感应电动机分岔现象分析及混沌控制
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摘要
本文系统地研究了感应电动机及其传动系统的分岔现象，探讨了感应电动机混沌控制及实际应用的理论与方法。
文中首先介绍感应电动机的建模及计算机仿真技术，建立了任意速参考坐标系下的电动机统一数学模型，由此根据感应电动机的不同控制策略和运行状态，导出状态变量方程描述的时域模型作为后继研究的基础。
其次分析了感应电动机及其传动系统的分岔现象。一是应用Lyapunov方法及中心流形定理研究了感应电动机本体的运动稳定性，揭示了感应电动机在输入功率不足以驱动负载时，电动机运行过程中将出现鞍结分岔，这对于分析感应电动机应用于垂直牵引如电梯、起重机的运动过程，避免发生故障具有重要的实际意义；二是针对常用的感应电动机间接磁场定向控制(IFOC)系统，研究了转子电阻这一个难以准确实时检测或估计的时变参数的影响，得出当PI速度调节器的参数设计不适应转子电阻的变化时，系统将出现Hopf分岔而发生振荡，由此得到Hopf分岔产生的条件，从而提出了PI速度调节器参数设计新方法，增强了系统运行的稳定性和可靠性，弥补了IFOC系统的不足。
诱发感应电动机的混沌运动或感应电动机的混沌反控制是一个很有实际意义的课题，如感应电动机的一个重要应用领域是驱动振动设备，提高振动的工作效率可以节省大量的电能。为此本文通过对IFOC系统的反馈控制实现了感应电动机的混沌振动，即混沌反控制，研究证实混沌振动可以有效地提高振动效率，并降低振动噪声，文中用Lyapunov指数和维数及功率谱方法量化了混沌反控制系统的性态，为其工程应用打下基础。
然后基于混沌理论提出了两种新的PWM产生策略——混沌SPWM和混沌SVPWM。针对常规PWM逆变器由于开关频率固定，输出波形在开关频率及倍频周围含有幅值较高的谐波成分的固有缺点，混沌SPWM和混沌SVPWM通过控制逆变器开关频率按混沌规律变化，改变逆变器输出谐波的频谱分布，降低谐波峰值，有效地抑制谐波的影响，减少感应电动机电流和转矩脉动，具有较好的实际应用价值。实验和仿真验证了研究的正确性。
最后，为进一步探索感应电动机的混沌控制，在A．Duchateau et al的多模型控制策略基础上提出了一种新的混沌控制方法。多模型控制策略是一种改进的OGY方法，通过在混沌系统的一条收敛轨道上设置一系列的局部线性模型，由线性反馈控制律把混沌系统引导到不动点。而本文的控制律由人工免疫算法产生，研究表明基于人工免疫算法的混沌多模型微扰控制方法能有效控制混沌并减少混
Bifurcation phenomenon in induction motor drives, together with theories and methods for chaotic control and its applications to induction motor drives are studied in this dissertation.
Firstly, Modeling and simulation techniques of induction motor are introduced. State equations based on reference frame transformation theory are employed as mathematical model to induction motor operating under different control strategies for the further research work.
Secondly, Bifurcations in induction motor and drives are concerned with. Stability of induction motor is analyzed with Lyapunov stability theory and center manifold theorem. It is shown that saddle-node bifurcation happens in induction motor when there is not enough input power to drive load. The result is useful in motion analysis of vertical traction such as elevator and crane that should avoid the occurrence of operation fault. Moreover, bifurcation in indirect field oriented control (IFOC) of induction motor drive is also analyzed. In IFOC system, with poor PI speed controller setting, oscillations may occur due to the existence of Hopf bifurcation provided the motor rotor resistance is not exactly estimated. Conditions for the emergence of Hopf bifurcation are derived and, guidelines for proper PI speed controller setting are proposed to improve stability and reliability of IFOC.
Thirdly, recent research has shown that chaotic oscillation could actually promote oscillating efficiency, save energy and reduce noise. Induction motor is widely used in driving oscillating machines. Thus, how to make it chaotic or how to obtain anti-control of chaos in it is a significant work. In this dissertation, anti-control of chaos in an induction motor is realized by a feedback control to IFOC. The chaotic drive's characteristics are measured by Lyapunov exponents, Lyapunov dimensions and power spectra of time series. The study, which our researches are preceding, lays the foundation for oscillating engineering applications.
