MODELING, ANALYSIS, AND IMPLEMENTATION OF LOGIC CONTROLLERS FOR MACHINING SYSTEMS USING PET

MODELING,ANALYSIS,AND IMPLEMENTATION OF LOGIC CONTROLLERS FOR MACHINING SYSTEMS USING PETRI NETS AND SFC

Euisu Park,Dawn M.Tilbury,and Pramod P.Khargonekar

NSF Engineering Research Center for Recon?gurable Machining Systems

2250GG Brown,2350Hayward St.

University of Michigan

Ann Arbor,Michigan48109-2125

{euisu,tilbury,pramod}@https://www.wendangku.net/doc/6015841217.html,

Keywords:logic controllers,machining systems,Petri nets,SFC

Abstract The logic control for high-volume machining systems,such as the trans-fer lines commonly used in the automotive manufacturing industry,must

achieve multiple functions in distinct control modes,and thus is quite

complex.A methodology for constructing the logic controller using Petri

nets is outlined.Each operation in the machining system is assigned ei-

ther a reversible or irreversible operation module,and an algorithm for

connecting these modules to form the control logic is presented.The

resulting logic controller is guaranteed to be live,safe,and reversible.

The logic controller can be implemented in SFC.

Introduction

Transfer lines are widely used in the automotive and other high-volume industries.In a transfer line machining system,several machine tools linked together provide complete processing of a complex machined part such as an engine block,transmission case,or cylinder head.The exact breakdown of operations is determined by the cycle time,which is in turn dictated by the required annual volume of parts to be produced.

A major goal of our research is to develop formal tools for analysis and synthesis of logicc ontrollers for recon?gurable machining systems as part of the NSF Engineering Research Center for Recon?gurable Ma-chining Systems.Recon?gurable systems must be modular.Since high

1

2DISCRETE EVENT SYSTEMS:ANALYSIS AND CONTROL volume transfer lines are widely used,in this work we focus on their logic controllers.It is our expectation that these results will have appropriate generalizations to other classes of manufacturing systems.

The outline of this paper is as follows.In Section1,we outline the logic control problem for high-volume machining systems such as transfer lines.Section2presents the modeling framework for logic control using Petri nets and summarizes the analytical results.Logic control imple-mentation in PLCs is discussed in Section3,and Section4concludes with a discussion of our ongoing and future work in this area.

1.MACHINING SYSTEMS BACKGROUND

The automaticmac hining systems c onsidered in this paper are high-volume transfer lines.A high-volume transfer line consists of a transfer mechanism,a number of machining stations,and?xturing mechanisms for each machining station[McDunn,1992,Graham,1992].Each sta-tion performs a particular process necessary to the overall production of the part using simple and fast motions.Each motion is called an oper-ation and a sequence of operations is associated with each station.The schematic diagram of a high volume transfer line is shown in Figure1. The numbered squares represent the locations of the engine blocks.

Cradle Mechanism

2 3 8 11

Figure1A high-volume transfer line

The typical cyclic sequence consists of the following operations:un-clamp?xtures,engage transfer,advance transfer,disengage transfer, clamp?xture,cycle machining station,and return transfer.This se-quence is repeated regularly under normal operation.Operations are overlapped and intertwined for maximal utilization.

1.1.CONTROL MODES

A logicc ontroller for an automaticmac hining system has multiple control modes:typically auto,hand,and manual.In the auto mode, operations are executed automatically except when faults are detected;

Modeling,Analysis,and Implementation of Logic Controllers3

1.0

1.0

0.5

1.5

Figure2Timing bar chart section.

then the machining system must stop.Hand mode is used by the opera-tor to coordinate multiple stations or validate the automatic process step by step.In manual mode,the operator has single station?ne operation control(such as jog motions)which are used for fault recovery.

In current industrial practice,the speci?cation of normal operation cycle is given by a timing bar chart,as shown in https://www.wendangku.net/doc/6015841217.html,ing this timing bar chart,logic controllers for the normal operation can be mod-eled[Park et al.,1999].However,because faults occur,each operation must have associated control logic for fault stop/fault diagnosis.If a fault is detected,the logic controller stops the operation and announces the fault to the operator.Because of the causal dependencies in the op-erations of a machining system,the entire machining system is stopped by any fault,and the system must wait for a re-start command from the operator to begin again.

