Process control
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This document discusses Ziegler-Nichols tuning method for proportional (P), proportional-integral (PI) and proportional-integral-derivative (PID) controllers. It provides the tuning parameters for each controller type based on the Ziegler-Nichols method. Simulation results including step response and Bode plots are presented for P and PI controllers designed using the Ziegler-Nichols tuning parameters. The P controller is stable but the PI controller is unstable based on the Bode plot results.
![Data need in Ziegler-Nichols tuning
method
R(S) U(t) C(S)
G(S)
m.file to find Ku and Pu
n = 1;
d = poly([0 -1 -5]); Gain margin frequency , w 2.2361
sys = tf(n,d) Ultimate gain, Ku 30
allmargin (sys)
Ultimate period Pu = 2 pi / w 2.8050
w=2.24
pu=2*pi/w Phase Margin 76.6603](https://image.slidesharecdn.com/processcontrolturki-130329231856-phpapp02/85/Process-control-2-320.jpg)
![Step Response of Proportional
Controller
M.file for step response
curve for P controller:
n=15;
d=poly([0 -1 -5]);
b1=tf(n,d);
b2=1;
sys=feedback(b1,b2);
step(sys)
bode(sys)
Step Peak Overshoot Settling Time Rise Time St.St. Value Offset
Response Amplitude
P 1.64 64.1 18 0.74 1 0](https://image.slidesharecdn.com/processcontrolturki-130329231856-phpapp02/85/Process-control-5-320.jpg)
![Step Response of PI Controller
M.File for step response
curve for PI controller:
n=12*[2.33 1];
d=[2.33 0];
b1=tf(n,d);
n2=1;
d2=poly([0 -1 -5]);
b2=tf(n2,d2);
b3=series(b1,b2);
b4=1;
sys=feedback(b3,b4);
step(sys)
bode(sys)
Step Peak Overshoot Settling Time Rise Time St.St. Value Offset
Response Amplitude
PI 2.01 101 109 0.74](https://image.slidesharecdn.com/processcontrolturki-130329231856-phpapp02/85/Process-control-8-320.jpg)
Process control
- 1. Prepared by: Turki Al hasani Ammar Khayat Adnan Ajohani Hamza Alsharef Mohammed Naji
- 2. Data need in Ziegler-Nichols tuning method R(S) U(t) C(S) G(S) m.file to find Ku and Pu n = 1; d = poly([0 -1 -5]); Gain margin frequency , w 2.2361 sys = tf(n,d) Ultimate gain, Ku 30 allmargin (sys) Ultimate period Pu = 2 pi / w 2.8050 w=2.24 pu=2*pi/w Phase Margin 76.6603
- 3. Ziegler-Nichols tuning method Controller type Kp tI td P 0.5 Ku = 15 ------ ------ PI 0.4 Ku = 12 0.83 Pu = 2.33 ------ PID 0.6 Ku = 18 0.5 Pu = 1.4025 0.125 Pu = 0.351
- 4. Method of Proportional Controller 15
- 5. Step Response of Proportional Controller M.file for step response curve for P controller: n=15; d=poly([0 -1 -5]); b1=tf(n,d); b2=1; sys=feedback(b1,b2); step(sys) bode(sys) Step Peak Overshoot Settling Time Rise Time St.St. Value Offset Response Amplitude P 1.64 64.1 18 0.74 1 0
- 6. Bode Diagram of Proportional Controller Bode Gain Frequency Phase Delay Stability Diagram Margin Margin Margin P 0.00245 2.24 - 0.0165 0 stable
- 7. Step Response for Proportional Integral Controller Design
- 8. Step Response of PI Controller M.File for step response curve for PI controller: n=12*[2.33 1]; d=[2.33 0]; b1=tf(n,d); n2=1; d2=poly([0 -1 -5]); b2=tf(n2,d2); b3=series(b1,b2); b4=1; sys=feedback(b3,b4); step(sys) bode(sys) Step Peak Overshoot Settling Time Rise Time St.St. Value Offset Response Amplitude PI 2.01 101 109 0.74
- 9. Bode Diagram for PI Controller Bode Gain Frequency Phase Delay Stability Diagram Margin Margin Margin PI - 13.4 1.56 - 15 2.99 Unstable