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EEE402 Exp06

This document provides instructions for designing a PID controller for a plant transfer function using root locus analysis and MATLAB. The design requirements specify the desired percent overshoot, settling time, and steady-state error. Using the SISO design tool, a PD controller is first designed by placing a closed-loop pole to meet constraints. Then a PID controller is designed by adding a pole and zero to the compensator. The uncompensated and compensated system responses are analyzed and the PID controller parameters are calculated to physically realize the controller.

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25 views3 pages

EEE402 Exp06

This document provides instructions for designing a PID controller for a plant transfer function using root locus analysis and MATLAB. The design requirements specify the desired percent overshoot, settling time, and steady-state error. Using the SISO design tool, a PD controller is first designed by placing a closed-loop pole to meet constraints. Then a PID controller is designed by adding a pole and zero to the compensator. The uncompensated and compensated system responses are analyzed and the PID controller parameters are calculated to physically realize the controller.

Uploaded by

mustafa27
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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1

UNITED INTERNATIONAL UNIVERSITY (UIU)


COURSE NO. EEE 402 (CONTROL SYSTEM LABORATORY)

EXPT. NO. 6
DESIGN A PID CONTROLLER USING ROOT LOCUS METHOD AND SISO DESIGN TOOL
Design Requirement:

K ( s 8)
and H(s) = 1, design a PID controller so
s 19 s 2 108s 180
that i) Compensated peak time = of uncompensated peak time ii) % OS = 20% and iii)
Steady-state error = 0
Given the transfer function, G ( s )

Procedure:
1.
2.
3.
4.
5.
6.
7.
8.

9.
10.
11.

Using SISO Design tool, create the design for a unity negative feedback system with
G(s) = K(s + 8) /( s + 3)(s + 6) (s + 10) and plot the root locus.
From Edit| SISO Tool Preferences window, select Options tab, select Zero/pole/gain
radio button under Compensator Format and click Ok.
Right click on the SISO Design Tool window and then click on Grid.
Right click on the SISO Design Tool window and then click on Design Constraints|
New from the appeared window. Select Constraint Type as Percent Overshoot, set
Percent Overshoot as 20 and click Ok.
Select the closed-loop pole at the intersection of shadowed region and the root locus.
Write down the value obtained in the C(s) text box. Also, write down the closed-loop
poles and damping ratio obtained from View| Closed Loop Poles.
Select Analysis| Response to Step Command. Write down the values of percent
overshoot, peak time, settling time and steady state error from the appeared window
of LTI Viewer for SISO Design Tool.
Calculate the imaginary part, d and real part, d of the compensated dominant pole
from the two-third value of uncompensated peak time obtained in Step 6.
Find the sum of angles, from the uncompensated systems poles and zeros to the
desired dominant pole calculated in Step 7. Then, calculate the location of
compensator zero, zc using the formula d /(zc d ) = tan ( 1800)
Set the value of the calculated compensated real zero to the root locus using the
window appeared after selecting Compensators| Edit| C, the value of which is
obtained in Step 8.
Repeat Step 6 and discuss your findings. This is the end of PD compensation.
Set another real zero at 0.5 and a pole at 0 using the window appeared after
selecting Compensators| Edit| C.

This sheet for Control System Laboratory has been prepared by:
Md. Iqbal Bahar Chowdhury, Assistant Professor, EEE, UIU.

2
12.

Repeat step 6 and discuss your findings. This is the end of PID compensation.

PostLab:
1.
Fill up the following table:
Uncompensated

PD-compensated

PID-compensated

Plant and
Compensator
Dominant
Poles
K

n
% OS
Ts
Tp
Kp
e()
Other poles
Zeroes
2.

3.

Note the value of K in the C(s) text box. Then using the values of compensated zeros,
poles and this gain, calculate the values of K 1, K2 and K3. Use following formula:
K ( s z c )( s 0.5) K 3 s 2 K 1 s K 2
K
G PID

K1 2 K 3 s
s
s
s
Physically realize the PID controller using the following formula

This sheet for Control System Laboratory has been prepared by:
Md. Iqbal Bahar Chowdhury, Assistant Professor, EEE, UIU.

G PID KGC

K ( s z c )( s 0.5)
K

1
R
C
RC
R2 C1 s 2 2 1 2
R
C
s
1
1

This sheet for Control System Laboratory has been prepared by:
Md. Iqbal Bahar Chowdhury, Assistant Professor, EEE, UIU.

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