Matlab : find a transfer function

Question

I am currently working on a project and I need to derive a transfer function such that it can be used with lsim() based on its analytical expression. I have the following code :

freq = logspace(-4,2,1000); 
w = 2*pi*freq;
tauR = 10e-6;                                                       
OmegaR = pi/(2*tauR);
T = 60e-3;                                 
H_a1 = ((4*1i*OmegaR*w.*sin(w.*(T+2*tauR)/2))./(w.^2-OmegaR^2)) .*...
 (cos(w.*(T+2*tauR)/2) + OmegaR*sin(w.*T/2)./w) .* (2*pi*freq).^(-2); 

Which correspond exactly to my transfer function Transfer function graph

But now I would like to express it as a ss object so that I can use it in lsim(H_a1, u, t) in order to see its effect. How can I do that ?

Here are the 4 things that I have tried so far without success

%1
H = H_a1 .* freq.';
H_AQG = tf(H, 1);

%2
H = arrayfun(H_a1, 2*pi*freq);
H_AQG = tf(H, 1);

%3
s = tf('s');
H_s1 = 1/(1 + (s/OmegaR)^2);
H_s2 = exp(-s*T/2);
H_AQG = H_s1 * H_s2;

%4
H_AQG = frd(H_a1,2*pi*freq);                            
H_AQG = fitmagfrd(H_AQG,40);