1.2.LOGIC CONTROL CHALLENGES

The major challenges in logic control for high-volume machining sys-tems arise from the overwhelming complexity of the system.In addition to the control of the machining operations,the logic controller handles all of the machine services(i.e.coolant,lubrication),the user interface, fault handling and diagnostics,and some safety interlocks(although crit-ical safety circuits are hardwired).As a result,a transfer line with ten

4DISCRETE EVENT SYSTEMS:ANALYSIS AND CONTROL

Logic Controller

(An Event Driven System)

Figure3Closed-loop system model.

to twelve stations may have as many as10,000I/O points,and up to 90%of the overall control logic may be used for exception handling.

Even though the functions of transfer-line logic controllers are stan-dard,programming the control logic takes approximately50%of the total construction time for each new machining system.The control logicis programmed in an unstruc tured programming language known as ladder diagram.Although cumbersome,it is still widely used for his-torical reasons.The complexity of the resulting low-level code,which can be a printout several inches tall,makes it di?cult or impossible to understand the overall operation of the controller.Debugging is a time-consuming process,and once the system is working,changes are only made reluctantly because there is no method for assessing the impact of a change on the overall system performance.

In practice,the control logic may only be veri?ed in the“cycle and debug”stage,after the mechanism has been built.No su?ciently pow-erful,versatile and simple to use software tool exists for verifying the correctness of logic controllers.Moreover,there is no uni?ed standard modeling method to represent the exception handling control logic with the automation control logic.As a result,it is not possible to conduct formal analysis and systematicdesign of the logicc ontroller.The goal of our research is to formalize the construction of a model of the logic controller which can manage the necessary complexity of an industrial set-up and be veri?ed as correct.

2.MODELING AND ANALYSIS

A block diagram of a machining system with its logic controller is shown in Figure3;the Petri net model is a supervisory controller rep-resenting the desired closed-loop system behavior.Control actions are assigned to the states of the Petri net model to generate control actions (as in Moore-Automata[Booth,1967]).The machining system is driven by the control actions and generates events.

Modeling,Analysis,and Implementation of Logic Controllers5 The Value

of Input

Notation Events

a active(a=1)

a↑rising edge

a↓falling edge

State Control Action O(operating)actuator on

C(completed)actuator o?

internal var.=1 IC(incomplete)actuator o?

announce fault

a.Event generation.

b.Operation block.

c.

Figure4Modeling framework elements.

2.1.MODELING FRAMEWORK

The reader is referred to[Murata,1989,David and Alla,1994,Reisig, 1982,DiCesare et al.,1993]for an overview of Petri nets.

Event generation.Sensor and operator command inputs are boolean variables;they can generate three di?erent events as shown in Figure4a. Operation model.An operation in a machining system is repre-sented by three states:operating,completed stop,and incomplete stop, and has an internal variable to keep track of its proper completion.By assigning the appropriate control actions to each state,an operation can be formally represented by a Petri net,as shown in Figure4b.

To prevent mechanical con?icts or reduce cycle time,there may be causal relationships between operations in di?erent stations.These causal relationships in the normal operation cycle are represented by dotted arrows in the timing bar chart;in the Petri net model,they can be represented by transition conditions which utilize internal variables. Superposition.Although the modes of a machining system o?er di?erent functionalities,they control the same set of operations.Thus the Petri net for each control mode is constructed by connecting the same set of places using transitions and arrows in such a manner that the speci?cations for that mode are met.The complete control logic can be obtained by combining the Petri nets for di?erent control modes using superposition as illustrated in Figure4c.Superposition is a well-known reduction rule and preserves properties such as liveness,safeness, and reversibility[Murata,1989].

6DISCRETE EVENT SYSTEMS:ANALYSIS AND CONTROL

IC

N

IC

t 3

a.R-module

b.I-module

Figure5The Petri net representation of the operation modules.

2.2.OPERATION MODULES

Because faults can happen at any time in a machining system,a logic controller should have fault recovery control logic for every operation. In general,a fault stop in an operation can be recovered by one of three methods:re-start the operation from the fault stop position directly, return to the operation’s initial position then re-start,or return to the station’s home position then re-start.A normal operation whose faults can only be recovered by the third method is de?ned as an irreversible operation;others are called reversible operation.Typically,motion-only operations operations are reversible.Metal-removal operations can be reversible or irreversible depending on the process.The operations used for fault recovery of normal operations are called fault recovery opera-tions.Because the normal operations in each station constitute a cyclic behavior,fault recovery operations are typically the same as normal operations.However,we consider the fault recovery operations to be di?erent operations because they are frequently executed with di?er-ent feed rates than their corresponding normal operations.Two types of operation modules are shown in Figure5:the reversible operation module(R-module)and the irreversible operation module(I-module). The superscripts N and F represent the normal and the fault recovery operation blocks of the operation O respectively.

