Description of the System

Fig. 5.2 shows the remote-controlled FMS, which is composed of 1) three processing machines, 2) three raw material suppliers, and 3) six automated conveyers. It is assumed that the raw materials are provided infinitely. The FMS corresponding to different products are specified in terms of recipes, i.e. the sequences of tasks to be carried out on discrete amounts of materials by employing all or part of the machines. This particular FMS is a multi-recipe system with three recipes for three different products described as follows:

Recipe 1) Product x-y: Load materials x and y to Machine 1 for processing. Then, convey

Recipe 2) Product x-z: Load materials x to Machine 1 and z to Machine 2 for processing, and then convey x and z to Machine 3. After processing x-z in Machine 3, unload the product.

Recipe 3) Product y-z: Load materials y to Machine 1 and z to Machine 2 for processing, and then convey y and z to Machine 3. After processing y-z in Machine 3, unload the product.

Machine 1

Export x-y, x-z, or y-z Machine 3

Machine 2 x

z y Raw Material Supplier

Conveyer_X1

Conveyer_Y1

Conveyer_13

Conveyer_23 Conveyer_Z2

Conveyer_3 Machine 1

Export x-y, x-z, or y-z Machine 3

Machine 2 x

z y Raw Material Supplier

Conveyer_X1

Conveyer_Y1

Conveyer_13

Conveyer_23 Conveyer_Z2

Conveyer_3

Fig. 5.2. Schematic diagram of the three-recipe FMS.

By applying the task-oriented concept, the PN model for the three recipes is constructed as shown in Fig. 5.3, which consists of 19 places and 22 transitions, respectively. Transitions drawn with dark symbols are events that are controllable by remote managers via the Internet. Corresponding notation is described in Table 5.1.

5.3.2 Design of the Supervisor

The three machines represent resources shared between the different recipes. Since more than one recipe may require access to the same resource, but each resource can only serve one recipe at a time, deadlock between different recipes may thus occur. The required specifications are as follows.

Spec-1: Raw material loading of x and y is allowed only when Machine 1 is available.

Spec-2: Raw material loading of z is allowed only when Machine 2 is available.

Spec-3: Material conveying to Machine 3 is allowed only when Machine 3 is available.

Spec-4: Liveness, i.e. no deadlock states, must be enforced throughout system operation.

t13 t15 p15 t16 p16

p17 t18 Convey x-y to M3

Convey z to M3

Controllable Event via Remote Manager

p1 t2 p2

t13 t15 p15 t16 p16

p17 t18 Convey x-y to M3

Convey z to M3

Controllable Event via Remote Manager Controllable Event via Remote Manager

Fig. 5.3. Preliminary PN model of the three-recipe FMS.

Table 5.1. Notations for the PN of the FMS in Fig. 5.3.

Place Description Transition Description

p1 Loading x-y to M1 t1 Cmd: start loading x-y to M1 p2 Loading x-y to M1 completed t2 Re: end loading x-y to M1 p3 Conveying x-y to M3 t3 Cmd: start conveying x-y to M3 p4 Conveying x-y to M3 completed t4 Re: end conveying x-y to M3 p5 Loading x to M1 t5 Cmd: start loading x to M1 p6 Loading x to M1 completed t6 Re: end loading x to M1 p7 Conveying x to M3 t7 Cmd: start conveying x to M3 p8 Conveying x to M3 completed t8 Re: end conveying x to M3 p9 Loading z to M2 t9 Cmd: start loading z to M2 p10 Loading z to M2 completed t10 Re: end loading z to M2 p11 Conveying z to M3 t11 Cmd: start conveying z to M3 p12 Conveying z to M3 completed t12 Re: end conveying z to M3 p13 Loading y to M1 t13 Cmd: start loading y to M1 p14 Loading y to M1 completed t14 Re: end loading y to M1 p15 Conveying y to M3 t15 Cmd: start conveying y to M3 p16 Conveying y to M3 completed t16 Re: end conveying y to M3 p17 Processing x-y in M3 t17 Cmd: start processing x-y p18 Processing x-z in M3 t18 Re: end processing x-y p19 Processing y-z in M3 t19 Cmd: start processing x-z

t20 Re: end processing x-z t21 Cmd: start processing y-z t22 Re: end processing y-z

In the specification model, Spec-1 and Spec-3 are built by using the mutual exclusion concept, while Spec-2 is modeled as the precondition of the associated tasks. The composed PN model of both the recipe and specifications is shown in Fig. 5.4. The supervisory arcs are shown with dashed lines and the places showing the supervisory positions are drawn thicker than those showing the task positions. The supervisory places ps1-4 (ps1 for Spec-1, ps2 for Spec-2, ps3-4 for Spec-3) are used to prevent the remote manager from issuing undesired commands leading to resource conflicts on the part of the system. Corresponding notation for the supervisory places is described in Table 5.2.

At this stage, the software package ARP (Maziero, 1990) is used again to verify the behavioral properties of the composed PN models. The validation result (without ps5) shows that one deadlock occurs with the places p2, p10, p12, and ps3 marked only. The

physical meaning of the deadlock state is that if both Machine 2 and Machine 3 are occupied with z for Product x-z or y-z, while Machine 1 is loaded for the Product x-y, then no product can be completed and the system is deadlocked. Hence, for Spec-4, the ps5 is further designed and added to the PN model, as shown in Fig. 5.4. Validation results (with ps5) reveal that the present PN model is live, bounded, and reversible. The liveness property means that the system can be executed properly without deadlocks, while boundedness indicates that the system can be executed with limited resources, and reversibility implies that the initial system configuration is always reachable. In this approach, the supervisor consists only of places and arcs, and its size is proportional to the number of specifications that must be satisfied.

Controllable Event via Remote Manager

p1 t2 p2

t13 t15 p15 t16 p16

p17 t18

Controllable Event via Remote Manager Controllable Event via Remote Manager

p1 t2 p2

t13 t15 p15 t16 p16

p17 t18

t13 t15 p15 t16 p16

p17 t18

Fig. 5.4. Composed PN model of the three-recipe FMS.

Table 5.2. Notations for supervisory places of the PN in Fig. 5.4.

Place Description

ps1 Spec-1: M1 is available for x-y, x, or y.

ps2 Spec-2: M2 is available for z.

ps3 Spec-3: M3 is available for x-y, x, or y.

ps4 Spec-3: M3 is available for x-y, or z.

ps5 (2-bound)

Spec-4: One token means x-y is not in M1 and z is not in M3. Another means x or y is in M3.

5.3.3 Design of the Local Controller

As mentioned in Section 5.2.4, the detailed operations of each task can also be designed and constructed with PN models. Fig. 5.5 (a)-(c) shows the PN model of the tasks Loading (from raw material supplier to M1 or M2 with processing), Conveying (from M1 or M2 to M3), and Processing (processed by M3 and unloaded), respectively.

M3: on

finished finished

Processing: t17-t18, t19-t20, t21-t22

M3: off Convey_3: on Convey_3: off Command:

x in M1 finished

Loading: t1-t2

Conveyer _13 for t1, t7, t15.

Conveyer_23 for t11.

Conveyer: on

in M1 or M2 finished

Loading: t5-t6, t9-t10,

Processing: t17-t18, t19-t20, t21-t22

M3: off Convey_3: on Convey_3: off Command:

x in M1 finished

Loading: t1-t2

Conveyer _13 for t1, t7, t15.

Conveyer_23 for t11.

Conveyer: on

in M1 or M2 finished

Loading: t5-t6, t9-t10,

Fig. 5.5. PN models of (a) loading, (b) conveying, and (c) processing tasks for FMS.