- Email: [email protected]
An application of AI control strategy to a walking beam reheating furnace
253
Applications
An Application of AI Control Strategy to a Walking Beam Reheating Furnace Jiang Jiong *
1. Introduction
Department of Industrial Management, Zhefiang University, Hangzhou, P.R. China
A hybrid knowledge-based model describing the dynamics of a slab walking beam reheating furnace is developed. Also, artificial intelligence (AI) technique is applied to design a hierarchical computer control strategy for the furnace. Part of this is successfully implemented on-line. The design procedure of hardware structure, software structure and man-machine interface are briefly introduced. The results show that the system is reliable and flexible for control. Better control performance and significant economic benefit are achieved since the system was put into use. Keywords: Modeling and simulation, Artificial intelligence, System implementation, Reheating furnace.
Dr. Jiang Jiong was born in Zhejiang, China in October 1962. He obtained his BS, MS and PhD degrees in Chemical Engineering at Zhejiang University in 1982, 1984 and 1987, respectively. Since 1987, he is with the Department of Industrial Management, Zhejiang University and now with the Faculty of Management, University of Toronto, Canada. Dr. Jiang's research interests are mainly in process modelling and control; distributed parameter system, decision system and manufacturing system. He is the author of about twenty papers in above areas and one of the National Award recipients in advanced science and technology in 1988. * Present address: 125 Lippincott st., Toronto, Ontario, Canada M5S 2P2. Elsevier Computers in Industry 13 (1989) 253-259 0166-3615/89/$3.50 © 1989 Elsevier Science Publishers B.V.
A list of papers and reports concerning the modeling and corresponding control strategies for reheating furnaces would p r o b a b l y cover a long page, but here, two facts shared b y most of them are enough to introduce the novel approaches presented in this paper. First, the models developed for the reheating furnaces, whether distributed or lumped ones, are difficult to be implemented on-line for optimal operation strategies, see for example [2,3,9,12]. Second, almost all of the works are dawdling on the w a y of simulation; in fact, the whole process of the reheating furnace is generally so complex that it is impossible to gain access to some i m p o r t a n t variables a n d information, although some parts of it can be precisely described even b y partial differential equations, such as the heat transfer in the reheating slabs [2,9,121. The novel approaches presented in this paper are, therefore, twofold: (1) C o m b i n i n g the qualitative methods emerging from knowledge-based systems [7] with the traditional analytic modeling technique to develop a hierarchical model for the goal of controlling final slab temperature and decreasing the fuel consumption. (2) Developing an integrated optimization control strategy which hybridizes quantitative and qualitative control based on the different abstraction hierarchies of the model. It is shown that the knowledge-based system technique and A I control not only provide an alternative representation m e t h o d that m a y be m o r e appropriate to the problem at hand, but also m a k e the optimization more implementable and feasible for practical use. Figure 1 shows the walking b e a m reheating furnace at the Fifth Rolling Mill of Tienjing,
254
Applications
Computers in Ind~s'try
Key Point/
Key Point /
f Inlet ~
/
f/
i/ •
•
1
•
Heat Zone 1=24.476M J
Key Point
J
~ 1 ~/
//
Outlet
•
Sz~ak
!
Slab Fig. 1. Walkingbeam reheatingfurnace.
PRC, for which the authors have developed a hierarchical computer control system [4-6]. The first level (low level) installed a micro-processor digital control system (YEWPACK packed control system which supports approximately 8 loops) for the control of air-fuel rate or so-called combustion control. On the second level (or upper level), a DESKTOP/10-SP computer from DG company was implemented. The L-bus of YEWPACK system and USAM-4-bus of DESKTOP system provide the communication interface between the two levels for the development of advanced control strategies which can be programmed by FORTRAN-77 language under RDOS. Previous studies of the furnace control system include modeling the heat transfer in slabs by partial differential equations or discrete state space formulation [4-6]. In both cases, some restrictive assumptions about distribution of the furnace temperature--such as "the furnace temperature is considered to be one dimensionally distributed along the length and linear between two neighbouring zones of temperature measurement" [4] or "the temperature may be represented by the product of a function of x alone (spatial variation in the temperature profile) and the normalized fuel rate of the corresponding zone" [5]--must be made due to the lack of information about the underlying physics. Since these relations are generally determined or verified from industrial experimental test data, the matching, of course, shows "excellent results" [5,12]. (The experimental test is generally made only once or twice to verify the model parameters because of the high cost of
the thermocouples and difficulty of the experiment.) So one may doubt "how about the optimization strategies completely based on these models which are used to estimate the behaviour of the poor furnace" [10]. The present paper consists of the development of a knowledge-based model which makes use of the expertise of the furnace operator to combine the traditional quantitative model in different hierarchies, formulation of the evaluation function to minimize the fuel consumption and presentation of a dynamic control problem based on AI strategy under the evaluation function which tends to guide the search for the optimal temperature setting.
