Is there a way to extract my 3 transfer function in matlab given these equations.

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Jorje German 2020-9-3

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https://ww2.mathworks.cn/matlabcentral/answers/588262-is-there-a-way-to-extract-my-3-transfer-function-in-matlab-given-these-equations

评论： Sam Chak 2020-9-10

采纳的回答： Sam Chak

在 MATLAB Online 中打开

I have these 3 equations

X1(s)*[m1*s^2 + c1*s+(k01+k12)] = F(s) + k12*X2(s)

X2(s)*[m2*s^2 + c2*s +(k12+k23)] = k12*X1(s)+k23*X3(s)

X3(s) [m3*s^2 + c3*s +(k23+k34)] = k23*X2(s)

and I am wondering if there is a possibility to be able to extract my 3 transfer functions, X1(s)/F(s), X2(s)/F(s), and X3(s)/F(s).

Ive really havent explore this part of Matlab and am interested to know if it is possible. I ask because currently I am doing it by hand and setting the left side S polynomial to be P1, P2, and P3 respectively.

but it is alot of algabra and I fear I will make a simple arithmetic mistake and ruin the whole thing.

Can this be done.

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Sam Chak 2020-9-3

I think the equations can be expressed in this form:

where you can algebraically solve

If

exists, then

,

Jorje German 2020-9-3

Interesting concept. I just showed my wife and she said, this is why you are still a student. I will try this method and play around in Matlab. Thank you. You have given me a direction to go to.

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Answer 1

Sam Chak 2020-9-3

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Hi Jorje German,

The transfer functions for your case in given in the first column of the

matrix. You can use the functions in Symbolic Math toolbox to simplify the rational expressions. Hope my answer helps.

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Jorje German 2020-9-8

编辑：Jorje German 2020-9-8

在 MATLAB Online 中打开

Would you be able to code that. I was able to input it in my calculator and selecting the rref(A) I was able to extract X1(s)/F(s) = (p2*p3-(k23)^2)/(p1*(p2*p3-(k23)^2)-p3*(k12)^2 this is the correct transfer function, which can be found below From input 1 to output..1...BUT how can I extract this so I can specifically use that transfer function and use it when sys=p41

M =
 
  From input 1 to output...
   1:  s^2 - s + 100
 
   2:  -100
 
   3:  0
 
  From input 2 to output...
   1:  100
 
   2:  -s^2 + s - 110
 
   3:  10
 
  From input 3 to output...
   1:  0
 
   2:  10
 
   3:  -s^2 + s - 10
 
Continuous-time transfer function.
ans =
 
  From input 1 to output...
                                                    
                s^4 - 2 s^3 + 121 s^2 - 120 s + 1000
                                                    
   1:  -------------------------------------------------------
                                                              
       s^6 - 3 s^5 + 223 s^4 - 441 s^3 + 3220 s^2 - 3000 s    
                                                              
                                                   - 3.659e-12
                                                              
                       -100 s^2 + 100 s - 1000
                                              
   2:  -------------------------------------------------------
                                                              
       s^6 - 3 s^5 + 223 s^4 - 441 s^3 + 3220 s^2 - 3000 s    
                                                              
                                                   - 3.659e-12
                                                              
                                -1000
                                     
   3:  -------------------------------------------------------
                                                              
       s^6 - 3 s^5 + 223 s^4 - 441 s^3 + 3220 s^2 - 3000 s    
                                                              
                                                   - 3.659e-12
                                                              
  From input 2 to output...
                                             
                       100 s^2 - 100 s + 1000
                                             
   1:  -------------------------------------------------------
                                                              
       s^6 - 3 s^5 + 223 s^4 - 441 s^3 + 3220 s^2 - 3000 s    
                                                              
                                                   + 5.192e-11
                                                              
                -s^4 + 2 s^3 - 111 s^2 + 110 s - 1000
                                                     
   2:  -------------------------------------------------------
                                                              
       s^6 - 3 s^5 + 223 s^4 - 441 s^3 + 3220 s^2 - 3000 s    
                                                              
                                                   + 5.192e-11
                                                              
                        -10 s^2 + 10 s - 1000
                                             
   3:  -------------------------------------------------------
                                                              
       s^6 - 3 s^5 + 223 s^4 - 441 s^3 + 3220 s^2 - 3000 s    
                                                              
                                                   + 5.192e-11
                                                              
  From input 3 to output...
                                    
                                1000
                                    
   1:  -------------------------------------------------------
                                                              
       s^6 - 3 s^5 + 223 s^4 - 441 s^3 + 3220 s^2 - 3000 s    
                                                              
                                                   + 5.545e-13
                                                              
                        -10 s^2 + 10 s - 1000
                                             
   2:  -------------------------------------------------------
                                                              
       s^6 - 3 s^5 + 223 s^4 - 441 s^3 + 3220 s^2 - 3000 s    
                                                              
                                                   + 5.545e-13
                                                              
                -s^4 + 2 s^3 - 211 s^2 + 210 s - 1000
                                                     
   3:  -------------------------------------------------------
                                                              
       s^6 - 3 s^5 + 223 s^4 - 441 s^3 + 3220 s^2 - 3000 s    
                                                              
                                                   + 5.545e-13
                                                              
Continuous-time transfer function.

Jorje German 2020-9-8

在 MATLAB Online 中打开

Here is my Original code. As you can see I only know how to use it in this form p41 = (p2*p3-(k23)^2)/(p1*(p2*p3-(k23)^2)-p3*(k12)^2); so I can use sys=p41 and plot certain plots. How can I extract p41 from the previous comment which is From input 1 to output..1 so I can plot it like the one below.

clear all
m1=1;
m2=1;
m3=1;
c1=1;
c2=1;
c3=1;
k01=0;
k12=100;
k23=10;
k34=0;
t = 0:0.01:10;
U1 = 10+2*t;
U2 = sin(t);
s = tf('s');
p1=(m1*s^2 + c1*s +(k01+k12)); 
p2=(m2*s^2 + c2*s +(k12+k23)); 
p3=(m3*s^2 + c3*s +(k23+k34));
p41 = (p2*p3-(k23)^2)/(p1*(p2*p3-(k23)^2)-p3*(k12)^2);
sys=p41;
p41
OPT = stepDataOptions('StepAmplitude', 100); % OPT means option to put in a step
[Y1, t1]=impulse(sys, 10);
[Y2, t2]=step(sys,10,OPT);
[Y3, t3]=lsim(sys,U1,t);
[Y4, t4]=lsim(sys,U2,t);
subplot(2,2,1)
plot(t1,Y1,'r')
hold on 
title ('Impulse Response')
xlabel ('Time (S)')
ylabel("Amplitude)")
grid on
subplot(2,2,2)
plot(t2,Y2,'r')
hold on 
title ('Step Response')
xlabel ('Time (S)')
ylabel("Amplitude)")
grid on
subplot(2,2,3)
plot(t3,Y3,'r')
hold on 
title ('Step Ramp Response')
xlabel ('Time (S)')
ylabel("Amplitude)")
grid on
subplot(2,2,4)
plot(t4,Y4,'r')
hold on 
title ('Sin Response')
xlabel ('Time (S)')
ylabel("Amplitude)")
grid on