Tune PID values from process or test data. Check rise, overshoot, and settling estimates instantly. Export results, review formulas, and compare practical tuning options.
This calculator helps you estimate controller settings from either a sustained oscillation test or a first-order plus dead-time process model. It supports P, PI, and PID modes, then simulates an estimated step response so you can compare speed and stability before field changes.
Closed-loop methods are useful when you can safely find the ultimate gain and period. Open-loop methods are better when you already have process gain, time constant, dead time, and a desired robustness target. Use the response plot to judge aggressiveness, overshoot, and settling behavior.
| Application | Method | Mode | Inputs | Kc | Ti | Td |
|---|---|---|---|---|---|---|
| Flow Loop | Ziegler-Nichols Closed-Loop | PID | Ku=6.2, Pu=1.8 | 3.72 | 0.9 | 0.225 |
| Pressure Loop | Tyreus-Luyben Closed-Loop | PI | Ku=4.8, Pu=2.6 | 1.5 | 5.72 | 0 |
| Thermal Loop | IMC Open-Loop | PID | K=1.5, Tau=18, Theta=4, Lambda=6 | 1.2 | 20 | 1.8 |
| Mixing Tank | SIMC Open-Loop | PI | K=2.2, Tau=12, Theta=2, Lambda=5 | 0.7792 | 12 | 0 |
| Level Loop | Cohen-Coon Open-Loop | PID | K=0.8, Tau=25, Theta=5 | 8.6458 | 11.3699 | 1.7544 |
The page reports the ideal controller form and also shows the parallel gains.
Ideal form: u(t) = bias + Kc [ e(t) + (1/Ti) ∫e(t)dt + Td de(t)/dt ] Parallel form: u(t) = bias + Kp e(t) + Ki ∫e(t)dt + Kd de(t)/dt Conversion: Kp = Kc Ki = Kc / Ti Kd = Kc × Td
Ziegler-Nichols and Tyreus-Luyben use the ultimate gain Ku and ultimate period Pu from a sustained oscillation test. Ziegler-Nichols is faster and more aggressive. Tyreus-Luyben is usually smoother and more robust.
Cohen-Coon uses process gain, time constant, and dead time. IMC and SIMC also use a lambda target. Larger lambda values usually reduce overshoot and improve robustness, but they slow the loop.
Start with IMC or SIMC when you have a process model and want smoother behavior. Start with Tyreus-Luyben when you only have ultimate test data and want a less aggressive closed-loop starting point.
It intentionally targets a faster response. That usually means larger gain and stronger correction. The tradeoff is higher overshoot and sometimes weaker robustness on noisy or delayed processes.
Lambda sets the desired closed-loop speed in IMC and SIMC tuning. Smaller lambda gives a faster loop. Larger lambda slows the response, reduces overshoot, and often improves robustness.
Yes. A negative process gain means the plant moves opposite to the manipulated variable. The computed controller gain will reflect that sign so the loop still acts with negative feedback.
P-only control reacts to current error but does not accumulate past error. Many plants therefore settle with a remaining offset. Adding integral action usually removes that steady-state error.
No. It is an engineering estimate based on the supplied model and a discrete simulation. Real valves, noise, saturation, filters, and nonlinear behavior can change the final plant response.
Use Cohen-Coon when you have a first-order plus dead-time fit and want an assertive open-loop tuning rule. It is useful for moderate dead time but can be too aggressive for fragile systems.
Use them as starting values, not blind final settings. Apply changes with limits, alarms, and operator awareness. Then trim the gains on the real process while watching stability, constraints, and safety.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.