Modeling and Simulation of a Fuzzy Supervisory Controller for an ...

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Modeling and Simulation of a Fuzzy Supervisory Controller for an Industrial Boiler Enrique Arriaga-de-Valle and Graciano Dieck-Assad SIMULATION 2006; 82; 841 DOI: 10.1177/0037549707076910 The online version of this article can be found at: http://sim.sagepub.com/cgi/content/abstract/82/12/841

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Modeling and Simulation of a Fuzzy Supervisory Controller for an Industrial Boiler Enrique Arriaga-de-Valle Graciano Dieck-Assad Electrical Engineering Department ITESM, Monterrey Campus 2501 E. Garza Sada Monterrey, NL Mexico, CP 64849 [email protected] In this paper we compare and discuss the performance of a boiler evaporator system when the system is controlled by a traditional PID-type strategy and when the system is enhanced by using fuzzy logic blocks to provide set-points for the system. The strategy used in fuzzy logic controllers (FLCs) is called fuzzy supervisory control and it generates set-points for the conventional controllers. The boiler under test is a VU-60 industrial system that produces 180,000 pounds of steam per hour. The mathematical model of the plant is a scaled version model of that obtained for a thermoelectric unit. The new model simpli1es the large-scale thermoelectric boiler model to an industrial small-scale type VU-60 boiler model based upon 1rst principle mass and energy balance equations. The main change consists of representing only the behavior of the drum–evaporator system, having a partial model of the combustion process, with a simpli1ed combustion control system and a three-element boiler feed-water controller. The control system for combustion and boiler feed-water receives a supervisory signal (or set-point tracking signal) that comes from the FLC to improve the performance of the overall control system. The behavior of the supervisory controller brings some advantages to the system performance, compared with the traditional control schemes. The comparison re2ects fuel improvements from 2.5% to 6.5% depending upon the steam load ramp regime. The simulations R R shell running under the MATLAB1 platform. are performed using the SIMULINK1 Keywords: boiler model, fuzzy controller, supervisory control.

1. Introduction One of the major problems in boiler control systems is the inverse effects of the two-phase liquid level control that generate the typical shrink & swell [1–4]. This phenomenon exists whenever the steam demand increases producing a drop in drum fluid pressure. The drum level controller replenishes the energy input to the system by increasing the feed-water rate to the drum tank and, therefore, the steam volume in the waterwalls increases.

SIMULATION, Vol. 82, Issue 12, December 2006 841–850 c 2006 The Society for Modeling and Simulation International 1

DOI: 10.1177/0037549707076910 Figures 1–6, 11–14 appear in color online: http://sim.sagepub.com

This results on increasing fluid level, even though the expected dynamic behavior would be a drop in water liquid level (inverse reaction). This inverse effect is present when the control system uses only the drum water level as a mass index in the evaporator system [6]. To compensate the inverse reaction several control schemes are available. The one that has been used for years is the three element controller [3–8] shown in the Figure 1. The elements correspond to the three variables that are used as indices of control variables: drum liquid level, feed-water flow, and steam flow. The feed-water flow control delays to react and compensate the shrink and swell phenomenon, regardless an instantaneous change in level and guarantees the equilibrium between steam out and water in (achieving a constant mass in the evaporator). A feed-forward steam flow signal compensates some of the dynamics of the feed-water valve and the sudden demands of steam flow. Finally, the third element is the drum level controller that maintains a constant drum level Volume 82, Number 12 SIMULATION


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Arriaga-de-Valle and Dieck-Assad

Figure 1. Drum level three-element controller

Figure 2. Steam pressure controller

using the flow demand as a set point and uses the drum level process variable as a feedback signal. New alternative control strategies have been applied to compensate for the shrink and swell phenomenon, as reported in Ziegler and Connel [6]. Many controllers provide anticipation signals to enhance the controller operation and to achieve a smooth and reliable control trajectory subject to stringent ramping conditions. Fuzzy logic has been applied, but only to control temperature and pressure, because of its inherent direct action [9]. In this paper we emphasize the use of this methodology for the evaporator control system. In particular, the VU-60 industrial boiler built by CERREY [11] shows a small drum design that has been exposed to rapid ramping loads using traditional PID controllers. The fuzzy logic controller (FLC) proposed here is intended to show the flexibility, adequacy and reliability of the boiler operation while using the fuzzy logic control action, particularly while having large ramping regimes where the shrink and swell effects are present. A computer simulation methodology is applied in order to verify the suitability of the modified controller to sustain the ramping regimes required by customers. Pressure is another critical variable to control in the boiler. This variable does not have the inverse reaction behavior that the drum level exhibits. There is a good possibility that the performance of the pressure controller can be improved in order to reduce the operation costs of the boiler. A conventional strategy for pressure control is shown in Figure 2.

