Process control
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This document provides information on tuning PID controllers using the Ziegler-Nichols tuning method. It summarizes the tuning parameters for P, PI, and PID controllers calculated using this method. It also includes the MATLAB code and results for simulating the step response of proportional and proportional-integral controllers designed using the Ziegler-Nichols tuning parameters. The step responses show the peak amplitude, overshoot, settling time, and other characteristics. Bode plots are also included showing the gain margin, phase margin, and stability for each controller type.
![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-130329232019-phpapp01/85/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-130329232019-phpapp01/85/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-130329232019-phpapp01/85/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