AIAPC Learning Library
Translate prediction and control horizons from sample counts into a timing example without treating it as a controller-design recommendation.
The prediction horizon describes how many future samples an MPC calculation evaluates. The control horizon describes the number or arrangement of independently chosen future control moves in the stated controller formulation. A horizon expressed as a sample count is not a duration until the sample time is known.
The example here uses a simple constant-sample-time, unblocked formulation. Other formulations can use move blocking or different conventions, so the configured controller documentation remains important.
Assume sample time Ts = 5 seconds, prediction horizon Np = 12 samples and control horizon Nu = 3 free moves. The prediction time is Np × Ts = 60 seconds. The three move intervals begin at the current decision time and the following two sample times.
| Setting or interval | Interpretation |
|---|---|
| Ts = 5 s | A control calculation interval of 5 seconds |
| Np = 12 | Predictions evaluated over 12 future sample steps |
| Np × Ts | A 60-second prediction span |
| Nu = 3 | Three free control moves in this stated formulation |
| Move interval starts | 0, 5 and 10 seconds from the current decision |
| Third interval ends | 15 seconds from the current decision |
In a common constant-after-last-free-move convention, later predicted input values are held at the last free move for the rest of that optimization. This does not mean the actual controller stops making decisions after 15 seconds.
The controller normally applies the first selected action, obtains updated information at the next interval and solves again. The predicted later moves are part of the current plan; they are not a promise that the plant will receive that unchanged sequence.
Changing the sample time also changes the interpretation of unchanged horizon counts. If Np remains 12 but Ts becomes 2 seconds, the prediction span becomes 24 seconds, not 60. Preserving 60 seconds with a 2-second sample time would require 30 prediction steps in this simple arithmetic comparison.
A longer look-ahead can represent more future behavior but also changes the computation. Whether a proposed setting is appropriate depends on dynamics, delays, model quality, constraints, objectives and the implementation. The synthetic values above do not establish stability or acceptable plant performance.
The industrial MPC guide explains predictions, objectives and constraints in the wider control cycle. Review MPC700 training for its step-response, control-matrix and related published topics. The FOPDT worked example provides a separate model-reading exercise; one simple model is not a complete multivariable MPC design.
Technical definitions are supported by the primary references below. The labelled numerical records, timelines and checklists are original teaching examples for this article. They do not establish site-specific design approval or a new course entitlement.
Browse the process-control learning library for the wider subject guides and course routes.
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