PID Tuning Calculator
Calculates P, PI and PID gains from a process model with five methods, simulates the closed-loop step response and a load disturbance, and compares them by overshoot, settling time and IAE.
// Inputs
Check the inputs (positive values, t₆₃ > t₂₈)
// Simulation
Frequently asked questions
Which PID tuning method should I choose?
Ziegler-Nichols is fast but aggressive with high overshoot. Cohen-Coon does better on processes with large dead time. IMC/Lambda balances speed and robustness with a single λ and gives no overshoot with a suitable λ. AMIGO is robustness-oriented and a good default. The tool simulates all methods and compares them by IAE, overshoot and settling time.
How do I find the process model (K, τ, θ)?
With the controller in manual and the process steady, apply a small step (Δu) to the input and record the output. Measure the times to reach 28.3% and 63.2% of the output change (t₂₈, t₆₃); the "From step data" tab calculates K, τ and θ with Smith's method.
What is the difference between Kp, Ti, Td and Kp, Ki, Kd?
Kp·(e + 1/Ti·∫e + Td·de/dt) is the ISA (ideal) form; in parallel form Ki = Kp/Ti and Kd = Kp·Td. Check which form and time unit (seconds / minutes / ms) the PID block in your PLC or drive uses.
How do I choose λ for IMC/Lambda?
λ is the desired closed-loop time constant. A large λ gives a slow but robust loop without overshoot; a small λ is fast but sensitive to model errors. λ ≥ θ is usual; λ = τ is a conservative starting point.
Why is the derivative filtered and taken on PV?
The derivative amplifies measurement noise, so it is filtered (N = 10 here). Taking the derivative of PV instead of the error avoids a jump in the output when the setpoint changes (derivative kick). The simulation uses this common practice.
What to do with dead-time dominant processes?
When θ/τ exceeds 1, PID performance is limited: the derivative helps little and aggressive settings become unstable. PI is usually enough; for very large dead time consider a Smith predictor or model-based control.
What is anti-windup?
When the controller output hits a limit, the integral keeps growing (windup) and causes large overshoot. The simulation uses conditional integration; use the "Controller output limit" option to see the effect of saturation and anti-windup.
How realistic is the simulation?
It uses a linear model with pure dead time. Nonlinear behaviour, noise, actuator speed and sample time can change the results on a real process. Use the calculated gains as a starting point and fine-tune on site.