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\title{Supervision and Control Industrial Refrigerator by Integration External and Bond Graph Models}
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\date{\small \em Received: 1 January 1970 Accepted: 1 January 1970 Published: 1 January 1970}

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\section[{I. Introduction}]{I. Introduction}\par
oday, we find that industrial systems are becoming more complex. This complexity requires the enlargement of the traditional model; so far this model is limited to control algorithms. The supervisory design of these systems must be evolved to take into account several valuable information processing systems (sensors and actuators) for which decision making is inevitable. This evolving needs and technological progress made in the field of sensors, actuators and communication field bus lead to the design of the supervision system has used intelligent systems (sensors and actuators) that incorporate a very large information capacity with automated process.\par
In this context several works have been carried out to provide the object-oriented functional (model external) and behavior (object-oriented model) functions to analyze the design of the intelligent equipment supervision system  {\ref (}   {\ref Samantary et al., 2008 )}. As far as the external model is concerned, this model uses the concepts of services, missions and mode of operation which offer to the user organizations based on modes of operation information on the behavior of the component in different operating situations (normal or defective).\par
The disadvantage of the external model is that it describes the industrial system in terms of functions, without taking into account parameters of physical and dynamic behavior. This consideration leads to certain ambiguity such as the location of defects. This is why the leap-graph model as a graphical modeling language of industrial systems element by element is a practical and useful complementary tool for obtaining behavioral and diagnostic models. In addition, the causal properties of this model can help design FDI (Fault Detection and Isolation FDI) algorithms  {\ref (}  \hyperref[b18]{Graisyhm, 1998;}\hyperref[b19]{Duthoit;}\hyperref[b19]{1997;}\hyperref[b20]{Staroswiecki, 1994;}\hyperref[b21]{Cassar et al., 1994)}.\par
This integration allows us to obtain behavioral knowledge about intelligent industrial systems, but it is limited since switching between modes is not determined. For this article is determined, hence the contribution of this article is to use the transfer function model to determine the output dimmer in each operating mode of the industrial system by inserting a switching program between the operating modes according to the necessary tipping conditions. In this way, it becomes possible to obtain, on the one hand, the behavioral knowledge of the intelligent industrial system for monitoring in case of faults and, on the other hand, to see the switchover between the modes of operation; and therefore, to ensure a modernized security standard.\par
In this article, the work is distributed as follows; the first section focuses on the concept of the supervisory system and these advantages in the automation of industrial systems. The second section will be determined on the concept of the external model and these advantages and disadvantages to describe an industrial system. The third section a brief introduction to the bond graph model in the interest of monitoring industrial systems, then the method of integrating the bond graph model with the external model, to complete the description of the industrial system is explained. In the fourth section we will use the concept of the bond graph transfer function model to determine the tilting of the operating worlds of the industrial system. Then, the design of PI controllers for each operating mode is proposed \hyperref[b0]{(Jeyashanthi and Santhi, 2020;}\hyperref[b1]{?edomir et al., 2019;}\hyperref[b2]{Kalaivani. and Lakshmi, 2014;}\hyperref[b3]{Lutfy, 2010)}. Finally, a conclusion to illustrate all the work we have done. 
\section[{II. Supervision by External, Bond Graph}]{II. Supervision by External, Bond Graph}\par
and Transfert Function Models a) Supervision System Supervision is generally defined as a task of controlling and monitoring the execution of an operation or work performed by other agents (men or machines), without going into the details of this execution. We have adopted the definition of the Research Group on Integrated Automation and Human Machine-Driven Systems, which stipulates that: supervision is the set of tools and methods used to conduct industrial installations both in normal operation and in the event of faults or disruptions for industrial system see figure  {\ref 1}.\par
Fig.  {\ref 1}: Supervision System for industrial system A supervisory system is active if it gathers all the events necessary to activate the decision-making see figure  {\ref 1}: ? Real-time: Decision-making will be effective and fast if the situational awareness is complete. ? In delayed time: Decision-making will be taken as appropriate and the analysis of concrete situations allows a formalization of the operations to be created for each provision.\par
A supervisory system can improve the process with: ? Continuous use of the system (no interruption), ? Minimization of fault tripping (speed and reliability), ? Optimization of the use of system components, ? Minimization of maintenance costs, ? Realization of benefits for industrialists (economic). 
