Fall 2001 16.318-1 TFs to State-Space Models The goal is to develop a state-space model given a transfer function for a system G(s There are many, many ways to do this But there are three primary cases to consider 1. Simple numerator y=G(s)= s3+a152+a28+a 2. Numerator order less than denominator order y=G(s) b1s2+b2+b3 3+a152+02S+a3 3. Numerator equal to denominator order bos+618+b28+b s3+a1s2+a28+a3 These 3 cover all cases of interestFall 2001 16.31 8–1 TF’s to State-Space Models • The goal is to develop a state-space model given a transfer function for a system G(s). – There are many, many ways to do this. • But there are three primary cases to consider: 1. Simple numerator y u = G(s) = 1 s3 + a1s2 + a2s + a3 2. Numerator order less than denominator order y u = G(s) = b1s2 + b2s + b3 s3 + a1s2 + a2s + a3 = N(s) D(s) 3. Numerator equal to denominator order y u = G(s) = b0s3 + b1s2 + b2s + b3 s3 + a1s2 + a2s + a3 • These 3 cover all cases of interest