开关变换器的二阶扩展状态空间模型

The state space average model of switching con-verters transforms time varying differential equations into time invariant differential equations by the averaging method in math.The model has merits of simple,clear physical conception and easy to design control system,but it exhibits significant steady-state error and delayed dynamic response in some special param-eters or state conditions.Besides,the conventional state space average model(CSSAM)can't reflect how much the switching period influences system performance.The averaging method based on exact time domain solution approximation for the state variable is established in this paper.Subsequently,a second-order state-space average model(SOSSAM)which extends the constant term in CSSAM to a combination of constant term and linear term of the switching period is proposed.This model inherits the advantages of CSSAM and improves accuracy of steady state performance and dynamic response of switching converters.Influence of switching period to system performance is reflected,which lays a foundation for analyzing system performance and designing a control system of switching converters.