This is mostly for my own reference, but I hope someone else will benefit from it. It’s mainly to play with transfer functions.

First, generate the transfer function:

% numerator coefficients for s^2 + 2s + 4
num = [1 2 4]
% denominator coefficients for s + 6
den = [ 1 6 ]
% build the transfer function
H = tf(num, den)
% now we can do fun stuff like get a bode plot
bode(H)
% or plot it over a range of frequencies, 100 to 200 radians/s
bode(H,{100,200})
% or we could get the gain and phase shift for a certain frequency, 4pi here
[gain, phase] = bode(H, 4pi)
% how about zeroes and poles? Okay...
tzero(H)
poles(H)

To add some more stuff, the transfer function can also be generated when you have the factored form of it to begin with:

% if the denominator looks like (s-1)(s-2)(s-3)
poles = [1 2 3]
% same for zeros: (s+1)(s+2)(s+3)
zeros = [-1 -2 -3]
% and finally, gain K
k = 1
% now we can get the system like so:
H = zpk(zeros, poles, k)

I may add more at a later point. Not too fancy stuff here, but pretty helpful to what I needed done.

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