精密指向机构非线性动力学建模与测控问题研究
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摘要
指向机构是一种回转型机电运动控制装置，在侦察、预警、制导、火控和通信等武器装备中得到大量应用。装备技术的飞速发展，对指向机构提出了越来越高的精度要求和轻量化要求。摩擦、质量不平衡、模态等因素已成为影响轻量化指向机构精度提高的关键因素，对这些因素的定量化分析建模，精确测量和补偿控制已经成为精密指向机构设计面临的关键问题。本文以提高指向机构控制精度为目标，围绕摩擦、质量不平衡、模态等影响因素，重点在非线性与模态参数时变性建模、关键参数辨识、鲁棒抗扰控制等方面开展工作，提出了较为完善、实用的指向机构非线性时变系统建模与测控方法。
论文的研究工作包含以下几个部分：
1．为了掌握摩擦、质量不平衡、模态等因素对指向机构控制性能的影响，进行了非线性动力学建模研究。依据两轴指向机构的动力学方程组，分析了机构的控制原理，基本掌握了摩擦、质量不平衡和模态影响控制性能的机理。以实现指向机构的精密测控为目的，对摩擦、模态的建模进行了深入研究。通过对轴承、动密封这两个关键运动副摩擦机理的研究，得到了摩擦力矩的模型描述。应用有限元方法，得到了指向机构的线性定常模态模型。
2．为了在机构制造装配阶段对摩擦、质量不平衡等非线性因素进行有效的工艺质量控制，针对指向机构制造装配过程对定量化性能检测的需要，研究了惯量、不平衡质量、摩擦等关键非线性动力学参数的精确测量和辨识方法。建立了指向机构的状态扩展离散动力学模型，分析比较了瞬时转速信号估计的三种数值微分算法，在此基础上，考虑工程实现中的机构运动的约束条件，综合应用最小二乘方法、非线性状态观测与控制方法提出了一种指向机构关键非线性模型参数的无偏辨识方法，经过实验验证，采用所研究的方法可以有效提高惯量、阻尼、摩擦和质量不平衡非线性动力学参数的测量和辨识精度。
3．在指向机构轻量化的要求下，结构模态特性对动态精度的影响已不容忽视，为此，研究了负载变化条件下模态参数变化模型的建模与辨识方法。分析了负载惯量变化对结构模态参数的影响机理，应用参数变化模型建模技术建立了指向机构的线性化模态参数变化模型。综合应用非线性最小二乘优化和主成分分析理论，提出了一种线性化模态参数变化模型的辨识方法。为轻量化、高动态、高精度指向机构的结构建模与分析提供了一种新的思路。
4．从控制的角度，摩擦、质量不平衡及模态变化都会以扰动的形式影响指向机构的控制精度。论文采用扰动观测技术对扰动特性进行了研究，分析和比较了DOB扰动观测器、状态扩展Kalman滤波器和时滞扰动观测器三种扰动观测技术的设计要点和性能特点：在设计方面，DOB扰动观测器的鲁棒稳定性可以应用非结构化不确定模型进行有效分析，与另外两种观测策略相比，其鲁棒性设计更加简单易行；在性能方面，状态扩展Kalman滤波器在干扰抑制能力、动态性和无偏性等方面的综合性能优于另外两种扰动观测器策略，但其鲁棒性设计方法尚不完善，有待进一步研究。以上比较分析为指向机构非线性控制方案的确定提供参考。
5．针对模型参数不确定性以及摩擦、质量不平衡等非线性扰动对控制精度的影响，研究了指向机构的非线性控制方法。建立了指向机构的参数化不确定模型。分析了摩擦力矩信号瞬时频率特性，定义了摩擦信号的瞬时功率大小度量以及伺服系统对信号瞬时功率的增益，用于估计摩擦引起的伺服轴尖峰跟踪误差，分析评价伺服回路的抗扰性能。基于以上系统分析方法，综合运用奇异值控制技术和DOB扰动观测技术，提出了一种双回路鲁棒跟踪伺服控制策略。通过改进奇异值控制器设计方法，使奇异值位置伺服回路包含两个积分器，能够有效抑制稳态跟踪误差；通过推导双回路综合的鲁棒稳定条件，得到了DOB回路的设计方法，能够有效提高双回路伺服控制的鲁棒稳定性。所提出的控制器设计方法为实现指向机构非线性伺服控制提供了一种较为有效的方案。
The precise pointing mechanism is a kind of mechatronic rotary motion controldevice, which has been widely applied in aspects including the reconnaissance,prewarning, guidance, fire control, communication, and other equipments. With therapid development of the equipment technology, the precision and lightweightrequirements on the pointing mechanism are higher and higher. The factors includingthe friction, mass unbalance, and modal are essential to the improvements of theprecision of the lightweight pointing mechanism; and, how to perform modeling to suchfactors, achieve the key parameters testing, and control arising positioning errors havebecome key issues in the research on the design technology. In the paper, the authortakes the enhancement of the pointing mechanism control precision as the objective andfocuses on the variability modeling, key parameter identification, and robustanti-disturbance control in case of nonlinearity and modality specific to the influentialfactors including the friction, mass unbalance, and modal, and puts forward the perfectand practical variability modeling, measurement and control methods in case ofnonlinear pointing mechanism.
