含摩擦环节伺服系统的分析及控制补偿研究
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摘要
伺服系统中由摩擦环节引起的爬行、振荡、跟踪误差等现象已成为阻碍系统
性能提高的严重障碍。为了克服这一障碍，本文深入地研究了伺服系统中出现的
爬行现象、分析了由摩擦导致的混沌振荡并提出了三种基于智能控制思想的摩擦
补偿方法。
本文首先综述了国内外在摩擦建模、系统分析以及摩擦补偿方面的研究现
状，总结了已有研究的不足之处，进而指出了这一领域发展趋势。
本文提出了两种分析含摩擦环节伺服系统爬行现象的方法，一种是基于非线
性传递函数理论的方法，另一种是以Newton-Raphson算法为基础的数值方法。
前者不但是一种完全解析化的方法，而且不要求系统具有好的低通滤波特性，同
时这种方法容易推广至高阶系统，因此克服了描述函数法和相平面法的缺陷；而
后者克服了模型复杂化给近似解析分析带来的困难和直接积分耗时、难以判断暂
态过程是否结束等传统数值方法的缺陷。因此采用这两种方法可以大大提高系统
分析的有效性和准确性。在这两种方法的基础上，本文还系统地研究了PD控制
的伺服系统中出现的爬行现象及其消除方法，找出了爬行现象与系统参数的关
系。
本文首次较为深入地研究了伺服系统中由摩擦导致的混沌现象，分析了系统
参数对系统动力学行为的影响及其通向混沌的道路，从而为系统的设计和综合提
供了依据。本文提出了一种系统地分析分段连续系统动力学行为的方法。在此基
础上，首次采用较完善的摩擦模型研究了强迫振动下，摩擦振子的混沌振荡行
为。分析了系统参数和摩擦模型对系统混沌行为的影响；发现了摩擦模型的选取
对系统动力学行为分析的重要性；揭示出在一定条件下，系统参数、环境条件或
润滑条件的改变都有可能使系统进入无序的混沌运动状态。
本文提出了三种基于智能控制思想的摩擦补偿方法，即基于自调整量化因子
模糊控制器的摩擦补偿方法、基于CMAC神经网络的摩擦补偿方法和将CMAC
网络与滑模控制器相结合的摩擦补偿方法。这三种方法都具备在线自调节能力或
自学习能力，从而大大减小了系统中出现的不确定性摩擦对系统性能的不利影
响。这些方法不仅克服了固定补偿和已有的基于模糊控制或神经网络的补偿方法
的缺陷，而且同一般自适应补偿方法相比，又具有实现简单、算法效率高、鲁棒
性强的优点，因此非常适合于工程应用。大量的仿真计算表明，这三种方法达到
了很好的补偿效果。
Friction presented in servo systems has become an impediment to improve their performance. To overcome this impediment, not only are stick-slip and chaos oscillation induced by friction analyzed, but also three friction compensation methods which is based on intelligent cybernetics are put forwarded in this thesis.
The literature relevant to friction modeling, system analyzing and friction compensation methods are outlined. The shortcomings of these studies are presented and future trends in this field are also described.
Two methods for analyzing stick-slip, which is presented in servo systems with friction, are put forwarded. One of these two methods is based on nonlinear transfer fi.inction; the other is a numerical method based on Newton-Raphson algorithm. The first method is an analytic method, by which the assumption that investigation of the first harmonic provides a reasonable approximation to the behavior to the true system is not necessary. It is also applicable for analyzing the high-order systems. So the shortcomings of describing function and phase plane analysis are overcome and the effectiveness and accuracy of the analysis is improved greatly. The other method can be used to analyze the system without any difficulty, which is raised by more and more complex models, this method also overcomes the shortcomings of brute-force approach, which is time consuming and difficult to tell when the steady sate has been achieved. Based on these methods, stick-slip presented in the servo systems governed by PD controller i
s analyzed systematically and the relationship between stick-slip and the parameters of these systems is revealed.
Chaos presented in servo systems induced by friction is studied by the first time. The impact of system parameters on the dynamics of the system and the route to chaos are analyzed. So this study provides a basis for system designing and synthesis. A method to analyze the dynamics of piecewise continuous system is presented, based on it, the chaotic oscillation of a harmonically forced spring-mass system with friction is studied. The impact of friction and other parameters on the chaotic oscillation of this system is analyzed. So the following conclusion is to be come to: First, the friction model is of great importance for the analyzing the dynamics of the servo systems with friction; Second, under some circumstances, chaos might be appeared as system parameters, circumstances and lubrication condition changing.
Three friction compensation methods based on intelligent cybernetics are put forwarded. One of these methods is based on self-tuned scaling factors fuzzy controller the others are based on CMAC. The controllers designed by all these methods have the ability of on-line auto tuning or self-learning, so the under-determined friction could be compensated. Not only do these three methods overcome the shortcomings of fixed compensation and the methods existed which is based on fuzzy logic and artificial neural networks, but also have the advantages of easy implementation, small computation load and robustness compared with traditional adaptive friction compensation methods: So these methods are applicable for engineering uses. Great effectiveness of these methods is demonstrated by a series of simulation.
