INTELLIGENT CONTROL MODEL AND ITS SIMULATION OF …

Manuscript submitted to doi:10.3934/xx.xx.xx.xxAIMS’ JournalsVolume X, Number 0X, XX 200X pp. X–XX

INTELLIGENT CONTROL MODEL AND ITS SIMULATION OF

FLUE TEMPERATURE IN COKE OVEN

Gongfa Li,Wei miao and Guozhang Jiang

College of Machinery and Automation

Wuhan University of Science and TechnologyWuhan, 430081, China

Yinfeng Fang, Zhaojie Ju and Honghai Liu

Intelligent Systems and Biomedical Robotics Group, School of ComputingUniversity of Portsmouth

Portsmouth PO1 3HE, United Kingdom

Abstract. In this paper, one-variable linear regression mathematical modelof top of regenerator temperature and flue temperature in machine side is builtusing the linear regress theory. The parameters of ARX model is determinedby identification method of least square method and the mathematical model

of flue temperature control is established. Applying the basis cascade controltheory, system adopts flue temperature and coal flue gas flow as controlledparameters of host circuit and subsidiary circuit respectively. The compoundFuzzy-PID control strategy is presented combined with the characteristics of

temperature system after analyzing the conventional PID control algorithmand fuzzy control algorithm. Using step signal and periodic signal to simulatethe conventional PID and compound Fuzzy-PID algorithm, the result has indi-cated: Compound Fuzzy PID control algorithm combines with the advantages

of fuzzy control and PID control algorithm, including fast response speed andstrong anti-interference ability. When external conditions change, the fuzzyPID compound control can show the strong adaptability and robustness whicheffectively improve the stability of the control system.

1. Introduction. Coke oven, important thermal equipment, has two main prod-ucts of the gas and coke. Among them, the coke is indispensable raw material inthe production of iron making, and its quality affect the quality of iron directly [1].Coking is a complex thermal process of intermittent operation, which compose ofa number of coking chamber and combustion chamber. Gas and air mix, diffuse,combust in the combustion chamber, and heat is passed to the coking chamber inthe form of radiation and convection. Coal is heated to produce the coke in theform of isolating air in the coking chamber. The flue gas generated by the burningof gas is emission through the regenerator and flue [2]-[3].

The flue temperature is the key of production in coke oven, whose stability haveimportant influence on cokes quality and production costs [4]. According to thecharacteristics of the production, many factors affect the relationship between the

2010 Mathematics Subject Classification. Primary: 93B52, 93C10; Secondary: 93C42.Key words and phrases. Flue temperature, linear regress theory, cascade control, compound

Fuzzy-PID control, simulate.∗ Corresponding author: G.F. Li.

1

http://dx.doi.org/10.3934/xx.xx.xx.xx

2 GONGFA LI,WEI MIAO, GUOZHANG JIANG

heating gas flow and top of regenerator temperature, including the period of coking,the types of coal, top of regenerator temperature and the production plan, whichcause the characteristic of strong nonlinear. Because of the large size of coke oven,it has large heat capacity and slow heating and cooling process. Due to complicatebody structure of coke oven and few detecting means, it is difficult to achieve precisecontrol applying the traditional control method [5]-[6].

There are three main categories of coke oven temperature control model, in-cluding feedback control model, feedforward control model and feedback controlcombined with feedforward control model [7]-[8]. Coke oven temperature controlis a complicated control system. In order to achieve the effective and accurate au-tomatic control, it is far from reach the desired control effect only to take singlecontrol model. The modern advanced coke oven temperature control systems ap-ply the control scheme that combined the feedback with feedforward control. Theartificial intelligence technology is introduced in control methods, including fuzzycontrol, neural network and genetic algorithm, and multi-level control system isalso combined with to achieve new control level of coke oven, which will become themain development trend of coke ovens automatic control technology [9]-[11].

The purpose of the coke oven heating systems control is timely adjustmentof heating supply automatic organization of reasonable combustion based on thechange of coke oven flue temperature, so that the temperature keep stable underthe action of various interference factors [12]. The heating system of coke oven iscomposed of two interrelated subsystems, including temperature system and suc-tion system (namely the negative pressure control system of combustion chamberand flue) [13]. This paper mainly studies the temperature control system.

In section 2, the control system of flue temperature is introduced and analysed.Additionally, the soft measurement model of coke oven and the mathematical modelof flue temperature control are established. Section 3 offers some control algorithm-s, such as conventional PID control algorithm, fuzzy PID control algorithm andcompound Fuzzy-PID control algorithm, according to the characteristics of fluetemperature control. Section 4 presents the simulation of step signal and periodicsignal for conventional PID control and compound Fuzzy-PID control. Finally, theconclusions are drawn in section 5.

