Process Model (FOPDT)
$$G(s)=\frac{K_p\,e^{-\theta s}}{\tau s+1}$$
Process Gain Kp
1.00
Time Constant τ (s)
10.0 s
Dead Time θ (s)
2.0 s
IMC Closed-Loop Time Constant
λ (s)
5.0 s
SIMC auto-sets λ = τ
Tuning Results
| Method | Kc | Ti (s) | Td (s) |
|---|
Theory Reference
Z-N: $K_c = \frac{1.2\tau}{K_p\theta}$, $T_i = 2\theta$, $T_d = 0.5\theta$
IMC: $K_c = \frac{\tau}{K_p(\lambda+\theta)}$, $T_i = \tau$, $T_d = \frac{\theta}{2}$
—
Best ISE Method
—
Rise Time (s)
—
Overshoot (%)
—
Settling Time 2% (s)
Note: Dead time is approximated with a 2nd-order Padé expansion. In practice, excessive dead time may cause Z-N tuned loops to become unstable.
Tuning Method Summary
- Ziegler-Nichols (Z-N): Empirical rules from open-loop step response. Fast but aggressive — typically ~30% overshoot and low stability margins.
- Cohen-Coon: Improves on Z-N for large dead-time ratios θ/τ. Explicitly accounts for the ratio τ/θ.
- IMC (λ tuning): Derived from Internal Model Control theory. The designer directly controls speed-vs-robustness trade-off via λ.
- SIMC (Skogestad IMC): Auto-sets λ = τ for an engineering-balanced response — widely regarded as the most practical single-parameter tuning rule.