\section[{b) External Model}]{b) External Model}\par
Industrial systems consist of a set of interconnected equipment. A hardware failure of one or more of these devices may jeopardize the achievement of some of the objectives for which the system was designed, so users should be warned by generating alarms. The latter must be sufficiently synthetic to express clearly the nature of the failure and its consequences. Research has developed modeling by external model \hyperref[b29]{Sallami et al., 2016;}\hyperref[b23]{Imhemed et al., 2007;}\hyperref[b25]{Maza et al., 2006;}\hyperref[b26]{Bayart et al., 1998;}\hyperref[b27]{Bayart et al., 1999)}. This model is based on the following notions: ? Concept of services, ? Concept of missions, ? Concept of operating modes.\par
Industrial systems consist of a set of equipment (heat exchanger, motor, pump, etc.) that are organized in such a way that the systems can meet the objectives for which they were designed. These devices are arranged in two ways: ? Low level: These are basic services; they are directly interfaced with the process (valves, tank, sensors...). ? High level: These are composed services; they consist of basic services (cooling circuits, water booster unit, desalination unit...).\par
Elementary services (of low level) are associated with each other to define so-called composite services; the latter realize what we call a mission. A hardware failure means the unavailability of certain basic services and may call into question the continuation of certain missions.\par
The missions were the first to take responsibility for managing and managing systems in accordance with the objectives of the specifications. But at a given moment, only a subset of these missions is necessary to meet the objectives set. Each of these subsets is referred to as the operating mode.\par
An operating mode (MEi) corresponds to a set of service versions represented by Si, this set is the grouping of the subsets that define the desired operating mode, so we have the following relation: MEi = \{S 1 , S 2 ??., S n \}.\par
At a given moment, the process is executed in an operating mode (represented by MEi), all the operating modes are available and interconnected to perform what we call operating mode management graph.\par
The request to change from one mode to another mode must be indicated for safety reasons because the system may fall on an operating mode MEj which is not available, hence the necessity of having a logical passage that leads The system on a mode of operation without getting into trouble. This passage is represented by a Boolean variable bij. The set of operating modes and the conditions of passage bij are described by a graph of management of the operating modes and which can be represented in figure  {\ref 2}. 
\section[{Fig. 2: Operating mode management graph c) Bond Graph Model}]{Fig. 2: Operating mode management graph c) Bond Graph Model}\par
The bond graph modeling tool was defined by Henry  {\ref Paynter (Henry, 1961)}, it is a language of graphical representation of physical systems, based on the modeling of the energy phenomena intervening within these systems. This energetic approach makes it possible to underline the analogies that exist between the different fields of physics (mechanics, electricity, hydraulics, thermodynamics, acoustics, etc.) and to represent in a homogeneous form the multidisciplinary physical systems . In this article, we will present the utility of the bond graph tool for the supervision of industrial systems. In the first part we will give the different approaches using the bond graph for the design of a supervisory system (qualitative and quantitative approach), the second part is devoted to the integration of the external model and the bond graph model for the supervision systems  {\ref (} Bond graph based modeling relies mainly on the concept of generalized stress and flux variables that allow the representation of balance sheets and energy exchanges between different elements of a system. In this approach, an energy exchange between two elements is represented by a half-arrow link indicating the direction of the transfer. These half-arrows are called "leaps", each is labeled by a force variable e and a flux variable f. The product of these two variables corresponds to the power "carried" by the leap. This power is counted positively in the direction of the halfarrow. The advantage of this modeling is that the choice of e and f depends only on the physical domain of the system to be represented in figure  {\ref 3}. 
