平面3-RRR柔性并联机器人机构弹性动力学建模与振动主动控制研究
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摘要
轻型、高速、高加速度、高精度柔性并联机器人在诸如电子装配,精密加工与测量，航空航天领域有着巨大的应用前景。然而在外力和惯性力的作用下，其柔性构件容易发生弹性变形。那不仅影响了系统的运动精度和定位精度，而且还会因为过大的应力导致柔性杆件疲劳、损伤。为了清楚地认识柔性并联机器人的动力学特性以及柔性构件与其他柔性构件、柔性构件和刚性构件之间的耦合机理。必须对其弹性动力学模型进行深入研究。为了抑制柔性构件的弹性振动，提高柔性并联机器人的性能。必须对柔性构件弹性振动控制问题进行系统地研究。然而，对于复杂的柔性并联机器人机械系统的弹性动力学建模与振动控制研究一直是非常具有挑战性的工作。本文以平面3-RRR柔性并联机器人为研究对象，对其弹性动力学建模和振动主动控制问题进行了理论和实验研究。主要内容如下：
（1）基于有限元方法和Lagrange方程，建立了平面3-RRR柔性并联机器人的弹性动力学方程。该方程考虑了刚体运动对柔性杆弹性变形运动的影响，还考虑了弹性变形运动对刚体运动的影响。同时只考虑柔性杆的轴向变形和横向变形，忽略其剪切变形。研究了系统间的各种约束关系，包括刚体运动约束、弹性变形运动约束以及动平台动力学约束。对系统动力学特性进行了研究，包括灵敏度、频率特性、模态分析和柔性杆的动态应力。比较研究了两类（3-RRR和3-PRR）平面完全3自由度柔性并联机器人动力学特性。最后比较分析了一步法（即KED方法）和两步法求解所建立的系统刚-柔耦合动力学方程。考虑横向弹性位移引起的轴向二阶耦合变形位移，把动力刚度项引入到系统弹性动力学方程中。建立了系统的一阶近似耦合（FOAC）模型，并与传统的零阶近似耦合（ZOAC）模型进行比较。
（2）系统高速、高加速度运动产生的惯性力将使柔性连杆发生弹性变形，从而在柔性连杆内产生弹性应力。在高精度的要求下，由温度变化而产生的热应力对系统精度的影响也至关重要。本文研究了平面3-RRR柔性并联机器人系统在环境温度改变的情况下，系统动力学特性随温度变化的规律。基于哈密尔顿原理和有限元方法，建立了一致温度影响下的平面3-RRR柔性并联机器人系统热-弹性动力学方程，从定性和定量两方面研究了柔性连杆最大等效应力随温度的变化情况以及动平台和柔性杆的弹性变形位移随温度的变化情况。商用软件ANSYS13.0被用来证明所建立的动力学模型的正确性。
(3)对平面3-RRR柔性并联机器人振动主动控制进行了理论和实验研究，在理论研究方面，基于所建立的系统总的动力学方程，设计了应变率反馈控制器和最优状态反馈控制器。研究发现：两种控制器都能有效的抑制系统的残余振动。相对应变率反馈控制，最优状态反馈控制在更低的控制电压下能取得更好的控制效果。同时，粘贴一对PZT片的控制效果明显比粘贴一片更好。在实验研究方面，仅考虑被动杆柔性且在每根柔性杆上粘贴2对压电陶瓷驱动器和一片压电传感器。基于应变率反馈控制策略设计了4种控制方案，分别是3根柔性杆同时控制、仅柔性杆1施加控制、仅柔性杆2施加控制、仅柔性杆3施加控制。比较研究了4种控制方案的优劣。实验结果表明：各柔性杆单独控制只能抑制自身的弹性振动，对其他柔性杆的振动没有起到抑制作用；3根柔性杆同时控制能有效抑制各柔性杆的弹性振动。
Light, high-speed, high-acceleration, high-precision flexible parallel robots are widelyused in industry, such as in the electronic assembly industry, precision machining andmeasurement field, aerospace industry and so on. The elastic deformation of its flexiblecomponents is very likely to be caused under the external force and inertia force. Thoseelastic deformations do not only affect kinematic accuracy and positioning precision, but alsocause fatigue and damage of the flexible components because of the heavy internal stress. Inorder to clearly understand the dynamic characteristics of the flexible parallel robots and thecoupling mechanism between the flexible component and the other flexible components, theflexible component and the rigid component, its dynamic model must be deeply researched.And, in order to suppress the elastic vibration of the flexible components and improve theperformance of the flexible parallel robots, the vibration control of the flexible componentsmust be systematically investigated. However, both elastodynamic modeling and vibrationcontrolling of complex flexible parallel robots have ever been a challenging task. In this paper,elastodynamic modelling and active vibration control of planer3-RRR flexible parallel robotsare systematically analyzed and studied. The main contributions in this thesis are listed asfollows:
(1) Based on the finite element method (FEM) and Lagrange equation, elastodynamicmathematics model was established, in which the coupling influence of the elasticdeformation motion and the rigid-body motion, the axial deformation displacement and thetransverse deformation displacement of flexible beam were considered while its sheardeformation was ignored. The different constraint relationships of the system including rigidmotion constraint, elastic deformation motion constraint and dynamic constraint of themoving platform are derived. The dynamic characteristics of the system including sensitivityanalysis, frequency characteristics, model analysis and dynamic stress analysis are studied.The dynamic characteristics of planar3-RRR and3-PRR flexible parallel robots are presented.A comparative analysis of one-step method (KED method) and two-step method for solvingrigid-flexible coupling nonlinear dynamic equations is given. In consideration of the second-order coupling quantity of the axial displacement caused by the transversedisplacement of flexible beam, the first-order approximation coupling (FOAC) model ofplanar3-RRR flexible parallel robots is presented, and compared with the conventionalzero-order approximation coupling (ZOAC) model.