2. Control model of coke oven flue temperature.

2.1. Analysis of temperature system.The flue temperature is the average value of the measurement of each combustion

chamber, which divided into the temperature of machine side and the temperatureof coke side [14]. The stability of flue temperature is the most important indica-tor heating system. Because of the characteristic of the coke ovens structure andits unique operation mode of production process, figure 1 shows two factors of in-fluencing the coke oven temperature [15]: (1)The change of gas composition andtemperature would affect flue temperature. (2)The change of environmental tem-perature and atmospheric pressure make the change of temperature and pressureof the coke oven, and also arouse the fluctuation of flue suction and combustionchambers temperature.

The control system of flue temperature is a complex industry control process, sothat there are no known theorems used to derive mathematical model. But for theproduction process of coke oven is a good experiment platform, the input/outputof temperature control system could be obtained by the test method, which solves

INTELLIGENT CONTROL MODEL AND ITS SIMULATION 3

Figure 1. Input/output and interference factors of combustion chamber

the problems that the experiment is difficult to design and the most informationcannot be got [16]. According to the data and information got by test method,mathematical model could be established using engineering testing technology andthe analysis theory, and then the parameters of system model could be determinedcombined with system identification.

The input and output data obtained by test methods is time series data of gasflow and temperature. Among them, the gas flow can be used directly measured byflow meter, and the flue temperature can be measured by soft measurement technol-ogy which can overcome the shortage of artificial directly measured [17]. Throughthe analysis of production process in coke oven, the regenerator is a heat transferstructure closely connected to the combustion chamber. After combusting in com-bustion chamber, the gas flow into the top of the regenerator when reversing. Thetop of regenerator temperature can reflect the combustion chamber temperature,and the same time, the regenerator is in the bottom of coke oven, which the interfer-ence to external heating system could be effectively isolated and the real reflectionof regenerator top temperature to straight temperature could be guaranteed [18].So in order get soft measurement model, it is necessary to analysis the data of thetop of regenerator temperature and flue temperature.

The production process of coke oven is taken as the experiment platform, inputand output data of the combustion chamber (namely the time series data of gasflow and flue temperature) could be obtained using the test methods. Among them,the gas flow can be measured by flow meter directly, and the flue temperaturecan be measured using soft measurement technology. The change curve of top ofregenerator temperature and flue temperature is shown in figure 2. From figure2, top of regenerator temperature and flue temperature is related, so that fluetemperature could be reflected indirectly by top of regenerator temperature.

2.2. Mathematical model of coke oven flue temperature.

2.2.1. Grey relation analysis of top of regenerator temperature and flue tempera-ture.


Figure 2. Changing curve of flue temperature in machine sideand top of regenerator temperature

The input gas flow and output flue temperature are measurable, but the processof the combustion of gas in the combustion chamber is very complicated, so the fluetemperature system could be regarded as a grey system [19]. Set top of regeneratortemperature and flue temperature at k time. Using the theory of gravy correlationto calculate [20]:

roi =1

N

N∑k=1

ζoi(k) (1)

where roi is the correlation of subsequence and mother sequence, N is the lengthof the sequence, ζoi(k) is the correlation coefficient.

ζoi =∆min + ρ∆max

∆oi + ρ∆max(2)

where ∆oi(k) represents the absolute difference of the two sequences at k time,namely ∆oi(k) = |x0(k) − xi(k)| , x0(k) is the mother sequence, xi(k) is the sub-sequence. ∆max and ∆min stands for the maximum and minimum values of theabsolute difference in each moment respectively. ρ is distinguish coefficient, whoserole is to improve the significance of difference between correlation coefficient. Setρ = 0.5.

The flue temperature Tx(k) was regarded as the research object, and grey rela-tional analysis was applied, which means that Tx(k) is mother series and Tc(k)ischild series. i = 1 here. According to the formula (1) and (2), the correlation degreewas calculated ro1 = 0.96. This shows that the correlation of top of regeneratortemperature and flue temperature in machine side is very big.

2.2.2. Soft measurement model of coke oven.The linear regress theory is applied to analysis the historical data of flue tem-

perature in machine side. Set top of regenerator temperature Tx, flue temperatureTc, then regression observations are (Tci, Txi). The linear regress equation of top of


regenerator temperature and flue temperature is assumed Tc = α + βTx [21]. The

least square method is used to estimate the estimator of (α, β) , that is (α̂, β̂)

α̂ = T̄ − β̂T̄x (3)

β̂ =

∑ni=1(Txi − T̄x)(Tci − T̄c)∑n

i=1(Txi − T̄x)2(4)

Calculated by the formula (3) and (4): α̂ = 785.0, β̂ = 0.468.The linear regress equation of top of regenerator temperature and flue tempera-

ture in machine side is:

Tci = 785.0 + 0.468Txi (5)

Formula (5) is a simple soft measurement model of coke oven.

