6_8 Ziegler Nichols tuning controller parameters and digital controllers.ppt

Session 6
Session 6
Automatic control Theory
Automatic control Theory
Dr. Saber Abdrabbo
Dr. Saber Abdrabbo

Sequence 6.8
Sequence 6.8
Ziegler Nichols tuning controller parameters
and digital controllers

Preview
Preview: Last Sequences covered structure and
: Last Sequences covered structure and
design of PID controllers
design of PID controllers

Present
Present: Current sequence covers design of
: Current sequence covers design of
PID controllers using Ziegler Nichols tuning
PID controllers using Ziegler Nichols tuning
Methods for practical applications with Matlab
Methods for practical applications with Matlab
code and digital PID controllers
code and digital PID controllers

Ziegler Nichols tuning controller parameters
Method (I) stability margin method:
-The controller is switched to pure P action.
-The gain of the P controller is continuously increased until the closed loop
shows permanent oscillations.
-The value of the gain at this state is denoted as the critical controller gain
(Ku).
-The length of period (critical period) of the oscillations is measured (Pu).
determines the controller tuning values according to the following
formulas

Example
Given the plant
Find Kp,Kd and Ki using Zeigler Nichols
Solution
By applying Rouths array hence
Kp=15
from Rrouth schema
(Third row from bottom)
30S2
+6000=0
Replace j by S
-30 2
+6000=0
p=14 rad/sec
)
200
30
(
400
)
( 2



S
S
S
S
Gp
1 200
30 400Kp
(6000-400Kp)/30 0
400Kp
3
2
1

Example (cont.)
Pu=2П/
For PID controller
Kp=7.5
Ki=40
Kd=0.5
Matlab code for Ziegler Nichols Method
clg, rlocus(ng,dg)
[km,pole]=rlocfind(ng,dg)
keyboard
wm=imag(pole);
kp=.5*km;
pu=2*pi/wm;
kd= 0.075*kp*pu
ki=1.2*kp/pu

Method (II) step response Method : The rules are based directly on the
slope of the tangent at the turning point and on the delay of the step
response. The transfer function will take the following form.
Where
is the pure time delay, and is time constant of the system
One has to observe that the measurement of the step response needs
only to be taken at the turning point T, as the slope of the tangent already
describes the ratio . Using the measured data and as well as the formula
given in the following table the controller tuning parameters can be
determined by simple calculations.
d
 

Conversion from continuous to digital
Conversion using c2dm
[numDz,denDz] = c2dm (num,den,Ts,'zoh')
[F,G,H,J] = c2dm (A,B,C,D,Ts,'zoh')
1. Transfer function
Example
Suppose you have the following continuous transfer function
M=1;
b=10;
k=20;
num=[1];
den=[M b k];
Ts=1/100;
[numDz,denDz]=c2dm(num,den,Ts,'zoh')

transient response
Suppose we have the following discrete transfer function
numDz=[1];
denDz=[1 -0.3 0.5];
[x] = dstep (numDz,denDz,51);
t = 0:0.05:2.5;
stairs (t,x)

2. State-Space
Matlab code
M=1;
b=10;
k=20;
A=[0 1;
-k/M -b/M];
B=[ 0;
1/M];
C=[1 0];
D=[0];
Ts=1/100;
[F,G,H,J] = c2dm (A,B,C,D,Ts,'zoh')

)
(
)
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
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Digital I Controller
Digital P and D controller
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 
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(
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1
(
2
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1
( k
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2
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( Z
E
Z
ZE
T
Z
U
Z
ZU 
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Digital PID Controller
or

Summary
Summary
Current sequence covered the following
Current sequence covered the following
1- Ziegler Nichols Method for tuning PID
1- Ziegler Nichols Method for tuning PID
parameters
parameters
2-Conversion from continuous system to digital
2-Conversion from continuous system to digital
systems
systems
3-Structure of PID digital controllers
3-Structure of PID digital controllers
1.
1. Matlab code to design PID controllers
Matlab code to design PID controllers

Assessment
Assessment
To view the assessment click on the
To view the assessment click on the
link below.
link below.
Good Luck
Good Luck

6_8 Ziegler Nichols tuning controller parameters and digital controllers.ppt

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