Substitute s for jw in a transfer function

Hi, I have a transfer function define by

G = ([1 2],[3 4 5]) (as an example)

I want to change the 's' for 'jw'. Does anyone know how to do it?

I've tried subs(G,{s},{1j*omega}) but it didn't work.

Answer 1

[Jon]

Hi,

I think you mean that you define your transfer function using (you forgot the tf() in your example)

G = tf([1 2],[3 4 5]) %(as an example))

Then if you want to evaluate it at a particular frequency, that is a specific value of jw, you can use

w = 3; % for example 3 radians/sec
val = evalfr(G,j*w)

You can also use the freqresp function to evaluate it for multiple values along the jw axis

[Jon]

If as Pat suggest you don't have the Control System Toolbox, you can do this a little more neatly using

num = [1,2]
den = [3,4,5]
w = 3; % for example 3 rad/s
val = polyval(num,j*w)/polyval(den,j*w)

You can also use i*w MATLAB defines by default i and j as sqrt(-1)

[Inés Bodoque]

It worked! Thank you very much

[kang]

can I use syms omega and use evalfr(G,j*omega)?

[Walter Roberson]

@kang

No, evalfr() is part of the Control System Toolbox, and there are no functions in the Control System Toolbox that accept symbolic expressions.

[Walter Roberson]

For 1 x 1 systems, G,

syms omega Omega
EVALFR = subs(poly2sym(G.Numerator{1}, Omega), Omega, 1j*omega) ./ ...
         subs(poly2sym(G.Denominator{1}, Omega), Omega, 1j*omega)

[Paul]

The numeric solution using polyval from this comment should use rdivide, ./, not mrdivide, /, for the general case where w is not a scalar. And safer to use 1j instead of j, which is a common variable name that can shadow the built-in function of the same name

num = [1,2];
den = [3,4,5];
w = [3 4]; % for example 3 and 4 rad/s
val = polyval(num,j*w)/polyval(den,j*w)   % wrong

val = -0.0110 - 0.1076i

val = polyval(num,1j*w)./polyval(den,1j*w)

val = 
  -0.0127 - 0.1433i  -0.0105 - 0.0969i

Answer 2

[Pat Gipper]

Matlab uses the reserved constant "i" which is set equal to sqrt(-1). Using your transfer function as defined try the following which will result in the variable "G" which will be a complex number.

num=1*i*w+2;den=3*(i*w)^2+4*i*w+5;G=num/den;

[Pat Gipper]

Based on some of your other questions it looks like you don't have access to the Control Systems Toolbox. So you need to do this arithmetic explicitly.

[Inés Bodoque]

Thank you for your answer! I need this for a project from one of my subjects and I am not allowed to use the Control Systems Toolbox, that's why I have to do it this way