- Email: [email protected]
Fuzzy model reference learning control of multi-stage flash desalination plants
DESALINATION Desalination 116 (1998) 157-164
ELSEVIER
Fuzzy model reference learning control of multi-stage flash desalination plants Abdulla Ismail Department of Electrical Engineering, UAE University, Al-Ain, United Arab Emirates. Tel. +971-3-5051582, Fax. +971-3-632382, E-mail. abdulla@ eclsun.uaeu.ac.ae
Received 27 February 1998; accepted 3 July 1998
Abstract The large scale process control of highly complex desalination plants has been largely dealt with conventional proportional-integral-derivative (PID) controllers. Although these conventional techniques may provide a minimum performance requirement, they fall short of the increasing control performance demand of robustness, optimality and adaptation to external disturbances. However, in the last few years, new emerging intelligent control techniques have been gaining acceptance for their attractive design and implementation advantages. These new control methods provides solutions for problems where no mathematical model of the system may exit and where uncertainties in the operating environment are significant. Among the widely spread desalination plants in need of efficient and reliable control mechanism are the distillation-based multi-stage flash (MSF). These complex non-linear systems with inter-coupled control loops have not been studied satisfactorily for their efficient performance during different operating conditions and under changing loads. While fuzzy control can provide effective practical solutions to complex industrial problems, as an alternative to conventional control methods, there are several drawbacks that may limit its use for some problems. One main drawback being the inability of the fuzzy controller, designed for the nominal plant, to perform adequately if significant and unpredictable plant variations may occur. Introducing the capability of a progressively learning mechanism into the system, along with basic ideas of fuzzy sets and control theory, will improve the performance of the overall controlled system when interacting with the environment. The fuzzy reference learning controller (FMRLC) utilises a learning mechanism which observes the plant outputs and adjusts accordingly the rules in a direct fuzzy controller such that the overall system performs satisfactorily. In this paper we would discuss the advantages of using FMRLC in controlling the top brine temperature (TBT) of the brine heater in an 18th stage MSF desalination plant. Comparisons with classical as well as direct fuzzy control of the same plant are investigated. Furthermore, some practical implementation issues of the proposed controller are discussed. Keywords: MSF desalination; Fuzzy control; Learning systems
1. Introduction Since the appearance of control systems, control engineers are working hard to
develop new theories and techniques to keep the controlled system stable and performing satisfactorily within the given operating conditions. A l t h o u g h c o n v e n t i o n a l PID
0011-9164/98/$ - see frontmatter© 1998ElsevierScienceB.V. All fightsreserved PII S0011-9164(98)00192-1
158
A. lsmail / Desalination 116 (1998) 157-164
controllers are being used widely in process industry and other applications, it is evident that these controllers suffer from serious drawbacks. Being dependant on the operating parameters of the system, PID controllers require a significant amount of tuning efforts in case of system parameters variation. Furthermore, the requirements of the different operating points of complex industrial systems and the associated m o d e l l i n g u n c e r t a i n t y pose serious challenges to modern control engineers. Fuzzy logic has open cited advantages over conventional PID control, including simpler design procedure and easier implementation. The design process is based on formulating a set of linguistic rules describing the desirable performance of the system. These rules, described by an expert in the field, can be easily programmed on a computer or stored on a custom-made VLSI chip or microcontroller. Tuning of fuzzy controllers are performed either by trial and error or by using some newly developed automatic tuning methods like the meta-rule based algorithm or the reinforcement based selflearning algorithm. Systems based on fuzzy logic have exhibited robustness and adaptation to unstructured and noisy environments. Recently, adaptive fuzzy control methodologies have been proposed to face the problem of model uncertainty and disturbance accommodation. In spite of the lack of systematic methods of tuning fuzzy controllers, current accumulated industrial experience proved the ease with which those limitations can be overcome. In this paper, we propose the use of an adaptive fuzzy technique, namely fuzzy model reference learning control (FMRLC), to regulate the top brine temperature (TBT) of large MSF desalination plants. The paper is organised as follows. Section 2 introduces the FMRLC technique and its design procedure. Section 3 shows a brief description of MSF plant control loops and in particular the TBT one. In section 4, the design of FMRLC for the TBT loop of an 18 stage MSF plant is
described. In section 5, simulation results of the performance of the proposed control system are illustrated and comparisons with those using non-adaptive fuzzy control are presented. Finally, some conclusions and future works on the subject are given.
