power and control system, Lecture notes of Control Systems

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1

Control System Toolbox (Part-I)

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Outline

• (^) Introduction
• (^) Transfer Function Models
  • (^) From Numerator & Denominator Coefficients
  • (^) From Zero-Pole-Gain
• (^) Pole-Zero maps
• (^) Simplification of Block Diagrams
  • (^) Series Blocks
  • (^) Parallel Blocks
  • (^) Feedback loops

Transfer Function Model Using Zeros, Poles and Gain

(ZPK model)

This transfer function can be stored into the

MATLAB

Zeros=-3;

Poles= [-1 -2];

K=100;

sys=zpk(Zeros,Poles,K)

To check your entry you can use the command

printsys as shown below:

printsys(num,den);

1 2

1

s p s p

K s z

s s

s

G s

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)

4 10

3 5

2

2

 

 



s s

s s

G ( s )

Series Blocks

S

9S + 17

9(S+3)

2S

**2

• 9s + 27**

num1 = [1 0];

den1 = [9 17];

num2 = 9*[1 3];

den2 = [2 9 27];

[num12, den12] = series (num1,den1,num2,den2);

printsys(num12,den12);

• (^) Blocks in series can be simplified by using series command

num1 = [1 0];

den1 = [9 17];

num2 = 9*[1 3];

den2 = [2 9 27];

num12 =conv(num1,num2);

den12 = conv(,den1,den2);

printsys(num12,den12);

Contd… Series Blocks

S

9S + 17

9(S+3)

2S

**2

• 9s + 27**

• (^) Blocks in series can also be simplified by using conv command

Closed-Loop Transfer Function (Unity Feedback)

R(S) - C(S)

S + 5

num = 9;

den = [1 5];

[numcl, dencl] = cloop(num, den,-1);

printsys(numcl,dencl)

• (^) Closed loop transfer function with unity feedback can be simplified

using cloop command.

Closed-loop transfer function

R(S) - C(S)

S + 1

S

um1 = 1;

en1 = [1 1];

um2 = 2;

en2 = [1 0];

umcl,dencl] = feedback(num1,den1,num2,den2,-1);

intsys(numcl,dencl)

• (^) If the feedback is not unity then we can use feedback command to

simplify the canonical form.

Exercise#

• (^) Simplify the following block diagram and determine the following.
  • (^) Closed loop transfer function (C/R)
  • (^) Poles
  • (^) Zeros
  • (^) Pole-Zero-map

R

C

( )

( )

3

7 1





s s

s 10

2 1

1

( s  )

2 1

1

( s  )

END OF TUTORIAL