基于状态反馈精确线性化的三相四桥臂逆变器的控制

Control of Three-phase Four-leg Inverter by State Feedback Exact Linearization

根据三相四桥臂逆变器的工作原理,应用开关函数建立了控制系统数学模型,引入开关周期平均算子将离散的系统转化为连续系统.根据系统的主要控制目标选取状态变量、输入变量和输出变量,得到适合于微分几何方法的3输入3输出的仿射非线性系统模型.根据非线性微分几何理论,从理论上证明了该模型满足多输入、多输出系统精确线性化的条件,推导出非线性状态反馈控制律.对非线性坐标变换后得到的线性系统,利用二次型最优控制策略时,根据无源性控制方法的思想,提出一种闭环系统能量函数,并推导出权矩阵的参数形式.将最优化得到的控制律进行逆变换来实现原系统的优化控制设计.仿真结果验证了该方法的有效性和正确性.

Based on the working principle of the three-phase four-leg inverter,the mathematical model of control systems is established by switching functions.The discrete system is then transformed into a continuous system by the average switch period operator.Further,the state variables,input variables and output variables are selected according to the main control objectives of the system and later three-input three-output affine nonlinear system models compatible with differential geometry methods are obtained.The resulting model is proved in the nonlinear differential geometry theory to meet conditions for the exact linearization of MIMO（multi-inputs and multi-outputs） systems and the nonlinear state feedback control laws are also deduced.For the resulting linear system after nonlinear coordinate transformation,a closed-loop system energy function is proposed by the idea of passivity control,when the quadratic optimal control strategy is adopted.Finally,the weight matrix in parametric form is deduced and the optimal control law of the original system is recovered by inverse transformation from the optimal control of linear systems.Simulation results demonstrate the effectiveness and correctness of the proposed control method.