2. Methodology

842 SIMULATION

2.1 Model Development The mathematical model of the evaporator system has been given previously in Dieck-Assad [1]. Two main equations from the model have been revised: the drum level and drum pressure equations. Both equations consider the level and pressure as state variables, and are obtained using mass and energy balances in the evaporator considering both liquid and steam phases. Figure 3 shows the control volumes of the evaporator. The following assumptions are made for this model: (i) the drum is a perfect cylinder1 (ii) the heat exchange surface between vapor and liquid is planar1 (iii) all the feed-water enters the downcomer tubes directly and returns through the waterwalls at fluid saturation conditions1 (iv) the circulation through the downcomers and waterwalls is constant1 (v) the water in both phases (liquid and vapor) at the drum is at saturated conditions. The main change implemented in this model is an additional integral term to produce a better shrink and swell model [10]. The heat source model described in [1] has

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MODELING AND SIMULATION OF A FUZZY SUPERVISORY CONTROLLER FOR AN INDUSTRIAL BOILER

The partial derivatives of densities with respect to drum pressure, P, are 12 v 1P

3

K 1 3 a1 4 2a2 P

(5)

12 l 1P

3

K 2 3 b1 4 2b2 P3

(6)

Now, applying the chain rule in equation (2) to the density terms with respect to time, and considering that the variation of the vapor volume is the same as the variation of liquid volume in the drum, we have Wsh 2 Wfe

3

Vv

4 2v

12 v 1 P 12 1 P 4 Vl l 1 P 1t 1 P 1t 1 Vv 1 Vl 4 2l 3 1t 1t

(7)

Substituting equations (3)–(6) into equation (7), we obtain Wsh 2 Wfe Figure 3. Control volumes for the mass and energy balances in the model

been simplified to consider variables such as excess oxygen and air temperature constants through the process. Also, additional model blocks have not been explicitly modeled, in order to further focus on just the evaporator system. Based upon the control volume VC.1 illustrated in Figure 3, the equations representing the evaporation systems are 2 1 1 2 v Vv 4 2 l Vl (1) Wsh 2 Wfe 3 1t Wsh 2 Wfe

3

Vv

12 v 1 Vv 4 2v 1t 1t

4

Vl

12 l 1 Vl 4 2l 1t 1t

(2)

where Wsh is the steam flow, Wfe is the feed-water flow, Vv is the drum vapor volume, Vl is the drum liquid volume, 2 v is the drum vapor density, and 2 l is the drum liquid density. The drum water density is considered a function only upon the drum pressure due to saturation conditions (see assumption v above), for both the liquid and vapor phases. Two quadratic interpolation functions provide an excellent fit to calculate these properties: 2v

3 a0 4 a1 P 4 a2 P 2

(3)

2l

3 b0 4 b1 P 4 b2 P 2 3

(4)

1P 1P 4 Vl K 2 1t 1t

3

Vv K 1

4

2 1 Vl 1 3 2l 2 2v 1t

(8)

Using assumption (i), the liquid volume at the drum tank is given as 5 3 4 R2D Vl 3 L d R 2 cos21 R 7 6 2 4R 2 D5 2R D 2 D 2 6 (9) where L d is the drum length, R is the drum radius, and D is the drum liquid level from the internal wall to the center of the drum cylinder. Taking the derivative of equation (9) with respect to time, we can explicitly write the variations of drum level with respect to time: 6 1D 1 Vl 3 2L d 2R D 2 D 2 3 1t 1t

(10)

Therefore, the cross-section “area zero” constant is: 6 A0 3 2L d 2R D 2 D 2 3 (11) Substituting equations (10) and (11) into equation (8), the following simplified flow balance equation is obtained 3