The study work of the paper includes following parts:
1. In order to master the impact of the factors including the friction, massunbalance, and modality on the control performance of the pointing mechanism, thenonlinearity dynamics modeling is studied and researched. In addition, based on thedynamics equation set of the two-axis pointing mechanism, its control principles areanalyzed, thus comprehending the mechanism of the friction, mass unbalance, andmodality impacting the control performance. In order to achieve precise measurementand control of the pointing mechanism, further study is performed to the friction andmodality modeling. By means of study on key kinematic pair friction mechanismsincluding the bearing and motive seal, the friction moment model description isobtained. Also, through research on the finite element method, the constant parametermodel of the modality is also obtained.
2. in order to perform effective process quality control to the friction, massunbalance, and other nonlinear factors during the mechanism fabrication andassembling stage, the exact identification methods for the inertia, unbalance mass,friction, and other key nonlinear dynamics parameters are studied and researched basedon the demands of the fabrication and assembling performance detection of the pointingmechanism. In addition, the state expansion and discrete dynamics model is establishedfor the pointing mechanism and three kinds of numerical differentiation algorithms for the instantaneous speed signal estimation are also analyzed and compared; on such basis,one unbiased identification method for the key nonlinearity model parameter of thepointing mechanism is proposed by means of the method of least squares and thenonlinear state observation and control methods and taking the mechanism restrictionsin the project into consideration. In a word, the applied research method can effectivelyimprove the identification precision of the inertia, damp, friction, mass unbalance, andnonlinear dynamics parameter.
3. Requested by the lightweight demand of the pointing mechanism, the impact ofthe structure modality characteristics on the precision can’t be ignored. On this account,the author studies and researches the modeling and identification method for themodality parameter variation model under changeable loads. In addition, the author alsoanalyzes the influential mechanism of the load inertia changes on the structure modalityparameter; furthermore, he applies the parameter variation model modeling technologyto establish the linear modality parameter variation model for the pointing mechanism.Also, applying the nonlinear least square optimization technology and the principalcomponent analysis technology, the author raises a kind of identification method for thelinear modality parameter variation model. In a word, the author offers a new thoughtfor the structure modeling and analysis of the high precision lightweight pointingmechanism.
4. From the control view, the changes of the friction, mass unbalance, and modalitywill impact the control precision of the pointing mechanism in form of disturbance. Theauthor performs studies and researches to the disturbance characteristics by means ofthe disturbance observation technology; summarizes and analyzes the design essentialsof three disturbance observation technologies including the DOB disturbance observer,state expansion Kalman filter, and time delay disturbance observer as well as analyzestheir own advantages and disadvantages from four aspects of the instantaneity,disturbance annihilation performance, noise annihilation performance, and steadyconvergence of the observation results. In a word, the author forms three schemes forthe disturbance compensation control of the pointing mechanism as well as offer ideasfor the subsequent design research on the nonlinear controller of the mechanism.
5. Considering the impact of the model parameter uncertainty and the transientcharacteristics of the friction moment on the control precision, the author studies andresearches a kind of robust and precise servo control design method for the pointingmechanism. In addition, the parameterization uncertainty model is also established forthe pointing mechanism. Moreover, the author also analyzes the instantaneousfrequency characteristics of the friction moment signal; defines the measure of theinstantaneous power of the friction signal and the gains of the servo system to the instantaneous power of the signal, so as to estimate the peak tracing error of the servoaxis arising from the friction and analyze the anti-interference performance of the servocircuit. Based on the above systematical analysis methods as well as applying thesingular value control technology and DOB disturbance observation technology, theauthor proposes a kind of dual-circuit robust tracking servo control strategy. With theimproved singular value controller design method, the singular value position servocircuit includes two integrators; thus, the steady tracking error can be effectivelyannihilated. Furthermore, the author also deduces the comprehensive robust steadyconditions for the dual-circuit as well as gives the DOB circuit design method on suchbasis. In a word, all the proposed control strategies can effectively improve the servoprecision of the pointing mechanism and the circuit robustness.
