Modify the Laplace variable in a transfer function

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

How should I proceed ?

Answer 1

[Star Strider]

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.

[Shreyas Dethe]

Thank you very much!

Can you please explain what is the function of simplify here ?

[Star Strider]

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!