LocalLinearizationAt an SOC point So, the vocy equation can be linearized locallyvo, = f(so),af(s) +(s-s)=+cs.y.01oCoCVOCVasLinearizedFunctionIs=.S0neartheoperatingpoints =(s -so)v= v(t) -vo=cs+v (t)+Ri(t)1oCVp0[ci,1]+ Ri(t)= Cx + Ri(t)ADVocvpna53.uedoC =[ci,1], x =vs1060.2080.3090.Stite of Charge (SOC)So
Local Linearization ocv 0 ocv ocv At an SOC point s0 , the vocv equation can be linearized locally v 0 s=s0 = f (s ), v v 0 + f (s) (s − s ) = v 0 + c s, 0 ocv 1 s s = (s − s0 ) v = v(t) − v 0 = c s + v (t) +Ri(t) ocv 1 p s = [c1 ,1] v + Ri(t) = Cx + Ri(t) p s C = [c1 ,1], x = v p s0 0 V ocv Linearized Function near the operatingpoint
The state equation is already linears(t) :1i(t)10s(t)0I福x+YL7101i(t)RRThen, an observer can be designed based on the linearized statespace model to estimate the SOC
The state equation is already linear 0 1 p p p Q 1 i(t) R C C 1 s(t) = s(t) = 1 i(t) Q 0 vp (t) = − vp (t)+ x = 0 − 1 x + 1 i RpCp C p Then, an observer can be designed based on the linearized state space model to estimate the SOC