control//feedback control//control loop//error signal

The error signal is the difference between what a control loop wants and what it measures, \(e=r-y\), and it is the only thing a classic controller looks at. A PID knows nothing about the plant; it only knows how far off the output is now, how far off it has been and how fast that is changing. Zero error means the loop is doing its job, and every measure of a loop's performance is some measure of how large the error gets and for how long.

The error signal is the difference between what a control loop wants and what it measures, e=r−ye=r-ye=r−y, and it is the only thing a classic controller looks at. A PID knows nothing about the plant; it only knows how far off the output is now, how far off it has been and how fast that is changing. Zero error means the loop is doing its job, and every measure of a loop's performance is some measure of how large the error gets and for how long.

The sign convention has to be fixed before any gain is set. With e=r−ye=r-ye=r−y, a positive error means the output is too low, and a heater's controller must answer it with more power; a cooling loop, where more actuation lowers the output, needs the opposite sign. Industrial controllers expose this as a setting, direct acting or reverse acting. A wrong sign turns negative feedback into positive feedback and the loop drives itself to a limit within seconds, so it is the first thing to check when a newly commissioned loop runs away.

The error is only as good as the measurement. Sensor noise enters it unchanged, and a sensor bias becomes an error the loop dutifully corrects, holding the true value off target by exactly that bias; no controller can see a mistake in its own measurement (sensor bias).

Integrated over a whole response, the error scores a tuning: the integral of its absolute value (IAE) or of its square (ISE) are the usual figures for comparing two tunings, and several tuning methods minimise one of them.

The present of the error is what the proportional term reacts to, its past what the integral term stores, and its trend what the derivative term extrapolates (PID controller).