control//feedback control//control loop//loop delay//Smith predictor

The Smith predictor is a control structure for plants with a long dead time that closes the loop around a model's prediction of the output without the delay, so that the controller can be tuned as if the delay were not there; it is a standard tool in process control, where conveyors, long pipes and analysers put seconds or minutes between an action and its measurement. Proposed by Otto Smith in 1957, it is the oldest form of the second defence against loop delay: when the delay cannot be removed, predict across it.

The Smith predictor is a control structure for plants with a long dead time that closes the loop around a model's prediction of the output without the delay, so that the controller can be tuned as if the delay were not there; it is a standard tool in process control, where conveyors, long pipes and analysers put seconds or minutes between an action and its measurement. Proposed by Otto Smith in 1957, it is the oldest form of the second defence against loop delay: when the delay cannot be removed, predict across it.

Picture a conveyor that carries ore from a feeder to a weighing belt two minutes downstream. A PI controller looking at the scale sees the effect of each feeder change only after two minutes, and must be tuned slowly enough not to oscillate. The predictor runs a model of the feeder and the belt in two versions, one without the transport delay and one with it, and feeds the controller

yc=y^0+(y−y^θ),y_c=\hat y_0+\bigl(y-\hat y_\theta\bigr),yc​=y^​0​+(y−y^​θ​),

where y^0\hat y_0y^​0​ is the model's output without delay, y^θ\hat y_\thetay^​θ​ the same output delayed by θ\thetaθ, and yyy the real measurement. If the model is exact, the bracket is zero and the controller sees a plant with no delay at all; whatever the model gets wrong, and every unmeasured disturbance, comes back through the bracket, late but corrected.

The delay still shows in the response. The output follows the setpoint θ\thetaθ later than the controller's internal picture, and a load disturbance is still seen only after it has travelled through the delay; what the predictor removes is the limit the delay put on the gains, which is where slow tuning came from.

It is only as good as its model of the delay. A delay misjudged by a fraction of itself can make the loop worse than a plainly detuned PI, so the structure suits plants whose transport time is steady or measured (a belt with a known speed, a pipe with a metered flow). The basic form also fails on plants that integrate or are unstable on their own, which need modified versions.

It belongs to a family that predicts with a model. An MPC predicts the whole trajectory by construction and handles constraints the predictor ignores, and an estimator can propagate the state forward over a slow sensor's latency, as a drone's EKF does with its GNSS fixes (delayed measurements). Where the delay is short, a well-tuned PID with a modest delay margin is usually enough and needs no model at all.