Modeling of controllers by NCES

The following examples serve to illustrate basic principles of mapping from commands of a programming language to NCES models. 

Data storage and assignment

Boolean variable cell can be modeled by the net having two places p₀ and p₁ and two transitions t_s and t_r as shown in the Figure 1. Setting of the variable is modeled by transition t_s and resetting by t_r.

Figure 1.  Model of a Boolean variable implementing SET and RESET commands.

Figure 2. Model of a Boolean variable implementing also ASSIGNMENT of a value.

Linear sequence of commands

Consider how a linear sequence of two commands (e.g. A; B) can be modeled in NCES. Transitions t₀, t₁ correspond to the commands A and B . Once t₀ fires it forces to start the model of the command A. Upon completion of A, the transition t₁ starts the model of command B.

Figure 3. Model of a two commands’ sequence.

Figure 4. Model of an assignment.

Conditional choice

Conditional choice of type IF X THEN Sequence A ELSE Sequence B can be modelled in NCES as shown in Figure 5. Transition t_A has incoming condition arc which relays value of X, and t_B has incoming condition arc marked with not X. Since the conditions are orthogonal, only one of the transitions is able to fire.

Figure 5. Model of a conditional choice operator.

Boolean operations

Since every Boolean variable is modeled by two places (as was shown in Figure 1), we do not need a specific model for getting negation of a Boolean variable. As for AND, and OR operations, they can be modeled as shown in Figure 6, a) and b)  correspondingly. Both models have two incoming event signals: compute and reset. Computation of the result takes one state transition.

 a).       b).

Figure 6. Models of Boolean operations.

© 2003, Martin Luther University of Halle-Wittenberg, Automation Technology Lab.
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