Vv K 1

1P 1P 4 Vl K 2 1t 1t

4

A1 A 0

1D 1t

(12)

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843

Wsh 2 Wfe



where

A1 3 2 l 2 2 v 3

(13)

The last term is referred to as the “equilibrium density parameter”. Now we analyze the energy balance in the waterwalls of the boiler or control volume VC.2, as shown in Figure 3. Using assumption (iii), the waterwalls energy balance equation is Wsh h eo 2 Wfe h v 4 Q sww 3

2 1 1 2 l h l Vl 4 2 v h v Vv 6 1t

(14)

Wsh h eo 2 Wfe h v 4 Q sww 5 5 4 4 12 1h l 12 1h v Vl 4 h v v 4 2 v Vv 3 hl l 4 2l 1t 1t 1t 1t 4

8

hl2l 2 hv2v

9 1 Vl

(15)

1t

where h eo is the enthalpy of water entering the drum tank, h v is the drum vapor enthalpy, h l is the drum liquid enthalpy, and Q sww is the heat flow rate between the furnace metal and the liquid circulating through the waterwalls. Note that the negative sign in the term corresponding to the drum vapor volume is because the increase or decrease in drum liquid volume corresponds to the decrease or increase in the drum liquid vapor (rate of change in Vl = – rate of change in Vl ). The enthalpies at the drum saturation conditions are also calculated using two quadratic interpolation functions of the drum steam pressure: hv

3 e0 4 e1 P 4 e2 P 2

(16)

hl

3

(17)

f0 4 f1 P 4 f2 P 2 3

Therefore, the derivatives of enthalpy with respect to drum pressure are: 1h v 1P

3

K 3 3 e1 4 2e2 P

(18)

1h l 3 K 4 3 f 1 4 2 f 2 P3 (19) 1P Substituting equations (5), (6), (18) and (19), equation (15) is simplified as follows: Wsh h eo 2 Wfe h v 4 Q sww 3 4h l K 2 4 2 l K 4 5Vl

1P 1t

4 4h v K 1 4 2 v K 3 5Vv 4 4h l 2 l 2 h v 2 v 5A0 844 SIMULATION

1P 1t

1D 3 1t

(20)

Rearranging and collecting the terms of equation (20), we have Wsh h eo 2 Wfe h v 4 Q sww 3 A4

1P 1D 4 A3 A0 1t 1t

(21)

where A4

3 4h l K 2 4 2 l K 4 5Vl 4 4h v K 1 4 2 v K 3 5Vv (22)

A3

3 4h l 2 l 2 h v 2 v 53

(23)

Finally, solving equations (12) and (21) for the derivatives of drum level and pressure, we obtain 1D 1t

3

Wfe [4A4 7 A2 52h eo ]2Wsh [4A4 7A2 52h v ]4Q sww 4A0 A1 A4 7A2 52A0 A3

1P 1t

3

Wfe [h eo 24A3 7A1 5]2Wsh [h v 24A3 7A1 5]4Q sww 3 (25) A4 24A2 A3 7A1 5

(24)

One last state equation integrates the overall process model of the boiler: the energy balance equation at the furnace waterwalls. This equation models the dynamics of the thermal properties of the metal tube and the heat radiated by the waterwalls: Q r 2 Q sww 1 Tmww 3 3 1t Mww cm

(26)

Here, Tmww is the effective temperature of the tube metal, Q r is the radiant heat transfer to the waterwall tubes, Q sww is the overall heat transferred from the waterwall metal to the steam-water mix at saturated conditions, Mww is the effective steam-water mass flowing through the waterwalls, and cm is the specific heat of the metal tubes. 2.2 Shrink and Swell Model The change in temperature and pressure in the evaporator system produces an unbalanced condition that generates a reverse effect in the drum level when increasing load conditions in the boiler. This phenomenon is called shrink and swell because of the vapor bubbles generated in the drum tank that generates the rise and drop of the drum level value. To model this effect, a first-order transfer function term equation is proposed as follows: 8h 3

K 4Wfe 2 Wsh 5 3 4s79 5 4 1

(27)

Here, 8h is the drum level adjustment, 9 is the bubble transit time to the drum liquid surface, Wfe is the feedwater flow, Wsh is the steam flow output to the high temperature exchangers such as the superheater, s is the complex frequency variable (s = j ) and K is a constant of the model in s kg21 . This equation assumes that the bubbles are lumped into a volume section of the drum cylinder and equation (27) describes a first-order behavior in transporting this volume to the very top of the liquid surface.