论文的研究工作包含以下几个部分：
1．为了掌握摩擦、质量不平衡、模态等因素对指向机构控制性能的影响，进行了非线性动力学建模研究。依据两轴指向机构的动力学方程组，分析了机构的控制原理，基本掌握了摩擦、质量不平衡和模态影响控制性能的机理。以实现指向机构的精密测控为目的，对摩擦、模态的建模进行了深入研究。通过对轴承、动密封这两个关键运动副摩擦机理的研究，得到了摩擦力矩的模型描述。应用有限元方法，得到了指向机构的线性定常模态模型。
2．为了在机构制造装配阶段对摩擦、质量不平衡等非线性因素进行有效的工艺质量控制，针对指向机构制造装配过程对定量化性能检测的需要，研究了惯量、不平衡质量、摩擦等关键非线性动力学参数的精确测量和辨识方法。建立了指向机构的状态扩展离散动力学模型，分析比较了瞬时转速信号估计的三种数值微分算法，在此基础上，考虑工程实现中的机构运动的约束条件，综合应用最小二乘方法、非线性状态观测与控制方法提出了一种指向机构关键非线性模型参数的无偏辨识方法，经过实验验证，采用所研究的方法可以有效提高惯量、阻尼、摩擦和质量不平衡非线性动力学参数的测量和辨识精度。
3．在指向机构轻量化的要求下，结构模态特性对动态精度的影响已不容忽视，为此，研究了负载变化条件下模态参数变化模型的建模与辨识方法。分析了负载惯量变化对结构模态参数的影响机理，应用参数变化模型建模技术建立了指向机构的线性化模态参数变化模型。综合应用非线性最小二乘优化和主成分分析理论，提出了一种线性化模态参数变化模型的辨识方法。为轻量化、高动态、高精度指向机构的结构建模与分析提供了一种新的思路。
4．从控制的角度，摩擦、质量不平衡及模态变化都会以扰动的形式影响指向机构的控制精度。论文采用扰动观测技术对扰动特性进行了研究，分析和比较了DOB扰动观测器、状态扩展Kalman滤波器和时滞扰动观测器三种扰动观测技术的设计要点和性能特点：在设计方面，DOB扰动观测器的鲁棒稳定性可以应用非结构化不确定模型进行有效分析，与另外两种观测策略相比，其鲁棒性设计更加简单易行；在性能方面，状态扩展Kalman滤波器在干扰抑制能力、动态性和无偏性等方面的综合性能优于另外两种扰动观测器策略，但其鲁棒性设计方法尚不完善，有待进一步研究。以上比较分析为指向机构非线性控制方案的确定提供参考。
5．针对模型参数不确定性以及摩擦、质量不平衡等非线性扰动对控制精度的影响，研究了指向机构的非线性控制方法。建立了指向机构的参数化不确定模型。分析了摩擦力矩信号瞬时频率特性，定义了摩擦信号的瞬时功率大小度量以及伺服系统对信号瞬时功率的增益，用于估计摩擦引起的伺服轴尖峰跟踪误差，分析评价伺服回路的抗扰性能。基于以上系统分析方法，综合运用奇异值控制技术和DOB扰动观测技术，提出了一种双回路鲁棒跟踪伺服控制策略。通过改进奇异值控制器设计方法，使奇异值位置伺服回路包含两个积分器，能够有效抑制稳态跟踪误差；通过推导双回路综合的鲁棒稳定条件，得到了DOB回路的设计方法，能够有效提高双回路伺服控制的鲁棒稳定性。所提出的控制器设计方法为实现指向机构非线性伺服控制提供了一种较为有效的方案。
The precise pointing mechanism is a kind of mechatronic rotary motion controldevice, which has been widely applied in aspects including the reconnaissance,prewarning, guidance, fire control, communication, and other equipments. With therapid development of the equipment technology, the precision and lightweightrequirements on the pointing mechanism are higher and higher. The factors includingthe friction, mass unbalance, and modal are essential to the improvements of theprecision of the lightweight pointing mechanism; and, how to perform modeling to suchfactors, achieve the key parameters testing, and control arising positioning errors havebecome key issues in the research on the design technology. In the paper, the authortakes the enhancement of the pointing mechanism control precision as the objective andfocuses on the variability modeling, key parameter identification, and robustanti-disturbance control in case of nonlinearity and modality specific to the influentialfactors including the friction, mass unbalance, and modal, and puts forward the perfectand practical variability modeling, measurement and control methods in case ofnonlinear pointing mechanism.
