The three-phase voltage pulse-width-modulation (PWM) inverter is a time-varying, multi-modal nonlinear system, for which we build the mathematical model with a switching function. By introducing the average switching-period operator, we transform the discrete-time system to a continuous-time system with a second order nonlinear model and a strict parameter feedback. By using back-stepping design approach, we select step by step the virtual control variable and Lyapunov function; so that each state variable has the appropriate asymptotic features and the whole system under a large disturbance has a global asymptotic stability. After the general expression of the feedback control law is determined, the specific feedback control law of the three-phase voltage source PWM inverter system is obtained by putting parameters into this expression. The effectiveness of the control method is validated by simulation experiments.%针对三相电压型脉冲调宽(pulse-width-modulation,PWM)逆变器这个时变的、多模态的非线性系统,应用开关函数建立了系统数学模型,引入开关周期平均算子将离散的系统化为连续系统,得到具有参数严格反馈形式的二阶非线性多输入多输出系统数学模型.并对此模型应用反向递推方法,通过逐步选择虚拟控制量和构造李雅普诺夫函数,使每个状态分量具有适当的渐近特性,实现整个系统在大扰动下的全局渐近稳定性,进而得到反馈控制律的一般表达式.将三相电压型PWM逆变器系统参数代入后得到其反馈控制规律.最后通过仿真实验验证了该方法的有效性和正确性.
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