Modify the Laplace variable in a transfer function
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I have a transfer function
H_analog = tf(Oc^N, lp_poles);
Where the variables are
Oc = 1.07;
N = 8;
lp_poles = 1x16 complex matrix (let's assume all 1's for now)
I want to transform the laplace variable from s to 
so as to get a new transfer function H_analog_new
so as to get a new transfer function H_analog_newHow should I proceed ?
采纳的回答
Star Strider
2019-4-5
You need to involve the Symbolic Math Toolbox for this.
syms s
sv = 1/(s^2 + 0.2059);
Oc = 1.07;
N = 8;
lp_poles = poly2sym(ones(1,16),s);
H_sym = subs((Oc^N)/lp_poles, {s},{sv});
H_sym = simplify(H_sym, 'Steps',50)
[H_num,H_den] = numden(H_sym);
Hn = sym2poly(H_num);
Hd = sym2poly(H_den);
H_analog_new = tf(Hn, Hd)
producing:
H_analog_new =
7.738e75 s^30 + 2.39e76 s^28 + 3.445e76 s^26 + 3.073e76 s^24 + 1.898e76 s^22 + 8.599e75 s^20
+ 2.951e75 s^18 + 7.812e74 s^16 + 1.609e74 s^14 + 2.576e73 s^12 + 3.182e72 s^10
+ 2.978e71 s^8 + 2.044e70 s^6 + 9.713e68 s^4 + 2.857e67 s^2 + 3.922e65
----------------------------------------------------------------------------------------------
4.504e75 s^30 + 1.841e76 s^28 + 3.753e76 s^26 + 5.182e76 s^24 + 5.588e76 s^22 + 5.166e76 s^20
+ 4.377e76 s^18 + 3.556e76 s^16 + 2.843e76 s^14 + 2.261e76 s^12 + 1.796e76 s^10
+ 1.426e76 s^8 + 1.133e76 s^6 + 8.994e75 s^4 + 7.142e75 s^2 + 5.671e75
Continuous-time transfer function.
Experiment to get the result you want.
2 个评论
Shreyas Dethe
2019-4-5
Star Strider
2019-4-5
My pleasure!
The simplify (link) call automatically rearranges the expression to provide a much more simplified expression. What it does depends on the expression, and here I want it to fully integrate the substituted ‘sv’ variable in the equation, rather than leaving every substituted value as the original ‘sv’ value. See the documentation I linked to for an extended discussion.
If my Answer helps you solve your problem, please Accept it!
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