2. Fuzzy model reference learning control (FMRLC) While fuzzy control can provide effective practical solutions to complex industrial problems, as an alternative to conventional control methods, there are several drawbacks that may limit its use for some problems. One main drawback being the inability of the fuzzy controller, designed for the nominal plant, to perform adequately if significant and unpredictable plant variations may occur. I n t r o d u c i n g the capability of a progressively learning mechanism into the system, along with basic ideas of fuzzy sets and control theory, will improve the performance of the overall controlled system when interacting with the environment. The fuzzy model reference learning controller (FMRLC) utilises a learning mechanism which observes the plant outputs and adjusts accordingly the rules in a direct fuzzy controller such that the overall system performs satisfactorily [4, 5]. The development of the concept of adaptive control went through some research studies, and usage in the industry. The first improvement was achieved when Mamdani proposed a Linguistic Self-Organizing Controller which can automatically synthesize and tune the membership functions in a direct fuzzy controller [6]. Some improvements of the technique and applications of the adaptive controller in some industrial problems were shown by Yamazaki [7], Scharf [8], Daley [9], Tanscheit [10], and Isaka [11]. Recently, Passino and Layne introduced the new concept of fuzzy model reference learning control (FMRLC) as an adaptive fuzzy control scheme [4]. The term learning was used instead of adaptive to distinct the
159
A. lsmail / Desalination 116 (1998) 157-164
Learning Mechanism
I
Plant
ytka9 r
T
Fig. 1. A schematic diagram of the fuzzy model reference learning control (FMRLC) system.
FMRLC from adaptive control since FMRLC tune, and to some extent, remember the values that it had tuned in the past, while the conventional adaptive one continues to tune the controller parameters without remembering the previous tuning process. A simple block diagram of the FMRLC is shown in Fig. 1. The FMRLC system consists of four main parts: the plant, the fuzzy controller, the r e f e r e n c e model, and the learning mechanism. The learning mechanism tunes the rule base of the fuzzy controller so that the closed loop system behaves like the reference model. The learning mechanism consists of two parts; a fuzzy inverse model and a knowledge base modifier. The fuzzy inverse model performs the function of mapping ye(kT) (representing the deviation from the desired behaviour), to changes in the process inputs p(kT) that are necessary to force ye(kT) to zero. The knowledge base modifier performs the function of modifying the fuzzy controller's rule-base to affect the needed changes in the process inputs. A fuzzy system is used to map ye(kT) and possibly functions of ye(kT), such as yc(kT) = (l/T) (ye(kT) -ye(kT-T)), to perform the necessary changes in the process inputs
p(kT). This map is called "fuzzy inverse model" since information about the plant inverse dynamics is used in its specification. Note that similar to the fuzzy controller, the fuzzy inverse model contains scaling factors gye, gyc, and gp. Given gye, gyc, and gp as inputs to the fuzzy inverse model, the rulebase for the fuzzy inverse model contains rules of the form IfyeisYe j andycisYc i,
thenpispm
where YeJ and Yci denotes linguistic values associated with the linguistic variables Yeand Yc,, respectively and pm denotes the linguistic value associated with the mth output fuzzy set. In any noisy environment, the actual plant output y(kT) will differ from the desired reference model output ym(kT), resulting in the error output ye(kT). This error will trigger the learning mechanism to modify its input to the knowledge base of the fuzzy controller, which in turn changes its input signal to the plant. Consequently, the closed loop system will behave accordingly such that the plant output matches that of the reference model. The fuzzy controller's rule base is
160
A. Ismail / Desalination 116 (1998) 157-164
8.H.
I~COVH~Y STAGES
IISIgt'fl~ STACBS
Sm--------#~
'
, - - l a na¢ ,~ I~ad
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,
"
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Fig. 2. A simplified schematic flow diagram of MSF plant model.
modified by the one-step back approach. Here the new control action, u(kT), would be the previously applied control action, u ( k T T), plus p(kT). Knowledge base modification is performed by shifting the centers Crn of the m e m b e r s h i p f u n c t i o n s of U, i.e. the consequent linguistic value associated with u, the linguistic variable associated with the fuzzy controller's output u(kT). This is carried out in two steps: - Find all the rules in the fuzzy controller whose premise certainty is ui[e(kT - T), c(kT - T)] > 0 "call this the active set of rules at kT-T" - For all the rules in the active set use cm(kT) = cm(kT - T) + p(kT) where cm(kT) is the center of the mth membership function at time kT. The selection of the scaling factors gl and g2 are carried out using on the following two approaches:
observe the plant and reference model response: If there exist unacceptable oscillations in the plant response, then increase g2 If the plant output is unable to keep up with the reference model response, then decrease g2.
