Up- and down-crossing aware truth states

[SouthEndMusic]

Motivation

The line below shows a range of a to-be-controlled parameter/state s, with indicated upper and lower bounds (ub, lb) and upper and lower setpoints (usp, lsp).

lb   *   lsp            usp    *    ub      
|---------|--------------|----------|

s ->

Quite common control use cases are of these types:

• Once s < lb, s must rise up to lsp;
• Once s > ub, s must fall down to usp.

Up to now, we used to view this problem as 'when the parameter s is in one of these starred (*) regions, there must be some memory that says whether s is on its way to a setpoint or not'.

However, DiscreteControl only takes action at changes of conditions. Therefore, it is useful to consider how the parameter s entered the starred regions. More specifically:

• s is on its way to lsp if it did an up-crossing at lb;
• s is on its way to usp if it did a down-crossing at ub.

Proposal by example

Say we have the following conditions for the situation described above:

1. s > lb
2. s > lsp
3. s > usp
4. s > ub

and also the control states 'rise' and 'fall', 'free' for making s rise, fall, and change freely respectively.

We introduce truth values in addition to T and F:

• U for an up-crossing, which is a special case of T;
• D for a down-crossing, which is a special case of F.

Then for the upper set point case, the control logic can be as follows (using the wildcard 'A' from #440):

• AAAT -> 'fall'
• AAAD -> 'fall'
• AATF -> 'free'
• AAFA -> 'free'

Note that the second case implies the third case. So, we say that crossing-type specific truth states take precedence.

Shortcoming

The above does not work when an extra condition on s is added within the relevant starred region.