Engineering explained · LOOP

One tank.
One loop.

If you have seen PID on a P&ID and nodded like you knew, this is what a control loop actually does. One tank, three devices, three sums. Then the survey of 26,000 real loops that should keep every engineer honest about how many of them work.

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01 The three things 02 Why a level never settles 03 Past, present, future 04 Tune one yourself 05 The survey

The three things.

A tank has to hold a level. Water comes in, water goes out. To make that happen on purpose rather than by luck you give it three devices, and the three together are the loop.

LT-101 is a differential pressure transmitter tapped above the top level and below the bottom one, which is how a level is actually measured. It sends the reading to LIC-101, the controller, on a dashed line because a dashed line is an electrical signal. LIC-101 compares the reading to the setpoint and drives LV-101, the globe valve on the outlet, shown cut open so you can see the plug the actuator moves. Same tag number on all three: one loop.

LT-101Reads. Turns a height of liquid into a number, four times a second, whether anyone is looking or not.

LIC-101Compares. Subtracts that number from where you wanted it. The difference is the error, and the error is the only thing the controller ever sees.

LV-101Moves. The only part of the loop that touches the process. Everything else is arithmetic.

Why a level never settles on its own.

Most things you control pull themselves back. Heat a room and it leaks heat to outside, faster the hotter it gets, so it finds a temperature. A level does not do that. Write the balance and the reason is right there:

A dh/dt = Q_in − Q_out There is no h on the right hand side. Nothing about being too full makes the tank empty itself. So any mismatch at all, however small, integrates: the level ramps, and it keeps ramping until it hits the top or the bottom.

Put numbers on it. A 3 m surge drum is 7.069 m² of area. Run it 5 m³/h out of balance, which is a valve a few percent off, and the level climbs at:

Area	π × 3² / 4	7.069 m²
Imbalance	Q_in − Q_out	5 m³/h
Ramp rate	5 / 7.069	0.71 m/h
Time to lose 2 m of freeboard	2 / 0.707	2.8 h

Under three hours from a valve that is barely wrong. That is why the loop exists, and it is also why the integral term matters more on a level than almost anywhere else.

Past, present, future.

The controller does three sums on one number, the error, and adds them up. Plot the error against time and all three are visible at once. The setpoint is the zero line, which is the trick that makes one curve carry the whole thing.

Something knocked the level at the left of the plot. The loop pulled most of it back and then left a small error sitting there. At the moment marked PRESENT: the green bar is how big the error is right now, the shaded region is every bit of error since the disturbance added together, and the orange tangent is where the error is going next.

P · nowPush in proportion to the error in front of you. Simple, fast, and on its own it always stops short: the push gets smaller exactly as the error does.

I · pastAdd the error up over time and push on the total. This is what removes the leftover. A small error that lasts all day is a big area, which is the whole point of the term.

D · futureLook at the slope and lean against it before the error arrives. It buys you damping. It also amplifies noise, which is why plenty of real loops run with it switched off.

More than 95% of the control loops in a plant are some version of those three sums. Learn this one and you have met almost all of them.

Tune one yourself.

The same 3 m drum. At 10 seconds something upstream steps the inflow up by 5 m³/h and leaves it there. The controller has to find a new valve position that matches it, without letting the level get away in the meantime.

Level loop, integrating process

Black is the level, on the left axis. Blue is the valve, on the right one. Orange dashes are the setpoint the controller is trying to hold.

Gain K_c 6.0 Integral time τ_I 300 s Derivative time τ_D off

furthest the level got from setpoint

error still there at the end

time to stay within 2 cm

Two things are worth doing. Set the gain to zero and watch the level walk off the top of the plot, which is section 02 happening in front of you. Then set the integral time to zero, which switches the integral off: the loop steadies the level but parks it somewhere that is not the setpoint, and no amount of gain closes that gap.

The survey that should keep every engineer humble.

A control company assessed 26,000 PID controllers in operating plants and graded how each one was performing. This is the result.

16% excellentdoing the job well

16% acceptabledoing the job

22% fairworking, badly

10% poormaking things worse than manual would

36% open loopin manual, or pinned against a limit. Not controlling anything.

Add the first two and you get 32%. About one loop in three was actually doing its job. More than a third were not closed at all: somebody put them in manual during a upset and nobody put them back.

It is not mysterious why. A big plant runs up to 5,000 regulatory loops with one engineer for every 200-400 of them. Nobody has time to tune 400 loops, so the ones that are loud get tuned and the rest sit there.

Which is the practical reason this matters to anyone building a model: a tank that will not drain is usually a loop, not a pump, and a model of the plant that does not know the loop exists will tell you the pump is fine and it will be right and useless.

Reflux Student builds the flowsheet under the loops.

Describe the process in a sentence and Reflux Student builds it in your own Aspen Plus, runs it, and reads the result back to you. Get the steady state right and the loops have something honest to sit on. You keep the judgment.