The study work of the paper includes following parts:
1. In order to master the impact of the factors including the friction, massunbalance, and modality on the control performance of the pointing mechanism, thenonlinearity dynamics modeling is studied and researched. In addition, based on thedynamics equation set of the two-axis pointing mechanism, its control principles areanalyzed, thus comprehending the mechanism of the friction, mass unbalance, andmodality impacting the control performance. In order to achieve precise measurementand control of the pointing mechanism, further study is performed to the friction andmodality modeling. By means of study on key kinematic pair friction mechanismsincluding the bearing and motive seal, the friction moment model description isobtained. Also, through research on the finite element method, the constant parametermodel of the modality is also obtained.
2. in order to perform effective process quality control to the friction, massunbalance, and other nonlinear factors during the mechanism fabrication andassembling stage, the exact identification methods for the inertia, unbalance mass,friction, and other key nonlinear dynamics parameters are studied and researched basedon the demands of the fabrication and assembling performance detection of the pointingmechanism. In addition, the state expansion and discrete dynamics model is establishedfor the pointing mechanism and three kinds of numerical differentiation algorithms for the instantaneous speed signal estimation are also analyzed and compared; on such basis,one unbiased identification method for the key nonlinearity model parameter of thepointing mechanism is proposed by means of the method of least squares and thenonlinear state observation and control methods and taking the mechanism restrictionsin the project into consideration. In a word, the applied research method can effectivelyimprove the identification precision of the inertia, damp, friction, mass unbalance, andnonlinear dynamics parameter.
3. Requested by the lightweight demand of the pointing mechanism, the impact ofthe structure modality characteristics on the precision can’t be ignored. On this account,the author studies and researches the modeling and identification method for themodality parameter variation model under changeable loads. In addition, the author alsoanalyzes the influential mechanism of the load inertia changes on the structure modalityparameter; furthermore, he applies the parameter variation model modeling technologyto establish the linear modality parameter variation model for the pointing mechanism.Also, applying the nonlinear least square optimization technology and the principalcomponent analysis technology, the author raises a kind of identification method for thelinear modality parameter variation model. In a word, the author offers a new thoughtfor the structure modeling and analysis of the high precision lightweight pointingmechanism.
4. From the control view, the changes of the friction, mass unbalance, and modalitywill impact the control precision of the pointing mechanism in form of disturbance. Theauthor performs studies and researches to the disturbance characteristics by means ofthe disturbance observation technology; summarizes and analyzes the design essentialsof three disturbance observation technologies including the DOB disturbance observer,state expansion Kalman filter, and time delay disturbance observer as well as analyzestheir own advantages and disadvantages from four aspects of the instantaneity,disturbance annihilation performance, noise annihilation performance, and steadyconvergence of the observation results. In a word, the author forms three schemes forthe disturbance compensation control of the pointing mechanism as well as offer ideasfor the subsequent design research on the nonlinear controller of the mechanism.
5. Considering the impact of the model parameter uncertainty and the transientcharacteristics of the friction moment on the control precision, the author studies andresearches a kind of robust and precise servo control design method for the pointingmechanism. In addition, the parameterization uncertainty model is also established forthe pointing mechanism. Moreover, the author also analyzes the instantaneousfrequency characteristics of the friction moment signal; defines the measure of theinstantaneous power of the friction signal and the gains of the servo system to the instantaneous power of the signal, so as to estimate the peak tracing error of the servoaxis arising from the friction and analyze the anti-interference performance of the servocircuit. Based on the above systematical analysis methods as well as applying thesingular value control technology and DOB disturbance observation technology, theauthor proposes a kind of dual-circuit robust tracking servo control strategy. With theimproved singular value controller design method, the singular value position servocircuit includes two integrators; thus, the steady tracking error can be effectivelyannihilated. Furthermore, the author also deduces the comprehensive robust steadyconditions for the dual-circuit as well as gives the DOB circuit design method on suchbasis. In a word, all the proposed control strategies can effectively improve the servoprecision of the pointing mechanism and the circuit robustness.
引文
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