Smith Predictor
The Smith predictor compensates for process dead time by using a model to predict the delayed output and control against the prediction.
The trouble with dead time
Pure time delay, dead time, is the hardest dynamic for feedback to handle: the controller cannot see the effect of its action until the delay elapses, so aggressive control causes oscillation and instability. A conventional controller must be detuned severely to remain stable when the delay is comparable to the process time constant, sacrificing performance. The Smith predictor breaks this limitation using a model of the process.
Predicting past the delay
The Smith predictor runs a model of the process split into its delay-free part and its pure delay. It feeds back the model's delay-free output to the controller immediately, giving the controller an undelayed picture to act on, while a second path corrects for model error by comparing the actual delayed output with the model's delayed output. Effectively, the controller regulates the delay-free model and the delay is moved outside the loop, so the controller can be tuned as if there were no delay.
Sensitivity to the model
The scheme's performance depends on model accuracy, especially the delay estimate. An incorrect delay degrades the compensation and, for unstable or integrating processes, can destabilize the loop, so modifications exist for those cases. Because it cancels the delay in the nominal model, the Smith predictor is more sensitive to delay mismatch than a well-tuned conventional controller, a trade-off between nominal performance and robustness.
- Model splits the process into delay-free and pure-delay parts
- Undelayed model output is fed back for immediate control
- A correction path handles model mismatch
- Effectively moves the delay outside the control loop
The Smith predictor is the classic form of model-based dead-time compensation, and modern MPC handles delay naturally within its prediction, generalizing the same idea. Filtered and modified Smith predictors improve robustness to delay uncertainty.
For a design-stage loop with significant transport delay, a Smith predictor would restore tight control that a conventional loop could not achieve, evaluated in simulation.