SP, PV, CV, and the Feedback Loop

The Core Idea

A feedback loop measures a process, compares that measurement with a target, and adjusts an output. The setpoint (SP) names the target, the process variable (PV) names the measured value, and the controller output (CV) names the controller's output command.

What you will learn

• Identify the target, measurement, command, and error in a feedback loop.

• Follow how a controller uses a measurement to adjust a process.

• Read a trace and mark overshoot, settling, and a persistent gap from the target.

Why it matters

These names let you read a trend and distinguish what was requested, what happened, and what the controller did about it.

Explained like you're five

Think of a thermostat. You choose how warm you want the room, a thermometer tells it how warm the room is, and it tells the heater how much heat to supply. It keeps checking the thermometer as the room changes.

That repeated measure → compare → adjust → measure again is a feedback loop. In this lesson, you operate a simulated heater and learn the names for those pieces.

The problem

Your small heater starts at 20 °C and should hold 50 °C. Its temperature sensor reports the measurement; its power command can range from 0% to 100%. The controller is already set up for you.

Names vary between vendors and textbooks. Rockwell's PID instructions call the output CV, the control variable; other documents call the same command the controller output (CO) or manipulated variable (MV). Some textbooks use controlled variable for the measurement, which is the PV here, so check which meaning a document uses.

Before running, point to the target, measurement, and output readouts below. At the starting temperature, does this heater need more heat or less heat? Say which signal the controller should change.

See it

Press Run and watch all 40 simulated seconds. The upper plot shows SP and PV in °C; the lower plot shows CV in %. The purple Reference run is a supplied measurement from a second run of the same heater, starting at the same temperature with the same target.

Pause partway through and name each live readout. Then resume and record the final temperature and output. Leave the prepared controller settings alone; Simulator speed changes how quickly you watch, and Restart repeats the same starting conditions.

Read and mark the trace

Use the finished plot to make these marks in your notes. Estimate from the lines; exact timestamps are not the goal. Use Open larger workspace if you need more room.

1. Label the fixed target line SP, the live temperature line PV, and the lower command line CV. Trace the first few seconds: which changes first, the command or the temperature?

2. Find the live PV's highest point. Record its approximate temperature and time, and draw a vertical mark from SP to that peak. A peak past the target is overshoot.

3. Mark the point after which live PV stays within 49.4–50.6 °C for the rest of the run. This is the lesson's settling band, ±0.6 °C around SP. Entering the band briefly is different from staying there.

4. At the right edge, mark the vertical gap between the purple reference PV and SP. Check its last several seconds: a gap that persists after the response levels out is offset. An early gap while PV is still moving toward SP is not yet evidence of offset.

Compare your marks with the prepared runs

The live heater peaks at about 51.1 °C, around 17 s: roughly 1.1 °C of overshoot above the 50 °C target. It stays inside the 49.4–50.6 °C band from about 26.4 s through the end of this run. You have observed settling over this window; a later disturbance could move it again.

The reference PV flattens near 40 °C, leaving about 10 °C of offset below SP. Both lines become nearly flat, but only the live response settles inside the target band. A flat line alone does not mean the target was reached.

The live CV finishes near 30% even though live PV is close to 50 °C. Keeping this heater warm takes continuing power. The command and the temperature have different units and different jobs.

What happened and why

The controller reads PV, compares it with SP, and changes CV. That command acts on the heater; the sensor reports the resulting temperature back as PV. The new measurement starts the next comparison, closing the loop.

At the start, PV is below SP, so this heating loop raises its output. As the temperature approaches the target, it adjusts the command again. Temperature takes time to change, so the output can already be falling while the heater is still warming.

Overshoot describes a peak beyond the target. Settling describes staying within a stated band for the observed remainder of the run. Offset describes a lasting difference from the target after the process levels out. Your marks distinguish these behaviors; later lessons explore how controller settings affect them.

Show the error calculation

With SP at 50 °C and PV at 20 °C, error is 50 − 20 = +30 °C. If PV reaches 51 °C, error is 50 − 51 = −1 °C. Error uses the same units as SP and PV; CV remains a percentage of commanded power.

The ±0.6 °C settling band is 2% of the 30 °C start-to-target change. Other processes may need a different tolerance, so state the band whenever you describe a settling time.

Check yourself

Without changing a gain, answer these from the trace:

• An operator asks for 50 °C, the sensor reads 40 °C, and the heater command is 20%. Name SP, PV, CV, and the sign of the error.

• If you move SP upward, which signal expresses the request, and which signal must you watch to find out whether it happened?

• Which prepared response fits the goal “hold 50 °C within ±0.6 °C by 30 s, with a peak below 52 °C”? Point to the evidence for each limit.

Check your explanation

SP is 50 °C, PV is 40 °C, CV is 20%, and error is positive. Raising SP changes the target; PV tells you whether the measured temperature follows. A changed command alone does not prove the process reached its target.

The live response meets the stated goal during this 40 s observation: it settles inside the band before 30 s and its peak stays below 52 °C. The reference response misses the target band even though it becomes steady. Neither “fastest” nor “flattest” alone defines a good response; use the process's stated limits.

Common mistakes

You can now describe what a feedback loop did using the target, measurement, command, and trace. Next, you will try making the output adjustments yourself.

Enable JavaScript to run the embedded simulator and complete the interactive exercises.