(2) In general, the strain and stress are caused not only by the external exciting force, butalso temperature change. The effect of temperature change on dynamic performances ofplanar3-RRR flexible parallel robots is studied in this paper. Based on the Hamilton principleand the finite element method, the general thermal-elastic coupling dynamic equations of the3-RRR systems are determined. The flexible link maximum stress and elastic displacement ofthe moving platform and the flexible links with respect to temperature changes are studiedusing qualitative and quantitative method. The commercial software ANSYS13.0is used toconfirm the validity of the theory model.
(3) The theoretical and experimental research for active vibration control of planar3-RRR flexible parallel robots. In theoretical study, both strain rate feedback controller andoptimal state feedback controller are designed based on general dynamic equations of thesystem. The simulation results reveal that two kinds of controllers can effectively suppressresidual vibration of the system. Moreover, comparing the strain rate feedback (SRF) control,the optimal state feedback control can obtain better control results in a lower control voltage.At the same time, the control result of pasting a pairs PZT film actuators is better than pastingjust one PZT film actuator. In experimental study, we only consider that passive links areflexible and each passive flexible link pastes two pairs of PZT actuator and one PZT filmsensor. Four control schemes that include three passive flexible links simultaneously control,only exert control to passive flexible link1, only exert control to passive flexible link2andonly exert control to passive flexible link3are designed based on the strain rate feedbackcontrol strategy. A comparative study is presented on four control schemes. The experimentalresults show that controlling one passive flexible link can only suppress elastic vibration itself.And when three passive flexible links simultaneously exert control, elastic vibration of allflexible links can be suppressed.
（1）基于有限元方法和Lagrange方程，建立了平面3-RRR柔性并联机器人的弹性动力学方程。该方程考虑了刚体运动对柔性杆弹性变形运动的影响，还考虑了弹性变形运动对刚体运动的影响。同时只考虑柔性杆的轴向变形和横向变形，忽略其剪切变形。研究了系统间的各种约束关系，包括刚体运动约束、弹性变形运动约束以及动平台动力学约束。对系统动力学特性进行了研究，包括灵敏度、频率特性、模态分析和柔性杆的动态应力。比较研究了两类（3-RRR和3-PRR）平面完全3自由度柔性并联机器人动力学特性。最后比较分析了一步法（即KED方法）和两步法求解所建立的系统刚-柔耦合动力学方程。考虑横向弹性位移引起的轴向二阶耦合变形位移，把动力刚度项引入到系统弹性动力学方程中。建立了系统的一阶近似耦合（FOAC）模型，并与传统的零阶近似耦合（ZOAC）模型进行比较。
（2）系统高速、高加速度运动产生的惯性力将使柔性连杆发生弹性变形，从而在柔性连杆内产生弹性应力。在高精度的要求下，由温度变化而产生的热应力对系统精度的影响也至关重要。本文研究了平面3-RRR柔性并联机器人系统在环境温度改变的情况下，系统动力学特性随温度变化的规律。基于哈密尔顿原理和有限元方法，建立了一致温度影响下的平面3-RRR柔性并联机器人系统热-弹性动力学方程，从定性和定量两方面研究了柔性连杆最大等效应力随温度的变化情况以及动平台和柔性杆的弹性变形位移随温度的变化情况。商用软件ANSYS13.0被用来证明所建立的动力学模型的正确性。
(3)对平面3-RRR柔性并联机器人振动主动控制进行了理论和实验研究，在理论研究方面，基于所建立的系统总的动力学方程，设计了应变率反馈控制器和最优状态反馈控制器。研究发现：两种控制器都能有效的抑制系统的残余振动。相对应变率反馈控制，最优状态反馈控制在更低的控制电压下能取得更好的控制效果。同时，粘贴一对PZT片的控制效果明显比粘贴一片更好。在实验研究方面，仅考虑被动杆柔性且在每根柔性杆上粘贴2对压电陶瓷驱动器和一片压电传感器。基于应变率反馈控制策略设计了4种控制方案，分别是3根柔性杆同时控制、仅柔性杆1施加控制、仅柔性杆2施加控制、仅柔性杆3施加控制。比较研究了4种控制方案的优劣。实验结果表明：各柔性杆单独控制只能抑制自身的弹性振动，对其他柔性杆的振动没有起到抑制作用；3根柔性杆同时控制能有效抑制各柔性杆的弹性振动。
Light, high-speed, high-acceleration, high-precision flexible parallel robots are widelyused in industry, such as in the electronic assembly industry, precision machining andmeasurement field, aerospace industry and so on. The elastic deformation of its flexiblecomponents is very likely to be caused under the external force and inertia force. Thoseelastic deformations do not only affect kinematic accuracy and positioning precision, but alsocause fatigue and damage of the flexible components because of the heavy internal stress. Inorder to clearly understand the dynamic characteristics of the flexible parallel robots and thecoupling mechanism between the flexible component and the other flexible components, theflexible component and the rigid component, its dynamic model must be deeply researched.And, in order to suppress the elastic vibration of the flexible components and improve theperformance of the flexible parallel robots, the vibration control of the flexible componentsmust be systematically investigated. However, both elastodynamic modeling and vibrationcontrolling of complex flexible parallel robots have ever been a challenging task. In this paper,elastodynamic modelling and active vibration control of planer3-RRR flexible parallel robotsare systematically analyzed and studied. The main contributions in this thesis are listed asfollows:
