基于非线性和柔性特性分析及补偿的直线电机精密运动控制
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摘要
现代的机电系统,例如先进机床、微电子和半导体制造装备、光学检测系统和芯片传输系统,通常需要高速高精度的直线运动。而直接驱动的直线电机系统消除了中间机械传动机构带来的一系列问题,例如齿隙、大摩擦力和惯性负载、结构的柔性,故而有潜力达到更高的速度和精度。但是为了实现高速高精度运动的目标,我们必须考虑直线电机系统存在的几个控制难点：明显的模型不确定、参数不确定和外干扰,各种非线性动力学,高频柔性动力学。本论文就是以直线电机的非线性和高频柔性作为两大研究重点。深入分析了定位力、摩擦力和非线性电磁驱动力三大主要的非线性动力学,对每一类非线性提出了更精确且又能用于实时补偿控制的数学模型,并通过时域辨识实验验证这些模型的有效性和准确性。将非线性自适应鲁棒控制技术和各种非线性的有效补偿相结合,提出各种非线性有效补偿的自适应鲁棒控制算法,这些控制算法在理论上保证优越的瞬态和稳态跟踪性能,并通过一系列的对比实验验证了这些非线性补偿对控制性能的进一步提升。另一方面,考虑现今控制器设计所忽略的高频柔性动力学,找出主导高频动力学的物理机制并建立可用于控制器分析和设计的高频动力学模型,通过频域辨识实验验证其模型的有效性。依据这些高频动力学信息,提出控制器参数选择的优化准则,在现有的刚性动力学控制器框架下获得了最优的控制性能。为了更进一步提升系统的闭环频宽,高频动力学也被引入到控制器的结构设计中。首先尝试了简单的零极相消技术,以消减主导柔性模态的影响。随后,提出了一种新型的基于μ-synthesis的自适应鲁棒控制策略。该算法使用自适应在线参数估计和有效的非线性前馈模型补偿,把传统μ-synthesis鲁棒控制难以实现的精确跟踪问题转化为镇定问题。而且利用μ-synthesis反馈控制设计可直接考虑高频动力学的优点设计出更高闭环频宽和更强抗干扰能力的鲁棒反馈控制。
本论文共分为六章,现分别简述如下：
第一章,详细介绍了直线电机精密运动控制的研究背景以及研究状况,归纳出直线电机高速高精度运动控制的几大难题。介绍各种控制方法在直线电机精密运动控制中的应用。阐述了直线电机系统存在的定位力、摩擦力和非线性电磁驱动力三大非线性动力学,以及它们的研究现状。分析了系统高频柔性动力学对控制性能的约束,以及现有的建模和辨识结果。最后概述了本论文的研究意义及研究内容。
第二章,简述了论文研究所使用的实验平台及其硬件性能参数。发展了直线电机的非线性刚性动力学模型。在原有周期性定位力模型的基础上,使用B样条函数提出了非周期定位力的数学模型,兼顾其整体上的周期特性和局部区间的非周期特性。分析原始LuGre动态摩擦力模型的耗散性问题和数字控制时的观测器失稳问题,提出改进型的LuGre动态摩擦力模型。针对直线电机电磁驱动力的非线性特性,提出了易于补偿控制实现的三阶多项式非线性电磁力模型。所有这些模型在准确描述非线性动力学特性的同时,也兼顾到了补偿控制器的实现难度。随后,对直线电机系统进行时域系统辨识,获得刚性动力学的各主要参数,验证各种非线性模型的有效性。
第三章,以简化的直线电机二阶刚性动力学为例,系统地阐述了自适应鲁棒控制的基本概念和各种变换形式,该控制方法从理论上保证系统在建模误差下的瞬态和稳态性能,以及只存在参数不确定时的渐进跟踪性能。将自适应鲁棒控制技术和各种非线性模型补偿有机结合起来,分别设计了非周期定位力补偿的自适应鲁棒控制算法、改进的LuGre动态摩擦力补偿的自适应鲁棒控制算法、非线性电磁力补偿的自适应鲁棒控制算法、以及各种非线性综合补偿的自适应鲁棒控制算法。通过对比实验,验证模型补偿的有效性和控制算法所能实现的优越控制性能。
第四章,首次分析了直线电机高频动力学的存在因素和物理特性,找出因平台旋转而产生的主导高频模态,并建立其数学模型。进行频域系统辨识,了解刚性动力学的有效频率范围和高频柔性模态的存在频段,验证所提的高频动力学模型的有效性。根据已知的高频动力学,通过实验和理论分析,讨论了高频动力学、控制器参数和系统闭环频宽之间的关系,提出了控制器参数选择的优化准则,在现有的刚性动力学控制器框架下实现最优的控制性能。
第五章,为了进一步提升系统的闭环频宽,高频动力学被引入到控制器的结构设计中。首先尝试了简单的零极相消技术,消减主导柔性模态的影响,故而提高了系统的闭环频宽上限。对于已知的非线性刚性动力学和高频柔性模态,打破原有的刚性动力学控制器设计结构,提出新型的基于μ-synthesis的自适应鲁棒控制策略。其自适应前馈环节可以拥有精确的在线参数估计和有效的非线性模型补偿,并把轨迹跟踪问题转化为镇定问题以便于μ-synthesis鲁棒反馈控制器设计；由于使用高频动力学作为名义模型的一部分,设计的μ-synthesis反馈环节可以达到更高的闭环频宽和更强的抗干扰能力。通过对比实验,验证了该方法所具有的优越控制性能。
第六章,归纳总结了本论文的主要工作,阐述研究结论和创新点,并对直线电机精密运动控制的研究进行了展望。
Modern mechatronic systems, such as advanced machine tools, microelectronic and semicon-ductor manufacturing equipment, optical inspection systems and dispensing processes systems often require high-speed and high-accuracy linear movement. Direct-drive linear motors eliminate gear related mechanical transmission problems such as backlash, large friction and inertial loads, and structural flexibility, and thus, have the potential of achieving higher speed and higher accuracy. But to realize its high-speed/high-accuracy potential, some control issues have to be solved:sig-nificant model uncertainties, parameter uncertainties and external disturbances; various nonlinear