2.2. Second approach -
-
-
-
Begin with go = 0, i.e. no adaptation, and simulate the system C h o o s e gp and g2 so that there is no saturation on the input universe of discourse Increase gp slightly and observe the response. You may need to tune gp and gp Continue to increase gp. You should get gp large enough for quick adaptation rate, but without getting into undesirable oscillations and instability.
2.1. First approach -
-
Select gl so that ye(kT) will not saturate the input MF c e r t a i n t y (near the endpoints) Choose gp = gu and let g2 = 0 Apply a step reference input r(kT) and
3. C o n t r o l l i n g M S F plants
MSF desalination is an evaporating and condensing process [1-3]. The heat energy required for evaporation is supplied by
A. Ismail / Desalination 116 (1998) 157-164
exhaust recovery boilers and auxiliary boilers. The energy supplied during evaporation is recovered in the condensation. The MSF unit is divided into three sections; a heat reject section, a heat recovery section, and a brine heater section as shown in Fig. 2 [12]. Control systems in desalination plants are responsible for keeping the parameters of the plant within the specified allowable design limits. The process variables which are to be set for acceptable operation of an MSF desalination plant are: - The top brine heater temperature (TBT): This directly affects the distillate production and the levels in each flash chamber. There is a maximum allowable value, depending upon the type of scale inhibitors added to the make-up feed. - Brine recycle flow: This directly affects the levels in each flash chamber and the steam consumption for a fixed TBT. The higher the flow rate, the lower the flashing efficiency with a reduction in the residence time in the stages and an increasing brine level in the stages. - Make-up flow: This makes up for the blow down flow and the distillate product flow out of the plant. It affects the temperature of the recirculating brine and thus affects the flashing process. - Low pressure (LP) steam temperature: This dictates the heat content of the system. - Sea water feed flow: This governs the fluid velocities in the tubes of the reject section. It affects the heat transfer in the heat reject section. - Sea water feed temperature: This directly affects the heat transfer in the reject section. It also affects the temperature of the make up and thus of the recirculating brine. - Brine heater condensate level: This ensures that the heat exchanger tubes are not submerged in condensed steam, since that will adversely affect the heat exchange. Brine level in the last stage: This affects the level of the brine in the preceding
161
,~i~ii!i~!i i;!i!!~;!i~; !ii~i;iliii!iiii;:, i~!il;~ii!i !i?ii!!!!i i!!;;~, Desired
........................... ..., I
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~
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~
. .....
i
::tie m p
Fig. 3. A schematic diagram of the F M R L C scheme.
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Fig. 4. The F M R L C for section.
TBT of the brine heater
stages, and helps to avoid drainage of the system. Distillate level in the last stage: This ensures that the distillate does not overflow the distillate tray. Of the control loops mentioned above, the one responsible for regulating the top brine temperature (TBT) is most important to control and automation problems. This is due the significant influence of TBT on the performance ratio of the plant. It is common practice in MSF plants that brine heaters are designed for minimum resistance time at the highest brine temperature. Furthermore, it is important to have a brine temperature sensor with a fast response in any evaporator working near the upper limit of brine temperature. Brine temperature control is exercised by using desuperheater where
1 62
A. l s m a i l / D e s a l i n a t i o n 116 (1998) 157-164 I
I
I00
_
_ _
i
i|
i=
100 RO
40
40
20
0
I
a 5
0
I0
I
15
0
20
0
2
4
TI... (..c)
Fig. 5. Time response of the brine heater with a slow step reference. Output of plant (solid line) and reference model (dashed line).
]J0
i
i
6 T ~-.
S
10
{Me)
Fig. 7. FMRLC and FLC for a slow reference model at 95°C. Output of plant (solid line) and reference model (dashed line).
I
t~O I
I
I
I
I
"
I
rgr
I00
#c 5O I
0IF 0
I
5
I
I
10
15
O~ 20
0
2
4
6
8
to
"rim{me) Fig. 6. Time response of the brine heater with a fast step reference. Output of plant (solid line) and reference model (dashed line).
