How a control loop works

In short. A control loop is a controller, a process and a measurement closed into a ring: the controller compares the set point with the measurement and changes the action on the process until they agree. Useful for naming signals correctly in a PLC project and for understanding what PID tuning actually adjusts.

Loop signals

Systems call the output MV (manipulated variable), CV (control variable) or OUT. This section uses u and avoids "CV": some packages use CV for the controlled, not the manipulated variable.

Why it works

The controller does not know an exact model of the process. It only sees the error and acts to reduce it. If PV is below the set point the steam valve opens a little; the temperature rises, the error shrinks and the valve movement slows down. This is negative feedback: the controller output opposes the deviation.

Feedback also compensates what nobody accounted for in advance: a change in water flow, fouling of the heat exchanger, drifting steam pressure. The price is that the controller reacts only after the deviation shows up in PV.

Open and closed loop

• Open loop (manual, MAN): the operator sets the output, the controller is not involved. Step tests are made in this mode — you watch how the process answers a change of the output. See step test and FOPDT model.
• Closed loop (automatic, AUTO): the controller computes the output. The behaviour depends both on the process and on the settings — this is what you judge from the step response.

Process properties that decide the tuning

Details: FOPDT model and when it does not fit.

Conventions of the "PID control" section

All articles of this section and all PID tools of the application use the same conventions:

• error: e = SP − PV;
• controller form: ideal (ISA) u = Kc·[e + (1/Ti)·∫e dt + Td·de/dt] unless stated otherwise (PID forms);
• time: seconds unless marked "min";
• normalisation: gains are given with units; a dimensionless Kc means % of output per % of PV range (normalisation);
• sign: a positive Kc with e = SP − PV is reverse action (direction of action);
• the process gain K (ΔPV/Δu) and the controller gain Kc (Δu/Δe) are different quantities and are never mixed;
• derivative filter: time constant Tf in seconds; N is always given together with its form (D filter).

Example

The model used for the examples of this section: heating with K = 1.8 °C/%, τ = 45 s, θ = 12 s. A PI controller with Kc = 1.04 %/°C, Ti = 45 s (SIMC tuning) brings PV to a 1 °C set-point step with 5.5 % overshoot in 74 s (±2 % band).

Open the example in the simulator

Typical mistakes

• The error is computed as PV − SP while the controller was tuned with formulas for SP − PV: the loop runs away. Check the block's convention.
• The controller works on an unfiltered or wrongly scaled PV: the settings seem to "drift" while the problem is the measurement.
• The actuator hits its limit (valve 100 %): the controller cannot do more while the integrator keeps accumulating — see saturation and anti-windup.

Limits

The picture describes one loop with one input and one output. Interacting loops, cascades and feedforward are separate structures: cascade, feedforward, split range.