Discrete Behavior

So far, all the examples we’ve seen have been of a purely continuous nature. This means that there have been no abrupt disturbances in the system. In this chapter, we’ll focus on how to express what we call “discrete behavior”. There are a wide variety of different engineering use cases for describing such behavior and we’ll explore these through the various examples presented in this chapter.

Normally, when we talk about discrete behavior we often refer to “events”. An event is something that occurs in our system that triggers some kind of discontinuity. Differential equations normally result in continuous solutions. But when events occur, they can introduce various kinds of discontinuities.

The simplest types of events are ones that happen at a particular time. These are, not surprisingly, called “time events”. Because these events are tied to time, we know what time they will occur even before they happen. Examples of time events would be things like changes triggered by some kind of digital clock that is activated at some specified frequency.

The other type of event we will encounter are so-called “state events”. These kinds of events are much trickier to handle. The reason is that we do not know a priori when these events will occur. Unlike time events, we have to actually wait for some signal in our system to cross some specified threshold. Generally speaking, we don’t know when that crossing will occur. Furthermore, determining the precise moment when the event occurs is somewhat expensive.

In this chapter, we’ll look at examples of both of these kinds of events and the various Modelica language features that can be used to describe when these events occur and how we describe responses to them.