Fig. 8. FMRLC and FLC for a fast reference model at 95°C. Output of plant (solid line) and reference model (dashed line).
temperature of the steam flowing into the heater is adjusted in accordance to the signals from the temperature sensor. Permissible TBT should be provided to avoid any harmful overheating consequences.
shown in Fig. 4. In this figure, the TBT input to the brine heater is controlled by the proposed adaptive fuzzy controller. A c o n t i n u o u s c o m p a r i s o n b e t w e e n the operating or actual top brine temperature (TBT) of the brine heater and a reference or desired TBT input is performed. The difference between the two values or the error is eliminated or minimized by the use of the fuzzy controller. The aim of the scheme is to automatically modify the control action into the brine heater by adjusting the parameters of the fuzzy logic controller through the
4. FMRLC of TBT loop Fig. 3 shows a schematic diagram of the system forming the FMRLC of TBT of the brine heater. Another illustrative view of the TBT control loop with FMRLC scheme is
163
A. Ismail / Desalination 116 (1998) 157-164
150
i
120 81
10rc 100 1w*C 80 50
60 40 I
I
t
1o
5
Time (~e)
15
20
20
0'0
Fig. 9. Time response of the brine heater with a fast step reference under a 100°C operating point. Output of plant (solid line) and reference model (dashed line).
5
t
m
i
l0
15
20
Fig. 11. Comparing the responses due to the FMRLC and the non-adaptive FLC at 100°C. Output of plant (solid line) and reference model (dashed line).
150 PIP
lit
150
10~C 100
pItD I~C
. . . . . . . . .
100
.
.
.
.
5O 0
I
I
I
J.
lO
15 I
Fig. 10. Time response of the brine heater with a fast step reference under a 105°C operating point. Output of plant (solid line) and reference model (dashed line).
learning mechanism. This will lead to an overall closed loop system with the required performance specifications.
5. Simulation results The simulation of the TBT is performed for two cases of reference model, a slow one and a relatively fast one. Furthermore, to test the capability of the learning mechanism, the F M R L C designed for the desired TBT of 95°C is applied to the 100°C and 105°C cases. Also, a final comparison of the proposed FMRLC system with the direct nonfuzzy case mentioned in [13] is performed. In Figs. 5 and 6, the responses of the system for a fast and a slow desired references along
5
I
10 T~.,,. (m:)
I
15
20
Fig. 12. Comparing the responses due to the FMRLC and the non-adaptive FLC at 105°C. Output of plant (solid line) and reference model (dashed line).
with an optimally tuned PID controlled one are shown. The performances of the closed loop system with FMRLC is quite satisfactory and superior to that of the PID controlled case. It is evident that F M R L C learns fast enough to adapt to the speed of the desired response. The PID controller was tuned for the best performance possible by using the Huang-Atherton criterion mentioned in [12]. Comparing the responses of the FMRLC system to the non-adaptive fuzzy controlled and the PID controlled systems in Figs. 7 and 8, it is evident that FMRLC is superior in both transient, overshoot and rise time, and steady state, settling time, responses. Being originally designed for the desired TBT operating point of 95°C, the FMRLC was able to adapt to the new desired TBT
164
A. lsmail / Desalination 116 (1998) 157-164
operating points of 100°C and 105°C as evident from the responses shown in Figs. 9 and 10, respectively. The response rise time is small and the steady state response is smooth with negligible oscillations. To prove the superior adaptive performance of FMRLC over direct nonadaptive fuzzy logic control, the two controllers were subjected to the changing situations of TBT of 100°C and 105°C respectively. The performance responses of the two cases are shown in Figs. 11 and 12, respectively. It is evident that the FMRLC has performed much better than the FLC in attempting to match the desired reference model. 6. Conclusions In this work, we have presented the application of fuzzy model reference learning control (FMRLC) to top brine temperature loop of large multi-stage flash (MSF) desalination plants. We have illustrated the learning capability of FMRLC to adapt to the control requirements of MSF plants under varying operating points. The FMRLC clearly outperformed the direct non-adaptive fuzzy controller in providing the necessary control actions to regulate the TBT with regard to different reference points. Further work on using FMRLC to other relevant control loops in MSF plants is under investigation. The nature of MSF plant complexity and model uncertainty would certainly urge the use of adaptive control techniques such as FMRLC compared to the direct non-adaptive fuzzy control. Acknowledgements The author would like gratefully to thank the Department of Electrical Engineering at the Ohio State University, particularly Prof. Kevin Passino, for hosting during the fullbright scholarship period and for