2. Modeling 2.1. Discrete State Space Model
A discrete state space model for the reheating furnace has been developed by discretizing the one-dimensional partial differential equations describing the unsteady heat conduction in slabs, which has been reported in several papers of the authors [4-6]. The model describes a cascade of transmission relations among 240 states in the corresponding positions of two transmission bands. The switching between the states depends on the movement of the walking step device driven seperately by electric-hydralic equipments. The state variables include the temperature difference (TD) between surface and center of slab and the
Computers in Industry
J. Jiong / A I Control Strategy 1200
temperature on surface of slab. The transmission relation of the states is described by
255
8
X(i) = T~j(t +, t-, -t, u(-t, ~, y), X ( j ) ) , i=j+l,
j-l,
j,
(1)
where X(i) ~ R" is the state space variable including the surface temperature and T D of the slab at state i (denoted by x s and x d respectively), t + is the entrance time of the slab to state i, t + is the exit time of the slab from state j, t is the related time intervals x, y are the length and width interval, of the related spatial variables, and u(t, ~, y) is the distribution of the furnace wall temperature in t along ~ and ~ which can be further related to u(t, ~, ) ) = f ( U ~ ( t ) ,
U2(t ) . . . . . Urn(i), ~, .p),
E
600 _
8
--
/.~ -
r~o
~
-
-
I
0
.
--
xs X
L
I
.
Measured - -
I
15
J
i
I
30
45
60
Time(Min.) 40 o v
(2) where Ul(t ) . . . . . Urn(t) are key point temperatures which are assumed as control variables. Figure 2 is the state transmission diagram which specifies the sequence of switching between the states. Model (1) is derived from a highly nonlinear partial differential equation under the assumption of the existence of an equivalent heat transfer coefficient [5,12] and some secondary effects being negligible after discretization. Simulation of the model has been carried out by computer and the results are compared with the experimental test data to verify the model (Fig. 3). As a matter of fact, this is rather a procedure to identify or determine the model parameters than to verify the model because the physical coefficients pre-assumed generally make the output of the model deviate from the experiment results in some extent. As a result, the traditional analytic modeling technique can only provide us with a relation with some "fuzziness" and not with a precise function of the temperature distribution of the furnace and slabs. On the other hand, model (1) is still too difficult to be used for on-line implementation of T
i-I ,i
T
i,i-1 Fig. 2. State transmission diagram.
~20
i/
8,
easured r~--
10
xd J
0
15
J
Model Output I
30
L
45
I
60
Time (Min.) Fig. 3. Comparison of simulation results with experimental data.
control without the help of expertise of the furnace operator, although it has been much simpler than many other furnace models [2,3,9], because the operation conditions of the furnace investigated are very poor [5].
2.2. Knowledge Based Model Two kinds of knowledge representation methods are used in this study to model the expertise of the furnace operation, which provide an alternative approach to compensate the ineffectiveness of classical modeling techniques. (1) Frame representation [1] is used to express the expertise about heating rules for a given grade of slabs, each frame is composed of several slots, some slots can be further divided into different sub-slots, the discrete state space model's knowledge is also combined into one of the sub-slot by imbedding it as a procedure (or so-called simula-
256
Applications
('ornputer.s in lndusti3"
tor). The following fragment is an example taken from one such typical frame.
distribution, [output variables]: temperature distribution of exit slab;
Steel grade: H08M,2S~; Physical parameters: subslot[1],[2] . . . . . ; Rolling temperature: 1200 ° C; TD of exit slab: "small" [Fuzzy set B with m e m bership/~ n (Xd)]; Constraints on key point temperature: U1 (much higher than) U2 (medium higher than) U3 [Fuzzy relation R with membership/~R(U1, U2, U3)]; Simulator: [input variables]: furnace temperature
where the physical parameters include the coefficients related to the heat transfer in the slabs, U~, U2 and U3 denote the key point temperatures of preheat zone, heat zone and soak zone respectively, and relations such as " m u c h higher" refer to the corresponding fuzzy subset and relation on given universes.
o•"
1200
La
1150
1100 22
18
20
.~ ,.-]
10
~
0
~
40
.to -]
26
Frequency of Stepping (1/Sec.) 1200
la
v
2 20
1100
1000
i
I
i
I
1000
i
I
,
o
/
g
12 oo
1100 Key Point Temperature for Heat Zone
40
1200
K
2o
1100
.~
~ g
,.2
1000
J
1000
i
:
1100
i
0
~
1200
Key Point Temperature for Soak Zone
Fig. 4. Analytical results based on the discrete state space model.
