Zhong-ming ZHANG，Xiao-su WU，En-ai CHEN，Xiao-kang ZHENG（Hangzhou Vocational and Technical College，Hangzhou 310018，China）

Study on the defects and improvement of sequential function chart

Zhong-ming ZHANG*，Xiao-su WU，En-ai CHEN，Xiao-kang ZHENG
（Hangzhou Vocational and Technical College，Hangzhou 310018，China）

In order to solve the problem that the current sequential function chart cannot express the conversion between automatic circulation and manual operation flexibly，taking the example of the typical work steps of hydraulic power sliding table as the research object，the paper brings forward a method by adding state variables and inserting some micro branches to hold the change process of dynamic memory between these two states.The sequential function chart and ladder diagram shows a more rigorous mapping relationship after redesign.By means of graph theory model establishment，we can find that the number of maximum flow has been increased than before after model reconstruction，but it still meets the needs of closure principle of graph，so as to maintain the stability of the control system.Through the observation of running the ladder diagram on the spot，the control program can shift between these two states with non-disturbance at the breakpoint，verifying the correctness and reliability of the new algorithm.

Hydraulic power sliding table，Sequential function chart，Automatic circulation，Mapping relationship，Model reconstruction

Hydromechatronics Engineering

http：//jdy.qks.cqut.edu.cn

E-mail：jdygcyw@126.com

1 Introduction

Sequential function chart becomes the vehicles which can express control information clearly due to its advantage to describe the action content and the changes of process variables so that it is widely accepted by different professionals.Some scholars’researches focus on the following two aspects：on the one hand，some papers［1-3］discussed the characteristics of sequential function chart such as universality，reliability and efficiency as well as industrial promotion，on the other hand，other papers［4-6］explored a new method witch can extract element hierarchy structure by means of activity on vertex network（AOV for short）in ladder diagram processing.However，there still exists a problem that the new technology cannot predict the error structure hidden deeply in some complicated sequential function chart.Therefore，it is more advised to discuss the state transitions based on current structure of sequential function chart.

The hydraulic power sliding table is a general part of the modular machine tool，on which some rotary tools are installed，aiming to drive the sliding table back and forward in accordance with the certain loop by means of hydraulic transmission system［7］.Because some modular machine tools are designed to perform some special or individual manufacturing tasks，technically，there is no real numerical control unit on it.In many situations，there are some special control systems consist of a programmable logical controller，position signal testing，relays，contractors and other components etc.for the modular machine tool.Generally speaking，the function design and panel appearance and operational methods of the control systems are developed by the customers and the engineers，some of the features such as precision error，flexibility and control method can be improved［8］.Some engineering projects containing transmission process be-tween automatic circulation and manual operation are unreasonable，on which there are some obvious defects，and possible serious accidents may happen due to improper operation sometimes.

2 Analysis of a typical case

2.1 Description of a hydraulic power sliding table

In order to study some problems of the control system of hydraulic power sliding table，here shows a typical form of the device depicted in Fig.1.The hydraulic motor converts the oil pressure and flow into angular displacement，driving the worktable forward and backward by the screw.In order to analyze the problem conveniently，some detail information of parameters such as oil pump，oil tank and solenoid valves of the pump station have been omitted.The symbols YV1，YV2 and YV3 represent solenoid valve coil and SQ1，SQ2 and SQ3 represent the position signals for the process of working feed，fast backward and return to the starting point of the worktable.These two kinds of signals are controlled or sampled by a programmable logic controller.

Fig.1 Schematic diagram of hydrauIic power station

2.2 Description of the work process

The automatic cycle process is described as follows. When the sliding table is on the position of starting point，press the start button and it will move forward at full speed and reach the maximum oil flow at the same time.When the sliding table hits the switch of working feed（SQ1），it will turn into the state of working feed，and the flow of hydraulic oil will be reduced and it is suitable for manufacturing.When the sliding table hits the switch of fast backward（SQ2），it means the manufacturing process is finished.After a period of time delay，it will fast rewind.When the sliding table hits the switch of start point（SQ3），it returns to the original position again.This cycle repeats itself ad infinitum.

2.3 Implementation of classical sequential function chart

IEC61131-3 is a standardized programming language specification for industrial control systems enacted by the International Electrotechnical Committee［9］.The sequential function chart（SFC for short）is a subset of the collection.The typical sequential function chart consists of steps，directed lines，conversion conditions，actions and etc.［10］.According to the principle we can draw the sequential function chart based on the PLC of Siemens 200 series，as shown in Fig.2.

Fig.2 SequentiaI function chart for singIe Ioop

From the perspective of formal logic we can find that there is a fatal flaw on the structure because it is a single loop which cannot express the variable states between automatic cycle and manual operation.Therefore，the classical sequential function chart is normally designed only for automatic cycle.