\section[{Fig. 3: Representation of a physical system by bond graph}]{Fig. 3: Representation of a physical system by bond graph}\par
This description is made in terms of components connected together by links through the ports they have, the components are classified by the number of ports they have, they are multiport or n-ports as described in. There are three types of Bond Graphs each used in a particular stage of the design process \hyperref[b22]{[22]}\hyperref[b23]{[23]}\hyperref[b25]{[24]}\hyperref[b26]{[25]}\hyperref[b27]{[26]}\hyperref[b28]{[27]}\hyperref[b29]{[28]}: ? Bond Graphs with words where the components represent subsystems described by black boxes, this level allows a first decomposition of the system to have an overall view of the energy exchanges implemented; ? Bicausal Bond Graphs where the components are indivisible elementary components and whose behavior is known (resistance, inductance, capacitor, etc.), this level is used at an advanced stage of the design process, where the components can be assimilated Perfect elementary components; ? Causal Bond Graphs which allow establishing the equations of the system.\par
In the sense of bond graphs, the services provided by the equipment of energy sources of the mechanical (motor), thermal (thermo resistance, potential energy or kinetic of a fluid) and hydraulic (pump) type energy sources are represented by sources At all times, an installation operates in an operating mode whose behavior is described by a bond graph model. Thus, each mode of operation (MEi) corresponds to a bond graph MBGi model represented by figure  {\ref 4}.\par
If Si is the set of jump graph elements and Vi is the version of each set, then the jump graph model is the sum of these sets associated with the MEi mode, ie the following relation:MBGi = MEi = \{S 1 (V 1 ) , S 2 (V 2 ) ..., S n (V n )\}.\par
The bond graph MBGi models of the system are linked by bij transitions, for each two jump graph models there are corresponding transition elements specific to them, for example in figure  {\ref 3}, the pattern graph respectively MBG 2 and MBG 3 are linked by the transition elements b 23 and b 32 . 
\section[{Fig. 4: Management graph of the MBGi using MEi}]{Fig. 4: Management graph of the MBGi using MEi}\par
From the point of view of industrial process monitoring, the causal properties of the bond graph are used for the detection and isolation of faults affecting the sensors, actuators or physical components of the process. Thus, the availability of the services (necessary for the realization of a mission) will be provided by the monitoring algorithm to the graph of management of operating modes. 
\section[{d) Transfer Function Model}]{d) Transfer Function Model}\par
Most physical systems can be described as operations that map responses from an input. These operations are transfer functions that explain the patterns of behavior between inputs and outputs. These transfer functions are obtained from linear or non-linear differential equations and can be in the form of a diagram containing all the information needed to simulate the system as a whole. At any time, the physical systems can operate in an operating mode whose behavior is described by a bond graph model   
\section[{III. Supervision and Control of Industrial Refrigerator}]{III. Supervision and Control of Industrial Refrigerator}\par
In this article, we will use the domestic static refrigerator to develop our contribution. This refrigerator is equipped with freezer and a cooling compartment. The volume of behavior is 150 L with two plastic containers containing water and ice. Our work in this article focuses on heat transfers in the refrigerator compartment (see figure \hyperref[fig_3]{6}) . 
\section[{a) External Model of Industrial Refrigerator}]{a) External Model of Industrial Refrigerator}\par
The industrial refrigerator provides cooling of the air and fulfills the following tasks: ? Mission 1: Check for leaks at the heat exchanger; ? Mission 2: Check the seal at the refrigerator door; ? Mission 3: Check for ice water leaks; ? Mission 4: Check for leaks at the water tank; ? Mission 5: Ensure the cooling of the auxiliaries using only the cold heat exchanger with the presence of the water tank and iced water; The tasks of the industrial refrigerator are those that are responsible for the management and management of the system in accordance with the objectives of the specifications. Indeed, at a given moment, only a subset of these missions is necessary to achieve the set objectives. Each of these subsets is called the operating mode.\par
For this cooling system, there are three modes of operation: ? Nominal operating mode: the refrigeration is ensured by two elements (the exchanger of cold and chilled water); ? Mode of operation without iced water: the refrigeration is ensured by a single element (the exchanger of cold); ? Mode of operation without water: the refrigeration is ensured by a single element (the exchanger of cold); ? Complete shutdown mode: the cooling air flow is stopped and maintenance can be ensured. 
\section[{Fig. 7: Different functions of the industrial refrigerator}]{Fig. 7: Different functions of the industrial refrigerator}\par
In case of hardware failure, the industrial refrigerator becomes unable to continue part of the missions for which it was designed. Operators of driving and maintenance must be informed. Manufacturers of the industrial refrigerator combine four (04) alarms. They are illustrated in table 2. This table gives for each defect a list of services and missions. through two elements (the exchanger of cold and iced water);\par
The model of the bond graph MBG 1 corresponds to figure 10 which corresponds to the modeling of the dual flow air treatment unit. 