2.2.3. The mathematical model of flue temperature control.The methods to identify the degree of system are Hankel Matrix method, residual

properties method, and AIC criteria and so on [22]. The residual properties methodwas used here.

The output (temperature) of coke oven system is and the input (blast furnacegas) is u(k) . The system model was regarded as ARX (Auto Regressive withXogenous input) model [23]:

A(q−1)y(k) = B(q−1)u(k) + e(k) (6)

A(q−1) = 1 + a1q−1 + a2q

−2 + · · ·+ anaq−n (7)

B(q−1) = b1q−nk + b2q

−nk−1 + · · ·+ bnbq−nb−nk+1 (8)

where e(k) is the white noise item, na and nb are the highest degree of polynomialA(q−1) and B(q−1) respectively, nk is the delay time of the system, q−1 q−nb−na+1

and are delay operators.The output of the model ARX:

y(k) = A−1(q−1)B(q−1)u(k) +A−1(q−1)ε(k) = ϕT (k)θζ(k) (9)

where ϕT (k) is regression matrix, θ is Model parameters to be identified of A(q−1)and B(q−1).

By using the historical data of flue temperature in machine side and gas flow andapplying least square method to identify the ARX model off-line, the mathematicalmodel in machine side was obtained:

(1) When coke oven gas was fixed and blast furnace gas was adjusted, the controlmodel of flue temperature system is formula (10):

y(k) = 232.65+0.6112y(k−1)+0.3632y(k−2)+0.0000933u(k−2)+0.001212u(k−3)(10)

(2) When blast furnace gas was fixed and coke oven gas was adjusted, the controlmodel of flue temperature system is formula (11):


y(k) = 268.10+0.5504y(k−1)+0.4209y(k−2)+0.001566u(k−1)−0.00009072u(k−2)(11)

3. Control algorithm of flue temperature.

3.1. Characteristics of flue temperature control.Although the established mathematical model can reveal essentially various nu-

merical relationships in the process of heat generation and transfer, practical appli-cations is often a lack of robustness and adaptability because of high requirements ofmonitoring points and accuracy and so many constraint conditions [24]-[25]. Due tothe disturbance variable can be reflected through the temperature deviation, whenstudying intelligent optimization control system of flue temperature, the gas flowcould be calculated according to output of flue temperature, instead of taking everydisturbance variables as input of the controller, so that interference factors couldbe suppressed [26].

The intelligent optimization control goal of flue temperature is to timely adjustheating load, automatically organize reasonable combustion and keep the furnacetemperature basically stable under the action of various interference factors basedon the changes of flue temperature. Control system mainly consists of two inter-related subsystems, namely the temperature optimization system and valve controlsystem. At the same time, because the work frequency of the valve control systemis far higher than the temperature optimization system, they are divided into twoindependent subsystems [27]-[28]. According to the above analysis, the flue tem-perature intelligent optimization control was divided into host circuit control andsubsidiary circuit control with the basis of feedback of temperature and gas flowand applying the idea of cascade control.

3.2. Control algorithm of flue temperature.

3.2.1. PID control algorithm.PID control, which is widely used in industrial process, has strong robustness,

simple structure, clear physical meaning of parameters, and the advantages of easyto implement.

The digital PID control is the most widely used control method in the process ofproduction, the system principle block diagram conventional PID control as shownin figure 3. The PID controller generates control deviation based on given values andactual output values and controls the object by controlled quantity that generatedby a linear combination of deviations proportion (P), integration (I) and differential(D) [29]. Its control rule is:

u(t) = Kp(e(t) +1

TI

∫ t

0

e(t)dt+TDde(t)

dt) (12)

Or the written form is transfer function:

G(s) =U(s)

E(s)= Kp(1 +

1

TIs+ TDs) (13)

where Kp represents proportionality coefficient, TI stands for integration timeconstant and TD is differential time constant.

In simple terms, the functions of each correction link in figure 3 are as follows[30]-[31]:


Integration

Ratio

Differentiation

Controlled Object

yout(k)rin(k) +

_

+

+

Figure 3. The flow diagram of PID control system

(1) Proportion link: It reflects deviation signal control system instantly andproportionally. Once deviation produced, controller immediately generates controleffect to reduce the deviation.