Figure 4. Fuzzy supervisory control

2.3 Combustion Model Equation (26) illustrates the energy balance between the radiant and convective heats, respectively. The radiant heat term is obtained using a simplified model as proposed in Dieck-Assad [1], Dieck-Assad et al. [2] and Stultz [7]. In fact, it is assumed that the combustion process is ideal with the required oxygen excess dictated by the boiler manufacturer’s predicted performance. Consider the flame enthalpy as a function of the heating value of the fuel, temperature, air flow and oxygen excess: h flame 3

Wfue H H V 4h air Wfue [ Afr f o1 4O2ex 4154 f o2 21] 3 Wfue Afr f o1 4O2ex 4154 f o2

(28)

Here, h flame is the flame enthalpy, HHV is the high heating value of the fuel, h air is the air enthalpy, Wfue is the fuel flow, O2ex is the oxygen excess, f o is the fuel air ratio and Afr is the oxygen excess factor. After the enthalpy calculation, the heat flow in the furnace is modeled as follows 1 2 (29) Q gas 3 Wflue h flame 2 h gas 1 2 where Wflue 3 Wfue O2ex Afr 4 f o is the flow of combustion gases. R was the technological platform on which Simulink1 the mathematical model was implemented. The graphical interface and user-friendly developing tools made the difference with respect to other simulation platforms. Also, the developing time was reduced tremendously. The three-element controller (Figure 1) and the fuel flow controllers (Figure 2) were included in the simulation. Equilibrium and model convergence conditions were obtained as initial test trials in the system. To verify the model, steady-state and transient tests were performed. The initial tests were taken from DieckAssad [1] and additional recent field tests were necessary to verify and validate the boiler model. 2.4 Proposed FLC Figure 4 shows the proposed scheme for the fuzzy controller. In this case, the FLC works as a function generator that receives the error obtained from the reference and actual value of the controlled variable. This way, the

Figure 5. Modi1ed three-element controller

main core of the system is stable and the tuning is simplified tremendously. For the input and output variables, we define three triangular membership functions corresponding to the magnitude of the input and the response. The proposed fuzzy set-point function generator would increase or decrease the set-point values for the controller, in order to accelerate or decelerate the response of the system and to eliminate steady-state errors under any operation regime. A fuzzy logic based function generator performs this supervisory function that permits the improvement of the controller characteristics. Figure 5 shows the fuzzy set-point three-element controller for the drum liquid level and Figure 6 illustrates the strategy for the fuzzy set-point steam pressure controller. Therefore, two reference values coexist in each controller: one that follows the trajectory of the load in the system (SP) that inputs the fuzzy generator system and another that varies according to the performance of the traditional PID-type controller loop. The drum level error, the steam pressure error, the rate of change in the drum level error and the rate of Volume 82, Number 12 SIMULATION


845


R3: R4: R5: R6: R7: R8: R9:

Figure 6. Modi1ed steam pressure controller

change in the pressure error are inputs to each of the fuzzy set-point generators. Their values have been conditioned to voltages in order to normalize the inputs to the fuzzy set-point generator system. The output variables from the fuzzy function generator (FSP) are the corrected set-points or references that input the conventional three-element or the steam pressure controller: drum level error, DL 3 Dref 2 D1 rate of change in drum level error, 8DLi 3 DLi 2 DL4t215 1 drum pressure error, p 3 pref 2 p1 rate of change in drum pressure error, 8pt 3 pi 2 p4t215 . Three fuzzy sets are proposed for the error: one represents the negative values, another represents the zero and the last represents the positive values. The same partition is used for the change in error variable. The limits on the domains of the sets or the support [12–14] of each of the sets are obtained using simulation runs of +10% and –10% of the overall boiler load at a rate of 20% and –20% per min, respectively. This rate of increase and decrease is the maximum rate recommended by the manufacturer for the VU-60 unit [11]. Figures 7 and 8 describe the membership functions for the error and the change in error, respectively. 2.5 Fuzzy Associative Rules The relations between the input and output fuzzy sets are as follows: R1: if e 0 and 8e 0, then 8sp 01 R2: if e 0 and 8e = 0, then 8sp 01 846 SIMULATION

if e 0 and 8e 0, then 8sp 01 if e = 0 and 8e 0, then 8sp 01 if e = 0 and 8e = 0, then 8sp = 01 if e = 0 and 8e 0, then 8sp 01 if e 0 and 8e 0, then 8sp 01 if e 0 and 8e = 0, then 8sp 01 if e 0 and 8e 0, then 8sp 0.