dynamics; high-frequency flexible modes. Thus, this dissertation focuses on major nonlinearities and flexibilities of linear motor driven systems. Physical modeling of cogging force, dynamic fric-tion and nonlinear electromagnetic field effect are developed and validated by the system identifica-tions in time domain. These novel nonlinear dynamical models capture the physical characteristics more accurately and also consider their complexity for compensation control design. The high performance adaptive robust control (ARC) technique is integrated with the effective nonlinearity compensations. Theoretically, these proposed control algorithms guarantee excellent transient and steady-state performance. And comparative experimental results also show the further improved tracking performance of the effective nonlinearity compensations. The physical cause of major high-frequency dynamics is identified. The corresponding mathematical model is then built, and verified by the system identification in frequency domain. With the knowledge of high-frequency dynamics, the optimal tuning guidelines of control gains are developed to maximize the tracking performance of the previously proposed control algorithms. To further increase the achievable close-loop bandwidth, the high-frequency dynamics neglected in the existing research are then ex-plicitly taken into consideration in the design of controllers. Specifically, the simple pole/zero can-celation technique is first incorporated into the control design to attenuate the major flexible mode effect. A novel μ-synthesis based adaptive robust control strategy is then developed. The proposed control algorithm uses adaptive model compensation having accurate on-line parameter estimation to effectively deal with various nonlinearity effect and to transform the difficult trajectory tracking control problem into a robust stabilization problem. The well-developed μ-synthesis based linear robust control technique is then employed to deal with the robust control issue associated with the high-frequency dynamics explicitly to achieve higher close-loop bandwidth and better disturbance rejection in the feedback control loop.
The dissertation consists of the following six chapters:
In Chapter1, the research background and history of precision motion control of linear motor driven systems are detailed. Specifically, the control issues associated with the high-speed/high-accuracy movement of linear motor drive systems are first pointed out, followed by a comprehen-sive literature survey of linear motor driven systems, including existing control methods dealing with nonlinearities such as cogging force, friction and nonlinear electromagnetic field effect and high-frequency flexible modes. A brief summary of the dissertation's contributions and significance is subsequently given.
