双连杆柔性机械臂的主动控制研究
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摘要
随着科学技术的发展,柔性构件在工程机构中大量使用。另外,机构运行速度加快,运行精度的要求也越来越高,由此构成所谓的柔性多体动力学系统或刚柔耦合动力学系统,柔性机械臂是这类系统的典型代表之一。柔性机械臂在作大范围刚体运动的同时,也将产生自身的小变形弹性振动,这两种运动相互耦合和相互影响,系统的动力学行为较为复杂,具有强非线性、强耦合、时变等特点。对于单杆柔性机械臂,系统中只存在单一的刚柔耦合,即系统大范围运动与柔性手臂弹性振动之间的耦合,动力学建模与控制相对来讲较为容易。而对于多杆柔性机械臂,系统中不但存在刚柔耦合,还存在各个柔性杆件弹性振动之间的柔柔耦合,动力学建模与控制难度较大。因为柔性机械臂在航空航天、机器人等许多高科技领域有着强烈的工程应用背景,因此对其动力学建模与控制的研究具有重要的理论意义和实际应用价值。
另一方面,压电材料由于具有良好的机电耦合特性,既可以作为传感器,也可以作为作动器,在结构振动主动控制领域得到了广泛应用。压电作动器通过粘贴或填埋方式与结构结为一体,因此非常适用于存在大范围运动的柔性构件的振动抑制。
本文在国家自然科学基金(编号:10772112,10472065)、教育部重点项目(编号:107043)、教育部博士点基金(编号:20070248032)和上海市教委科研重点项目(编号:09ZZ17)的资助下,开展压电双杆柔性机械臂的动力学建模与主动控制的研究,主要内容和成果总结如下:
(1)在大量阅读文献的基础上,较为全面地综述了柔性机械臂的研究进展。
(2)研究了压电双杆柔性机械臂的动力学建模问题,并且进行了系统大范围已知和未知两种情况下的动力学仿真,通过仿真揭示对机械臂系统进行主动控制的必要性。该部分的工作是为后续主动控制的设计提供模型保证。
(3)研究了双杆柔性机械臂的线性最优控制问题。研究中,只采用两个杆件关节扭矩进行系统的位置主动控制,不采用压电作动器。研究结果表明:关节扭矩控制律能够使得系统到达指定位置,并可抑制柔性杆件的弹性振动,但是在系统到达指定位置的时间指标上效果欠佳。
(4)研究了压电柔性双杆机械臂的非线性控制问题,进行了压电控制律和关节扭矩控制律的综合设计。关节扭矩用于保证系统的大范围刚体运动,压电作动器用于控制柔性杆件的弹性变形,综合设计这两个控制律,以实现系统的轨迹跟踪与振动控制。研究结果表明:非线性控制方法不但可以使得系统跟踪预期的理想轨迹,柔性杆件的弹性振动可以同时得到抑制,而且在到达时间指标上具有良好性能。
(5)考虑到PD控制方法在实际工程中的大量使用,研究了压电柔性双杆机械臂的模糊PD控制问题。研究中,使用模糊控制器对PD控制的控制参数进行在线调整,形成专家模糊PD控制器,并且与常规PD控制方法的效果进行了对比研究。研究结果表明:在PD控制的增益参数取值较好时,常规PD控制方法与模糊PD控制方法皆可以取得良好的控制效果,但是模糊PD控制方法的控制代价小于常规PD控制方法;当PD控制增益参数取值不理想时,常规PD控制方法的控制效果较差,有可能导致系统响应出现发散,而模糊PD控制方法仍能取得满意的控制效果。模糊控制器能够有效地在线调节PD控制中的增益参数,使之达到良好的控制效果,减少了常规PD控制方法繁冗的参数调节。
柔性机械臂的动力学与控制问题是一个极具挑战性的研究课题,许多方面还需要进一步深入研究与探讨,因此在论文的最后,对本文的研究工作和成果进行了全面总结,对未来的研究问题进行了展望。
With the development of science and technology, lightweight and flexible components have been widely used in mechanism. Meanwhile, the requirements on operating speed and precision of mechanism become higher and higher. Research in this area comes to the so-called flexible multibody dynamic system or rigid-flexible coupling dynamic system. The flexible manipulator is a typical application in this area. When the manipulator moves with a large-scale movement, elastic vibration of flexible arm will occur synchronously. These two motions are coupled and affect each other, which results in the complicated dynamics of system such as strong nonlinearity and coupling etc. For the flexible one-link manipulator, single rigid-flexible coupling exists in the system, i.e., the coupling of large motion of the system with the elastic vibration of flexible arm, so the problem of dynamic modeling and control for the system is relatively easier. But for the flexible multi-link manipulator, the system exist not only the rigid-flexible coupling but also the flexible-flexible coupling between elastic vibrations of each flexible arms, so the work of modeling and control for the system is very difficult. Since flexible manipulator system has lots of applications in high tech engineering areas such as aerospace, aviation and robot, it is of importance, both theoretically and practically, to study its dynamic modeling and active control method.
