LABORATORY MANUAL CONTROL SYSTEM DESIGN B.TECH …

LABORATORY MANUAL

CONTROL SYSTEM DESIGN

B.TECH

7TH SEMESTER

DEPARTMENT OF ELECTRICAL ENGINEERING

JHARKHAND RAI UNIVERSITY

KAMRE, RANCHI

LAB MANUAL CONTROL SYSTEM DESIGN

S. No. NAME OF EXPERIMENT PAGE

No.

1 BODE PLOT FOR A TRANSFER FUNCTION 3-4

2 POLE –ZERO PLOT OF A GIVEN TRANSFER 5-6

FUNCTION

3 PD,PI CIONTROLLER DESIGN IN TIME AND 7-10

FREQUENCY DOMAIN

4 PID CIONTROLLER DESIGN IN TIME AND 11-12

FREQUENCY DOMAIN

5 PHASE LEAD DESIGN IN TIME AND FREQUENCY 13-14

DOMAIN

6 PHASE LAG COMPENSATOR DESIGN IN TIME AND 15-16

FREQUENCY DOMAIN

7 ROOT LOCUS FOR A TRANSFER FUNCTION 17-18

8 TRANSFER FUNCTION OF DC MOTOR AND 19-20

PERFORMANCE IN TIME AND FREQUENCY

DOMAIN.

2


EXPERIMENT NO:01

BODE PLOT FOR A TRANSFER FUNCTION

AIM: To plot the bode plot for a given transfer and find its gain and phase margin.

SOFTWARE REQUIRED: MATLAB

THEORY:

Bode plot is a graphical representation for determining the stability of the control

system. It consist of two different plots. Magnitude plot 20 10

Phase plot, phase angle

Magnitude plot is the log of magnitude of a sinusoidal transfer function and other

is plot of phase angle, both plots are plotted the frequency. The curves are drawn

on semi log paper using log scale for frequency and linear scale for magnitude (in

decibels) or phase angle (in degrees).

= (1+ )(1+ )

(1+ )(1+ )

1 2

N- Number of poles at origin i.e. N defines the type of system =

Magnitude:

(1+ )(1+ )

(1+)(1+

2) 1

20

+ 20 1 + 2 2

= 20+ 201 + 2 2 −

10

20 2 − 20 1 + 2 2 − 20 1 + 2 2

1 2

Phase:

3

LAB MANUAL CONTROL SYSTEM DESIGN ∠ =

0 = −1 + −1 + −1 − −1 − −1 1 − −1 2

Example:== 1000

(1+0.1 )(1+0.001 )

PROGRAM:

PROCEDURE:

1. Open MATLAB. 2. Generate the transfer function. 3. Give command as: bode (tf) to generate the bode plot. 4. Find out the value of gain margin and phase margin.

RESULT: Thus the bode plot of a given transfer function is plotted and GM

and PM is obtained.

4


EXPERIMENT NO: 02

POLE –ZERO PLOT OF A GIVEN TRANSFER FUNCTION

AIM:To plot the pole –zero plot of a given transfer function.

SOFTWARE REQUIRED: MATLAB.

THEORY: ( ) = = ( + 1)( + 2)

( ) ( + 1)( + 2)

K= gain factor.

Poles: those values of s for which G(s) tends to infinity. = 1, = 2

Zeroes: those values of s for which G(s) tends to zero. = 1, = 2

Example = ( +1)( +2) ( +3)( +4)

PRORAM:

5


PROCEDURE:

1. Open MATLAB. 2. Generate transfer function. 3. Give command as: pzmap(tf) for plotting pole zero plot. 4. Observe the position of pole and zero.

RESULT: Thus the pole-zero plot is obtained and the position is analyzed.

6


EXPERIMENT NO:03

PD,PI CIONTROLLER DESIGN IN TIME AND FREQUENCY

DOMAIN

AIM: To design the PD,PI controller for a given transfer function in time

and frequency domain.

SOFTWARE RQUIRED: MATLAB

THEORY:

PD controller- proportional derivative controller

R(s) E(S)

U(S)

2

Y(s)

( + 2 )

( ) = +

= + = (1 + )

Time domain

Give the step input and analyze rise time, overshoot, and settling time, bandwidth.

Frequency domain

Using bode plot analyze the phase and gain margin.

7


PI (proportional integral COTROLLER):

2

R(s) E(s)

U(s)

( + 2 )

Y( (s)

=+ ∗ ( )

= +

Time domain

Give the step input and analyze rise time, overshoot, and settling time,

bandwidth. Frequency domain


8


PROGRAM:

PROCEDURE:

FOR PD CONTROLLER

TIME DOMAIN

1. For a transfer function of any system, give values of parameters. 2. Declare the gain values of both controllers. 3. Get the overall transfer function of the closed loop control system. 4. Give the unit step signal as input signal to the transfer function. 5. Get the output plot and analyze the parameters.

FREQUENCY DOMAIN

1. For a transfer function of any system, give values of parameters. 2. Declare the gain values of both controllers. 3. Get the overall transfer function of the closed loop control system. 4. Give the command as: bode(tf). 5. Get the output plot in frequency domain and analyze the parameters.