In Chapter2, the hardware equipment and their specifications used in the experiments are introduced. Rigid-body dynamics of linear motor drive systems are presented with a focus on better modeling of major nonlinearities inherited to the linear motor drive systems. Specifically, an aperiodic cogging force model is built by using B-spline functions, which captures both periodic and aperiodic characteristics of cogging force. The modified LuGre dynamic friction model is proposed to solve the passive problem and the observer instability problem of the existing ones. A third order polynomial model is developed to precisely describe the nonlinear electromagnetic field effect as well. All the proposed models not only provide a more accurate description of the nonlinearity under study, but also can be easily used in the subsequent controller design for more effective on-line model compensation. The system identifications in time domain are then carried out, validating the effectiveness of all proposed models.
In Chapter3, based on the rigid-body dynamics of linear motor drive systems, the concepts and various implementations of adaptive robust control (ARC) strategy are introduced. Theoretically, the presented ARC can achieve a guaranteed transient and steady-state performance in the pres-ence of both parametric uncertainties and model uncertainties, as well as zero steady-state tracking error when subjected to parametric uncertainties only. The adaptive robust control technique is subsequently integrated with more effective compensations of various nonlinearities, including the adaptive robust control with aperiodic cogging force compensation, the adaptive robust control with dynamic friction compensation using modified LuGre model, the adaptive robust control with elec-tromagnetic nonlinearity compensation, and the adaptive robust control with integrated compen-sation of all major nonlinearities of linear motor drive systems. Comparative experimental results show the effectiveness of the proposed nonlinearity compensations and the excellent performance of the proposed control algorithms.
In Chapter4, physical causes of the high-frequency dynamics of linear motor drive systems are analyzed. The stage rotation is found to be the cause of the major flexible mode of linear motor driven systems. The corresponding mathematical model is then built to capture this ef-fect and system identifications in frequency domain are carried out to verify the effectiveness of the proposed model on the high-frequency dynamics of linear motors. With the knowledge of these high-frequency dynamics, the relationship among high-frequency dynamics, control gains and close-loop bandwidth is established, and the optimal tuning guidelines on control gains are de-veloped to maximize the tracking performance of the rigid-body dynamics based control algorithms of linear motors in implementation.
In Chapter5, to further increase the achievable close-loop bandwidth, the high-frequency dy-namics are explicitly taken into consideration in the design of controllers. Specifically, the simple pole/zero cancelation of known high-frequency dynamics is first incorporated to attenuate the ma-jor flexible mode effect so that the upper bound on the achievable close-loop bandwidth of the rigid-body dynamics based control algorithms can be raised. With the knowledge of nonlinear rigid-body dynamics and the structure of high-frequency flexible modes, a novel μ-synthesis based adaptive robust control algorithm is then proposed. Its adaptive feedforward loop has accurate on-line parameter estimation and effective nonlinearity compensation, which makes it possible to convert the difficult tracking control problem into a robust stabilization problem. By treating ma-jor high-frequency dynamics as a part of the nominal model, the μ-synthesis feedback loop of the proposed novel ARC strategy can achieve higher close-loop bandwidth and better disturbance re-jection. Comparative experiments are conducted and the results show the better performance of the proposed control algorithms over existing ones.
In Chapter6, the research work of this dissertation is summarized. Major innovations are highlighted, and some future research directions are discussed.