(2) The second class of knowledge is derived from the computer simulation experience of the discrete state space model and control experience of the authors [4]. They are expressed in the syntax of production-rules system. Since the production rules are relations between fuzzy sets [11], we use the following steps to decide the corresponding linguistic rules which can be viewed as qualitative results abstracted from the analytic results based on the discrete state space model (Fig. 4). (A) Define fuzzy sets on the universe of discourse for the temperature and temperature difference of slab at the outlet. (B) Determine the membership of fuzzy sets defined by step (A), which is rather subjective. (C) Make use of the functional relation shown in Fig. 4 to define the fuzzy set and their corresponding membership for operational conditions. The following examples illustrate the linguistic rules derived. Rule 1. If x S is positive big and x a is positive small, then decrease U3 slightly. Rule 2. If x s is positive big and x d is negative small, then increase U2 slightly. The memberships of fuzzy sets for "positive big" and "positive small" (x~) and "slight" (U2 and U3) are shown in Fig. 5. In the implementation, the linguistic rules can be expressed by a so-called decision table [10] which can be easily p r o g r a m m e d on line; the max-membership method can be applied to transform fuzzy values and non-fuzzy values. As mentioned before, the knowledge model presented above makes the AI technique applicable to solving the control problem with significant efficiency. The AI technique introduced in our
J. Jiong / AI Control Strategy
Computers in Industry "Small Positive"
"Big Positive"
1.0
257
output slabs is "big", then even the fuel rate of the soak zone.
3. Designing Control Strategy by AI Technique 3.1. A I Formulation of the Problem r~
0.0
After the description of the hybrid model, we introduce the index of performance as follows: 3 tl 0
E 10
20
30
Temperature Difference
40
x(o) = Xo,
"Slightly"
0.0 1050
1100
1150
(3)
i=1 j=0
subject to (1) and
xd
1.0
1000
K
E r,j(U~(tj)),
1200
Key Point Temperature for heat zone and preheat zone Fig. 5. M e m b e r s h i p f u n c t i o n s .
study is somewhat like a nonlinear programming optimization technique, and it is very flexible and greatly reduces the computation carried out on line. There are also some production rules based on the author's experience which play an important role in the control of fuel rate of each zone. They are derived from the inspection of expert operation over a long period of time. Most of these rules are very effective when the furnace is out of the normal operation state. Examples are: Rule 3. If one of the transmission bands has stopped for a given time, then reduce the fuel rate to a certain extent. Rule 4. If both transmission bands are at the same stepping rate, and the temperature covariance of
R1(Vl(-t), V2(-t), V30)) < R,
(4)
where R is a given fuzzy relation. As compared with the non-restrictive dynamic control formulation presented by [9], the specification of desired performance here is direct, which does not have to transform the control behaviour into the required quadratic mathematical description. As well-known, the index is refered to the heuristic evaluation function in AI technique rather than to the objective function. Under the above formulation, the first part of the inference engine designed for control is given as follows. (1) Deriving the weight coefficients or functions r i and /~d, /xs, R with the help of first kind knowledge (expressed by the frame structure). (2) Forward reasoning chaining to the node ordering search with the key point temperatures as state variables under the evaluation function, using the production rule to correct the search direction in order to satisfy the constraints (4). In this step, the generate-test technique is used [8]. The second part of the inference engine is the application of production rules based on the control experience on a higher level of hierarchy, which are always active to correct and detect the control actions in order to make them more feasible and receivable to the operator. The rules shown in the example take into consideration some practical factors and simulate the judgement of the operator. In Table 1 the steps taken by the inference engine of the AI controller are shown. For example, if the rolling slab is of type H08Mn2S i, the final state of the key point temper-
258
Applications
Computers in Industry
Table 1 Steps of the inference engine of the AI controller
then decrease or increase the setting temperature smoothly to the desired one.
(1) (2) (3)
3.2. Implementation
(4) (5)
Detection of process variables. Derivation of control action using forward chaining. Matching the datum with control action to testify whether the results are receivable, or else correct them with the experience of the expert operator. Providing the explanation if asked to do so. Implementation of the control action.