Examining some of the rules, for R1 in the extreme case, if the error (e) is negative (meaning that the output variable y is larger than the reference variable, yref , in other words, y is beyond the desired value), and if the change in error (8e) is negative (meaning that the output signal tends to increase far from the reference value), then the reference must be decreased below its real value. In this way, the presence of a larger error in the slave controller (conventional PID-type loop) will force the response of the overall loop to accelerate in the direction of the reference or set-point value. Rule R9 illustrates the opposite case. If the error is positive (yref > y, meaning that the output value is below the reference), and if the value of the change in error is positive (this implies that the output variable tends to decrease), then the increment in the reference must be positive. This will increase the error and the state feedback controller will react as if a larger step change was received. Again, the speed of response will accelerate towards the reference value. There are three output fuzzy sets: one when the increment in the reference value is negative, another when the increment in the reference value is zero and the last when the increment in the reference value is positive. Figure 9 shows the output variable fuzzy sets. All the variables involved in the fuzzy set-point generator illustrate triangular or trapezoidal membership functions. 2.6 Defuzzi1cation Once the error and the change of error are translated from the crisp domain into the fuzzy environment via the fuzzification procedure, the output fuzzy sets are found using the fuzzy associative table. This table will show the fired or activated rules after the fuzzification has occurred. For instance, a drum level error of –0.25 in and a rate of change in drum level error of –11 in h21 would fire rules R1, and R4. These rules determine the active output fuzzy sets and the membership bound given for the set is obtained from the minimum value between the membership values of the error and the change of error. This is using min(DL , 8DL ) or the Zadeh–Sup–Min inference to start the defuzzification process [15–19]. The resulting crisp value for the output variable (change in the reference or set-point) is obtained using the height method illustrated in Lee [16], Mamdani and King [20], Mamdani [21] and Langari and Ying [22]. This method obtains the sum of the domain center values of the




Figure 7. Error fuzzy sets for drum level D and drum pressure p

Figure 8. Rate of change of error fuzzy sets for drum level D and drum pressure p

Figure 9. Fuzzy sets for function generator SP outputs

maximum output fuzzy sets multiplied by their membership values and dividing by the sum of their membership values. Figure 10 illustrates this procedure. The mathematical expression for this defuzzification method is 8 9

m k31 p 4k5 k p 0 8 9

m (30) 3 k31 k p where 0 represents the membership value for the resulting increment in the reference value, p 4k5 is the center (middle support value) of each output fuzzy set, and k 4 p 5 is the membership value for these centers from their output fuzzy sets.

Figure 10. The height defuzzi1cation method

3. Results and Discussion 3.1 Model Validation The computational model obtained is compared with the measurements from the real boiler at steady state as well

as during transient conditions. In steady state, four steam loads were studied and these are shown in Tables 1–4. In all cases, a small steady-state error is observed for the feed-water flow. This error might be produced by a purge Volume 82, Number 12 SIMULATION


847


Table 1. Measurement versus simulation comparison for a load of 56 5 103 lb h–1 @56 103 lb h–1

Real

Simulated

Steam 2ow (lb h–1 )

56.25 5 103

56.25 5 103 0.00%

Gas 2ow (lb h )

3.09 5 10

3.18 5 103

2.72%

Drum water level (in)

21.28

21.28

0.00%

Drum pressure (psia)

453.84

453.84

0.00%

Feed-water 2ow (lb h–1 ) –1

56.25 5 103 3

Error

56.25 5 103 0.00%


Real


65.73 5 103 65.73 5 103 0.00%

Feed-water 2ow (lb h–1 )

Simulated

Error

65.90 5 103 65.73 5 103 –0.26%

Gas 2ow (lb h )

