永磁同步电机的混沌控制方法研究
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摘要
永磁同步电动机(PMSM)具有体积小、重量轻、反应快、效率高等优点,随着电力电子技术和控制技术的发展,永磁同步电动机交流伺服系统已经在现代高性能伺服系统中得到了极为广泛的应用,尤其是近年来,随着永磁材料的迅速发展,电力电子和控制技术的进步,永磁同步电机将越来越多地替代传统电机,应用前景非常的乐观,因而对永磁同步电机的研究是非常有意义的。
本篇论文首先研究了永磁同步电机的混沌行为,研究表明,永磁同步电机对输入参数非常敏感,当参数落入某个区域时,永磁同步电机会产生混沌现象,由于这种混沌现象对于永磁同步电机来说是非常有害的,应该给予抑制。所以,本文研究的重点是对永磁同步电机中的混沌现象实施控制。另外,系统可能由于机械磨损,建模误差,或者测量误差导致参数的不确定性,于是,在研究的过程中考虑了参数不确定的情况,针对参数不确定的永磁同步电机,分析了混沌现象的存在,然后也研究其混沌现象的控制策略。
对于永磁同步电机的混沌控制策略的研究,主要做了以下工作:(1)研究了参数固定永磁同步电机的脉冲控制策略,通过Lyapunov方法得出使其稳定运行的充分条件,然后对参数不确定的永磁同步电机设计脉冲控制器,并通过矩阵分析,将系统不确定矩阵进行了有效的表示,在此基础上,得到了参数不确定的永磁同步电机系统渐近稳定和指数稳定的充分条件。(2)提出了永磁同步电机模糊控制的数学模型,并针对参数固定和参数不确定的永磁同步电机设计相应的模糊控制器,并分别得出了参数固定和参数不确定的永磁同步电机的稳定性条件。(3)在研究脉冲控制和模糊控制的基础上,提出模糊脉冲控制的混沌数学模型,设计一种能够综合利用脉冲控制和模糊控制优点的控制器,并研究其稳定性,得出了参数固定和参数不确定的两种永磁同步电机的渐近稳定和指数稳定的充分条件,同时也指出,当脉冲间距比较大的时候,模糊脉冲控制的控制难度越来越大,理论上虽然存在相应的模糊脉冲控制器,但在实际应用中会增大成本,因此不利于实际利用,于是,在脉冲间隔比较小的情况小,做相应的模糊脉冲控制是非常有效的。本文对所提出的方法都做了数值模拟,模拟结果表明所得的结果对于永磁同步电机的稳定性控制是有效的。
在实际运行中的永磁同步电机,由于电压的不稳定,工作环境的瞬间振动等,有可能导致电机系统出现扰动现象,于是本文最后对具有扰动的永磁同步电机进行研究,重点研究具有脉冲扰动的永磁同步电机,同样考虑了其中参数固定和参数不确定的两种情况,首先提出数学模型,然后设计相应的控制规则,并研究其稳定性,得到了参数固定和参数不确定的永磁同步电机渐近稳定和指数稳定的充分条件。最后针对上面的研究结果,进行了相应的数值模拟,数值实验进一步证实了本论文所研究结果的有效性。
总而言之,本文把脉冲理论、模糊理论引入到永磁同步电机系统是一种全新的思想,根据脉冲微分方程的基本理论、模糊控制的基本理论和Lyapunov稳定性理论,研究在脉冲控制、模糊控制以及模糊脉冲控制框架下的永磁同步电机系统稳定和控制问题,为永磁同步电机的应用和发展打下了良好的基础。
Permanent magnet synchronous motors (PMSMs) have superior features such as compact size, high torque/weight ratio, high torque/inertia ratio and absence of rotor losses, and advantages of higher efficiency compared with induction motors. With the development of electronic technology and control technology, the PMSMs are widely applied in high performance servosystem. Especially in rencent years, the conventional motors were superseded by PMSMs due the development of permanent-magnet material and control echnology. The foreground application is very optimistic. So it is important to sduty the permanent magnet synchronous motors.
