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**OPTIMUM
PID CALCULATION**

Examples
based on Zieglar-Nichols's tuning rule

**1. Example using data
captured using a paperless recorder of a level increasing process**

2. Process rate = (PV2 - PV1) / (T2 - T1) = (80% - 60%)/(32.4 s - 12.8 s) = 1.0204 % / s

3. Controller output difference = MV2 - MV1 = 64.9% - 40.5% = 24.4%

4. RR = process rate / controller output = 1.0204 / 24.4 = 0.04182 / s

5. For level process, use PI mode. Hence, based on Z-N tuning rule:

P = 111.1 x 0.04182 x 2.6 = 12.1%

I = 3.33 x 2.6 = 9 s

**3. Example using data
captured using a chart recorder of a level increasing process**

1. Chart speed = 1000 mm
/ hr = 3.6 s / mm

2. x-axis (time's scale)
= 10 mm = 36 s , y-axis (measurement's scale) = 10 mm thick
mark = 10 %

3. Td = 1 mm = 3.6 s

4. Time difference between
point A and B = 6 mm = 21.6 s

5. Process rate = (68% -
52%) / 21.6 s = 0.7407 % / s

6. Controller output change
= MV2 - MV1 = 44.3% - 25.9% = 18.4%

7. RR = process rate / step
input = 0.7407 / 18.4 = 0.04026 / s

8. Level process ==> Mode
= PI

P = 111.1
x 0.04026 x 3.6 = 16.1%

I = 3.33
x 3.6 = 12 s

**TEST
YOUR SELF**: Can you calculate the optimum PI for this level decreasing
process