本论文共分为六章,现分别简述如下：
第一章,详细介绍了直线电机精密运动控制的研究背景以及研究状况,归纳出直线电机高速高精度运动控制的几大难题。介绍各种控制方法在直线电机精密运动控制中的应用。阐述了直线电机系统存在的定位力、摩擦力和非线性电磁驱动力三大非线性动力学,以及它们的研究现状。分析了系统高频柔性动力学对控制性能的约束,以及现有的建模和辨识结果。最后概述了本论文的研究意义及研究内容。
第二章,简述了论文研究所使用的实验平台及其硬件性能参数。发展了直线电机的非线性刚性动力学模型。在原有周期性定位力模型的基础上,使用B样条函数提出了非周期定位力的数学模型,兼顾其整体上的周期特性和局部区间的非周期特性。分析原始LuGre动态摩擦力模型的耗散性问题和数字控制时的观测器失稳问题,提出改进型的LuGre动态摩擦力模型。针对直线电机电磁驱动力的非线性特性,提出了易于补偿控制实现的三阶多项式非线性电磁力模型。所有这些模型在准确描述非线性动力学特性的同时,也兼顾到了补偿控制器的实现难度。随后,对直线电机系统进行时域系统辨识,获得刚性动力学的各主要参数,验证各种非线性模型的有效性。
第三章,以简化的直线电机二阶刚性动力学为例,系统地阐述了自适应鲁棒控制的基本概念和各种变换形式,该控制方法从理论上保证系统在建模误差下的瞬态和稳态性能,以及只存在参数不确定时的渐进跟踪性能。将自适应鲁棒控制技术和各种非线性模型补偿有机结合起来,分别设计了非周期定位力补偿的自适应鲁棒控制算法、改进的LuGre动态摩擦力补偿的自适应鲁棒控制算法、非线性电磁力补偿的自适应鲁棒控制算法、以及各种非线性综合补偿的自适应鲁棒控制算法。通过对比实验,验证模型补偿的有效性和控制算法所能实现的优越控制性能。
第四章,首次分析了直线电机高频动力学的存在因素和物理特性,找出因平台旋转而产生的主导高频模态,并建立其数学模型。进行频域系统辨识,了解刚性动力学的有效频率范围和高频柔性模态的存在频段,验证所提的高频动力学模型的有效性。根据已知的高频动力学,通过实验和理论分析,讨论了高频动力学、控制器参数和系统闭环频宽之间的关系,提出了控制器参数选择的优化准则,在现有的刚性动力学控制器框架下实现最优的控制性能。
第五章,为了进一步提升系统的闭环频宽,高频动力学被引入到控制器的结构设计中。首先尝试了简单的零极相消技术,消减主导柔性模态的影响,故而提高了系统的闭环频宽上限。对于已知的非线性刚性动力学和高频柔性模态,打破原有的刚性动力学控制器设计结构,提出新型的基于μ-synthesis的自适应鲁棒控制策略。其自适应前馈环节可以拥有精确的在线参数估计和有效的非线性模型补偿,并把轨迹跟踪问题转化为镇定问题以便于μ-synthesis鲁棒反馈控制器设计；由于使用高频动力学作为名义模型的一部分,设计的μ-synthesis反馈环节可以达到更高的闭环频宽和更强的抗干扰能力。通过对比实验,验证了该方法所具有的优越控制性能。
第六章,归纳总结了本论文的主要工作,阐述研究结论和创新点,并对直线电机精密运动控制的研究进行了展望。
Modern mechatronic systems, such as advanced machine tools, microelectronic and semicon-ductor manufacturing equipment, optical inspection systems and dispensing processes systems often require high-speed and high-accuracy linear movement. Direct-drive linear motors eliminate gear related mechanical transmission problems such as backlash, large friction and inertial loads, and structural flexibility, and thus, have the potential of achieving higher speed and higher accuracy. But to realize its high-speed/high-accuracy potential, some control issues have to be solved:sig-nificant model uncertainties, parameter uncertainties and external disturbances; various nonlinear dynamics; high-frequency flexible modes. Thus, this dissertation focuses on major nonlinearities and flexibilities of linear motor driven systems. Physical modeling of cogging force, dynamic fric-tion and nonlinear electromagnetic field effect are developed and validated by the system identifica-tions in time domain. These novel nonlinear dynamical models capture the physical characteristics more accurately and also consider their complexity for compensation control design. The high performance adaptive robust control (ARC) technique is integrated with the effective nonlinearity compensations. Theoretically, these proposed control algorithms guarantee excellent transient and steady-state performance. And comparative experimental results also show the further improved tracking performance of the effective nonlinearity compensations. The physical cause of major high-frequency dynamics is identified. The corresponding mathematical model is then built, and verified by the system identification in frequency domain. With the knowledge of high-frequency dynamics, the optimal tuning guidelines of control gains are developed to maximize the tracking performance of the previously proposed control algorithms. To further increase the achievable close-loop bandwidth, the high-frequency dynamics neglected in the existing research are then ex-plicitly taken into consideration in the design of controllers. Specifically, the simple pole/zero can-celation technique is first incorporated into the control design to attenuate the major flexible mode effect. A novel μ-synthesis based adaptive robust control strategy is then developed. The proposed control algorithm uses adaptive model compensation having accurate on-line parameter estimation to effectively deal with various nonlinearity effect and to transform the difficult trajectory tracking control problem into a robust stabilization problem. The well-developed μ-synthesis based linear robust control technique is then employed to deal with the robust control issue associated with the high-frequency dynamics explicitly to achieve higher close-loop bandwidth and better disturbance rejection in the feedback control loop.