In this paper, the chaos fo PMSMs is investigated firstly. The study indicates that PMSMs are sensitive to the parameters, the chaotic phenomena will happen if the parameters fall into some area. Because the chaos is baneful to the PMSMs, we must restrain it for PMSMs. So the emphasis of this paper is studying the method of controlling chaos of PMSMs. Furthermore, the values of parameters of the PMSM model are not constant, but span some interval. The main reason is that the permanent magnetic-flux will vary with the temperature rise of permanent-magnet material and rotary inertia will vary with the attrition of the device, or modelling errors, measurement inaccuracy, and so on. The parameters uncertains will be considerd in our study. So we investigate the chaos and the control strategy for PMSMs with parameters uncertains.
As for the study of the chaotic control strategy for PMSMs, the main results in this paper can be described as follows: (1) The impusive control strategy for PMSMs with fixed parameters si investigated firstly. Then the sufficient conditions of the robust stability are established by employing the method of Lyapunov functions. Then the impulsive controller is designed for PMSMs with uncertain parameters. After the uncertain matrixes which represent the variable system parameters are formulated through matrix analysis, the asymptotical/exponential stability criteria of fuzzy control are established. (2) The fuzzy control mathematics model is established, and the fuzzy controllers for PMSMs with fixed and uncertain parameters are designed respectively. (3) Based on the above study, the chaotic fuzzy impulsive control model is brought forward. The fuzzy impulsive controller which containing the merits of fuzzy and impulsive controller is designed. The stability of fuzzy impulsive control is investigated, and the asymptotical/exponential stability criteria of fuzzy impulsive control are established for PMSMs with fixed and uncertain parameters. Our results indicate that the fuzzy impulsive control is difficult with the increase of pulse spacing, the theoretical controller exists but the control cost will increase. So the fuzzy impulsive control is effective for small pulse spacing. The numerical simulations illustrate the affectivity of all the above control strategy.
Otherwise, the disturbances exist in PMSMs due to the instability of voltage, concussion of running circumstance and so on. So the PMSMs with disturbances especially impulsive effects are investigated in the end of this paper. As the analysis of the above, the PMSMs with fixed parameters and uncertain parameters are considered. Firstly, the chaotic mathematics model is brought forward. Then the control rules are designed. And the asymptotical/exponential stability criteria for PMSMs with impulsive effects are established. Furthermore, the numerical simulations illustrate the affectivity of the above control strategy for PMSMs with impulsive effects.
In a word, it is creative to apply the impulsive theory and fuzzy theory to PMSMs. The stability of PMSMs is investigated by the theory of impulsive differential equation, fuzzy control and Lyapunov function. It is important for the application and development of PMSMs.
本篇论文首先研究了永磁同步电机的混沌行为,研究表明,永磁同步电机对输入参数非常敏感,当参数落入某个区域时,永磁同步电机会产生混沌现象,由于这种混沌现象对于永磁同步电机来说是非常有害的,应该给予抑制。所以,本文研究的重点是对永磁同步电机中的混沌现象实施控制。另外,系统可能由于机械磨损,建模误差,或者测量误差导致参数的不确定性,于是,在研究的过程中考虑了参数不确定的情况,针对参数不确定的永磁同步电机,分析了混沌现象的存在,然后也研究其混沌现象的控制策略。
对于永磁同步电机的混沌控制策略的研究,主要做了以下工作:(1)研究了参数固定永磁同步电机的脉冲控制策略,通过Lyapunov方法得出使其稳定运行的充分条件,然后对参数不确定的永磁同步电机设计脉冲控制器,并通过矩阵分析,将系统不确定矩阵进行了有效的表示,在此基础上,得到了参数不确定的永磁同步电机系统渐近稳定和指数稳定的充分条件。(2)提出了永磁同步电机模糊控制的数学模型,并针对参数固定和参数不确定的永磁同步电机设计相应的模糊控制器,并分别得出了参数固定和参数不确定的永磁同步电机的稳定性条件。(3)在研究脉冲控制和模糊控制的基础上,提出模糊脉冲控制的混沌数学模型,设计一种能够综合利用脉冲控制和模糊控制优点的控制器,并研究其稳定性,得出了参数固定和参数不确定的两种永磁同步电机的渐近稳定和指数稳定的充分条件,同时也指出,当脉冲间距比较大的时候,模糊脉冲控制的控制难度越来越大,理论上虽然存在相应的模糊脉冲控制器,但在实际应用中会增大成本,因此不利于实际利用,于是,在脉冲间隔比较小的情况小,做相应的模糊脉冲控制是非常有效的。本文对所提出的方法都做了数值模拟,模拟结果表明所得的结果对于永磁同步电机的稳定性控制是有效的。
在实际运行中的永磁同步电机,由于电压的不稳定,工作环境的瞬间振动等,有可能导致电机系统出现扰动现象,于是本文最后对具有扰动的永磁同步电机进行研究,重点研究具有脉冲扰动的永磁同步电机,同样考虑了其中参数固定和参数不确定的两种情况,首先提出数学模型,然后设计相应的控制规则,并研究其稳定性,得到了参数固定和参数不确定的永磁同步电机渐近稳定和指数稳定的充分条件。最后针对上面的研究结果,进行了相应的数值模拟,数值实验进一步证实了本论文所研究结果的有效性。