Figure 6 is the schematic diagram of the hierarchical computer system. The desktop computer acquires data from the Y E W P A C K controller at the rate of 1 second, the whole knowledge-based model is programmed in FORTRAN; the advantage of this is that it is very suitable for carrying out the computation or a real time implementation. Of course, it shares the disadvantage of difficulties in the design of the man-machine interface and adding new rules to the designed system. The only interface we provided now is of the menu type, the operator can add or delete rules by manipulating input data and switches. In fact, researchers in the area of AI control have stopped looking for the universal knowledge representation language that will solve all problems [1] and the language used for implementation is usually not LISP and PROLONG or another AI language but BASIC or FORTRAN [10]. The system implemented has the following properties.
atures for preheat zone, heat zone and soak zone after reasoning are 870°C, 1210°C and 1150°C, respectively for the steady state operation condition with walking step length 0.22 m and frequency of stepping 6 / m i n . If no other {situation)-(action) rule is triggered, the key point temperatures will be sent directly to the process controller as the setting temperature for each zone. If a rule such as Rule 5 is applied, then the value of setting temperature will be revised before it is transmitted. Rule 5. If the operational condition is not in a constraint region and the difference of the setting temperature with the measured one is positive big,
Production Scheduling Information And Management Information
~
~
~
~
M:nhinelnterface
Predicationof SlabTemperature Quantitative Models (Simulator)
L_ll
AI Control Production Strategy .... Scheduling (Inference (Management Engin) Information)
i-- KnowledgeBase i i i
u er
Level
--] Setting
Setting
I
I DDC Combustion Control
F1
r nn
n n n n n
Setting
i
DDC Combustion Control
Temperature Measured
I
I
Temperature Measured
rl
Lower Level
DDC Combustion Control Temperature Measured
F-I
n n n n o o
Fig. 6. Schematic diagram of the hierarchical computer system.
1 Heatingand Rolling Process
Computers in lndustry
(1) With the assistance of qualitative knowledge derived from the discrete state space model simulator, the action on the AI control strategy is completely the same as the process taken by the furnace control expert (human expert), so it is more receivable than the general optimal strategies [4,5] to the operator. (2) The optimum objective is translated into a heuristic function to guide the search for the solution. Using the elimination (generate-test) technique, the search algorithm is equivalent to a branch and bound method [8]; the advantage of the formulation is that the final state is always reachable although it is generally not the optimal one in a rigorous sense in the given time interval which is not enough for the solution of optimization on line. In fact, it simulate the judgement of a human expert, the result is satisfactory and not necessary optimal. Although the search is mostly dependent on the experience, the hybridization of the knowledge from different sources can help the controller to reason how to get access to the final state. (3) Since the slab on the same grade a n d size is generally rolled in batch, the dynamic compensation can be taken into consideration by combining the experience into the knowledge base, which can largely reduce the search space and save computation time. The implemented program takes about 256 kb (shell) and 2 × 368 kb (background) space, the analysis can be made based on the general control results collected. In summary, compared with general control methods [4,5] and man-manipulation, the following conclusions can be made. (1) The AI strategy is easier to implement than the traditional optimal system design technique. Also, the interface of the system is very flexible and receivable to the furnace operator. (2) The covariance of the slab temperature at the outlet is greatly reduced, which means improved rolling quality of the steel and increased throughput. (3) About 5 percent of the fuel consumption and 0.295 percent of the steel consumption caused by overheating are reduced after a part of the system is implemented.
J. Jiong / AI Control Strategy
259
4. Conclusions The novel approach to the control of a reheating furnace falls into two categories, the hybridization of the traditional quantiative method and the human expert to deal with the poor and complex system where traditional modeling techniques are difficult to apply, implementation of a desired system to show that AI control does compensate some deficiency of the technique presented. The study presented in this paper cannot be viewed as of particular significance, it can be extended to a more general reheating furnace such as a push type furnace, and even to other industrial processes.
References [1] H. Frederick, Building Expert System, Addison-Wesley, New York, 1983. [2] F. Hollander and R. Husiman, "Design, development and performance of on-line computer control system in a 3-zone reheating furnace", Iron and Steel Engineer, Vol. 59, 1982, pp. 44. [3] Y. Iwahashi and K. Takanshi, "Computer control system for continuous reheating furnace", Proc. IFAC 8th World Congress, Vol. 5, 1981, pp. 2526. [4] J. Jiang, Y. Yang and Y. Lu, "Development of a computer control system for a walking beam reheating furnace", Metallurgical Process Control, Vol. 8, 1989, pp. 3. [5] J. Jiang, Y. Yang and Y. Lu, "Optimal control of reheating furnace by nonlinear programming technique", Inf. Control, Vol. 10, 1989, p. 10. [6] Y. Lu, "Application of morden control techniques to industrial control - with working samples", in Advanced Control Techniques Move from Theory to Practice, edited by H. Morris, E. Kompass and T. Williams, Purdue University, West Lafayette, IN, U.S.A., 1986. [7] W. Negotia, Fuzzy System, Abacus Press, Tunbridge wells, England, 1982. [8] N.J. Nillson, Principle of Artificial Intelligence, Tioga Press, Palo Alto, CA, 1980. [9] H.E. Pike and S. Citron, "Optimization study of a slab reheating furnace", Automatica, Vol. 6, 1972, pp. 41. [10] D.Q. Qian, J.P. Chen and J. Jiang, "Artificial intelligence control: A survey", Proc. Chinese Automation Society, Control Theory and Application, 1988, pp. 101. [11] R.M. Tong, "A retrospective view of fuzzy control system", Fuzzy sets and Systems, Vol. 4, 1984, pp. 199. [12] Y. Yang and Y. Lu, "Development of a computer control model for slab reheating furnace", Computers in Industry, Vol. 7, 1986, pp. 145.
