一类齿隙非线性控制系统的研究
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摘要
齿隙非线性作为机械传动系统中一种最主要的非线性,广泛存在于各种机床、机器人、天文望远镜、雷达、火炮、导弹发射架、航空航天飞行器等系统中,是影响传动系统动态性能和稳态精度的重要因素。由于齿隙具有不可微的非线性特性,对它的补偿非常困难,这使得对于性能和可靠性有着极高要求的高精度传动控制系统在设计和工程实现上都面临着严峻的挑战。因此,对机械传动系统中存在的齿隙非线性展开深入研究,具有重要的理论意义和工程应用价值。
本文研究了一类齿隙非线性系统的控制问题,主要内容如下:
(1)研究了驱动系统的齿隙非线性控制问题。首先针对存在有界不确定未知参数的输入端齿隙非线性系统,在研究低阶系统的基础上,提出了具有普遍意义的基于模型跟踪的高阶系统鲁棒控制策略。随后,针对内部包含齿隙非线性的传动系统提出了一种切换控制策略,在系统主、从动部分的接触阶段采用PID控制,使系统输出跟踪期望目标;在齿隙期间采取基于时间次优的滑模控制,保证驱动部分快速通过齿隙的同时,在齿隙终了与从动部分实现无碰撞接触;并设计了基于稳定性理论的切换监督机制,保证系统在跟踪期望目标的过程中能够保持BIBO稳定。
(2)以具有代表性的双电机驱动齿隙非线性系统为对象,研究了冗余驱动系统(齿隙非线性传动系统由施加偏置力矩的两组驱动子系统和一组从动子系统组成)的基于Backstepping方法的齿隙非线性控制问题。引入标志函数重新描述齿隙非线性,应用Backstepping方法设计了基于状态反馈的控制策略;并进一步针对参数未知的控制对象,设计了基于Backstepping方法的状态反馈自适应控制策略。
(3)研究了存在未知摩擦、未知齿隙非线性的冗余驱动系统的模型参考自适应控制(MRAC)问题。以冗余驱动补偿后的近似线性系统为研究对象,针对驱动子系统参数一致的情况,设计了基于状态反馈的MRAC鲁棒控制策略;进而,针对系统中由于未得到完全补偿的齿隙非线性、变刚性系数等产生的力矩扰动,及各驱动子系统间由于参数不一致产生的同步协调问题,通过变换系统模型,设计了基于状态反馈的MRAC鲁棒同步控制策略。
(4)研究了存在未知摩擦、未知齿隙等非线性的驱动系统的神经网络控制问题。首先以单电机驱动系统为研究对象,在对齿隙非线性进行分解的基础上,采用函数链神经网络(Function Link Neural Net简称FLNN)对未知非线性进行辨识,应用Backstepping方法设计了基于FLNN的鲁棒自适应控制策略。之后,进一步研究了以双电机驱动系统为对象的冗余驱动系统的神经网络控制问题,引入同步误差反馈,设
As a main nonlinearity in mechanical drive systems, backlash exists broadly in various systems such as machine tools, robots, astronomical telescopes, radars, artilleries, missile launchers, aerocrafts etc., and is an important factor influencing the dynamic and static properties of drive systems. Due to the non-differentiable trait of backlash, its compensation is much difficult. This brings austere challenge to the high-precision drive systems that have strict demand to quality and reliability. So, making deep study into the backlash nonlinearity in mechanical drive systems is much important both in theory and engineering.In this dissertation, a class of backlash nonlinear control systems is studied. The main ideas are as follows:(1) Drive systems with backlash nonlinearity are studied. First, this paper presents a robust nonlinear control scheme for input backlash systems with parametric uncertainties. A model reference controller is developed and robust global convergence of the tracking error is proved by Lyapunov method. Furthermore, a switching control scheme with PTO (proximate time optimal) compensation is presented for the systems containing inner backlash. With a linear PID controller used in contact period, a sliding control with PTO surface is switched into when system enters the backlash. Then, a supervising mechanism is introduced to find suitable time switching between linear PID control and PTO sliding control, ensuring BIBO stability of the whole system. The design can effectively eliminate the colliding disturbance resulting from the backlash and improve the robustness of the controller.(2) Based on dual-motors drive systems with backlash nonlinearity, the paper present studies on the nonlinearity still existing in the redundant system (consist of dual driving sub-systems with pre-loaded torque bias and one driven sub-system). By selecting control Lyapunov function through Backstepping approach, a state feedback scheme is developed to completely eliminate the influence of backlash in system. Then, an adaptive control scheme for backlash nonlinearity in such system with unknown parameters is proposed in the same way. The scheme can effectively keep tracking to the reference input while ensure the stability of overall system.(3) A model reference adaptive control (MRAC) is proposed for redundantly driven systems with unknown nonlinearities such as friction and backlash. First, the system is