On the other hand, with good mechanical-electric coupling quality, piezoelectric material can make both a sensor and an actuator, which explains its wide application in active vibration control systems. Piezoelectric actuator can make part of a component by means of either adhering or embedding, which is useful for vibration control of flexible components with large-scale movement.
This dissertation studies the dynamic modeling and active control of flexible two-link manipulator. This research was funded by the National Natural Science Foundation of China (Grant Nos. 10772112 and 10472065), the Key Project of Ministry of Education of China (Grant No. 107043), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20070248032) and the Key Project of Education Committee of Shanghai (Grant No. 09ZZ17). The main research and achievements are as follows:
(1) The dynamic modeling theories and vibration control of flexible manipulators are comprehensively reviewed. The research extent and contents of this dissertation are put forward.
(2) The dynamic modeling of flexible two-link manipulator is studied. Numerical simulations with known and unknown large motion of the system are carried out to demonstrate the necessity of active control for the system. The study in this section provides dynamic model for the following control studies for the system.
(3) This dissertation discusses the linear optimal control of flexible manipulator, where the two joint torques are only used to drive the system and PZT actuator is not used. Simulation results indicate that, with linear optimal controller, the flexible arm can reach an expected position with suppressed vibration, however the time taken to position is longer than expected.
(4) Nonlinear control strategy of the flexible manipulator is studied in this dissertation. The PZT controller and the joint controller are synthetically designed, where the joint controller is used to guarantee the large motion of the system and the PZT controller is used to control the vibration of the two flexible arms. Simulation results indicate that, nonlinear control strategy works well with precise positioning, suppression of vibration and time control.
(5) Due to the wide applications of PD control strategy in practical engineering, fuzzy PD control method is studied for the flexible two-link manipulator in this dissertation. Fuzzy controller is used to adjust the control weighting coefficient of PD strategy to compose the expert fuzzy PD controller. The fuzzy PD controller is compared with the classical PD controller. Simulation results indicate that, when the control weighting coefficient is better chosen, the classical PD controller and the fuzzy PD controller can both achieve better control effectiveness, but the control cost of the classical PD controller is larger than that of the fuzzy PD controller. When the control weighting coefficient is worse chosen, the control effectiveness of the classical PD controller becomes worse and instability of control system may possibly occur, whereas the fuzzy PD controller may also achieve a better control effectiveness. This indicates that the fuzzy controller may effectively adjust the control weighting coefficient of PD strategy to obtain a better control effectiveness, it may reduce the parameter adjusting work using the classical PD strategy.
The topic of dynamic modeling and control of the piezoelectric flexible manipulator is challenging both in mechanics and in control engineering, where many aspects need further study and more efforts. At conclusion, a summary of work done in this dissertation is given and some problems of interest are also brought forward for future research.
另一方面,压电材料由于具有良好的机电耦合特性,既可以作为传感器,也可以作为作动器,在结构振动主动控制领域得到了广泛应用。压电作动器通过粘贴或填埋方式与结构结为一体,因此非常适用于存在大范围运动的柔性构件的振动抑制。
本文在国家自然科学基金(编号:10772112,10472065)、教育部重点项目(编号:107043)、教育部博士点基金(编号:20070248032)和上海市教委科研重点项目(编号:09ZZ17)的资助下,开展压电双杆柔性机械臂的动力学建模与主动控制的研究,主要内容和成果总结如下:
(1)在大量阅读文献的基础上,较为全面地综述了柔性机械臂的研究进展。
(2)研究了压电双杆柔性机械臂的动力学建模问题,并且进行了系统大范围已知和未知两种情况下的动力学仿真,通过仿真揭示对机械臂系统进行主动控制的必要性。该部分的工作是为后续主动控制的设计提供模型保证。
(3)研究了双杆柔性机械臂的线性最优控制问题。研究中,只采用两个杆件关节扭矩进行系统的位置主动控制,不采用压电作动器。研究结果表明:关节扭矩控制律能够使得系统到达指定位置,并可抑制柔性杆件的弹性振动,但是在系统到达指定位置的时间指标上效果欠佳。
(4)研究了压电柔性双杆机械臂的非线性控制问题,进行了压电控制律和关节扭矩控制律的综合设计。关节扭矩用于保证系统的大范围刚体运动,压电作动器用于控制柔性杆件的弹性变形,综合设计这两个控制律,以实现系统的轨迹跟踪与振动控制。研究结果表明:非线性控制方法不但可以使得系统跟踪预期的理想轨迹,柔性杆件的弹性振动可以同时得到抑制,而且在到达时间指标上具有良好性能。
(5)考虑到PD控制方法在实际工程中的大量使用,研究了压电柔性双杆机械臂的模糊PD控制问题。研究中,使用模糊控制器对PD控制的控制参数进行在线调整,形成专家模糊PD控制器,并且与常规PD控制方法的效果进行了对比研究。研究结果表明:在PD控制的增益参数取值较好时,常规PD控制方法与模糊PD控制方法皆可以取得良好的控制效果,但是模糊PD控制方法的控制代价小于常规PD控制方法;当PD控制增益参数取值不理想时,常规PD控制方法的控制效果较差,有可能导致系统响应出现发散,而模糊PD控制方法仍能取得满意的控制效果。模糊控制器能够有效地在线调节PD控制中的增益参数,使之达到良好的控制效果,减少了常规PD控制方法繁冗的参数调节。
柔性机械臂的动力学与控制问题是一个极具挑战性的研究课题,许多方面还需要进一步深入研究与探讨,因此在论文的最后,对本文的研究工作和成果进行了全面总结,对未来的研究问题进行了展望。
