Model Predictive Control 3 - Understanding the input and output horizons and control weighting in generalised predictive control

Looks at choices of input horizon equal to 2 and demonstrates that for many cases this is not sufficiently flexible to give good predictions and thus cannot lead to an expectation of good closed-loop behaviour.

Gives a number of illustrations of GPC predictions with short output horizons and demonstrates how the associated predictions are often very poor which in turn suggests the GPC optimisation is ill-posed and not to be trusted.

Demonstrates that the input weighting parameter has a limited range of efficacy which is linked to the horizons. Moreover, it is shown that the required horizons for a well-posed optimisation are strongly linked to the choice of this weighting. Also demonstrates that the parameter must be used with care with unstable open-loop systems.

Gives a number of illustrations of GPC predictions with long output horizons and demonstrates how the associated predictions can be very good and thus lead to a GPC optimisation which is well-posed and can be be trusted. However, also shows this insight does not necessarily apply to systems with poor open-loop unstable dynamics (e.g. unstable) and moreover is dependent on an appropriate choice of input horizon.

Uses overlays of predictions with many different choices of control horizon to demonstrate how this parameter affects the prediction. It is made clear that the input horizon cannot be considered in isolation from the output horizon. In general one can only have confidence in the predictions if both the input and output horizons are large.

Demonstrates through example how some 'popular' choices for the horizons can actually lead to every poor behaviour. Uses this as a motivation for the need to investigate and understand the role of the horizons and weighting more carefully.

Draws together the insights of the previous 7 videos and proposes a systematic choice for the input and output horizons to ensure that the GPC optimisation is well posed and therefore likely to give a sensible answer. Demonstrates the approach with some numerical examples.

Discusses how the basic set up of GPC is not appropriate for designing a compensator for unstable open-loop systems and that any control law that 'works' is likely to do so more by luck than good design and thus should be treated with caution. Gives a brief review of historical adaptions to cope with these scenarios.