性能提高的严重障碍。为了克服这一障碍，本文深入地研究了伺服系统中出现的
爬行现象、分析了由摩擦导致的混沌振荡并提出了三种基于智能控制思想的摩擦
补偿方法。
本文首先综述了国内外在摩擦建模、系统分析以及摩擦补偿方面的研究现
状，总结了已有研究的不足之处，进而指出了这一领域发展趋势。
本文提出了两种分析含摩擦环节伺服系统爬行现象的方法，一种是基于非线
性传递函数理论的方法，另一种是以Newton-Raphson算法为基础的数值方法。
前者不但是一种完全解析化的方法，而且不要求系统具有好的低通滤波特性，同
时这种方法容易推广至高阶系统，因此克服了描述函数法和相平面法的缺陷；而
后者克服了模型复杂化给近似解析分析带来的困难和直接积分耗时、难以判断暂
态过程是否结束等传统数值方法的缺陷。因此采用这两种方法可以大大提高系统
分析的有效性和准确性。在这两种方法的基础上，本文还系统地研究了PD控制
的伺服系统中出现的爬行现象及其消除方法，找出了爬行现象与系统参数的关
系。
本文首次较为深入地研究了伺服系统中由摩擦导致的混沌现象，分析了系统
参数对系统动力学行为的影响及其通向混沌的道路，从而为系统的设计和综合提
供了依据。本文提出了一种系统地分析分段连续系统动力学行为的方法。在此基
础上，首次采用较完善的摩擦模型研究了强迫振动下，摩擦振子的混沌振荡行
为。分析了系统参数和摩擦模型对系统混沌行为的影响；发现了摩擦模型的选取
对系统动力学行为分析的重要性；揭示出在一定条件下，系统参数、环境条件或
润滑条件的改变都有可能使系统进入无序的混沌运动状态。
本文提出了三种基于智能控制思想的摩擦补偿方法，即基于自调整量化因子
模糊控制器的摩擦补偿方法、基于CMAC神经网络的摩擦补偿方法和将CMAC
网络与滑模控制器相结合的摩擦补偿方法。这三种方法都具备在线自调节能力或
自学习能力，从而大大减小了系统中出现的不确定性摩擦对系统性能的不利影
响。这些方法不仅克服了固定补偿和已有的基于模糊控制或神经网络的补偿方法
的缺陷，而且同一般自适应补偿方法相比，又具有实现简单、算法效率高、鲁棒
性强的优点，因此非常适合于工程应用。大量的仿真计算表明，这三种方法达到
了很好的补偿效果。
Friction presented in servo systems has become an impediment to improve their performance. To overcome this impediment, not only are stick-slip and chaos oscillation induced by friction analyzed, but also three friction compensation methods which is based on intelligent cybernetics are put forwarded in this thesis.
The literature relevant to friction modeling, system analyzing and friction compensation methods are outlined. The shortcomings of these studies are presented and future trends in this field are also described.
Two methods for analyzing stick-slip, which is presented in servo systems with friction, are put forwarded. One of these two methods is based on nonlinear transfer fi.inction; the other is a numerical method based on Newton-Raphson algorithm. The first method is an analytic method, by which the assumption that investigation of the first harmonic provides a reasonable approximation to the behavior to the true system is not necessary. It is also applicable for analyzing the high-order systems. So the shortcomings of describing function and phase plane analysis are overcome and the effectiveness and accuracy of the analysis is improved greatly. The other method can be used to analyze the system without any difficulty, which is raised by more and more complex models, this method also overcomes the shortcomings of brute-force approach, which is time consuming and difficult to tell when the steady sate has been achieved. Based on these methods, stick-slip presented in the servo systems governed by PD controller i
s analyzed systematically and the relationship between stick-slip and the parameters of these systems is revealed.
Chaos presented in servo systems induced by friction is studied by the first time. The impact of system parameters on the dynamics of the system and the route to chaos are analyzed. So this study provides a basis for system designing and synthesis. A method to analyze the dynamics of piecewise continuous system is presented, based on it, the chaotic oscillation of a harmonically forced spring-mass system with friction is studied. The impact of friction and other parameters on the chaotic oscillation of this system is analyzed. So the following conclusion is to be come to: First, the friction model is of great importance for the analyzing the dynamics of the servo systems with friction; Second, under some circumstances, chaos might be appeared as system parameters, circumstances and lubrication condition changing.
Three friction compensation methods based on intelligent cybernetics are put forwarded. One of these methods is based on self-tuned scaling factors fuzzy controller the others are based on CMAC. The controllers designed by all these methods have the ability of on-line auto tuning or self-learning, so the under-determined friction could be compensated. Not only do these three methods overcome the shortcomings of fixed compensation and the methods existed which is based on fuzzy logic and artificial neural networks, but also have the advantages of easy implementation, small computation load and robustness compared with traditional adaptive friction compensation methods: So these methods are applicable for engineering uses. Great effectiveness of these methods is demonstrated by a series of simulation.
引文
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