Hybrid dynamic systems - Modeling and simulation

For a long time, the massive development of automation in the 20th century followed two types of technology, implemented according to their own methodologies and by personnel from different backgrounds: discrete-event systems and continuous systems.

Discrete-event systems are systems with elements characterized by two states: open or closed, on or off, out or in... The corresponding "all-or-nothing" (TOR) equipment is classically managed using Boolean algebra, derived from the work of 19th-century English logicians, then, taking into account the chronology of states and their sequencing, using state-transition methods accompanied by graphical representation: state graphs, Petri nets, Grafcet.

As for continuous systems, they are made up of elements characterized by a measurement that can take on an infinite number of values: temperature of a room or object, speed of a mobile, level in a reservoir... The management of these systems calls on mathematical tools suited to the representation of continuous dynamics: differential equations with various transformations (Laplace, Fourier...), state methods in matrix form.

This division into two categories of systems is not perfect, both in terms of the problems addressed – many industrial assemblies comprising elements of both types – and in terms of the equipment used. For example, spool valves and solenoid valves belong a priori to the TOR world, but proportional spool valves and solenoid valves, which do not differ fundamentally from the former, are used in the continuous world. Similarly, it's not easy to classify an element with ten possible values, for example, in one of these two system categories.

It is, however, the widespread use of computer tools that has made the need for unifying methods more acute, as the computer has become the fundamental tool for study and the digital processor the fundamental tool for control, for both of the above-mentioned categories.

However, simulation software is not the same, and the specialization of control processors (programmable logic controllers (PLCs) for the discrete part, regulators for the continuous part) persists. When the same processor and software are used, the graphics and programming mode for the discrete and continuous parts may nevertheless differ. This dichotomy results in problems of consistency of description and readability, and makes diagnosis difficult in the event of a fault.

In addition to being a tool common to both discrete and continuous systems, the internal operation of the control processor, which means that data acquisition and processing cannot be carried out simultaneously, has led to a relativization of the notion of continuous/discrete time. Time,...