how to get tf answer for this problem?

2022 1 12
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a=[40]
a = 40
b=[0.05 1]
b = 1×2
0.0500 1.0000
c=[1]
c = 1
d=[0.5 1]
d = 1×2
0.5000 1.0000
e=[0.8]
e = 0.8000
f=[1 1]
f = 1×2
1 1
g=[0.1]
g = 0.1000
h=[0.04 1]
h = 1×2
0.0400 1.0000
T1=tf(a,b)
T1 = 40 ---------- 0.05 s + 1 Continuous-time transfer function.
T2=tf(c,d)
T2 = 1 --------- 0.5 s + 1 Continuous-time transfer function.
T3=tf(e,f)
T3 = 0.8 ----- s + 1 Continuous-time transfer function.
T4=tf(g,h)
T4 = 0.1 ---------- 0.04 s + 1 Continuous-time transfer function.
A=(T1*T2*T3)
A = 32 ---------------------------------- 0.025 s^3 + 0.575 s^2 + 1.55 s + 1 Continuous-time transfer function.
B=(T1*T2*T4)
B = 4 ---------------------------------- 0.001 s^3 + 0.047 s^2 + 0.59 s + 1 Continuous-time transfer function.
C=1+B+A
C = 2.5e-05 s^6 + 0.00175 s^5 + 0.04333 s^4 + 0.5701 s^3 + 5.341 s^2 + 27.22 s + 37 ------------------------------------------------------------------------------- 2.5e-05 s^6 + 0.00175 s^5 + 0.04333 s^4 + 0.4381 s^3 + 1.537 s^2 + 2.14 s + 1 Continuous-time transfer function.
A/C
ans = 0.0008 s^6 + 0.056 s^5 + 1.386 s^4 + 14.02 s^3 + 49.17 s^2 + 68.48 s + 32 ------------------------------------------------------------------------------------------------------------------------ 6.25e-07 s^9 + 5.813e-05 s^8 + 0.002128 s^7 + 0.0419 s^6 + 0.5302 s^5 + 4.678 s^4 + 25.42 s^3 + 68.81 s^2 + 84.57 s + 37 Continuous-time transfer function.
i want A to be like this 32/((1+.05s)(1+0.5s)(1+s)) is this possible

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Star Strider
Star Strider 2022-1-12
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1 个投票