Applications
An Application of AI Control Strategy to a Walking Beam Reheating Furnace Jiang Jiong *
1. Introduction
Department of Industrial Management, Zhefiang University, Hangzhou, P.R. China
A hybrid knowledge-based model describing the dynamics of a slab walking beam reheating furnace is developed. Also, artificial intelligence (AI) technique is applied to design a hierarchical computer control strategy for the furnace. Part of this is successfully implemented on-line. The design procedure of hardware structure, software structure and man-machine interface are briefly introduced. The results show that the system is reliable and flexible for control. Better control performance and significant economic benefit are achieved since the system was put into use. Keywords: Modeling and simulation, Artificial intelligence, System implementation, Reheating furnace.
Dr. Jiang Jiong was born in Zhejiang, China in October 1962. He obtained his BS, MS and PhD degrees in Chemical Engineering at Zhejiang University in 1982, 1984 and 1987, respectively. Since 1987, he is with the Department of Industrial Management, Zhejiang University and now with the Faculty of Management, University of Toronto, Canada. Dr. Jiang's research interests are mainly in process modelling and control; distributed parameter system, decision system and manufacturing system. He is the author of about twenty papers in above areas and one of the National Award recipients in advanced science and technology in 1988. * Present address: 125 Lippincott st., Toronto, Ontario, Canada M5S 2P2. Elsevier Computers in Industry 13 (1989) 253-259 0166-3615/89/$3.50 © 1989 Elsevier Science Publishers B.V.
A list of papers and reports concerning the modeling and corresponding control strategies for reheating furnaces would p r o b a b l y cover a long page, but here, two facts shared b y most of them are enough to introduce the novel approaches presented in this paper. First, the models developed for the reheating furnaces, whether distributed or lumped ones, are difficult to be implemented on-line for optimal operation strategies, see for example [2,3,9,12]. Second, almost all of the works are dawdling on the w a y of simulation; in fact, the whole process of the reheating furnace is generally so complex that it is impossible to gain access to some i m p o r t a n t variables a n d information, although some parts of it can be precisely described even b y partial differential equations, such as the heat transfer in the reheating slabs [2,9,121. The novel approaches presented in this paper are, therefore, twofold: (1) C o m b i n i n g the qualitative methods emerging from knowledge-based systems [7] with the traditional analytic modeling technique to develop a hierarchical model for the goal of controlling final slab temperature and decreasing the fuel consumption. (2) Developing an integrated optimization control strategy which hybridizes quantitative and qualitative control based on the different abstraction hierarchies of the model. It is shown that the knowledge-based system technique and A I control not only provide an alternative representation m e t h o d that m a y be m o r e appropriate to the problem at hand, but also m a k e the optimization more implementable and feasible for practical use. Figure 1 shows the walking b e a m reheating furnace at the Fifth Rolling Mill of Tienjing,
254
Applications
Computers in Ind~s'try
Key Point/
Key Point /
f Inlet ~
/
f/
i/ •
•
1
•
Heat Zone 1=24.476M J
Key Point
J
~ 1 ~/
//
Outlet
•
Sz~ak
!
Slab Fig. 1. Walkingbeam reheatingfurnace.
PRC, for which the authors have developed a hierarchical computer control system [4-6]. The first level (low level) installed a micro-processor digital control system (YEWPACK packed control system which supports approximately 8 loops) for the control of air-fuel rate or so-called combustion control. On the second level (or upper level), a DESKTOP/10-SP computer from DG company was implemented. The L-bus of YEWPACK system and USAM-4-bus of DESKTOP system provide the communication interface between the two levels for the development of advanced control strategies which can be programmed by FORTRAN-77 language under RDOS. Previous studies of the furnace control system include modeling the heat transfer in slabs by partial differential equations or discrete state space formulation [4-6]. In both cases, some restrictive assumptions about distribution of the furnace temperature--such as "the furnace temperature is considered to be one dimensionally distributed along the length and linear between two neighbouring zones of temperature measurement" [4] or "the temperature may be represented by the product of a function of x alone (spatial variation in the temperature profile) and the normalized fuel rate of the corresponding zone" [5]--must be made due to the lack of information about the underlying physics. Since these relations are generally determined or verified from industrial experimental test data, the matching, of course, shows "excellent results" [5,12]. (The experimental test is generally made only once or twice to verify the model parameters because of the high cost of
the thermocouples and difficulty of the experiment.) So one may doubt "how about the optimization strategies completely based on these models which are used to estimate the behaviour of the poor furnace" [10]. The present paper consists of the development of a knowledge-based model which makes use of the expertise of the furnace operator to combine the traditional quantitative model in different hierarchies, formulation of the evaluation function to minimize the fuel consumption and presentation of a dynamic control problem based on AI strategy under the evaluation function which tends to guide the search for the optimal temperature setting.
