Design philosophy

This page discusses the design process for model predictive control applications.

Model design

The concept is that a layout should be defined, which include all available sensors as states and some states that either; describe a critical feature, or is necessary for model coherency and accuracy. Beyond these rules as few states as possible should be included in the model. The motivation is that this model must be linear to be suitable for mpc. Each model state, that is not defined with an observation (measurement), must be estimated. An estimated state in a linearised model will, introduce some kind of prediction error, which is undesirable.

Model reduction

The next step in the design process attempts to remove states from the initial design, using a similar reasoning as above: Even with full observation coverage for the model states, parameters could be poorly identified, or some non-linearity could make the optimisation program ill-conditioned.

Control applications should be centered around a few, well-defined objectives, that gives the system stability and provides fast (a relative concept ..) response to environmental changes. It follows that a few states - the ones directly associated with a control objective - are more critical to predict accurately, compared to other states. Therefore, the model should only states that are critical to obtain accurate operation, and the states required for model coherency.

A secondary consideration is in cases, where it is possible to chose between several states in the reduction process: It is often better to choose the state that causes a larger gradient in the model dynamics, pressure loss for instance, since parameter identification with a clear gradient in general yields a better model. Also, it should be considered an advantage to include a larger range of dynamics in the model.

Design goals

This defines a design process where the model should have as few states as possible, backed mostly by observations, describing the dynamics in the objective function, while maintaining coherency. For a water distribution model we can define three objectives:

• Accurate boundary conditions for demand to residents and exchange flow to other pressure zones.
• Water level in elevated storage.
• Critical pressure as measured in the distribution well / station closest to the critical resident.