# I ask for help with commands TransferFunctionModel + StateSpaceModel

Given system of ODE:

$$\begin{cases} \dot{x}=G+u_1 \ \dot{z}=-z+\frac{df}{dt} \ \dot{G}=-G+z \cdot u_2 \end{cases}$$

where $$f=-x^2$$,

$$u_1=\frac{d}{dt}(\alpha \sin(\omega \cdot t))$$ and $$u_2=\alpha \sin(\omega \cdot t)$$

f = -x[t]^2; asys = AffineStateSpaceModel[{x'[t] == G[t] + u1[t], z'[t] + z[t] == D[f, t], G'[t] + G[t] == z[t]  u2[t]}, {{x[t], 1}, {G[t], 0}, {z[t], 0}}, {u1[t], u2[t]}, {x[t], z[t], G[t]}, t]; 

And here is the result of the numerical calculation:

pars = {\[Alpha] = 0.5, \[Omega] = 2 Pi 5, xs = 1, xe = 0}; s1 = \[Alpha] Sin[\[Omega] t]; or = OutputResponse[asys, {D[s1, t], s1}, {t, 0, 500}] Plot[{or[[1]] - s1, xe}, {t, 0, 25}, PlotRange -> All, PlotPoints -> 100] 

Next, I try to get the transfer function of the system:

tf = TransferFunctionModel[asys] 

And results:

or = OutputResponse[tf, {D[s1, t], s1}, {t, 0, 500}] Plot[{or[[1]]}, {t, 0, 5}, PlotRange -> All, PlotPoints -> 100] 

Should the results be the same, and if not, why not?