supporting the outcome of this paper. Further thanks go to the Water and Electricity Department of Abu-Dhabi, and in particular to Dr. Darwish A1-Gobaisi, for providing the necessary information about MSF plants. References [1]
S. Spiegler, Principles of Desalination: Parts A & B, 2nd Ed., Academic Press, New York, 1980. [2] E. Howe, Fundamentals Of Water Desalination, Environmental Science & Technology Series, Vol. 1, Marcel Decker, 1970. [3] R. Bakish, Desalination Processes - A Bird's Eye View, Fairleigh Dickinson University Press, 1973. [4] J. Layne and K. Passino, Fuzzy model reference learning control, Proc. 1st IEEE Conference on Control Applications, Dayton, OH, 1992. [5] K. Passino and S. Yurkovich, Fuzzy control: Theory and applications, Addison Wesley, 1997. 16] T. Procyk and E. Mamdani, A linguistic selforganizing process controller, Automatica, 15 (1979). [7] T. Yamazaki, An improved algorithm for a selforganizing controller and its experimental analysis, Ph.D. Thesis, London University, 1982. [8] E. Scharf and N. Mandic, The application of a fuzzy controller to the control of a multi-degreeof-freedom robot arm, Industrial applications of fuzzy control, M. Sugeno, Amsterdam, The Netherlands, 1985. [9] S. Daley and K.F. Gill, A design study of a selforganizing fuzzy logic controller, Proc. I. Mech. E., 1986. [ 10] R. Tanscheit and E. Sharf, Experiments with the use of a rule-based self-organizing controller for robotics applications, Fuzzy Sets and Systems, 1988. l l l ] A. Isaka, A. Sebald, A. Karimi, N. Smith, and M. Quinn, On the design and performance evaluation of adaptive fuzzy controllers, Proc. 1988 Conference on Decision and Control, December 1988. [12] A. Woldai et al., Simulation aided design development of an adaptive scheme with optimally tuned PID controller for a large multistage flash desalination plant: part I, part II, and Part III, 5th IFAC Symp. on Adaptive System in Control and Signal Processing, June 1995. [13] A. Ismail and E. Abu-khousa, Fuzzy control of multistage flash (MSF) desalination plant, IDA World Congress on Desalination and Water Sciences, Vol. VII, November 1995.
ELSEVIER
Fuzzy model reference learning control of multi-stage flash desalination plants Abdulla Ismail Department of Electrical Engineering, UAE University, Al-Ain, United Arab Emirates. Tel. +971-3-5051582, Fax. +971-3-632382, E-mail. abdulla@ eclsun.uaeu.ac.ae
Received 27 February 1998; accepted 3 July 1998
Abstract The large scale process control of highly complex desalination plants has been largely dealt with conventional proportional-integral-derivative (PID) controllers. Although these conventional techniques may provide a minimum performance requirement, they fall short of the increasing control performance demand of robustness, optimality and adaptation to external disturbances. However, in the last few years, new emerging intelligent control techniques have been gaining acceptance for their attractive design and implementation advantages. These new control methods provides solutions for problems where no mathematical model of the system may exit and where uncertainties in the operating environment are significant. Among the widely spread desalination plants in need of efficient and reliable control mechanism are the distillation-based multi-stage flash (MSF). These complex non-linear systems with inter-coupled control loops have not been studied satisfactorily for their efficient performance during different operating conditions and under changing loads. While fuzzy control can provide effective practical solutions to complex industrial problems, as an alternative to conventional control methods, there are several drawbacks that may limit its use for some problems. One main drawback being the inability of the fuzzy controller, designed for the nominal plant, to perform adequately if significant and unpredictable plant variations may occur. Introducing the capability of a progressively learning mechanism into the system, along with basic ideas of fuzzy sets and control theory, will improve the performance of the overall controlled system when interacting with the environment. The fuzzy reference learning controller (FMRLC) utilises a learning mechanism which observes the plant outputs and adjusts accordingly the rules in a direct fuzzy controller such that the overall system performs satisfactorily. In this paper we would discuss the advantages of using FMRLC in controlling the top brine temperature (TBT) of the brine heater in an 18th stage MSF desalination plant. Comparisons with classical as well as direct fuzzy control of the same plant are investigated. Furthermore, some practical implementation issues of the proposed controller are discussed. Keywords: MSF desalination; Fuzzy control; Learning systems
