Transcription of 7.2.5. Perturbation and linearization
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7.2.5. Perturbation and linearization
fundamentals of power Electronics!Chapter 7: AC equivalent circuit modeling!27! Perturbation and linearization !Ldi(t)Tsdt=d(t)vg(t)Ts+d'( t)v(t)TsCdv(t)Tsdt= d'(t)i(t)Ts v(t)TsRig(t)Ts=d(t)i(t)TsConverter averaged equations:! nonlinear because of multiplication of the time-varying quantity d(t) with other time-varying quantities such as i(t) and v(t).! fundamentals of power Electronics!Chapter 7: AC equivalent circuit modeling!28!Construct small-signal model:"Linearize about quiescent operating point!If the converter is driven with some steady-state, or quiescent, inputs!d(t)=Dvg(t)Ts=Vgthen, from the analysis of Chapter 2, after transients have subsided the inductor current, capacitor voltage, and input current!i(t)Ts,v(t)Ts,ig(t)Tsreach the quiescent values I, V, and Ig, given by the steady-state analysis as!
Fundamentals of Power Electronics! 29! Chapter 7: AC equivalent circuit modeling! Perturbation! So let us assume that the input voltage and duty cycle are equal to
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