plotting transfer function / time domain version

Hi guys,

I am trying to plot a Laplace domain function I have, however when I use fplot or step() the graph shows nothing at all. How do I fix this?

Code Below:

clear 
clc

P = [8.925*10^-20 11.925*10^-15 17.995*10^-10 6.625 10^5];
poles = roots(P);
poles = poles';

Q = [2.25*10^-20 5.25*10^-15 1.5*10^-5 3*10^-5];
zeros = roots(Q);
zeros = zeros';

FT = tf(zeros,poles);

syms s t z

snum = poly2sym(zeros,s);
sden = poly2sym(poles,s);

step(FT);

FT_time_domain = ilaplace(snum/sden);
FT_time_domain = simplify(FT_time_domain,'Steps',10);
FT_time_domain = collect(FT_time_domain, exp(-t))

Answer 1

[Star Strider]

I’m assuming here that ‘Q’ is the numerator polynomial and ‘P’ is the denominator poplynomial. (If that is not correct, it is easy to switch them.)

Try something like this —

P = [8.925*10^-20 11.925*10^-15 17.995*10^-10 6.625 10^5];
poles = roots(P);
poles = poles';

Q = [2.25*10^-20 5.25*10^-15 1.5*10^-5 3*10^-5];
zeros = roots(Q);
zeros = zeros';

FT = tf(Q,P)

FT =
 
         2.25e-20 s^3 + 5.25e-15 s^2 + 1.5e-05 s + 3e-05
  --------------------------------------------------------------
  8.925e-20 s^4 + 1.193e-14 s^3 + 1.8e-09 s^2 + 6.625 s + 100000
 
Continuous-time transfer function.

syms s t z

snum = poly2sym(Q,s);
sden = poly2sym(P,s);

FTsym = vpa(snum / sden, 5)

FTsym = 

step(FT);

FT_time_domain = ilaplace(snum/(sden*s));                   % Step Response Requires: snum/sden*(1/s)
FT_time_domain = simplify(FT_time_domain,'Steps',10);
FT_time_domain = collect(FT_time_domain, exp(-t))

FT_time_domain = 

figure
fplot(FT_time_domain, [0 1.5E-5])
xlabel('Time (s)')
ylabel('Amplitude (units)')

The system appears to be unstable.

EDIT — (17 Apr 2023 at 13:02)

Initially forgot the multiplication to produce a step response in the symbolic code. Now added, with comment.

.

Answer 2

[Sam Chak]

Hi @Miller

If you want to use the step(sys) function, then the sys must be a SISO or MIMO Linear System Model.

In your case, it can descibed by a transfer function model in the s-domain.

Q = [2.250e-20  5.250e-15  1.500e-5  3e-5];
P = [8.925e-20 11.925e-15 17.995e-10 6.625 10^5];
G = tf(Q, P)

G =
 
         2.25e-20 s^3 + 5.25e-15 s^2 + 1.5e-05 s + 3e-05
  --------------------------------------------------------------
  8.925e-20 s^4 + 1.193e-14 s^3 + 1.8e-09 s^2 + 6.625 s + 100000
 
Continuous-time transfer function.

step(G)

p = pole(G)     % two of the poles have positive real parts, thus the system is unstable.

p = 
   1.0e+06 *

  -4.2411 + 0.0000i
   2.0613 + 3.6406i
   2.0613 - 3.6406i
  -0.0151 + 0.0000i