2. Modeling 2.1. Discrete State Space Model
A discrete state space model for the reheating furnace has been developed by discretizing the one-dimensional partial differential equations describing the unsteady heat conduction in slabs, which has been reported in several papers of the authors [4-6]. The model describes a cascade of transmission relations among 240 states in the corresponding positions of two transmission bands. The switching between the states depends on the movement of the walking step device driven seperately by electric-hydralic equipments. The state variables include the temperature difference (TD) between surface and center of slab and the
Computers in Industry
J. Jiong / A I Control Strategy 1200
temperature on surface of slab. The transmission relation of the states is described by
255
8
X(i) = T~j(t +, t-, -t, u(-t, ~, y), X ( j ) ) , i=j+l,
j-l,
j,
(1)
where X(i) ~ R" is the state space variable including the surface temperature and T D of the slab at state i (denoted by x s and x d respectively), t + is the entrance time of the slab to state i, t + is the exit time of the slab from state j, t is the related time intervals x, y are the length and width interval, of the related spatial variables, and u(t, ~, y) is the distribution of the furnace wall temperature in t along ~ and ~ which can be further related to u(t, ~, ) ) = f ( U ~ ( t ) ,
U2(t ) . . . . . Urn(i), ~, .p),
E
600 _
8
--
/.~ -
r~o
~
-
-
I
0
.
--
xs X
L
I
.
Measured - -
I
15
J
i
I
30
45
60
Time(Min.) 40 o v
(2) where Ul(t ) . . . . . Urn(t) are key point temperatures which are assumed as control variables. Figure 2 is the state transmission diagram which specifies the sequence of switching between the states. Model (1) is derived from a highly nonlinear partial differential equation under the assumption of the existence of an equivalent heat transfer coefficient [5,12] and some secondary effects being negligible after discretization. Simulation of the model has been carried out by computer and the results are compared with the experimental test data to verify the model (Fig. 3). As a matter of fact, this is rather a procedure to identify or determine the model parameters than to verify the model because the physical coefficients pre-assumed generally make the output of the model deviate from the experiment results in some extent. As a result, the traditional analytic modeling technique can only provide us with a relation with some "fuzziness" and not with a precise function of the temperature distribution of the furnace and slabs. On the other hand, model (1) is still too difficult to be used for on-line implementation of T
i-I ,i
T
i,i-1 Fig. 2. State transmission diagram.
~20
i/
8,
easured r~--
10
xd J
0
15
J
Model Output I
30
L
45
I
60
Time (Min.) Fig. 3. Comparison of simulation results with experimental data.
control without the help of expertise of the furnace operator, although it has been much simpler than many other furnace models [2,3,9], because the operation conditions of the furnace investigated are very poor [5].
2.2. Knowledge Based Model Two kinds of knowledge representation methods are used in this study to model the expertise of the furnace operation, which provide an alternative approach to compensate the ineffectiveness of classical modeling techniques. (1) Frame representation [1] is used to express the expertise about heating rules for a given grade of slabs, each frame is composed of several slots, some slots can be further divided into different sub-slots, the discrete state space model's knowledge is also combined into one of the sub-slot by imbedding it as a procedure (or so-called simula-
256
Applications
('ornputer.s in lndusti3"
tor). The following fragment is an example taken from one such typical frame.
distribution, [output variables]: temperature distribution of exit slab;
Steel grade: H08M,2S~; Physical parameters: subslot[1],[2] . . . . . ; Rolling temperature: 1200 ° C; TD of exit slab: "small" [Fuzzy set B with m e m bership/~ n (Xd)]; Constraints on key point temperature: U1 (much higher than) U2 (medium higher than) U3 [Fuzzy relation R with membership/~R(U1, U2, U3)]; Simulator: [input variables]: furnace temperature
where the physical parameters include the coefficients related to the heat transfer in the slabs, U~, U2 and U3 denote the key point temperatures of preheat zone, heat zone and soak zone respectively, and relations such as " m u c h higher" refer to the corresponding fuzzy subset and relation on given universes.
o•"
1200
La
1150
1100 22
18
20
.~ ,.-]
10
~
0
~
40
.to -]
26
Frequency of Stepping (1/Sec.) 1200
la
v
2 20
1100
1000
i
I
i
I
1000
i
I
,
o
/
g
12 oo
1100 Key Point Temperature for Heat Zone
40
1200
K
2o
1100
.~
~ g
,.2
1000
J
1000
i
:
1100
i
0
~
1200
Key Point Temperature for Soak Zone
Fig. 4. Analytical results based on the discrete state space model.