\section[{Fig. 8: Bond graph model in normal operation MBG 1}]{Fig. 8: Bond graph model in normal operation MBG 1}\par
In this mode of operation ME 2 , operation with a single element (the heat exchanger). The bond graph model for this (MBG2) can be easily deduced, then we obtain the link graph model shown in figure \hyperref[fig_4]{9}, which corresponds to the modeling of the industrial refrigerator with the cold heat exchanger only. In this mode of operation ME 3 , operation with a single element (the heat exchanger) and also without water. The bond graph model for this MBG 3 can be easily deduced, and then we obtain the link graph model shown in figure \hyperref[fig_5]{10}, which corresponds to the modeling of the industrial refrigerator with the cold exchanger only and without the model of the water. To determine the residues using the redundant analytical relationship method. In our case we will change the temperature sensors (De 1 , De 2 , De 3 and De 4 ) by residues (r 1 , r 2 , r 3 and r 4 ) which are at the junctions 0 1 , 0 2 , 0 3 and 0 4 . ? For the junction ''0 1 '', the conservation relation is:\par
The first residual r 1 can be written as:\par
(1) ? For the junction ''0 2 '', the conservation relation is:   The first residual r 2 can be written as:f 3 -f 4 -f 5 +f 9 -+f 10 =0 ) De - De ( R 1 f ) De - De ( R 1 f ) De - De ( R 1 f dt dDe C f ) De - MSe ( R 1 f 4 1 i 10 3 1 w ç 2 1 d 5 1 e 4 1 e 3 = ? = ? = ? = ? = ? f 7 -f 8 =0 dt dDe C f ) De - De ( R 1 f 2 d 4 2 1 d 7 = ? = ? ) - ( R 1 - ) - ( R 1 - ) - ( R 1 - C - ) - (\textbf{1}4 1 i\par
(2) ? For the junction ''0 3 '', the conservation relation is:f 13 -f 12 =0 ) De - De ( R 1 f dt dDe C f 3 1 w 12 3 w 13 = ? = ?\par
The third residual r 3 can be written as:\par
(3) ? For the junction ''0 4 '', the conservation relation is:f 16 -f 15 =0 ) De - De ( R 1 f dt dDe C f 4 1 i 15 4 i 16 = ? = ?\par
The fourth residual r 4 can be written as: \hyperref[b3]{(4)} The residues are grouped with the elements of the industrial refrigerator in table  {\ref 3}. We obtain a boolean matrix (0 or 1). The columns are associated with the residues r 1 , r 2 , r 3 and r 4 and the lines are the fifteen elements.\par
Table  {\ref 3}: Matrix of faults signatures for the industrial refrigerator r 1 r 2 r 3 r 4F 1 :MSe 1 0 0 0 F 2 :Ce 1 0 0 0 F 3 :Cd 0 1 0 0 F 4 :Ci 0 0 0 1 F 5 :Cw 0 0 1 0 F 6 :Re 1 0 0 0 F 7 :Rd 1 1 0 0 F 8 :Ri 1 0 0 1 F 9 :Rw 1 0 1 0 F 10 :De1 1 1 1 1 F 11 : De2 1 1 0 0 F 12 : De3 1 0 1 0 F 13 : De4 1 0 0 1 dt dDe C - ) De - De ( R 1 r 3 w 3 1 w 3 = ) De - De ( R 1 - dt dDe C r 4 1 i 4 i 4 = dt dDe C - ) De - De ( R 1 r 2 d 2 1 d 2 = i. Normal Operation\par
In this mode of operation the industrial system operates under the favorable conditions where the trend of the residues converges towards zero (figure  {\ref 11}   
\section[{Abnormal Operation}]{Abnormal Operation}\par
In this mode of operation the industrial system operates in unfavorable conditions from where the residues do not converge towards zero and the temperature trends indicate new values. To analyze this system we will insert four faults (four alarms).\par
Alarm 01: This fault corresponding to a fault (leakage) of the exchanger of the industrial refrigerator modeled by the element Ce, this fault causes a decrease in the amount of cooling potential (Figure  {\ref 14}). This element exists in the equation of the residue r 1 for each operating mode MBG 1 , MBG 2 and MBG 3 (figure  {\ref 13}), from which only the residue r1 is sensitive to this defect in with the table 3 of signature of the defects (this defect is localized by this residue r 1 ). However, if this component is defective, all operating modes are According to this table 3, we can note that the elements F 1 , F 2 , F 3 , F 4 , F 5 and F 6 are sensitive by a single residue. While the elements F 7 , F 8 , F 9 , F 10 , F 11 , F 12 and F 13 have several residues that are sensitive. To solve this monitoring problem, a linear combination of these different residues with other residues is necessary to eliminate some redundant variables.\par
