1. Control System Toolbox (Part-I)

2. Outline Introduction Transfer Function Models Pole-Zero maps
From Numerator & Denominator Coefficients
From Zero-Pole-Gain
Pole-Zero maps
Simplification of Block Diagrams
Series Blocks
Parallel Blocks
Feedback loops

3. Transfer Function Model Using Numerator & Denominator Coefficients
This transfer function can be stored into the MATLAB
num = 100;
den = [ ];
sys=tf(num,den)
To check your entry you can use the command printsys as shown below:
printsys(num,den);
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4. Transfer Function Model Using Zeros, Poles and Gain (ZPK model)
This transfer function can be stored into the MATLAB
Zeros=-3;
Poles= [ ];
K=100;
sys=zpk(Zeros,Poles,K)
To check your entry you can use the command printsys as shown below:
printsys(num,den);
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5. Poles & Zeros
We can find poles with the help of following MATLAB command.
poles = roots(den)
We can find Zeros with the help of following MATLAB command
zeros = roots(num)
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6. contd….. Poles & Zeros
We can plot the poles of the above transfer function marked by the symbol ‘x’.
plot(poles,’x’)
To plot the poles and zeros of any transfer function there is a built in function pzmap in the MATLAB
pzmap(num,den)
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7. Series Blocks
Blocks in series can be simplified by using series command S
9S + 17
9(S+3)
2S2 + 9s + 27
num1 = [1 0];
den1 = [9 17];
num2 = 9*[1 3];
den2 = [ ];
[num12, den12] = series (num1,den1,num2,den2);
printsys(num12,den12);
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8. Contd… Series Blocks
Blocks in series can also be simplified by using conv command S
9S + 17
9(S+3)
2S2 + 9s + 27
num1 = [1 0];
den1 = [9 17];
num2 = 9*[1 3];
den2 = [ ];
num12 =conv(num1,num2);
den12 = conv(,den1,den2);
printsys(num12,den12);
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9. Parallel Block
Blocks in parallel can be simplified by using parallel command
num1 = [1 2];
den1 = [ ];
num2 = [1 3];
den2 = [ ];
[num, den]=parallel(num1,den1,num2,den2);
printsys(num,den);
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10. Closed-Loop Transfer Function (Unity Feedback)
Closed loop transfer function with unity feedback can be simplified using cloop command.
C(S)
R(S) - 9
S + 5
num = 9;
den = [1 5];
[numcl, dencl] = cloop(num, den,-1);
printsys(numcl,dencl)
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11. Closed-loop transfer function
If the feedback is not unity then we can use feedback command to simplify the canonical form.
C(S)
R(S) - 1
S + 1 2 S
num1 = 1;
den1 = [1 1];
num2 = 2;
den2 = [1 0];
[numcl,dencl] = feedback(num1,den1,num2,den2,-1);
printsys(numcl,dencl)
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12. Exercise#1
Simplify the following block diagram and determine the following (Assume K=10).
Closed loop transfer function (C/R)
Poles
Zeros
Pole-zero-map

13. Exercise#2
Simplify the following block diagram and determine the following.
Closed loop transfer function (C/R)
Poles
Zeros
Pole-Zero-map + - R C

14. End of Tutorial You can Download this tutorial from
End of Tutorial
11/11/2018