Modeling,Analysis,and Implementation of Logic Controllers7 2.3.STATION CONTROL LOGIC

Each station controller manages the sequential behavior of its opera-tions in all three control modes,and keeps track of the internal variables which are used to encode the dependencies between stations.

Connection Algorithm.In each station,three types of operation sequences are possible:normal,reverse,and fault recovery.Some nor-mal sequences of reversible operations need to be reversed to their initial state for the repeatable steps in hand mode;the reverse sequence is nec-essary for this.If each operation is represented by its operation module, only the fault recovery sequences for irreversible operations need to be developed because the fault recovery sequences for reversible operations are included in the reversible operation modules.

A station can be considered an ordered sequence of operations;the ordering is derived from the timing bar chart and starts with the home operation,which is de?ned based on mechanical stability and may not be the?rst operation listed.A systematic procedure can be used to construct the complete station logic control structure.

1Assign an operation module for each operation listed in the timing bar chart.

2Create the normal operation cycle.

3Create the reverse sequences for the repeatable steps in hand mode.

4Create the fault recovery sequence for irreversible operations. More details on this procedure can be found in[Park et al.,2000].

Internal variables reset.Internal variable information is stored and updated within the operation modules.If a normal operation is completed,the value of the internal variable assigned for that operation is changed from0to1;if its fault recovery operation is completed,the value is re-set from1to0.For repetitive cyclic operation,all the internal variables in each station must be re-set from1to0whenever the cycle is?nished.The initial state of a system for cyclic operation is de?ned as the beginning moment of its timing bar chart;this is the time during the cycle when all the internal variables must be re-set.

2.4.ANALYSIS

Each station logic controller is constructed by connecting its operation modules according to the algorithm in Section2.3.The resulting Petri net structure of a station logic controller can be characterized by the following proposition.

8DISCRETE EVENT SYSTEMS:ANALYSIS AND CONTROL Proposition1The Petri net representation of a station logic controller constructed according to the algorithm in Section2.3is a strongly con-nected state machine.

Therefore,the following well known properties of state machines can be used for analysis.

Theorem1([Murata,1989])A state machine(N,M0)is live if and only if N is strongly connected and M0has at least one token;a state machine(N,M0)is safe if and only if M0has at most one token.A live state machine(N,M0)is safe if and only if M0has exactly one token.

Theorem2([DiCesare et al.,1993])A live state machine is reversible.

The following proposition is thus straightforward to prove.

Proposition2A station logic controller constructed according to the algorithm in Section2.3is live,safe,and reversible.

In our formal representation,therefore,the control logic for a ma-chining system can be modeled by a set of Petri nets;each Petri net

is live,safe,and reversible.However,the Petri nets for station logic controllers are implicitly connected by internal variable conditions to encode the operation dependencies between stations.Improper internal variable conditions can lead to deadlocks in the logic control.To prohibit these deadlocks,we introduce the operation causality condition.Within each station,the operations are totally ordered according to the timing bar https://www.wendangku.net/doc/6015841217.html,bining the station operations with the operations whose internal variable conditions appear in that station results in a partially ordered set.This partial ordering is de?ned as the operation ordering for the station.

De?nition1(Operation Causality Condition)A logic controller is said to satisfy the operation causality condition if the operations order-ings in station logic controllers do not con?ict with each other.

Using the operation causality condition,we can develop the following theorem for the properties of the logic controller which consists of a number of station logicc ontrollers.

Theorem3The logic controller is live,safe and reversible if and only

if each station logic controller is live,safe,reversible,and the operation causality condition is satis?ed.

Since the liveness,safeness,and reversibility properties of the Petri net model for each station logic controller are guaranteed by following the connection algorithm in Section2.3,the control logic can be easily veri?ed by checking the operation causality condition.