With the development of science and technology, lightweight and flexible components have been widely used in mechanism. Meanwhile, the requirements on operating speed and precision of mechanism become higher and higher. Research in this area comes to the so-called flexible multibody dynamic system or rigid-flexible coupling dynamic system. The flexible manipulator is a typical application in this area. When the manipulator moves with a large-scale movement, elastic vibration of flexible arm will occur synchronously. These two motions are coupled and affect each other, which results in the complicated dynamics of system such as strong nonlinearity and coupling etc. For the flexible one-link manipulator, single rigid-flexible coupling exists in the system, i.e., the coupling of large motion of the system with the elastic vibration of flexible arm, so the problem of dynamic modeling and control for the system is relatively easier. But for the flexible multi-link manipulator, the system exist not only the rigid-flexible coupling but also the flexible-flexible coupling between elastic vibrations of each flexible arms, so the work of modeling and control for the system is very difficult. Since flexible manipulator system has lots of applications in high tech engineering areas such as aerospace, aviation and robot, it is of importance, both theoretically and practically, to study its dynamic modeling and active control method.
On the other hand, with good mechanical-electric coupling quality, piezoelectric material can make both a sensor and an actuator, which explains its wide application in active vibration control systems. Piezoelectric actuator can make part of a component by means of either adhering or embedding, which is useful for vibration control of flexible components with large-scale movement.
This dissertation studies the dynamic modeling and active control of flexible two-link manipulator. This research was funded by the National Natural Science Foundation of China (Grant Nos. 10772112 and 10472065), the Key Project of Ministry of Education of China (Grant No. 107043), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20070248032) and the Key Project of Education Committee of Shanghai (Grant No. 09ZZ17). The main research and achievements are as follows:
(1) The dynamic modeling theories and vibration control of flexible manipulators are comprehensively reviewed. The research extent and contents of this dissertation are put forward.
(2) The dynamic modeling of flexible two-link manipulator is studied. Numerical simulations with known and unknown large motion of the system are carried out to demonstrate the necessity of active control for the system. The study in this section provides dynamic model for the following control studies for the system.
(3) This dissertation discusses the linear optimal control of flexible manipulator, where the two joint torques are only used to drive the system and PZT actuator is not used. Simulation results indicate that, with linear optimal controller, the flexible arm can reach an expected position with suppressed vibration, however the time taken to position is longer than expected.
(4) Nonlinear control strategy of the flexible manipulator is studied in this dissertation. The PZT controller and the joint controller are synthetically designed, where the joint controller is used to guarantee the large motion of the system and the PZT controller is used to control the vibration of the two flexible arms. Simulation results indicate that, nonlinear control strategy works well with precise positioning, suppression of vibration and time control.
(5) Due to the wide applications of PD control strategy in practical engineering, fuzzy PD control method is studied for the flexible two-link manipulator in this dissertation. Fuzzy controller is used to adjust the control weighting coefficient of PD strategy to compose the expert fuzzy PD controller. The fuzzy PD controller is compared with the classical PD controller. Simulation results indicate that, when the control weighting coefficient is better chosen, the classical PD controller and the fuzzy PD controller can both achieve better control effectiveness, but the control cost of the classical PD controller is larger than that of the fuzzy PD controller. When the control weighting coefficient is worse chosen, the control effectiveness of the classical PD controller becomes worse and instability of control system may possibly occur, whereas the fuzzy PD controller may also achieve a better control effectiveness. This indicates that the fuzzy controller may effectively adjust the control weighting coefficient of PD strategy to obtain a better control effectiveness, it may reduce the parameter adjusting work using the classical PD strategy.
The topic of dynamic modeling and control of the piezoelectric flexible manipulator is challenging both in mechanics and in control engineering, where many aspects need further study and more efforts. At conclusion, a summary of work done in this dissertation is given and some problems of interest are also brought forward for future research.
引文
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