(2) Integral link: It mainly used to eliminate static error and improve the indis-crimination degree of system. The strength of the integral action depends on theintegral time constant .

(3) Differential link: It can reflect the change trend (rate of change) of deviationsignal. And before the deviation signal value becomes too large, the system isintroduced in an effective early correction signal, thus the movement speed of systemis accelerated and the adjusting time is reduced.

3.2.2. Fuzzy PID control algorithm.Fuzzy control, a kind of nonlinear control, belongs to the category of intelligent

control. One of the main characteristics of Fuzzy control has both the systematictheory and much practical application background. Some control problems, suchas time varying and nonlinearity, could be solved well using Fuzzy control withoutbuilding accurate control model [32]-[33]. The fuzzy reasoning algorithm is shownin figure 4.

Initiation

Input the clear variables

Input the quantitative

factors and calculate

Fuzzy the inputs

If finish the inputs fuzziness?

Fuzzy inference

Defuzzy the outputs

Calculate the output quantization factor

If finish the outputs fuzziness?

Output the clear variable

Ending

Figure 4. Flow chart of fuzzy reasoning algorithm


According to the time-variation of flue temperature, the fuzzy controller needto be more accommodating, so that it can apply to the different controlled objectand also obtain satisfactory control characteristic [34]-[35].So the adjustable controlrule of fuzzy controller should be applied. The control rule of fuzzy controller isexpressed by analytical expression:

U = − < (E + EC)/2 > (14)

where E is the fuzzy quantity of deviation between target flue temperature andmeasured flue temperature in coke oven. EC is the fuzzy quantity of deviationschange rate. U is the fuzzy quantity of gas flows increment. < · · · > representsrounding operation.

Can be seen from (14) above, the control action depends on the error and errorchange rate, and both weighted equally. In order to adapt to different characteristicsof the object under the condition of different coke oven production, an adjustmentfactor is introduced and on the basis of the formula (14). Then a control rule withadjustment factor is obtained [36]:

U = − < (αE + (1− α)EC)/2 >,α ∈ [0, 1] (15)

By adjusting the size of α , different weighted degree of error and error changecould be changed. When the deviation becomes big, the main task of control systemis to eliminate the deviation as soon as possible, and the weight of deviation E shouldbe larger. When the deviation becomes big, the main task of control system is tomake the system stable as soon as possible.

3.2.3. Compound Fuzzy-PID control of flue temperature.According to the characteristics of heating and combustion process in coke oven

and the theory of classic control and fuzzy control, the compound Fuzzy-PID controlis presented. Figure 5 shows the block diagram of the compound Fuzzy-PID control:

TS +

Bang-Bang

Control

Fuzzy Control

│e1│ 6°C

│e1│=6°C

de/dtec

u1

+

+

u2

us

uPID

e2Gas Valve Coke Oven

-TC -

Figure 5. Compound Fuzzy-PID control structure

Apply the basis cascade control theory, system adopts flue temperature andcoal flue gas flow as controlled parameters of host circuit and subsidiary circuitrespectively. As shown in figure 5, the purpose of subsidiary circuit is to overcomethe frequent fluctuation of main pipeline pressure, and its control law is adjusted byPID. The subsidiary circuit is used to stabilize the gas pressure and ensure relativelystable of gas flow rate and the set value of the gas pressure control system couldbe adjusted with interval time according to high and low of flue temperature. Thefuzzy control is used in the host circuit [37]. Because the fuzzy control does notdepend on the mathematical model of controlled objects, the adjustment factorcould be changed flexible in control rule according to the production condition.


In figure 5, Ts is the set value of flue temperature given by the technological re-quirements, usis the feedforward input values of heating gas flow, u1 is the outputvalue of fuzzy control or Bang-Bang control, u is the input of gas flow after hostcircuits correction, u2 is the feedback value of gas flow in subsidiary circuit, Tc isfeedback value of flue temperature, e1 is the deviation value of target flue temper-ature and feedback value in coke oven, ec is the deviations change value of targetflue temperature and feedback value in coke oven, e2 is the deviation value of gasflows input value in host circuit and feedback value in subsidiary circuit.

4. Simulation of coke oven flue temperature.

4.1. Simulation object model and the simulation conditions.The simulation object model is the mathematical model in machine side. Ac-

cording to the actual production, the simulation conditions are as follows:(1) The parameters of the conventional PID controller is adjusted by Zieg1er-

Nicho1s parameter adjustment method. Here set Kp = 0.18, KI = 0.06 , KD = 0.1.