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Almost.
Use the zpk function to do the format transformation.
a=[40];
b=[0.05 1];
c=[1];
d=[0.5 1];
e=[0.8];
f=[1 1];
g=[0.1];
h=[0.04 1];
T1=tf(a,b);
T2=tf(c,d);
T3=tf(e,f);
T4=tf(g,h);
A=(T1*T2*T3)
A = 32 ---------------------------------- 0.025 s^3 + 0.575 s^2 + 1.55 s + 1 Continuous-time transfer function.
Azpk = zpk(A)
Azpk = 1280 ------------------ (s+20) (s+2) (s+1) Continuous-time zero/pole/gain model.
B=(T1*T2*T4)
B = 4 ---------------------------------- 0.001 s^3 + 0.047 s^2 + 0.59 s + 1 Continuous-time transfer function.
Bzpk = zpk(B)
Bzpk = 4000 ------------------- (s+25) (s+20) (s+2) Continuous-time zero/pole/gain model.
C=1+B+A
C = 2.5e-05 s^6 + 0.00175 s^5 + 0.04333 s^4 + 0.5701 s^3 + 5.341 s^2 + 27.22 s + 37 ------------------------------------------------------------------------------- 2.5e-05 s^6 + 0.00175 s^5 + 0.04333 s^4 + 0.4381 s^3 + 1.537 s^2 + 2.14 s + 1 Continuous-time transfer function.
Czpk = zpk(C)
Czpk = (s+34.37) (s+20) (s+8.593) (s+2) (s^2 + 5.036s + 125.3) ------------------------------------------------------- (s+25) (s+20)^2 (s+2)^2 (s+1) Continuous-time zero/pole/gain model.
AC = A/C
AC = 0.0008 s^6 + 0.056 s^5 + 1.386 s^4 + 14.02 s^3 + 49.17 s^2 + 68.48 s + 32 ------------------------------------------------------------------------------------------------------------------------ 6.25e-07 s^9 + 5.813e-05 s^8 + 0.002128 s^7 + 0.0419 s^6 + 0.5302 s^5 + 4.678 s^4 + 25.42 s^3 + 68.81 s^2 + 84.57 s + 37 Continuous-time transfer function.
ACzpk = zpk(AC)
ACzpk = 1280 (s+25) (s+20)^2 (s+2)^2 (s+1) ----------------------------------------------------------------- (s+34.37) (s+20)^2 (s+8.593) (s+2)^2 (s+1) (s^2 + 5.036s + 125.3) Continuous-time zero/pole/gain model.
Amr = minreal(A)
Amr = 1280 ------------------------ s^3 + 23 s^2 + 62 s + 40 Continuous-time transfer function.
Amrzpk = zpk(Amr)
Amrzpk = 1280 ------------------ (s+20) (s+2) (s+1) Continuous-time zero/pole/gain model.
Bmr = minreal(B)
Bmr = 4000 --------------------------- s^3 + 47 s^2 + 590 s + 1000 Continuous-time transfer function.
Bmrzpk = zpk(Bmr)
Bmrzpk = 4000 ------------------- (s+25) (s+20) (s+2) Continuous-time zero/pole/gain model.
Cmr = minreal(C)
Cmr = s^5 + 50 s^4 + 733 s^3 + 8144 s^2 + 5.074e04 s + 7.4e04 ------------------------------------------------------- s^5 + 50 s^4 + 733 s^3 + 2864 s^2 + 4180 s + 2000 Continuous-time transfer function.
Cmrzpk = zpk(Cmr)
Cmrzpk = (s+34.37) (s+8.593) (s+2) (s^2 + 5.036s + 125.3) ------------------------------------------------ (s+25) (s+20) (s+2)^2 (s+1) Continuous-time zero/pole/gain model.
ACmr = minreal(AC)
ACmr = 1280 s^3 + 8.32e04 s^2 + 1.792e06 s + 1.28e07 -------------------------------------------------------------------------- s^6 + 88 s^5 + 2957 s^4 + 5.155e04 s^3 + 566600 s^2 + 4.228e06 s + 1.48e07 Continuous-time transfer function.
ACmrzpk = zpk(ACmr)
ACmrzpk = 1280 (s+25) (s+20)^2 --------------------------------------------------- (s+34.37) (s+20)^2 (s+8.593) (s^2 + 5.036s + 125.3) Continuous-time zero/pole/gain model.
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arian hoseini
arian hoseini 2022-1-12
can we do something about (s+20)^2
the answer i need is this1280(s + 25)/( s 4 + 48s 3 + 637s 2 + 6870s + 37000)
by the way thank u ...ur solution is perfect
Star Strider
Star Strider 2022-1-12
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Ran in:
My pleasure!
The form you need is not an option in any of the representations I looked through. The zpk representation is as close as it is possible to get. Dividing the transfer function by (s+20)^2 changes nothing about it.
If you absolutely must have that representation, you will need to write it yourself, or possibly use the Symbolic Math Toolbox. Special representations such as that are simply not possible in the Control System Toolbox.
s = tf('s');
a=[40];
b=[0.05 1];
c=[1];
d=[0.5 1];
e=[0.8];
f=[1 1];
g=[0.1];
h=[0.04 1];
T1=tf(a,b);
T2=tf(c,d);
T3=tf(e,f);
T4=tf(g,h);
A=(T1*T2*T3);
% Azpk = zpk(A);
B=(T1*T2*T4);
% Bzpk = zpk(B)
C=1+B+A;
% Czpk = zpk(C)
AC = A/C;
% ACzpk = zpk(AC)
% Amr = minreal(A)
% Amrzpk = zpk(Amr)
% Bmr = minreal(B)
% Bmrzpk = zpk(Bmr)
% Cmr = minreal(C)
% Cmrzpk = zpk(Cmr)
ACmr = minreal(AC);
ACmrzpk = zpk(ACmr)
ACmrzpk = 1280 (s+25) (s+20)^2 --------------------------------------------------- (s+34.37) (s+20)^2 (s+8.593) (s^2 + 5.036s + 125.3) Continuous-time zero/pole/gain model.
.

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