Work out pid tuning estimate instantly with clear inputs, formula shown and shareable results.
First-order-plus-dead-time models let a controller be tuned from three numbers: process gain, time constant and dead time. Ziegler-Nichols gives fast but oscillatory response, Cohen-Coon suits dead-time-dominant loops, and IMC/lambda tuning gives a smooth non-oscillatory response that most process plants prefer.
FOPDT tuning
Ziegler-Nichols: Kp = 1.2 tau / (K theta), Ti = 2 theta, Td = 0.5 theta; IMC uses a lambda closed-loop time constant
IMC or lambda tuning. It is stable, has one intuitive knob (desired closed-loop speed) and will not leave the loop oscillating.
Tau/theta above about 4 is easy to control; below 1 the loop is dead-time dominated and needs conservative tuning or a model-based controller.