Fourthly, two new PWM schemes: chaos-based SPWM and chaos-based SVPWM are brought forward. There are cluster harmonics around the multiples of switching frequency in conventional SPWM and SVPWM output waves owing to their fixed switching frequencies. Chaos-based PWM strategies utilize a chaotic changing switching frequency to spread the harmonics continuously to a wideband area so that
文中首先介绍感应电动机的建模及计算机仿真技术，建立了任意速参考坐标系下的电动机统一数学模型，由此根据感应电动机的不同控制策略和运行状态，导出状态变量方程描述的时域模型作为后继研究的基础。
其次分析了感应电动机及其传动系统的分岔现象。一是应用Lyapunov方法及中心流形定理研究了感应电动机本体的运动稳定性，揭示了感应电动机在输入功率不足以驱动负载时，电动机运行过程中将出现鞍结分岔，这对于分析感应电动机应用于垂直牵引如电梯、起重机的运动过程，避免发生故障具有重要的实际意义；二是针对常用的感应电动机间接磁场定向控制(IFOC)系统，研究了转子电阻这一个难以准确实时检测或估计的时变参数的影响，得出当PI速度调节器的参数设计不适应转子电阻的变化时，系统将出现Hopf分岔而发生振荡，由此得到Hopf分岔产生的条件，从而提出了PI速度调节器参数设计新方法，增强了系统运行的稳定性和可靠性，弥补了IFOC系统的不足。
诱发感应电动机的混沌运动或感应电动机的混沌反控制是一个很有实际意义的课题，如感应电动机的一个重要应用领域是驱动振动设备，提高振动的工作效率可以节省大量的电能。为此本文通过对IFOC系统的反馈控制实现了感应电动机的混沌振动，即混沌反控制，研究证实混沌振动可以有效地提高振动效率，并降低振动噪声，文中用Lyapunov指数和维数及功率谱方法量化了混沌反控制系统的性态，为其工程应用打下基础。
然后基于混沌理论提出了两种新的PWM产生策略——混沌SPWM和混沌SVPWM。针对常规PWM逆变器由于开关频率固定，输出波形在开关频率及倍频周围含有幅值较高的谐波成分的固有缺点，混沌SPWM和混沌SVPWM通过控制逆变器开关频率按混沌规律变化，改变逆变器输出谐波的频谱分布，降低谐波峰值，有效地抑制谐波的影响，减少感应电动机电流和转矩脉动，具有较好的实际应用价值。实验和仿真验证了研究的正确性。
最后，为进一步探索感应电动机的混沌控制，在A．Duchateau et al的多模型控制策略基础上提出了一种新的混沌控制方法。多模型控制策略是一种改进的OGY方法，通过在混沌系统的一条收敛轨道上设置一系列的局部线性模型，由线性反馈控制律把混沌系统引导到不动点。而本文的控制律由人工免疫算法产生，研究表明基于人工免疫算法的混沌多模型微扰控制方法能有效控制混沌并减少混
Bifurcation phenomenon in induction motor drives, together with theories and methods for chaotic control and its applications to induction motor drives are studied in this dissertation.
Firstly, Modeling and simulation techniques of induction motor are introduced. State equations based on reference frame transformation theory are employed as mathematical model to induction motor operating under different control strategies for the further research work.
Secondly, Bifurcations in induction motor and drives are concerned with. Stability of induction motor is analyzed with Lyapunov stability theory and center manifold theorem. It is shown that saddle-node bifurcation happens in induction motor when there is not enough input power to drive load. The result is useful in motion analysis of vertical traction such as elevator and crane that should avoid the occurrence of operation fault. Moreover, bifurcation in indirect field oriented control (IFOC) of induction motor drive is also analyzed. In IFOC system, with poor PI speed controller setting, oscillations may occur due to the existence of Hopf bifurcation provided the motor rotor resistance is not exactly estimated. Conditions for the emergence of Hopf bifurcation are derived and, guidelines for proper PI speed controller setting are proposed to improve stability and reliability of IFOC.
Thirdly, recent research has shown that chaotic oscillation could actually promote oscillating efficiency, save energy and reduce noise. Induction motor is widely used in driving oscillating machines. Thus, how to make it chaotic or how to obtain anti-control of chaos in it is a significant work. In this dissertation, anti-control of chaos in an induction motor is realized by a feedback control to IFOC. The chaotic drive's characteristics are measured by Lyapunov exponents, Lyapunov dimensions and power spectra of time series. The study, which our researches are preceding, lays the foundation for oscillating engineering applications.
Fourthly, two new PWM schemes: chaos-based SPWM and chaos-based SVPWM are brought forward. There are cluster harmonics around the multiples of switching frequency in conventional SPWM and SVPWM output waves owing to their fixed switching frequencies. Chaos-based PWM strategies utilize a chaotic changing switching frequency to spread the harmonics continuously to a wideband area so that
引文
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