,这就很好地解决了扰动抑制能力与跟踪性能之间的矛盾,为控制器设计提供了很大的灵活性。为解决ZPETC的跟踪性能易受系统参数变化影响的缺点,提出了变增益ZPETC,以有效地克服建模误差与参数变化的影响,从而提高了ZPETC本身的参数鲁棒性。为克服ZPETC在补偿相位误差的同时所引起的自身增益损失,进一步改善跟踪性能,提出了L_2最优ZPETC,通过选取适当的目标函数,利用L_2范数优化设计数字前置滤波器,将此滤波器和ZPETC串联成新的前馈控制器来提高前馈增益,进一步提高了跟踪精度。
本文通过仿真和实验研究,验证了所采用的基本理论和提出的控制方法是行之有效的。
Taking the project supported by National Natural Science Foundation of China (The research of high precision micro-feed servo system driven permanent-magnet linear AC motor) as background, this dissertation researches on the permanent magnet synchronous linear motor(PMLSM) servo feeding system used in modern advanced NC machine tool. For the characteristic of direct drive and the double high requirements of robustness and tracking performance for high precision servo system in NC machine tool, it is very difficult to obtain dual gains between rejecting disturbance and tracking performance using traditional single degree of freedom controller, therefore in the dissertation the proposed scheme is to design a novel two-degree-of-freedom(2-DOF) controller to ensure the robustness and high precision and high speed positioning and tracking performance of the system, on the basis of the feedback control, combining with feedforward control.
Robust feedback controller and feedforward controller are designed respectively in 2-DOF control system. Robust feedback controller ensures the stability and the robust restraining disturbance ability of the system, and robust feedforward controller solves mainly the problem of the tracking ability of the system output. 2-DOF control can design and adjust controllers independently to obtain the best state of the restraining disturbance ability and tracking performance. Robust feedback controller consists of the following elements: a disturbance observer in the velocity loop, a velocity P controller( PI controller), a PD feedback controller and a repetitive controller in the position loop. Robust feedforward controller adopts zero phase error tracking controller (ZPETC). According to the characteristic of the controlled plant and controllers, the external disturbance modes and the requirement of servo drive, the controllers are designed.
For the parameters uncertainties for PMLSM servo system and nonlinear disturbances including the friction, a disturbance observer is utilized in the velocity loop to eliminate and attenuate the bad influences of the factors. A PD controller is used in the position loop to construct an asymptotically stable system. However, the periodic force disturbance is generated by specially existing end effect of PMLSM, which can not be rejected effectively by the disturbance observer. For it, a repetitive controller is designed in the position loop to restrain the periodic disturbances. The performance of restraining disturbance is improved. To enhance high-speed response and high accuracy positioning and tracking performance, a ZPETC is added to the closed-loop feedback control system as feedforward controller.
Combining ZPETC with robust feedback controller, a novel 2-DOF control system is designed to solve the conflict between the fast tracking performance and the interference rejection in the linear servo system. ZPETC depends on the model of the system and is sensitive to the parameters changes of the system. For it, the variable gain ZPETC is presented to overcome the influences modeling error and the parameters changes. Thus the robustness of ZPETC is greatly enhanced. ZPETC is used to compensate for the phase error, but this will also cause gain error. To improve the tracking performance of the ZPETC, the optimal design scheme of feedforward controller based on L_2-norm is proposed. The optimal digital pre-filter (DPF) is designed by selecting proper objective function and cascaded to ZPETC. The scheme can ensure the phase error of the system to be zero, at the same time, the gain performance of the system is greatly improved. The tracking precision is enhanced.
Finally, for the proposed methods, the simulations and experiments are conducted, which verify the feasibility of the theory studies and simulation results of the proposed control methods.
引文
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