The dissertation consists of the following six chapters:
In Chapter1, the research background and history of precision motion control of linear motor driven systems are detailed. Specifically, the control issues associated with the high-speed/high-accuracy movement of linear motor drive systems are first pointed out, followed by a comprehen-sive literature survey of linear motor driven systems, including existing control methods dealing with nonlinearities such as cogging force, friction and nonlinear electromagnetic field effect and high-frequency flexible modes. A brief summary of the dissertation's contributions and significance is subsequently given.
In Chapter2, the hardware equipment and their specifications used in the experiments are introduced. Rigid-body dynamics of linear motor drive systems are presented with a focus on better modeling of major nonlinearities inherited to the linear motor drive systems. Specifically, an aperiodic cogging force model is built by using B-spline functions, which captures both periodic and aperiodic characteristics of cogging force. The modified LuGre dynamic friction model is proposed to solve the passive problem and the observer instability problem of the existing ones. A third order polynomial model is developed to precisely describe the nonlinear electromagnetic field effect as well. All the proposed models not only provide a more accurate description of the nonlinearity under study, but also can be easily used in the subsequent controller design for more effective on-line model compensation. The system identifications in time domain are then carried out, validating the effectiveness of all proposed models.
In Chapter3, based on the rigid-body dynamics of linear motor drive systems, the concepts and various implementations of adaptive robust control (ARC) strategy are introduced. Theoretically, the presented ARC can achieve a guaranteed transient and steady-state performance in the pres-ence of both parametric uncertainties and model uncertainties, as well as zero steady-state tracking error when subjected to parametric uncertainties only. The adaptive robust control technique is subsequently integrated with more effective compensations of various nonlinearities, including the adaptive robust control with aperiodic cogging force compensation, the adaptive robust control with dynamic friction compensation using modified LuGre model, the adaptive robust control with elec-tromagnetic nonlinearity compensation, and the adaptive robust control with integrated compen-sation of all major nonlinearities of linear motor drive systems. Comparative experimental results show the effectiveness of the proposed nonlinearity compensations and the excellent performance of the proposed control algorithms.
In Chapter4, physical causes of the high-frequency dynamics of linear motor drive systems are analyzed. The stage rotation is found to be the cause of the major flexible mode of linear motor driven systems. The corresponding mathematical model is then built to capture this ef-fect and system identifications in frequency domain are carried out to verify the effectiveness of the proposed model on the high-frequency dynamics of linear motors. With the knowledge of these high-frequency dynamics, the relationship among high-frequency dynamics, control gains and close-loop bandwidth is established, and the optimal tuning guidelines on control gains are de-veloped to maximize the tracking performance of the rigid-body dynamics based control algorithms of linear motors in implementation.
In Chapter5, to further increase the achievable close-loop bandwidth, the high-frequency dy-namics are explicitly taken into consideration in the design of controllers. Specifically, the simple pole/zero cancelation of known high-frequency dynamics is first incorporated to attenuate the ma-jor flexible mode effect so that the upper bound on the achievable close-loop bandwidth of the rigid-body dynamics based control algorithms can be raised. With the knowledge of nonlinear rigid-body dynamics and the structure of high-frequency flexible modes, a novel μ-synthesis based adaptive robust control algorithm is then proposed. Its adaptive feedforward loop has accurate on-line parameter estimation and effective nonlinearity compensation, which makes it possible to convert the difficult tracking control problem into a robust stabilization problem. By treating ma-jor high-frequency dynamics as a part of the nominal model, the μ-synthesis feedback loop of the proposed novel ARC strategy can achieve higher close-loop bandwidth and better disturbance re-jection. Comparative experiments are conducted and the results show the better performance of the proposed control algorithms over existing ones.
In Chapter6, the research work of this dissertation is summarized. Major innovations are highlighted, and some future research directions are discussed.
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