本文研究了一类齿隙非线性系统的控制问题,主要内容如下:
(1)研究了驱动系统的齿隙非线性控制问题。首先针对存在有界不确定未知参数的输入端齿隙非线性系统,在研究低阶系统的基础上,提出了具有普遍意义的基于模型跟踪的高阶系统鲁棒控制策略。随后,针对内部包含齿隙非线性的传动系统提出了一种切换控制策略,在系统主、从动部分的接触阶段采用PID控制,使系统输出跟踪期望目标;在齿隙期间采取基于时间次优的滑模控制,保证驱动部分快速通过齿隙的同时,在齿隙终了与从动部分实现无碰撞接触;并设计了基于稳定性理论的切换监督机制,保证系统在跟踪期望目标的过程中能够保持BIBO稳定。
(2)以具有代表性的双电机驱动齿隙非线性系统为对象,研究了冗余驱动系统(齿隙非线性传动系统由施加偏置力矩的两组驱动子系统和一组从动子系统组成)的基于Backstepping方法的齿隙非线性控制问题。引入标志函数重新描述齿隙非线性,应用Backstepping方法设计了基于状态反馈的控制策略;并进一步针对参数未知的控制对象,设计了基于Backstepping方法的状态反馈自适应控制策略。
(3)研究了存在未知摩擦、未知齿隙非线性的冗余驱动系统的模型参考自适应控制(MRAC)问题。以冗余驱动补偿后的近似线性系统为研究对象,针对驱动子系统参数一致的情况,设计了基于状态反馈的MRAC鲁棒控制策略;进而,针对系统中由于未得到完全补偿的齿隙非线性、变刚性系数等产生的力矩扰动,及各驱动子系统间由于参数不一致产生的同步协调问题,通过变换系统模型,设计了基于状态反馈的MRAC鲁棒同步控制策略。
(4)研究了存在未知摩擦、未知齿隙等非线性的驱动系统的神经网络控制问题。首先以单电机驱动系统为研究对象,在对齿隙非线性进行分解的基础上,采用函数链神经网络(Function Link Neural Net简称FLNN)对未知非线性进行辨识,应用Backstepping方法设计了基于FLNN的鲁棒自适应控制策略。之后,进一步研究了以双电机驱动系统为对象的冗余驱动系统的神经网络控制问题,引入同步误差反馈,设
As a main nonlinearity in mechanical drive systems, backlash exists broadly in various systems such as machine tools, robots, astronomical telescopes, radars, artilleries, missile launchers, aerocrafts etc., and is an important factor influencing the dynamic and static properties of drive systems. Due to the non-differentiable trait of backlash, its compensation is much difficult. This brings austere challenge to the high-precision drive systems that have strict demand to quality and reliability. So, making deep study into the backlash nonlinearity in mechanical drive systems is much important both in theory and engineering.In this dissertation, a class of backlash nonlinear control systems is studied. The main ideas are as follows:(1) Drive systems with backlash nonlinearity are studied. First, this paper presents a robust nonlinear control scheme for input backlash systems with parametric uncertainties. A model reference controller is developed and robust global convergence of the tracking error is proved by Lyapunov method. Furthermore, a switching control scheme with PTO (proximate time optimal) compensation is presented for the systems containing inner backlash. With a linear PID controller used in contact period, a sliding control with PTO surface is switched into when system enters the backlash. Then, a supervising mechanism is introduced to find suitable time switching between linear PID control and PTO sliding control, ensuring BIBO stability of the whole system. The design can effectively eliminate the colliding disturbance resulting from the backlash and improve the robustness of the controller.(2) Based on dual-motors drive systems with backlash nonlinearity, the paper present studies on the nonlinearity still existing in the redundant system (consist of dual driving sub-systems with pre-loaded torque bias and one driven sub-system). By selecting control Lyapunov function through Backstepping approach, a state feedback scheme is developed to completely eliminate the influence of backlash in system. Then, an adaptive control scheme for backlash nonlinearity in such system with unknown parameters is proposed in the same way. The scheme can effectively keep tracking to the reference input while ensure the stability of overall system.(3) A model reference adaptive control (MRAC) is proposed for redundantly driven systems with unknown nonlinearities such as friction and backlash. First, the system is
引文
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