1. Introduction Since the appearance of control systems, control engineers are working hard to
develop new theories and techniques to keep the controlled system stable and performing satisfactorily within the given operating conditions. A l t h o u g h c o n v e n t i o n a l PID
0011-9164/98/$ - see frontmatter© 1998ElsevierScienceB.V. All fightsreserved PII S0011-9164(98)00192-1
158
A. lsmail / Desalination 116 (1998) 157-164
controllers are being used widely in process industry and other applications, it is evident that these controllers suffer from serious drawbacks. Being dependant on the operating parameters of the system, PID controllers require a significant amount of tuning efforts in case of system parameters variation. Furthermore, the requirements of the different operating points of complex industrial systems and the associated m o d e l l i n g u n c e r t a i n t y pose serious challenges to modern control engineers. Fuzzy logic has open cited advantages over conventional PID control, including simpler design procedure and easier implementation. The design process is based on formulating a set of linguistic rules describing the desirable performance of the system. These rules, described by an expert in the field, can be easily programmed on a computer or stored on a custom-made VLSI chip or microcontroller. Tuning of fuzzy controllers are performed either by trial and error or by using some newly developed automatic tuning methods like the meta-rule based algorithm or the reinforcement based selflearning algorithm. Systems based on fuzzy logic have exhibited robustness and adaptation to unstructured and noisy environments. Recently, adaptive fuzzy control methodologies have been proposed to face the problem of model uncertainty and disturbance accommodation. In spite of the lack of systematic methods of tuning fuzzy controllers, current accumulated industrial experience proved the ease with which those limitations can be overcome. In this paper, we propose the use of an adaptive fuzzy technique, namely fuzzy model reference learning control (FMRLC), to regulate the top brine temperature (TBT) of large MSF desalination plants. The paper is organised as follows. Section 2 introduces the FMRLC technique and its design procedure. Section 3 shows a brief description of MSF plant control loops and in particular the TBT one. In section 4, the design of FMRLC for the TBT loop of an 18 stage MSF plant is
described. In section 5, simulation results of the performance of the proposed control system are illustrated and comparisons with those using non-adaptive fuzzy control are presented. Finally, some conclusions and future works on the subject are given.
2. Fuzzy model reference learning control (FMRLC) While fuzzy control can provide effective practical solutions to complex industrial problems, as an alternative to conventional control methods, there are several drawbacks that may limit its use for some problems. One main drawback being the inability of the fuzzy controller, designed for the nominal plant, to perform adequately if significant and unpredictable plant variations may occur. I n t r o d u c i n g the capability of a progressively learning mechanism into the system, along with basic ideas of fuzzy sets and control theory, will improve the performance of the overall controlled system when interacting with the environment. The fuzzy model reference learning controller (FMRLC) utilises a learning mechanism which observes the plant outputs and adjusts accordingly the rules in a direct fuzzy controller such that the overall system performs satisfactorily [4, 5]. The development of the concept of adaptive control went through some research studies, and usage in the industry. The first improvement was achieved when Mamdani proposed a Linguistic Self-Organizing Controller which can automatically synthesize and tune the membership functions in a direct fuzzy controller [6]. Some improvements of the technique and applications of the adaptive controller in some industrial problems were shown by Yamazaki [7], Scharf [8], Daley [9], Tanscheit [10], and Isaka [11]. Recently, Passino and Layne introduced the new concept of fuzzy model reference learning control (FMRLC) as an adaptive fuzzy control scheme [4]. The term learning was used instead of adaptive to distinct the
159
A. lsmail / Desalination 116 (1998) 157-164
Learning Mechanism
I
Plant
ytka9 r
T
Fig. 1. A schematic diagram of the fuzzy model reference learning control (FMRLC) system.
