基于Lyapunov理论的交流传动系统建模和稳定性分析

Modeling and Stability Analysis of AC Drive System Based on Lyapunov Theory

为完整分析PWM整流器-逆变器-电机串联交流传动系统的稳定性跟随主要系统参数变化的规律,基于各子系统的开关函数模型,结合空间矢量脉宽调制算法的开关函数在dq坐标系下的等效表达式,建立整个系统的状态空间模型,采用偏微分法进行线性化处理,得到系统的增量方程;基于Lyapunov第一法,采用MATLAB MAT语言对系统的稳定性进行分析.仿真结果表明:在传动系统全速度范围内,增大PWM整流器滤波参数和电机定转子电阻有利于增加系统的稳定性,电机定转子电感的变化对系统稳定性的影响呈双极性变化.因此,合理选择系统设计参数,能够使系统保持较大的稳定区域,避免系统振荡现象的发生.

With the variation of the main system parameters, for a complete stability analysis of pulse width modulation （PWM） rectifier-voltage source inverter-motor serial AC drive system, this paper builds the switch function models of each subsystem, and the whole system state space model was established under the equivalent expression of space vector PWM modulation （SVPWM） algorithm. System linearization under partial differential method was used and incremental equation of the system was achieved. Based on Lyapunov first method, Matlab MAT language was used for system stability analysis. Simulation results show that, in full drive speed range, increasing the PWM rectifier filter parameters and the motor stator and rotor resistance help to increase system stability, the motor stator and rotor inductance impact on system stability was bipolar changed. Therefore, a reasonable system design parameters choice can enable the system to maintain a large stable region and prevent system oscillation phenomenon.