3.77 5 103

3.71 5 103

–1.55%


25.93

25.93

0.00%


445.44

445.44

0.00%

–1


Real

Simulated

Error

135.36 5 103 135.36 5 103 0.00%


Feed-water 2ow (lb h ) 141.88 5 103 135.36 5 103 –4.60% –1

Gas 2ow (lb h–1 )

8.04 5 103

7.65 5 103

–4.77%


25.84

25.84

0.00%


474.63

474.63

0.00%


Real

Simulated 170.74 5 10

Gas 2ow (lb h–1 )

9.87 5 103

9.67 5 103

–2.02%


25.73

25.73

0.00%


502.17

502.17

0.00%

Steam 2ow (lb h )

3

are defined, the FLC is tested for the control of feed-water flow and fuel gas flow. Both variables present some numerical instability, as shown in Figure 13. This increases the simulation time up to the point that it is not practical to wait for the whole transition to see the tendency in controlling the feed-water flow using the FLC. Regardless of this problem, the results obtained for fuel gas flow are reasonable, as illustrated in Figure 14. The summarized results are shown in Table 5. The fuel gas flow control uses the steam pressure as the process variable. The deviation of this variable was just 1

Error

170.74 5 10

–1

Figure 11. Drum level behavior and error comparing simulation and measurements

3

0.00%

Feed-water 2ow (lb h–1 ) 175.40 5 103 170.74 5 103 –2.66%

located before the sensor position. This way, the flow will always be higher in the simulation values. The simulation of the transient behavior was performed using a load ramp of 1.9% per min. The results for the critical variables are shown in Figures 11 and 12. The error in the feed-water flow is due to a non-minimal phase effect that was not replicated exactly in the model simulation. 3.2 Tuning the FLC and Performance As mentioned earlier, several tests were performed in order to define the membership functions. Table 5 illustrates the results obtained from the tests, particularly the fuel used during the transient trajectory. Once the diffuse sets 848 SIMULATION

Figure 12. Feed-water 2ow behavior and error comparing simulation and measurements




Figure 13. Fuel pressure behavior for a load trajectory of 20% per min.

Figure 14. Fuel gas 2ow behavior for a load trajectory of 20% per min (2ow in # h21 )

Table 5. Fuel used during the transient trajectory Fuel gas 2ow (5103 lb h–1 ) Using FLC

Without FLC

8

Load

Slope

change

(% per min)

10–100%

20

38.4

41.4

–6.5%

100–10%

–20

48.7

49.9

–2.4%

psia with respect to the reference value when the FLC was used, both during steady state before the transient period and afterwards. Considering that the steam pressure nominal condition is about 400 psia, the error is negligible. 4. Conclusions In this paper we have presented a performance evaluation of two industrial boiler control systems using a computer simulation. The boiler simulation is based upon the Dieck-Assad model [1,2], which was modified and scaled to fit the requirements of the VU-60, 180,000 # h21 rated capacity industrial-type boiler. The most important variations are the use of a lower number of state variables and the development of a newer graphical userfriendly platform. We show that the difference between the fuzzy supervisory control (FLC) and the conventional fuel gas control is less than 7%. The main concern about the FLC is the problem obtained in the numerical solution, which means that the equation system is ill conditioned, and the numerical instability. The behavior of the supervisory controller has advantages for the system performance, compared with traditional three-element level and steam pressure controllers. The boiler develops a reduction of 6.5% in fuel flow when ramping up (at 20% per min) from 10% to 100% load. Moreover, it shows an-

other reduction of 2.5% in fuel flow when ramping down (at –20% per min) from 100% to 10% load. MATLAB requires about 5 min to reach a solution using the supervisory controller and just 3 min to obtain the numerical solution using a conventional fuel gas controller. Also, boiler simulations help in the analysis of the shrink and swell phenomenon obtained at very fast ramps, such as +20% and –20% per min. There are some possible improvements, as follows: 6 improvements in the module creation that could simulate other parts of the plant, such as the combustion system, in order to analyze efficiency and other economic aspects of the boiler1 6 improvement in the numerical method used to solve the simulation model, particularly for illconditioned equations or other numerical instabilities presented1 6 tests of additional fuzzy controllers to this problem and the verification of these schemes in field tests. References [1] Dieck-Assad, G. 1990. Development of a state space boiler model for process optimization. Simulation 55:201–213. [2] Dieck-Assad, G., G. Masada, and R. Flake. 1987. Optimum set point scheduling in a boiler turbine system. IEEE Transactions on Energy Conversion 2:388–395. [3] De Lorenzi, O. 1953. Combustion Engineering. New York: McGraw Hill. [4] Dolezal, R., and V. Ludvík. 1970. Process Dynamics: Automatic Control of Steam Generation Plant. New York: Elsevier. [5] Gunn, R., D. Horton, and R. Horton. 1988. Industrial Boilers. Avon, UK: Longman. Volume 82, Number 12 SIMULATION