In some manufacturing processes on the spot，a suspended animation can occur at any time due to equipment failure so that the automatic cycle has to be changed into manual operation.During the pause，the technician can address some failures temporarily.This is so called“breaking point”，when the fault is eliminated，the state will be returned to automatic cycle from manual operation again.At this“breaking point”，the control system should run continuously until the automatic cycle is finished.

3 Reconstruction of sequential function chart

3.1 Add new definition of input/output variables

Due to the inherent flaws of the sequential function chart，we need to reconstruct the original SFC design. Three sets of important signals should be added here. The first signal I0.7 represents the conversion between automatic and manual.When I0.7=0，it means the state of automatic while 1 means manual.The second sets are signals ranged from I0.3 to I0.5，which can drive solenoid valve coils directly at the state of manual.The third set signals ranged from S19.0 to S19.4，which can keep the information related to each step，comparing to the M signal，the S signal is nonvolatile memory.These new added signals laid the groundwork for sequential function chart redesign.

3.2 Design a new sequential function chart

A prominent part of designing sequential function chart is that when you compose the code of ladder diagram you can do it step by step and avoid missing［11］.In developing the technical standards for SFC，more consideration is focused on the common of various PLC manufacturers in terms of processing order issues，the International Electrotechnical Commission did not offer a special case in dealing with the“autocycle”and“manual operation”，so there is a structural flaw in current sequential function chart［12］.It may lead to a serious damage to the workers and equipment on the spot due to a misconceived designing of program.

Fig.3 is a new designed sequential function chart which contains state transition director.Compared with sequential function chart with a single automatic cycle，a major structure still can be found clearly，which is a virtual step at S19.0 and four real steps from S19.1 to S19.4.Two states can be set in each action step，when the transfer switch I0.7 is set to logic“0”（upper connected），it is an automatic process and vice versa is manual process.The signal I0.7 is divided into I0.7_1 and I0.7_2 which formed certain micro cycles in order（cycle1-8）to keep the current variable states respectively so that the two states can be transferred each other with no disturbed［13］.

Further analyzing the sequential function chart depicted in Fig.3，we can find that there are two input signals for a special target ranged from Q0.5 to Q0.7 while there is only one input signal at former expression mentioned.It means that there are two possibilities to drive coil Q，one is automatic control signal and the other is manual one.The cubicle switches I0. 7 play and important role to realize the transition from one state to another.

Fig.3 SequentiaI function chart with state conversation

4 Implementation of algorithm

4.1 Design of ladder diagram

Ladder diagram as shown in Fig.4 is designed in accordance with the new designed sequential function chart，along with the transition which abides by the method recommended by the IEC61131-3.The program consists of 18 independent modules，just parts of them are provided due to space limitations.Following is a brief description of each module，the N1 is an initial module，N2 to N5 are the variables setting module ranged from step1 to step4，N6 to N13 are transition module between auto loop and manual mode，N14 to N18 are the output module.Further detail information is depicted on the ladder diagram.

4.2 Testing of different function

Download the ladder diagram to the programmable logical controller in order to generate executable codes so that the different function can be tested according to the following steps.

Firstly，periodic testing is executed at the automatic cycle as follows.Place the switch I0.7 in auto state，press the start button I0.6，the program will perform an automatic cycle：fast forward，working feed，time delay and fast rewind.

Secondly，testing of transferring from auto to manual is executed as follows.At the state of auto，for instance of second step，when the switch I0.7 is placed in manual state，the auto state will be halted，the target relay Q0.5，Q0.6 and Q0.7 can be driven by pressing I0.3，I0.4 and I0.5 directly in order to deal with some temporary failures.

Thirdly，testing of transferring from manual to auto is executed as follows.When the switch I0.7 is placed in auto state again，the program will run continuously from step2 until the end of the automatic cycle.

The experiment results show that the new designed ladder diagram can realize the state transition in the current work step from automatic to manual correctly and then it can return to automatic state again without disturbance and finish the rest steps continuously.It improves the safety，stability and flexibility of the special control system for modular machine tools because the two states can be switched each other smoothly.

Although it makes the sequential function chart looks more sophisticated by means of adding some variables and micro circulation branches based on the single loop，it presents some special features such as transparency，rigorous and cross-reference running through the whole process of carefully designation and transition.

Fig.4 Ladder diagram after modeIing reconstruction

5 Graph theory model establishments

5.1 Description of graph theory model

So far we have solved the problem that convert sequential function chart into ladder diagram，on the other hand，we can further analyze the new features from a new perspective of graph theory model establishment.Fig.5 is a directed graph with single automatic cycle while Fig.6 which inserted some amendment flows，it is clear that the latter has more branches than former.Now a graph theory model can be created and it will be compared to each other in order to find some new characteristics of the latter.