FOR PI CONTROLLER

TIME DOMAIN


9


FREQUENCY DOMAIN


Now compare the parameters for both type of controllers.

RESULT:Thus the PD,PI controller for a given transfer function is designed and

parameters are analyzed in time and frequency domain.

10


EXPERIMENT NO:04

PID CIONTROLLER DESIGN IN TIME AND FREQUENCY

DOMAIN

AIM: To design the PID controller for a given transfer function in time

and frequency domain.

SOFTWARE RQUIRED: MATLAB

THEORY:

PD controller- proportional derivative controller

R(s) E(S)

U(S)

2

Y(s)

( + 2 )

=+

( )

+ ∗ ( )

= + +

11


Time domain

Give the step input and analyze rise time, overshoot, and settling time, bandwidth.

Frequency domain


PROGRAM:

PROCEDURE:

TIME DOMAIN


FREQUENCY DOMAIN


Analyze the parameters of PID controller.

RESULT:Thus the PID controller for a given transfer function is designed

and parameters are analyzed in time and frequency domain.

12


EXPERIMENT NO:05

PHASE LEAD DESIGN IN TIME AND FREQUENCY DOMAIN

AIM: To design a phase Lead and a phase Lag compensator in time and frequency

Domain.

SOFTWARE REQUIRED: MATLAB

THEORY:

R(s) E(s) U(s) G(s)

C(s)

Transfer function of compensator of phase lead compensator

= 1+

, 0< < 1

1+

PROGRAM:

13


PROCEDURE

TIME DOMAIN

1. For a transfer function of any system, give values of parameters. 2. Declare the gain values of compensator. 3. Get the overall transfer function of the closed loop control system. 4. Give the unit step signal as input signal to the transfer function. 5. Get the output plot and analyze the parameters.

FREQUENCY DOMAIN

1. For a transfer function of any system, give values of parameters. 2. Obtain bode plot for this transfer function and analyze the GM,PM. 3. Declare the gain values of compensator. 4. Get the overall transfer function of the closed loop control system. 5. Give the command as: bode(tf). 6. Get the output plot in frequency domain and analyze the PM,GM.

RESULT: Thus we plotted the phase lead plot and obtained the maximum

phase lead that can be added to any system.

14


EXPERIMENT NO:06

PHASE LAG COMPENSATOR DESIGN IN TIME AND

FREQUENCY DOMAIN

AIM: To design a phase Lag compensator in time and frequency

domain. SOFTWARE REQUIRED: MATLAB THEORY:

R(s) E(s)

U(s) G(s)

C(s)

Transfer function of compensator of phase lead compensator (1+ )

= (1+ )

, > 1

PROGRAM:

15


PROCEDURE

PHASE LAG COMPENSATOR

TIME DOMAIN

1. For a transfer function of any system, give values of parameters. 2. Declare the gain values of compensator. 3. Get the overall transfer function of the closed loop control system. 4. Give the unit step signal as input signal to the transfer function. 5. Get the output plot and analyze the parameters.

FREQUENCY DOMAIN

1. For a transfer function of any system, give values of parameters. 2. Obtain bode plot for this transfer function and analyze the GM,PM. 3. Declare the gain values of compensator. 4. Get the overall transfer function of the closed loop control system. 5. Give the command as: bode(tf). 6. Get the output plot in frequency domain and analyze the PM,GM.

RESULT:Thus we plotted the phase lead plot and obtained the maximum phase

lead added to the transfer function of any system

16


EXPERIMENT NO:07

ROOT LOCUS FOR A TRANSFER FUNCTION

AIM:Draw a root locus for a given transfer

function. SOFTWARE REQUIRED: MATLAB

THEORY:

Roots of characteristics equation corresponds to a particular value of system

parameter can be then located on the locus or the value of the parameter for

a desired root location can be determined from the locus. =

( + )

Characteristic equation is 2 + + = 0

2

= −

+, − [(

) − ]

1,2 2

2

PROGRAM:

17


PROCEDURE:

1. Generate the transfer function of a system 2. Give command as: rlocus(tf). 3. Analyze the root locus by changing the gain.

RESULT: Thus we obtained the root locus plot.

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EXPERIMENT NO: 08

TRANSFER FUNCTION OF DC MOTOR AND PERFORMANCE

IN TIME AND FREQUENCY DOMAIN.

AIM:To obtain the transfer function of a DC motor and its bode plot and time

responses specification.

SOFTWARE REQUIRED:MATLAB

THEORY

PROGRAM

19


PROCEDURE

TIME DOMAIN

1. Obtain the transfer function. 2. Give input as step signal as: step(tf) 3. Analyze the performance specifications.

FREQUENDY DOMAIN

1. Obtain the transfer function. 2. Obtain the bode plot by giving command as :bode(tf) 3. Analyze the performance specifications

RESULT: Thus we obtained the transfer function and performance specification

in time and frequency domain.

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LABORATORY MANUAL CONTROL SYSTEM DESIGN B.TECH …

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