总而言之,本文把脉冲理论、模糊理论引入到永磁同步电机系统是一种全新的思想,根据脉冲微分方程的基本理论、模糊控制的基本理论和Lyapunov稳定性理论,研究在脉冲控制、模糊控制以及模糊脉冲控制框架下的永磁同步电机系统稳定和控制问题,为永磁同步电机的应用和发展打下了良好的基础。
Permanent magnet synchronous motors (PMSMs) have superior features such as compact size, high torque/weight ratio, high torque/inertia ratio and absence of rotor losses, and advantages of higher efficiency compared with induction motors. With the development of electronic technology and control technology, the PMSMs are widely applied in high performance servosystem. Especially in rencent years, the conventional motors were superseded by PMSMs due the development of permanent-magnet material and control echnology. The foreground application is very optimistic. So it is important to sduty the permanent magnet synchronous motors.
In this paper, the chaos fo PMSMs is investigated firstly. The study indicates that PMSMs are sensitive to the parameters, the chaotic phenomena will happen if the parameters fall into some area. Because the chaos is baneful to the PMSMs, we must restrain it for PMSMs. So the emphasis of this paper is studying the method of controlling chaos of PMSMs. Furthermore, the values of parameters of the PMSM model are not constant, but span some interval. The main reason is that the permanent magnetic-flux will vary with the temperature rise of permanent-magnet material and rotary inertia will vary with the attrition of the device, or modelling errors, measurement inaccuracy, and so on. The parameters uncertains will be considerd in our study. So we investigate the chaos and the control strategy for PMSMs with parameters uncertains.
As for the study of the chaotic control strategy for PMSMs, the main results in this paper can be described as follows: (1) The impusive control strategy for PMSMs with fixed parameters si investigated firstly. Then the sufficient conditions of the robust stability are established by employing the method of Lyapunov functions. Then the impulsive controller is designed for PMSMs with uncertain parameters. After the uncertain matrixes which represent the variable system parameters are formulated through matrix analysis, the asymptotical/exponential stability criteria of fuzzy control are established. (2) The fuzzy control mathematics model is established, and the fuzzy controllers for PMSMs with fixed and uncertain parameters are designed respectively. (3) Based on the above study, the chaotic fuzzy impulsive control model is brought forward. The fuzzy impulsive controller which containing the merits of fuzzy and impulsive controller is designed. The stability of fuzzy impulsive control is investigated, and the asymptotical/exponential stability criteria of fuzzy impulsive control are established for PMSMs with fixed and uncertain parameters. Our results indicate that the fuzzy impulsive control is difficult with the increase of pulse spacing, the theoretical controller exists but the control cost will increase. So the fuzzy impulsive control is effective for small pulse spacing. The numerical simulations illustrate the affectivity of all the above control strategy.
Otherwise, the disturbances exist in PMSMs due to the instability of voltage, concussion of running circumstance and so on. So the PMSMs with disturbances especially impulsive effects are investigated in the end of this paper. As the analysis of the above, the PMSMs with fixed parameters and uncertain parameters are considered. Firstly, the chaotic mathematics model is brought forward. Then the control rules are designed. And the asymptotical/exponential stability criteria for PMSMs with impulsive effects are established. Furthermore, the numerical simulations illustrate the affectivity of the above control strategy for PMSMs with impulsive effects.
In a word, it is creative to apply the impulsive theory and fuzzy theory to PMSMs. The stability of PMSMs is investigated by the theory of impulsive differential equation, fuzzy control and Lyapunov function. It is important for the application and development of PMSMs.
引文
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