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[6] Ziegler, J. G., and J. R. Connel. 1997. Detecting the reverse reaction. Chemical Engineering. New York: McGraw Hill. [7] Stultz, S. C. 1978. Steam: Its Generation and Use. Barberton, OH: Babcock & Wilcox. [8] Singer, J. 1981. Combustion: Fossil Power Systems, 3rd edn. Windsor, CT: Combustion Engineering Inc. [9] Van Landigham, H., and T. Nishithi. 1996. Knowledge-based adaptive fuzzy control of drum level in a boiler system. In SouthCon ’96 Conference Record, Orlando, FL, pp. 454–459. [10] Arriaga-de-Valle, E. 1999. Simulación y Evaluación de un Esquema de Control Inteligente en una Caldera Industrial Usando Simulink. Master’s Thesis, ITESM, Monterrey, Mexico. [11] CERREY. 1998. VU-60, 180000 lbm/hour combustion engineering boiler, Monterrey, Mexico. [12] Zadeh, L. A. 1992. The calculus of fuzzy if/then rules. AI Expert 7(3):23–27. [13] Driankov, D., and H. Hellendoorn. 1993. An Introduction to Fuzzy Control. Berlin: Springer. [14] Zimmerman, H. J. 1994. Fuzzy Set Theory and Its Applications, 2nd edn. Dordrecht: Kluwer. [15] Ordóñez, R., J. Zumberge, J. T. Spooner, and K. M. Passino. 1997. Adaptive fuzzy control: experiments and comparative analyses. IEEE Transactions on Fuzzy Systems 5(2):167–188. [16] Lee, C. C. 1990. Fuzzy logic in control systems: Fuzzy logic controller, Parts I and II. IEEE Transactions on Systems, Man and Cybernetics 20(2):404–435. [17] Johnston, R. 1994. Fuzzy logic control. GEC Journal of Research 11(2):99–109. [18] Zhao, Z-Y., M. Tomizuka, and S. Isaka. 1993. Fuzzy gain scheduling of PID controllers. IEEE Transactions on Systems, Man, and Cybernetics 23(3):1392–1398.

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[19] He, S. Z., Tan, S. H., Xu, F. L., and Wang, P. Z. 1993. PID selftuning control using a fuzzy adaptive mechanism. In Proceedings of the 2nd IEEE International Conference on Fuzzy Systems, San Francisco, CA, pp. 559–563. [20] Mamdani, E. H., and P. J. King. 1977. The application of fuzzy control systems to industrial processes. Automatica 13:235–242. [21] Mamdani, E. H. 1976. Applications of fuzzy algorithms for control of simple dynamic plants. Proceedings of the IEEE 121:1585– 1588. [22] Langari, R., and H. Ying. 1994. Analytical aspects of fuzzy control. In Proceedings of the 1994 NAFIPS/IFIS/NASA Conference, San Antonio, TX.

Enrique Arriaga-de-Valle obtained his MS degree in electronics systems engineering in December 1999 from the ITESM, Monterrey campus. He graduated as an Electronics and Communications Engineer at the ITESM campus Estado de México in December 1997. During his graduate studies at ITESM, he worked in the research group that modeled industrial boilers for CERREY, Monterrey, Mexico. Graciano Dieck-Assad is a full Professor of Electrical and Electronics Engineering at the ITESM, Monterrey campus. From 1994 to 2003 he was the EE chair at the ITESM. In August 2006, he was appointed as the Director of Research and Graduate Studies in Electronics and Information Technology at the ITESM. Presently, his research interests are bioMEMS, microsystems and energy systems modeling.



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