PID Tuning Cheat Sheet
PID tuning on one page: Ziegler–Nichols tables, Cohen–Coon, lambda tuning for self regulating and integrating loops, PID algorithm forms and a troubleshooting guide.
Download
A one page A4 sheet to print, pin up in the workshop or keep on your phone. Everything on it is also shown below.
Download PDF A4 · 79 KBZiegler–Nichols closed loop (ultimate gain)
| Mode | Kc | Ti | Td |
|---|---|---|---|
| P | 0.5 Ku | ||
| PI | 0.45 Ku | Pu ÷ 1.2 | |
| PID | 0.6 Ku | Pu ÷ 2 | Pu ÷ 8 |
Ku: gain at sustained oscillation, Pu: its period.
Ziegler–Nichols open loop (step test)
| Mode | Kc | Ti | Td |
|---|---|---|---|
| P | τ ÷ (K θ) | ||
| PI | 0.9 τ ÷ (K θ) | 3.33 θ | |
| PID | 1.2 τ ÷ (K θ) | 2 θ | 0.5 θ |
K: process gain, τ: time constant, θ: dead time.
Lambda tuning (PI)
| Self regulating | Kc = τ ÷ (K (λ + θ)), Ti = τ |
| Integrating (level) | Kc = (2λ + θ) ÷ (K (λ + θ)²), Ti = 2λ + θ |
| Choose λ | τ to 3τ, and at least 3θ for robustness |
Cohen–Coon PID
| Kc | (1 ÷ K)(τ ÷ θ)(4/3 + θ ÷ 4τ) |
| Ti | θ (32 + 6θ/τ) ÷ (13 + 8θ/τ) |
| Td | 4θ ÷ (11 + 2θ/τ) |
PID algorithm forms
| Ideal (ISA) | u = Kc [e + (1 ÷ Ti) ∫e dt + Td de/dt] |
| Parallel | u = Kp e + Ki ∫e dt + Kd de/dt, Ki = Kc ÷ Ti, Kd = Kc × Td |
| Series to ideal | Kc = Kc′ (1 + Td′/Ti′), Ti = Ti′ + Td′, Td = Ti′Td′ ÷ (Ti′ + Td′) |
Units you will meet
| Proportional band | PB % = 100 ÷ Kc |
| Reset rate | repeats/min = 1 ÷ Ti (min) |
| Integral time | min/repeat or s/repeat |
Typical starting values
| Loop | Kc | Ti | Td |
|---|---|---|---|
| Flow | 0.3 to 0.8 | 0.05 to 0.2 min | 0 |
| Liquid pressure | 0.5 to 2 | 0.1 to 0.5 min | 0 |
| Gas pressure | 2 to 10 | 1 to 5 min | 0 |
| Level (averaging) | 1 to 5 | 5 to 20 min | 0 |
| Temperature | 1 to 10 | 2 to 20 min | 0.1 to 2 min |
Starting points only; always tune on the real process.
Troubleshooting
| Symptom | Try |
|---|---|
| Fast oscillation | Lower Kc |
| Slow oscillation | Increase Ti (less integral) |
| Sluggish, offset lasts long | Raise Kc or shorten Ti |
| Noisy output | Reduce Td, filter PV |
| Oscillates at constant amplitude | Check valve stiction first |
Controller action
- Reverse acting: output falls when PV rises (most heating and level outflow loops)
- Direct acting: output rises when PV rises (cooling, level inflow control)
- Wrong action makes the loop run away to a limit
Related Calculators and Tools
Frequently Asked Questions
What are the Ziegler–Nichols PID settings?
Kc = 0.6 Ku, Ti = Pu ÷ 2 and Td = Pu ÷ 8 from the closed loop test.
How do I convert gain to proportional band?
PB % = 100 ÷ Kc. A gain of 2 is a 50 % proportional band.
Which tuning method is most robust?
Lambda tuning, because you choose the closed loop speed directly and it does not aim for an oscillatory response.
Learn more on the blog
PID controller tuning explained
A practical guide on instrumentationblog.in that explains the theory behind this cheat sheet.
Read Full Article