(1) Based on the finite element method (FEM) and Lagrange equation, elastodynamicmathematics model was established, in which the coupling influence of the elasticdeformation motion and the rigid-body motion, the axial deformation displacement and thetransverse deformation displacement of flexible beam were considered while its sheardeformation was ignored. The different constraint relationships of the system including rigidmotion constraint, elastic deformation motion constraint and dynamic constraint of themoving platform are derived. The dynamic characteristics of the system including sensitivityanalysis, frequency characteristics, model analysis and dynamic stress analysis are studied.The dynamic characteristics of planar3-RRR and3-PRR flexible parallel robots are presented.A comparative analysis of one-step method (KED method) and two-step method for solvingrigid-flexible coupling nonlinear dynamic equations is given. In consideration of the second-order coupling quantity of the axial displacement caused by the transversedisplacement of flexible beam, the first-order approximation coupling (FOAC) model ofplanar3-RRR flexible parallel robots is presented, and compared with the conventionalzero-order approximation coupling (ZOAC) model.
(2) In general, the strain and stress are caused not only by the external exciting force, butalso temperature change. The effect of temperature change on dynamic performances ofplanar3-RRR flexible parallel robots is studied in this paper. Based on the Hamilton principleand the finite element method, the general thermal-elastic coupling dynamic equations of the3-RRR systems are determined. The flexible link maximum stress and elastic displacement ofthe moving platform and the flexible links with respect to temperature changes are studiedusing qualitative and quantitative method. The commercial software ANSYS13.0is used toconfirm the validity of the theory model.
(3) The theoretical and experimental research for active vibration control of planar3-RRR flexible parallel robots. In theoretical study, both strain rate feedback controller andoptimal state feedback controller are designed based on general dynamic equations of thesystem. The simulation results reveal that two kinds of controllers can effectively suppressresidual vibration of the system. Moreover, comparing the strain rate feedback (SRF) control,the optimal state feedback control can obtain better control results in a lower control voltage.At the same time, the control result of pasting a pairs PZT film actuators is better than pastingjust one PZT film actuator. In experimental study, we only consider that passive links areflexible and each passive flexible link pastes two pairs of PZT actuator and one PZT filmsensor. Four control schemes that include three passive flexible links simultaneously control,only exert control to passive flexible link1, only exert control to passive flexible link2andonly exert control to passive flexible link3are designed based on the strain rate feedbackcontrol strategy. A comparative study is presented on four control schemes. The experimentalresults show that controlling one passive flexible link can only suppress elastic vibration itself.And when three passive flexible links simultaneously exert control, elastic vibration of allflexible links can be suppressed.
引文
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