Descripción y Análisis de los Procesos Productivos

4.3.2.1 Circuit Petri Net Construction

CiPNs are necessary to track the flow of current in electrical systems or subsystems. A CiPN is required for every electrical ciruit identified in a given system. Once the components have been identified in a given circuit the decision tables of those components can be searched. Moving through each row of the decision tables, the component states/modes that can cause current/no current within a circuit are identified.

From this information the Petri nets for ‘current in circuit n’ and ‘no current in circuit n’ are developed. For the Petri net ‘current in circuit n’, all components in circuit n need to pass current. For ‘no current in circuit n’, it only takes one component in circuit n to not pass current.

Construction Procedure

1. Take circuit list n and create a place representing “Current in circuit n” and a place representing “No Current in circuit n”.

2. For “Current in circuit n” and “No Current in circuit n” identify the rows in the decision tables of the components in circuit list n that have an out column that represents this circuit having current and no current.

3. For each row identified:

(a) If “–” exists in either state or mode column then ignore that row. (b) Else, identify type in state or mode column.

4. For “Current in circuit n”, create a single immediate transition and for “No Current in circuit n” create an immediate transition for each row identified in step 2.

5. Create a single headed inhibit arc from the transition(s) to the places representing “Current in circuit n” and “No Current in circuit n”.

M FS PS1 PS2 OUT OUT OUT OUT 1 OUT IN IN IN IN IN OUT 1 OUT 2 OUT 2 IN J1 J2

Figure 4.10: Example of a system with multiple circuits

6. For each state or mode type identified for “Current in circuit n”, create a double headed arc from the place representing this state or mode in the CPN to the transition.

7. For each state or mode type identified for “No Current in circuit n” create a double headed arc from the place representing this state or mode in the CPN to the transition representing that row.

Each CiPN connects to a component within the circuit list through the transitions created from the decision tables. The component that is identified is determined by the software by using the system topology information and the circuit list.

To demonstrate the procedure the example given in Figure 4.3 is extended to include another circuit as shown in Figure 4.10. In this new system there are two power supplies, P S1 and P S2, a fuse F a motor, M and two junctions, J 1 and J 2 as labelled in the diagram. From the diagram there are two circuits that exist in this system and are listed below:

1. { P S1, J 1, F S, M, J 2 } 2. { P S2, J 1, F S, M, J 2 }

The procedure begins with step one using the circuit lists given above. Taking circuit 1 first, a place is created to represent ‘current in circuit 1’ and another to represent ‘no current in circuit 1’. Each row of each component decision table is considered, to find any rows that result with an output (out) with C or N C. As seen in Figure 4.11b, all rows of each of the tables have a C or N C output and therefore all must be considered for the next step. Step three moves through each of the rows identified in step two and identifies which state (or mode when applicable) of the component leads to either current or no current. Figure 4.11c shows the states identified for each of the three components. Figure 4.11d shows the Petri net representation of the information found in this step. These

places representing the components’ states are linked to the places within the individual CPNs, similar to those found in Section 4.3.1.1. The next step, step four, generates a single transition which links to the ‘current in circuit 1’ place. Step four also generates a transition for every component state that can contribute to ‘no current in circuit 1’. Figure 4.11e shows these transitions. Step five adds the arcs between the transition and the places for ‘current in circuit 1’ and ‘no current in circuit 1’. A single, single-headed inhibit arc is required between the transition and the places. An inhibit arc is required to ensure that firing of the transition will not occur constantly. Steps 6 and 7 generate double-headed arcs from the component state places and the transition. All arcs from the places representing component states that lead to current connect to the same transition, as seen in Figure 4.11g. Each component state that leads to no current have an individual arc to connect to, as seen in Figure 4.11h.

This same procedure was also applied to the circuit 2 list producing the Petri net in Figure 4.12.

If a component with multiple operational modes was included in the circuit, such as the toggle switch then the method would be the same, except instead of the state identified in step three it would be the component’s mode.

The CiPNs indicate the current state of the circuit at a given time, therefore a Petri net extension is required to track the changes within the circuit. An example of this extension can be found in Figure 4.13. Another purpose of this extension is to ensure that there is not a constant flow of tokens from the CiPN. The first iteration of the connection of the CiPN to the SPN proved that a simple link between them would cause a significant increase in the number of tokens moving around the SPN. This would cause multiple tokens to exist in a single place at any given time. The method demonstrated here reduced the likelihood of too many tokens moving through the SPN.

Where the connection between the CiPN and the SPN occurs is an automated decision made by the software. From the initiating component a flow of connections is explored. When the first component in the circuit is found, this becomes the connecting component. The software establishes the connection between the CiPN and the SPN on this component.