How can I do summation in transfer function?

s = tf('s');
sys_Foster = tf(R_Foster(1)/(1+R_Foster(1)*C_Foster(1)*s)+R_Foster(2)/(1+R_Foster(2)*C_Foster(2)*s)+R_Foster(3)/(1+R_Foster(3)*C_Foster(3)*s));
[N_tf,D_tf] = tfdata(sys_Foster);

If I have a transfer function like the code show

How can I perform sys_Foster not only summation for 3 terms but i terms, where i is size(R_Foster)

I have tried the code below

for i = 1:size(R_Foster)
    sys_Foster_i(i) = tf(R_Foster(i)/(1+R_Foster(i)*C_Foster(i)*s))
end
    sys_Foster = sum(sys_Foster_i)

but got wrong answer.

Answer 1

[Paul]

One approach

R_Foster = 1:3;
C_Foster = 11:13;
sys_Foster = tf(0)

sys_Foster =
 
  0
 
Static gain.

for ii = 1:3
    sys_Foster = sys_Foster + tf(R_Foster(ii),[R_Foster(ii)*C_Foster(ii) 1])
end

sys_Foster =
 
     1
  --------
  11 s + 1
 
Continuous-time transfer function.


sys_Foster =
 
       46 s + 3
  ------------------
  264 s^2 + 35 s + 1
 
Continuous-time transfer function.


sys_Foster =
 
       2586 s^2 + 268 s + 6
  -------------------------------
  10296 s^3 + 1629 s^2 + 74 s + 1
 
Continuous-time transfer function.

sys_Foster

sys_Foster =
 
       2586 s^2 + 268 s + 6
  -------------------------------
  10296 s^3 + 1629 s^2 + 74 s + 1
 
Continuous-time transfer function.

[larry liu]

Thanks a lot! It really solve my problem.

I have another question like below:

syms s
        [N_tf,D_tf] = numden(R_Foster(1)/(1+R_Foster(1)*C_Foster(1)*s)+R_Foster(2)/(1+R_Foster(2)*C_Foster(2)*s)+...
        R_Foster(3)/(1+R_Foster(3)*C_Foster(3)*s))
        D = sym2poly(N_tf);
        N = sym2poly(D_tf);

The same as the original question, How can I transform 3 terms to i terms instead? thank you!

[Paul]

It looks like the assignments to D and N are backwards.

Once you have N and D do you just want to create a tf object? I'm not sure what the desired end result is ...

R_Foster = 1:3;
C_Foster = 11:13;
syms s
[N_tf,D_tf] = numden(R_Foster(1)/(1+R_Foster(1)*C_Foster(1)*s)+R_Foster(2)/(1+R_Foster(2)*C_Foster(2)*s)+...
    R_Foster(3)/(1+R_Foster(3)*C_Foster(3)*s));
%D = sym2poly(N_tf);
%N = sym2poly(D_tf);
N = sym2poly(N_tf);
D = sym2poly(D_tf);
tf(N,D)

ans =
 
       2586 s^2 + 268 s + 6
  -------------------------------
  10296 s^3 + 1629 s^2 + 74 s + 1
 
Continuous-time transfer function.

[larry liu]

What I really want is that turn the code into

syms s
[N_tf, D_tf]=numden(R_foster(i)/(1+R_foster(i)*C_foster(i)*s))

wher i is 1,2,⋯to size(R_foster)

but I run the code. the result is strange.

[larry liu]

the result is not the same as summation each term.

[Paul]

Now I'm very confused as to what the goal actually is. In this answer I showed how to use a loop to add three first order transfer functions together using the Control System Toolbox functions. In this comment I showed how to create the same tf object but adding together the first order transfer functions using the Symbolic Toolbox to get the same result. Maybe you want to use the Symbolic Toolbox but in a loop?

R_Foster = sym(1:3);
C_Foster = sym(11:13);
syms s
H(s) = sym(0);
for ii = 1:numel(R_Foster)
    H(s) = H(s) + R_Foster(ii)/(1+R_Foster(ii)*C_Foster(ii)*s);
end
H(s) % this is a symfun object

ans = 

[num,den] = numden(H(s));
H(s) = num/den % still a symfun object

H(s) = 

H(s) = expand(num)/expand(den)  % still a symfun object

H(s) = 

If none of this solves the problem, please be more clear about the problem actually is. Do you want a Symbolic result or a Control System Toolbox result? Does the result need to be in a specific format? Etc.

[larry liu]

@Paul Thanks a lot! I got the answer I want. You really solve my problem. Really aprreciate.