Reference ID: MET-D8DC | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
A PID controller is the workhorse of industrial process control. It continuously adjusts a final element—usually a control valve or a variable-speed pump—so that a measured process variable (PV) tracks a desired set-point (SP). Tuning the three PID parameters (gain Kc, integral time Ti, derivative time Td) is therefore a daily task for every process engineer. The sheet below uses the classical Cohen–Coon (open-loop) method, which is ideal for self-regulating processes that can be approximated by a first-order-plus-dead-time (FOPDT) model. Typical applications include flow, pressure, temperature, and level loops on skids in food & beverage, water treatment, fine chemicals, and pharmaceuticals.
Methodology & Formulas
Convert volumetric flow to SI units
\[ Q_{\text{nom}} = \frac{Q_{\text{nom,m}^3\text{/h}}}{3600} \]
Calculate average velocity
\[ A = \frac{\pi D^{2}}{4}, \qquad v = \frac{Q_{\text{nom}}}{A} \]
For sluggish, lag-dominated loops such as heat exchangers or ovens, use a Lambda-tuned PI controller followed by manual adjustment of the derivative term:
Set Lambda to 1.5× the dominant time constant (τ) to avoid overshoot.
Calculate Kc = τ/(Kp·(λ + θ)) and Ti = τ, where Kp is the process gain and θ the dead time.
Add derivative only if noise is low; start with Td = 0.2·Ti and halve Kc to retain stability.
Verify with a small set-point step; if overshoot > 1 %, increase λ by 10 % and repeat.
A new valve usually changes both gain and dead time. Perform a simple open-loop bump test:
Put controller in manual, step the output 5 %, and record the PV response.
From the steepest slope draw a tangent; the intersection with the baseline gives the new θ and τ.
Calculate the dimensionless ratio θ/τ. If it is > 0.5, use a PI controller; if < 0.2, add derivative.
Apply Ziegler–Nichols or Lambda rules with the updated model, then reduce Kc by 20 % to account for valve non-linearity.
Test under automatic mode with a 2 % set-point change and fine-tune by trimming Kc ±10 % until decay ratio is ¼.
Continuous cycling when SP and load are constant is usually caused by non-tuning issues:
Stiction in the final element: check valve positioner and, if air-operated, add a booster or replace packing.
Measurement noise amplified by high derivative: switch to a PI controller or filter PV with a 0.5–1 s first-order lag.
Reset windup during saturation: verify output limits and use external anti-windup that matches the DCS block.
Interacting loops (e.g., cascade or feedforward) fighting each other: put secondary on tighter tuning or decouple gains.
Rapid valve motion on fast flow loops shortens actuator life. Reduce wear while keeping deviation low:
Halve Kc and double Ti; this keeps the integral gain (Kc/Ti) unchanged so offset remains zero.
Add a 0.2–0.5 s PV filter to hide turbulence without affecting set-point tracking.
Limit controller output velocity to 5 % s⁻¹ using a rate-of-change clamp in the DCS.
If overshoot is acceptable, switch to I-only control (very high Kc, Ti = 0.1 s) for pure flow loops with short dead times.
Worked Example – PID Tuning for a Water-Flow Loop
A field engineer needs a fast-responding flow controller on a 38 mm stainless-steel line that meters 1 m³ h⁻¹ of water at 20 °C. The installed valve and transmitter give an effective dead time of 0.3 s. Using the open-loop step-test data, determine PI controller settings that keep the overshoot below 5 %.
