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Using ss2tf when your matrices are variables without values yet

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syms m b k
A = [0 (1/m+1/b);-k (-k/m-k/b)]
B = [0;k]
C = [0 1]
D = [0]
[b,a] = ss2tf(A,B,C,D)
I would like to get the transfer function of those matrices but the ss2tf function requires the matrices to be numerical. Is there a way to get a symbolic answer or am I looking at the wrong function?
  2 Comments
Walter Roberson
Walter Roberson on 11 Aug 2024
To be explicit:
ss2tf() does not work on symbolic variables. Very few of the functions in the Control System Toolbox will work with symbolic variables (the ones that do work are more or less by accident.)
Paul
Paul on 11 Aug 2024
Edited: Paul on 11 Aug 2024
ss2tf is not listed on the Control System Toolbox Functions page nor (very surprisingly to me) on the Signal Processing Toolbox Functions page. It's been out of vogue from the CST for so long that I'm always a bit surprised when I see it brought up and wonder why users are asking about it. Not sure when it was taken of the SPT doc; maybe that's been more recent and the reason users still try to use it.
FWIW, tf2ss is still a documented function in the SPT, and it does happen to work with symbolic inputs.

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Accepted Answer

Star Strider
Star Strider on 10 Aug 2024
Edited: Star Strider on 10 Aug 2024
I would not use the Symbolic Math Toolbox for this!
For undefined variables, use anonymous functions for them, and then pass the arguments to them later —
A = @(b,k,m) [0 (1/m+1/b);-k (-k/m-k/b)]
A = function_handle with value:
@(b,k,m)[0,(1/m+1/b);-k,(-k/m-k/b)]
B = @(k) [0;k]
B = function_handle with value:
@(k)[0;k]
C = [0 1]
C = 1x2
0 1
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
D = [0]
D = 0
[n,d] = ss2tf(A(1,2,3),B(2),C,D)
n = 1x3
0 2 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
d = 1x3
1.0000 2.6667 2.6667
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
EDIT — (10 Aug 2024 at 13:55)
Also —
A = @(b,k,m) [0 (1/m+1/b);-k (-k/m-k/b)]
A = function_handle with value:
@(b,k,m)[0,(1/m+1/b);-k,(-k/m-k/b)]
B = @(k) [0;k]
B = function_handle with value:
@(k)[0;k]
C = [0 1]
C = 1x2
0 1
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
D = [0]
D = 0
TFfcn = @(b,k,m) ss2tf(A(b,k,m),B(k),C,D);
b = 1;
k = 2;
m = 3;
[n,d] = TFfcn(b,k,m)
n = 1x3
0 2 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
d = 1x3
1.0000 2.6667 2.6667
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
.

More Answers (1)

Paul
Paul on 10 Aug 2024
Hi Wynand,
For a low-order problem like this, you can use the Symbolic toolbox to evaluate the equtation that computes the transfer function from the state space matrices. If you try it without success, feel free to post back here showing the code you tried and what the problem is.
Also, assuming this model represents some sort of mass-spring-damper system, I suggest reviewing the derivation of the state space matrices, because the A and B matrices don't look correct. For example, 1/b does not have the same units as 1/m.
syms m b k
A = [0 (1/m+1/b);-k (-k/m-k/b)]
A = 
B = [0;k]
B = 
C = [0 1];
D = [0];
%[b,a] = ss2tf(A,B,C,D)
  8 Comments
Wynand
Wynand on 15 Aug 2024
Edited: Wynand on 15 Aug 2024
Good day @Sam Chak
I redid my work and go to this transfer function
syms k m b s
T = k/(m*s^2+b*s+k)
T = 
This seems to be inline with the equation you have as well. Thank you for you engagement
Sam Chak
Sam Chak on 15 Aug 2024
Please note that your transfer function does not include the gravity term 'mg'. Either you did not account for the effect of gravity, or you canceled out the effect of gravity in the force term , as follows:
which results in
.
If the latter is the case, then the transfer function is valid:
.
Your next step is to design a stabilizing equation such that the elevator reaches the target floor at the desired settling time without overshoot. Note that if you use the popular unconstrained Proportional–Derivative equation, the elevator will reach all target floors at the same settling time. For high-rise buildings, this assumption is somewhat unrealistic.
Additionally, please consider researching Otis Elevator, Kone Elevator, Toshiba Elevator, and Schindler's Lifts if possible.

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