affected. Therefore, switching to other modes of operation is not allowed because this element exists in operation mode without chilled water and in operating mode without water tank. In this case, the available mode is the stop mode MBG 4 .  \hyperref[fig_3]{16}). These phenomena are readable on the graph-hop model and can be quantified by the equations. This element exists in the equation of the residue r 2 for each operating mode MBG 1 , MBG 2 and MBG 3 (figure  {\ref 15}), from which only the residue r2 is sensitive to this defect in accordance with the table 3 of signature of the defects (this defect is localized by this modes of operation are affected. Therefore, switching to other operating modes is not allowed because this element exists in the operation mode without chilled water and in the operating mode without water tank, in this case the available mode is the stop mode MBG 4 .   {\ref 18}). These phenomena are readable on the bond graph model and can be quantified by the equations. This element exists in the equation of the residue r 4 for the operating mode MBG 1 (figure  {\ref 17}), from which only the residue r4 is sensitive to this defect in accordance with the table 3 of signature of the defects (this defect is localized by this residue r 4 ). However, if this component is defective this operating mode will be affected. Therefore, the transition to other modes of operation is allowed eg MBG 2 , MBG 3 or MBG 4 .\par
Fig.  {\ref 18}: Evolution of the temperature with fault in the ice water Alarm 04: This fault corresponding to a fault (leakage) at the water of the industrial refrigerator modeled by the element Cw, this defect causes a decrease in the amount of cooling potential (figure  {\ref 20}). These phenomena are readable on the graph-hop model and can be quantified by the equations. This element exists in the equation of the residue r 3 for the operating mode MBG 1 and MBG 2 (figure \hyperref[fig_4]{19}), from which only the residue r 3 is sensitive to this defect in accordance with the table 3 of signature of the defects (this defect is localized by this residue r 3 ). However, if this component is defective these modes of operation will be affected. Therefore, the transition to other modes of operation is allowed eg MBG 3 or MBG 4 . If the normal operating mode is the current mode, in the event of a fault, it is necessary to take into account the automatic changeover to another mode. In this case, we find that the two available modes are MBG 2 , MBG 3 or MBG 4 .  The transfer function of the industrial refrigerator in normal operation H 1 (s) is the outlet temperature Tex (s) with respect to the inlet temperature Te (s): + = + +\textbf{(5)}\par
From the bond graph model MBG 2 industrial refrigerator in operation without iced water (figure \hyperref[fig_4]{9}), we can construct the block diagram of the below shown with duplicate links system (effort and flow) figure 24. The transfer function of the industrial refrigerator without iced water H 2 (s) is the outlet temperature Tex (s) with respect to the inlet temperature Te (s): \par
From the bond graph model MBG 3 industrial refrigerator in operation without iced water (figure \hyperref[fig_5]{10}), we can construct the block diagram of the below shown with duplicate links system (effort and flow) figure 23: The transfer function of the industrial refrigerator without water H 3 (s) is the outlet temperature Tex (s) with respect to the inlet temperature Te (s):3 2 0.05283 ( ) 0.05682 s H s s s = +\textbf{(7)}\par
Figure 24 shows the evaluation of the transfer function for the three modes of operation (normal operating mode, reduced operating mode and stop mode). \par
Then, we will consider the recursive equation for each model. So by fixing a sampling time Ts=1s and a first holder folder we obtained the following recursive equations for the three models: By implementing these control laws, we obtained the evolution of the temperature of the refrigerator for the three modes. \par
The determination of the K p and K i parameters leads to the following control laws: ( ) ( ) ( ) ( )   
\section[{G}]{G}\par
From Figure 25, it is noted that the designed PI controllers allow the regulation of the temperature in spite of the variation of the set-point and the switching between modes. 