Fig.5 Directed graph with singIe automatic cycIe

Fig.6 Directed graph with amendment fIows

For an arbitrary directed graph，a common expression could be written out［14］as follows.

G=（V（G），A（G））（1）

For this particular graph a group of expression of vertices and edges collection on the basis of graph theory［15］could be defined as follows：

V（G）=｛s，a，b，c，d，e，f，g，h｝（2）

A（G）=｛sa，ab，bc，…，dh，hd，ds｝（3）

Where V（G）represents a vertices collection and A（G）represents edges collection.

5.2 Model establishment and analysis

A set of state point collection is given as bellows：

S=｛x1，x2，…，xn｝（4）

A set of revise state point collection is given below：

R=｛y1，y2，…yn-1｝（5）

On collection S the first kind of effective edges sub collection can be constructed as bellows：

A=｛xixi+1|i=1，2，…，n-1｝（6）

Similarly，on collection R the second kind of effective edges sub collection can be constructed as bellows，too：

B=｛xiyixixi+1|i=1，2，…，n-1｝（7）

Thus the calculation of maximum flow of the graph theory model is

It is subject to Li=xixi+1∈A or Li=xiyixixi+1∈B and i=1，2，…，n-1.

Among them C（LiLi+1）represents the line capacity of LiLi+1.

Actually，if a proper path L1，L2，…Li…Ln-1…is assumed to be existed，then the problem of searching a maximum flow of the graph can be solved.To the particular graph，let n=4 and then give these assignments to each variable as the following forms：x1=a，x2=b，x3=c，x4=d.

In order to discuss the methods of searching routines，for each effective edge，we can assign capacity 0 to collection A and capacity 1 to collection B.In the process of graph traversal，the meaning of the weight can be expressed as：0 must be passed through while 1 conditional executed.If some state in the testing point xkis assumed to be out of order，the expression C（xk·xk+1）=1 will be available.And finally the current issue can be converted into the solution of calculating maximum flow of the graph theory model.

Comparing Fig.5 and Fig.6 wen can conclude that after modeling reconstruction，although the maximum flow of the graph has been increased in number and it reduces the efficiency of searching nodes or routines to a certain extent，it still presents its strict closeness［16］.This is an important underlying mechanism to keep the stability of the control system.

6 Conclusions

Program designers or engineers should retain correct SFC and correspondent ladder diagram codes in the form of archive for the users no matter how complicated it is and this is a fundamental condition to keep the stability，traceability as well as expendability for the control system of the module machine tools.It is suggested that we should encourage people to use common vocabulary adaptive many kinds of controller，avoiding use specific statements in order to facilitate the transplantation of ladder diagram.We should keep the balance between the universality of typical sequential function chart and individuality of special control system on the spot.On the other hand，fault diagnosis based on graph theory modeling is a new development direction related to machine tool repairing and remanufacturing.

Acknowledgements

This paper is supported by Department of Education of Zhejiang Province（No.jg2013281）and Hangzhou Education Bureau（No.［2013］55-23）.

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順序功能圖的缺陷與改進(jìn)研究

張中明*，吳曉蘇，陳恩愛，鄭小康
杭州職業(yè)技術(shù)學(xué)院，杭州 310018

為了解決現(xiàn)有順序功能圖無法靈活地表達(dá)自動(dòng)循環(huán)與手動(dòng)操作之間的工作狀態(tài)轉(zhuǎn)換問題，以液壓動(dòng)力滑臺(tái)典型工作步驟為研究對(duì)象，提出了增設(shè)狀態(tài)變量并插入微小分支回路的方法來保存兩種狀態(tài)之間的動(dòng)態(tài)存儲(chǔ)器變化過程。研究表明：重新設(shè)計(jì)后的順序功能圖與梯形圖之間呈現(xiàn)出了更為嚴(yán)格的映射關(guān)系。通過圖論建模發(fā)現(xiàn)，模型重構(gòu)后連通圖的最大流數(shù)量比之前有所增加，但是仍然符合圖的封閉性原則，從而維持了控制系統(tǒng)的穩(wěn)定性。通過現(xiàn)場觀察梯形圖的運(yùn)行過程，控制程序在兩種狀態(tài)之間實(shí)現(xiàn)了斷點(diǎn)無擾動(dòng)切換，驗(yàn)證了新算法的正確性與可靠性。

液壓動(dòng)力滑臺(tái)；順序功能圖；自動(dòng)循環(huán)；映射關(guān)系；模型重構(gòu)

10.3969/j.issn.1001-3881.2015.12.022Document code：A

TG502.32

10 September 2014；revised 22 December 2014；accepted 6 April 2015

*Corresponding author：Zhong-ming ZHANG，Senior engineer，

Associate professor.E-mail：zhangzhongming-8@163.com