Modeling,Analysis,and Implementation of Logic Controllers9 3.IMPLEMENTATION USING SFC

Currently,PLCs are the most popular devices for implementing logic controllers.As an international standard,the IEC1131-3programming languages were developed for PLCs[Lewis,1995].Since the?rst revi-sion of the IEC1131-3standard published in1993,the PLCs from major manufacturers can be programmed using some of the programming lan-guages provided in the standard.One of the standard languages is SFC (Sequential Function Chart).It is based on Grafcet which was inspired from Petri nets and in fact,the structures of SFC and Grafcet are almost the same.The comparison of Grafcet and Petri nets along with SFC can be found in[David,1995].

A live,safe,and reversible Petri net which has mutually exclusive transitions can be implemented directly in SFC[David,1995].The logic controller developed in this paper consists of live,safe,and reversible Petri nets with mutually exclusive transitions.Therefore,it can be di-rectly implemented in SFC.

4.DISCUSSION

The machining systems which are considered in this paper,namely high volume transfer lines,have similar structures and functions.How-ever,programming a logic controller is still a time consuming job and always requires a“cycle and debug”stage to correct errors.This is due to the unstructured nature of the control logic and the lack of a veri?ca-tion method.If all or part of the logic can be generated automatically and the correctness of control logic can be veri?ed before the mechanism has been built,the e?ects would be tremendous in the machining system industry.

Our formal representation of a logicc ontroller provides a method to automatically generate veri?ed control code from the timing bar chart. The logic controller proposed in this work has a formal Petri net struc-ture and its correctness has been veri?ed by the properties of Petri nets and the operation causality condition.Moreover,the control logic for each station consists of operation modules.The control logic for each operation module is a function of input and output variables for the corresponding sensors and actuators;each operation module can be re-peatedly generated by replacing the names of those variables.

There is a trend towards decentralized implementations of logic con-trol,with controllers for individual machining stations connected by a network.Although there is some reduction in controller complexity,a decentralized architecture requires an added level of coordination be-tween controllers.Incremental ramp-up and testing of individual sta-

10DISCRETE EVENT SYSTEMS:ANALYSIS AND CONTROL tions along with reduced wiring are the major bene?ts of decentraliza-tion.The modular logic control structure considered in this paper can naturally be implemented in a decentralized fashion.

In an industrial application,the actual logic controllers should include auxiliary c ontrol logicfor hydraulicpumps,lubric ation,and safety de-vices.In addition,the level of communication achievable between station logicc ontrollers strongly depends on the c hosen network.To address these and other practical issues,we are currently working with one of our industrial partners to extend the proposed methodology in appro-priate directions with the ultimate goal of implementing this control methodology in industrial machining systems development. References

[Booth,1967]Booth,T.L.(1967).Sequential Machines and Automata Theory.John Wiley and Sons,Inc.,New York.

[David,1995]David,R.(1995).Grafcet:A Powerful Tool for Speci?-cation of Logic Controllers.IEEE Transactions on Control Systems Technology,3(3):253–268.

[David and Alla,1994]David,R.and Alla,H.(1994).Petri Nets for Modeling of DynamicSystems—A Survey.Automatica,30(2). [DiCesare et al.,1993]DiCesare,F.,Harhalakis,G.,Proth,J.M.,Silva, M.,and Vernadat,F.B.(1993).Practice of Petri nets in Manufac-turing.Chapman&Hall,New York,?rst edition.

[Graham,1992]Graham,B.A.(1992).Changing Control Methodology for Multi-Station Machine Tools.In IPC’92:Enabling Flexibility. [Lewis,1995]Lewis,R.W.(1995).Programming Industrial Control Sys-tems using IEC1131-3.Institution of Electrical Engineers,London. [McDunn,1992]McDunn,T.P.(1992).The Simple Approach to Trans-fer Line Control.In IPC’92:Enabling Flexibility,pages297–306. [Murata,1989]Murata,T.(1989).Petri Nets:Properties,Analysis and Applications.Proceedings of the IEEE,77(5):541–580.

[Park et al.,1999]Park,E.,Tilbury,D.M.,and Khargonekar,P.P. (1999).Modular LogicController for Mac hining Systems:F ormal Representation and Performance Analysis using Petri Nets.IEEE Transactions on Robotics and Automation,16(6):1046–1061.

[Park et al.,2000]Park,E.,Tilbury,D.M.,and Khargonekar,P.P. (2000).A Modeling and Analysis Methodology for Modular Logic Controllers of Machining Systems with Auto,Hand,and Manual Con-trol Modes.In Proc.2000American Control Conference,Chicago. [Reisig,1982]Reisig,W.(1982).Petri Nets.Springer-Verlag,Berlin.