(2) According to the technological requirements, the flue temperature in machineside is set 1260◦C. Because the coke oven exists hysteresis quality, sampling timeshould not too short and set 20s.

(3) When the system is adopts the simulation of compound Fuzzy-PID, the ad-justment factor is set α = 0.45.

4.2. Simulation of control model.

4.2.1. Simulation of conventional PID control.The system equation of the formula (10) was simulated with step signal and

periodic signal respectively, whose simulation curves were shown in figure 6 and 7respectively. The step response curve shows that the system has long transition timeand exist oscillation for a short time. In the periodic response curve, the overshootamount of system decreased obviously after several periods.

Figure 6. Response of conventional PID step signal for the ma-chine side

The system equation of the formula (11) was simulated with step signal andperiodic signal respectively, whose simulation curves were shown in figure 8 and 9.Although the step response curve response faster, the system still appear oscillation


Figure 7. Response of conventional PID periodic signal for themachine side

for a short period of time after it keeping stable for a long time; the control effectof periodic signal was not ideal, which need to be further improved.


Can be seen from the results of simulation, the system still exist many defects,such as the long transition time and large overshoot amount, etc.

4.2.2. Simulation of compound Fuzzy-PID control.When the System equation was formula (10), the step response curve and periodic

response curve were shown in figure 10 and figure 11. In the step response curve,the dynamic characteristics were improved compared with figure 6: there was shorttransition time, no overshoot and oscillation in the system. It also can be seen fromthe periodic response curve that oscillation times was reduced obviously.

When the System equation was formula (11), the step response curve and periodicresponse curve were shown in figure 12 and figure 13. Through comparing figure



Figure 10. Response of compound Fuzzy-PID step signal for themachine side

12 with figure 8 and comparing figure 13 with figure 9, it showed that the dynamiccharacteristics of the control system was improved greatly by the compound Fuzzy-PID algorithm. The transition time of step response curve became shorter andthere is no Oscillation after system became stable. At the same time, the overshootamount of the periodic response curve was decreased from ±20◦C to less than ±5◦C.

Can be seen from the simulation results, the compound Fuzzy-PID control hadeffectively control in coke oven heating process. Through the simulation of math-ematical model with different retardation time and parameters, the designed con-troller had strong adaptability and robustness and good control effect.

4.3. Simulation analysis.


Figure 11. Response of compound Fuzzy-PID periodic signal forthe machine side

Figure 12. Response of compound Fuzzy-PID step signal for themachine side

The compound Fuzzy-PID control method had better tracking performance andresponse speed and stronger anti-interference ability compared with the conven-tional PID control, which effectively reduced the fluctuation of furnace tempera-ture, improved the quality of the coke and reduced the energy consumption. It hadgreat referential value and practical value for the complex problem of coke oventemperature control.

(1) In terms of overshoot amount, the overshoot amount of the compound Fuzzy-PID control algorithm was smaller than the conventional PID control algorithm, andwas small overshoot or no overshoot;

(2) In terms of anti-interference characteristics, can be seen from the figure 10and figure 13, the compound Fuzzy-PID control algorithm had less fluctuation andshorter adjusting time;


Figure 13. Response of compound Fuzzy-PID periodic signal forthe machine side

(3) In terms of robustness, when the set point of temperature and the modelparameters of controlled objects were changed, the compound Fuzzy-PID controlalgorithm showed a strong adaptation;

(4) In terms of transition time, the transition time of the compound Fuzzy-PIDcontrol algorithm is short and its convergence rate is rapid, so that the effect ofhysteresis quality of controlled object to the system became weakened.

5. Conclusions.The intelligent control of flue temperature is important to stabilize furnace tem-

perature, improve coke quality, reduce gas consumption, reduce the workers labourintensity and extend the service life of coke oven. According to the actual situationof a coking plant, the temperature control system was studied using coking tech-nique, automatic control, grey theory and fuzzy control methods, which achievedgood results.

In this study, the relationship between top of regenerator temperature and fluetemperature was analyzed qualitatively. Grey correlation degree was calculatedusing grey theory and the soft measurement model of coke oven is determined bythe linear regress theory. Combined with the time series of historical data, theARX model of flue temperature and gas flow was established applying the theoryof system identification. Apply the basis cascade control theory, system adoptsflue temperature and coal flue gas flow as controlled parameters of host circuitand subsidiary circuit respectively. The simulation curves was analysed applyingthe methods of conventional PID control and compound Fuzzy-PID control, whichverified the adaptability and robustness of the compound Fuzzy-PID control.

Acknowledgments. This research was supported by Hubei Provincial Depart-ment of Education (Q20141107).

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