PID Loop

Closed-loop controller on a process model. Step the setpoint or a load, then move the gains. The dim pens are the run from before that change.

Process seconds. Touch the trend to read a point.

Running

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SP — · CO — · e —

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Run

Operate point

Setpoint step

Load step %CO

Response

Rise time: —
Overshoot: —
Settling: —
SS error: —
IAE: —
Integrator: —

Tuning

Standard (ISA). Kc multiplies the whole parenthesis.

Kc %CO/%PV

Ti s

Td s

—

Output

CO low CO high

Anti-windup Derivative on PV Derivative filter

Filter N

Plant

—

Gain K %PV/%CO

Rate K %/s per %CO

Lag τ s

ωn rad/s

ζ damping

Dead time θ s

Reverse action raises CO when PV is below setpoint. That is the right match for a positive process gain; direct action on this model runs the wrong way. Parallel is u = Kp e + Ki ∫e dt + Kd de/dt. Standard (ISA) is u = Kc (e + 1/Ti ∫e dt + Td de/dt). Same controller. FOPDT is the tuning-sheet model. The level is a chest whose outflow is matched at mid-scale valve, so CO can fill or drain it. P-only leaves an offset on a self-regulating loop. Integral removes it, and it is what winds up while the valve sits on a stop. Derivative on PV does not kick when the setpoint steps. The model advances in fixed 20 ms steps of process time, and dead time is a delay line on the output.