(2) The second class of knowledge is derived from the computer simulation experience of the discrete state space model and control experience of the authors [4]. They are expressed in the syntax of production-rules system. Since the production rules are relations between fuzzy sets [11], we use the following steps to decide the corresponding linguistic rules which can be viewed as qualitative results abstracted from the analytic results based on the discrete state space model (Fig. 4). (A) Define fuzzy sets on the universe of discourse for the temperature and temperature difference of slab at the outlet. (B) Determine the membership of fuzzy sets defined by step (A), which is rather subjective. (C) Make use of the functional relation shown in Fig. 4 to define the fuzzy set and their corresponding membership for operational conditions. The following examples illustrate the linguistic rules derived. Rule 1. If x S is positive big and x a is positive small, then decrease U3 slightly. Rule 2. If x s is positive big and x d is negative small, then increase U2 slightly. The memberships of fuzzy sets for "positive big" and "positive small" (x~) and "slight" (U2 and U3) are shown in Fig. 5. In the implementation, the linguistic rules can be expressed by a so-called decision table [10] which can be easily p r o g r a m m e d on line; the max-membership method can be applied to transform fuzzy values and non-fuzzy values. As mentioned before, the knowledge model presented above makes the AI technique applicable to solving the control problem with significant efficiency. The AI technique introduced in our
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output slabs is "big", then even the fuel rate of the soak zone.
3. Designing Control Strategy by AI Technique 3.1. A I Formulation of the Problem r~
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After the description of the hybrid model, we introduce the index of performance as follows: 3 tl 0
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Key Point Temperature for heat zone and preheat zone Fig. 5. M e m b e r s h i p f u n c t i o n s .
study is somewhat like a nonlinear programming optimization technique, and it is very flexible and greatly reduces the computation carried out on line. There are also some production rules based on the author's experience which play an important role in the control of fuel rate of each zone. They are derived from the inspection of expert operation over a long period of time. Most of these rules are very effective when the furnace is out of the normal operation state. Examples are: Rule 3. If one of the transmission bands has stopped for a given time, then reduce the fuel rate to a certain extent. Rule 4. If both transmission bands are at the same stepping rate, and the temperature covariance of
R1(Vl(-t), V2(-t), V30)) < R,
(4)
where R is a given fuzzy relation. As compared with the non-restrictive dynamic control formulation presented by [9], the specification of desired performance here is direct, which does not have to transform the control behaviour into the required quadratic mathematical description. As well-known, the index is refered to the heuristic evaluation function in AI technique rather than to the objective function. Under the above formulation, the first part of the inference engine designed for control is given as follows. (1) Deriving the weight coefficients or functions r i and /~d, /xs, R with the help of first kind knowledge (expressed by the frame structure). (2) Forward reasoning chaining to the node ordering search with the key point temperatures as state variables under the evaluation function, using the production rule to correct the search direction in order to satisfy the constraints (4). In this step, the generate-test technique is used [8]. The second part of the inference engine is the application of production rules based on the control experience on a higher level of hierarchy, which are always active to correct and detect the control actions in order to make them more feasible and receivable to the operator. The rules shown in the example take into consideration some practical factors and simulate the judgement of the operator. In Table 1 the steps taken by the inference engine of the AI controller are shown. For example, if the rolling slab is of type H08Mn2S i, the final state of the key point temper-
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Table 1 Steps of the inference engine of the AI controller
then decrease or increase the setting temperature smoothly to the desired one.
(1) (2) (3)
3.2. Implementation
(4) (5)
Detection of process variables. Derivation of control action using forward chaining. Matching the datum with control action to testify whether the results are receivable, or else correct them with the experience of the expert operator. Providing the explanation if asked to do so. Implementation of the control action.
Figure 6 is the schematic diagram of the hierarchical computer system. The desktop computer acquires data from the Y E W P A C K controller at the rate of 1 second, the whole knowledge-based model is programmed in FORTRAN; the advantage of this is that it is very suitable for carrying out the computation or a real time implementation. Of course, it shares the disadvantage of difficulties in the design of the man-machine interface and adding new rules to the designed system. The only interface we provided now is of the menu type, the operator can add or delete rules by manipulating input data and switches. In fact, researchers in the area of AI control have stopped looking for the universal knowledge representation language that will solve all problems [1] and the language used for implementation is usually not LISP and PROLONG or another AI language but BASIC or FORTRAN [10]. The system implemented has the following properties.