\section[{IV. Conclusions}]{IV. Conclusions}\par
In this article we used three models to determine the supervision of an industrial system. Indeed the external model provides a functional description for an industrial system; this task is insufficient to supervise the behavior of all elements of the system. To complete the inadequacy of this task, we have introduced another model called bond graph. The bond graph model is a tool based on a physical knowledge of the industrial system; this model bond graph models the industrial system element by element. This modeling, which clearly represents the physical phenomena of the industrial system, improves the surveillance system and the security (fault detection and localization). The use of the model of the transfer function by the bond graph model allowed us to see the ready for each mode of operation (normal operating mode, reduced operating mode and stop mode), also the model of the function transfer allowed us to see the swing of the industrial system for these modes. By considering these representations, we designed PI controllers in order to regulate the temperature for each mode.\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{51}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Fig. 5 :Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Fig. 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9}\includegraphics[]{image-6.png}
\caption{\label{fig_4}Fig. 9 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{10}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Fig. 10 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_6}G}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-9.png}
\caption{\label{fig_8}G}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-10.png}
\caption{\label{fig_9}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1112}\includegraphics[]{image-11.png}
\caption{\label{fig_10}Fig. 11 :Fig. 12 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1314}\includegraphics[]{image-12.png}
\caption{\label{fig_11}Fig. 13 :Fig. 14 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1516}\includegraphics[]{image-13.png}
\caption{\label{fig_12}Fig. 15 :Fig. 16 :}\end{figure}
       \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.5054989816700611\textwidth}P{0.04039375424304141\textwidth}P{0.042124915139171756\textwidth}P{0.25794297352342155\textwidth}P{0.004039375424304141\textwidth}}
\multicolumn{2}{l}{Alarmes Defaults}\tabcellsep Service Level 0\tabcellsep \multicolumn{2}{l}{Service Level 1 Missions}\\
\tabcellsep Leak\tabcellsep \tabcellsep \tabcellsep \\
A-01\tabcellsep exchanger\tabcellsep \multicolumn{2}{l}{No cooling Reduced cooling}\tabcellsep 1, 7\\
\tabcellsep level\tabcellsep \tabcellsep \tabcellsep \\
A-02\tabcellsep Leak door level\tabcellsep No sealing\tabcellsep Bad seal\tabcellsep 2\\
A-03\tabcellsep Leak iced water level\tabcellsep Not iced water\tabcellsep Reduced iced water\tabcellsep 3\\
A-04\tabcellsep Leak water level\tabcellsep No water\tabcellsep Reduced amount of water\tabcellsep 4\\
\multicolumn{3}{l}{Alarm A-01: This fault is associated with the leakage at}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{the level of the exchanger of the industrial refrigerator,}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{the mission concerned with this element are 1 where}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{operating modes are threatened ME 1 , ME 2 and ME 3 . The}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{absence of these missions makes the modes in}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{question unavailable. If the normal operating mode (or}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{the operation mode without ice, or the operating mode}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{without a water tank) is the current mode, in the event of}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{a fault, the automatic changeover to another mode must}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{be taken into account. In this case, we find that the available mode is the stop mode ME 4 .}\tabcellsep \multicolumn{2}{l}{Alarm A-04: This fault is associated with the leakage at the water level, the mission concerned with this element}\\
\multicolumn{3}{l}{Alarm A-02: This fault is associated with the leak at the}\tabcellsep \multicolumn{2}{l}{is the missions 4 the operating modes are threatened}\\
\multicolumn{3}{l}{door level, the mission concerned with this element is}\tabcellsep \multicolumn{2}{l}{ME 1 and ME 2 . The absence of these missions makes the}\\
\multicolumn{3}{l}{the mission 2 from which the operating modes are}\tabcellsep \multicolumn{2}{l}{modes in question unavailable. If the normal operating}\\
\multicolumn{3}{l}{threatened ME 1 , ME 2 and ME 3 . The absence of this}\tabcellsep \multicolumn{2}{l}{mode is the current mode, in the event of a fault, it is}\\
\multicolumn{3}{l}{mission makes the modes in question unavailable. If the}\tabcellsep \multicolumn{2}{l}{necessary to take into account the automatic}\end{longtable} \par
  {\small\itshape [Note: normal operating mode (or the operation mode without ice, or the operating mode without a water tank) is the current mode, in the event of a fault, the automatic changeover to another mode must be taken into account. In this case, we find that the available mode is the stop mode ME 4 .Alarm A-03: changeover to another mode. In this case, we find that the two available modes are ME 3 or ME 4 .b) Bond Graph Modeling TreatmentIn this mode of operation ME 1 , the refrigeration of the auxiliaries is ensured by the circulation of the air]} 
\caption{\label{tab_3}Table 2 :}\end{figure}
 			\footnote{© 2022 Global Journals ( ) G Supervision and Control Industrial Refrigerator by Integration External and Bond Graph Models} 			\footnote{© 2022 Global Journals ( )} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\end{document}
