IMC PID Designer

Pick a process model, set its parameters, and let IMC tuning rules compute the PID parameters automatically. Compare setpoint and disturbance step responses as you adjust the model or the desired closed-loop time constant λ.

1. Select a process model

Transfer function with parameters

Current numerical transfer function

2. Model parameters

Closed-loop time constant λ (s): 1.0

Smaller λ = faster, more aggressive response. Larger λ = slower, more robust.

Simulation time (s): 50

3. IMC tuning rule

Controller gain K_c —

Integral time τ_I —

Derivative time τ_D —

Filter time τ_F —

Parallel PID: K_p=K_c, K_i=K_c/τ_I, K_d=K_c·τ_D

4. Closed-loop step responses

Setpoint step

y(t) r(t) u(t)

Disturbance step

Unit step disturbance enters at the process input; setpoint held at zero.

IMC PID Designer

1. Select a process model

2. Model parameters

3. IMC tuning rule

4. Closed-loop step responses

Tuning formulas