MATLAB: How to get the transfer function G(s) = (X2(s)-W(s))/W(s)

transfer function

According to the site below, how can I get the transfer function G(s) = (X2(s)-W(s))/W(s)
Control Tutorials for Matlab and Simulink
%%Parameters
m1 = 2500;   % (kg)

m2 = 320;    % (kg)
k1 = 80000;  % (N/m)

k2 = 500000; % (N/m)
b1 = 350;    % (N*s/m)

b2 = 15020;  % (N*s/m)
%%Transfer Function (Open Loop)
% Displacement Of Sprung Mass G(s) = X1(s)/W(s)
num1 = [(0) (0) (b1*b2) (b1*k2+b2*k1) (k1*k2)];
den1 = [(m1*m2) (m1*b1+m1*b2+m2*b1) (m1*k1+m1*k2+m2*k1+b1*b2) (b1*k2+k1*b2) (k1*k2)];
G1 = tf(num1,den1);
% Suspension Deflection G(s) = (X1(s)-X2(s))/W(s)
num2 = [(0) (-m1*b2) (-m1*k2) (0) (0)]; 
den2 = [(m1*m2) (m1*b1+m1*b2+m2*b1) (m1*k1+m1*k2+m2*k1+b1*b2) (b1*k2+k1*b2) (k1*k2)];
G2 = tf(num2,den2);
% Tire Deflection G(s) = (X2(s)-W(s))/W(s)
% num3 = [];
% den3 = [];
% G3 = tf(num3,den3);

Best Answer

It seems to me that you just copy it from the website and paste it to a tab in your Editor, just like I copied it and pasted it here:
M1 = 2500;
M2 = 320;
K1 = 80000;
K2 = 500000;
b1 = 350;
b2 = 15020;
s = tf('s');
G1 = ((M1+M2)*s^2+b2*s+K2)/((M1*s^2+b1*s+K1)*(M2*s^2+(b1+b2)*s+(K1+K2))-(b1*s+K1)*(b1*s+K1));
G2 = (-M1*b2*s^3-M1*K2*s^2)/((M1*s^2+b1*s+K1)*(M2*s^2+(b1+b2)*s+(K1+K2))-(b1*s+K1)*(b1*s+K1));
If you want to know how it was derived, that is described in detail on the page.
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