atures for preheat zone, heat zone and soak zone after reasoning are 870°C, 1210°C and 1150°C, respectively for the steady state operation condition with walking step length 0.22 m and frequency of stepping 6 / m i n . If no other {situation)-(action) rule is triggered, the key point temperatures will be sent directly to the process controller as the setting temperature for each zone. If a rule such as Rule 5 is applied, then the value of setting temperature will be revised before it is transmitted. Rule 5. If the operational condition is not in a constraint region and the difference of the setting temperature with the measured one is positive big,
Production Scheduling Information And Management Information
~
~
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M:nhinelnterface
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AI Control Production Strategy .... Scheduling (Inference (Management Engin) Information)
i-- KnowledgeBase i i i
u er
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i
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I
I
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F-I
n n n n o o
Fig. 6. Schematic diagram of the hierarchical computer system.
1 Heatingand Rolling Process
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(1) With the assistance of qualitative knowledge derived from the discrete state space model simulator, the action on the AI control strategy is completely the same as the process taken by the furnace control expert (human expert), so it is more receivable than the general optimal strategies [4,5] to the operator. (2) The optimum objective is translated into a heuristic function to guide the search for the solution. Using the elimination (generate-test) technique, the search algorithm is equivalent to a branch and bound method [8]; the advantage of the formulation is that the final state is always reachable although it is generally not the optimal one in a rigorous sense in the given time interval which is not enough for the solution of optimization on line. In fact, it simulate the judgement of a human expert, the result is satisfactory and not necessary optimal. Although the search is mostly dependent on the experience, the hybridization of the knowledge from different sources can help the controller to reason how to get access to the final state. (3) Since the slab on the same grade a n d size is generally rolled in batch, the dynamic compensation can be taken into consideration by combining the experience into the knowledge base, which can largely reduce the search space and save computation time. The implemented program takes about 256 kb (shell) and 2 × 368 kb (background) space, the analysis can be made based on the general control results collected. In summary, compared with general control methods [4,5] and man-manipulation, the following conclusions can be made. (1) The AI strategy is easier to implement than the traditional optimal system design technique. Also, the interface of the system is very flexible and receivable to the furnace operator. (2) The covariance of the slab temperature at the outlet is greatly reduced, which means improved rolling quality of the steel and increased throughput. (3) About 5 percent of the fuel consumption and 0.295 percent of the steel consumption caused by overheating are reduced after a part of the system is implemented.
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4. Conclusions The novel approach to the control of a reheating furnace falls into two categories, the hybridization of the traditional quantiative method and the human expert to deal with the poor and complex system where traditional modeling techniques are difficult to apply, implementation of a desired system to show that AI control does compensate some deficiency of the technique presented. The study presented in this paper cannot be viewed as of particular significance, it can be extended to a more general reheating furnace such as a push type furnace, and even to other industrial processes.
References [1] H. Frederick, Building Expert System, Addison-Wesley, New York, 1983. [2] F. Hollander and R. Husiman, "Design, development and performance of on-line computer control system in a 3-zone reheating furnace", Iron and Steel Engineer, Vol. 59, 1982, pp. 44. [3] Y. Iwahashi and K. Takanshi, "Computer control system for continuous reheating furnace", Proc. IFAC 8th World Congress, Vol. 5, 1981, pp. 2526. [4] J. Jiang, Y. Yang and Y. Lu, "Development of a computer control system for a walking beam reheating furnace", Metallurgical Process Control, Vol. 8, 1989, pp. 3. [5] J. Jiang, Y. Yang and Y. Lu, "Optimal control of reheating furnace by nonlinear programming technique", Inf. Control, Vol. 10, 1989, p. 10. [6] Y. Lu, "Application of morden control techniques to industrial control - with working samples", in Advanced Control Techniques Move from Theory to Practice, edited by H. Morris, E. Kompass and T. Williams, Purdue University, West Lafayette, IN, U.S.A., 1986. [7] W. Negotia, Fuzzy System, Abacus Press, Tunbridge wells, England, 1982. [8] N.J. Nillson, Principle of Artificial Intelligence, Tioga Press, Palo Alto, CA, 1980. [9] H.E. Pike and S. Citron, "Optimization study of a slab reheating furnace", Automatica, Vol. 6, 1972, pp. 41. [10] D.Q. Qian, J.P. Chen and J. Jiang, "Artificial intelligence control: A survey", Proc. Chinese Automation Society, Control Theory and Application, 1988, pp. 101. [11] R.M. Tong, "A retrospective view of fuzzy control system", Fuzzy sets and Systems, Vol. 4, 1984, pp. 199. [12] Y. Yang and Y. Lu, "Development of a computer control model for slab reheating furnace", Computers in Industry, Vol. 7, 1986, pp. 145.