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加权矩阵的选取在最优反馈系统的综合设计中具有重要意义。该文基于无源性控制思想,提出一种二次型性能指标。应用状态空间平均建模法,建立电流连续型(current conduction mode,CCM)Buck变换器的仿射非线性模型。采用状态反馈精确线性化方法,推导出非线性状态反馈表达式,实现非线性系统的线性化。进一步,利用二次型最优控制对状态反馈反馈系数进行优化设计。所得控制律简单、容易实现。数值仿真验证了该控制方案的优越性,仿真波形对比分析显示与传统无源性控制方法相比,基于该控制方法的系统静态误差小,启动性能优越,且开关频率固定,对输入电压扰动和负载扰动均具有较强的鲁棒性。
The selection of weight matrix is of great importance in the comprehensive design of the optimal feedback system. Based on the idea of passive control, this paper proposes a quadratic performance index. An affine nonlinear model of the current conduction mode (CCM) Buck converter is established by using the state space average modeling method. Using the state feedback precise linearization method, the nonlinear state feedback expression is derived to realize the linearization of the nonlinear system. Further, quadratic optimal control is used to optimize the state feedback feedback coefficient. The resulting control law is simple and easy to implement. Numerical simulation shows the superiority of this control scheme. Compared with the traditional passive control method, the simulation results show that the system based on this control method has the advantages of small static error, excellent starting performance and fixed switching frequency, Load disturbances are robust.