FMRLC from adaptive control since FMRLC tune, and to some extent, remember the values that it had tuned in the past, while the conventional adaptive one continues to tune the controller parameters without remembering the previous tuning process. A simple block diagram of the FMRLC is shown in Fig. 1. The FMRLC system consists of four main parts: the plant, the fuzzy controller, the r e f e r e n c e model, and the learning mechanism. The learning mechanism tunes the rule base of the fuzzy controller so that the closed loop system behaves like the reference model. The learning mechanism consists of two parts; a fuzzy inverse model and a knowledge base modifier. The fuzzy inverse model performs the function of mapping ye(kT) (representing the deviation from the desired behaviour), to changes in the process inputs p(kT) that are necessary to force ye(kT) to zero. The knowledge base modifier performs the function of modifying the fuzzy controller's rule-base to affect the needed changes in the process inputs. A fuzzy system is used to map ye(kT) and possibly functions of ye(kT), such as yc(kT) = (l/T) (ye(kT) -ye(kT-T)), to perform the necessary changes in the process inputs
p(kT). This map is called "fuzzy inverse model" since information about the plant inverse dynamics is used in its specification. Note that similar to the fuzzy controller, the fuzzy inverse model contains scaling factors gye, gyc, and gp. Given gye, gyc, and gp as inputs to the fuzzy inverse model, the rulebase for the fuzzy inverse model contains rules of the form IfyeisYe j andycisYc i,
thenpispm
where YeJ and Yci denotes linguistic values associated with the linguistic variables Yeand Yc,, respectively and pm denotes the linguistic value associated with the mth output fuzzy set. In any noisy environment, the actual plant output y(kT) will differ from the desired reference model output ym(kT), resulting in the error output ye(kT). This error will trigger the learning mechanism to modify its input to the knowledge base of the fuzzy controller, which in turn changes its input signal to the plant. Consequently, the closed loop system will behave accordingly such that the plant output matches that of the reference model. The fuzzy controller's rule base is
160
A. Ismail / Desalination 116 (1998) 157-164
8.H.
I~COVH~Y STAGES
IISIgt'fl~ STACBS
Sm--------#~
'
, - - l a na¢ ,~ I~ad
l
,
"
"
I'I I
"
Fig. 2. A simplified schematic flow diagram of MSF plant model.
modified by the one-step back approach. Here the new control action, u(kT), would be the previously applied control action, u ( k T T), plus p(kT). Knowledge base modification is performed by shifting the centers Crn of the m e m b e r s h i p f u n c t i o n s of U, i.e. the consequent linguistic value associated with u, the linguistic variable associated with the fuzzy controller's output u(kT). This is carried out in two steps: - Find all the rules in the fuzzy controller whose premise certainty is ui[e(kT - T), c(kT - T)] > 0 "call this the active set of rules at kT-T" - For all the rules in the active set use cm(kT) = cm(kT - T) + p(kT) where cm(kT) is the center of the mth membership function at time kT. The selection of the scaling factors gl and g2 are carried out using on the following two approaches:
observe the plant and reference model response: If there exist unacceptable oscillations in the plant response, then increase g2 If the plant output is unable to keep up with the reference model response, then decrease g2.
2.2. Second approach -
-
-
-
Begin with go = 0, i.e. no adaptation, and simulate the system C h o o s e gp and g2 so that there is no saturation on the input universe of discourse Increase gp slightly and observe the response. You may need to tune gp and gp Continue to increase gp. You should get gp large enough for quick adaptation rate, but without getting into undesirable oscillations and instability.
2.1. First approach -
-
Select gl so that ye(kT) will not saturate the input MF c e r t a i n t y (near the endpoints) Choose gp = gu and let g2 = 0 Apply a step reference input r(kT) and
3. C o n t r o l l i n g M S F plants
MSF desalination is an evaporating and condensing process [1-3]. The heat energy required for evaporation is supplied by
A. Ismail / Desalination 116 (1998) 157-164
exhaust recovery boilers and auxiliary boilers. The energy supplied during evaporation is recovered in the condensation. The MSF unit is divided into three sections; a heat reject section, a heat recovery section, and a brine heater section as shown in Fig. 2 [12]. Control systems in desalination plants are responsible for keeping the parameters of the plant within the specified allowable design limits. The process variables which are to be set for acceptable operation of an MSF desalination plant are: - The top brine heater temperature (TBT): This directly affects the distillate production and the levels in each flash chamber. There is a maximum allowable value, depending upon the type of scale inhibitors added to the make-up feed. - Brine recycle flow: This directly affects the levels in each flash chamber and the steam consumption for a fixed TBT. The higher the flow rate, the lower the flashing efficiency with a reduction in the residence time in the stages and an increasing brine level in the stages. - Make-up flow: This makes up for the blow down flow and the distillate product flow out of the plant. It affects the temperature of the recirculating brine and thus affects the flashing process. - Low pressure (LP) steam temperature: This dictates the heat content of the system. - Sea water feed flow: This governs the fluid velocities in the tubes of the reject section. It affects the heat transfer in the heat reject section. - Sea water feed temperature: This directly affects the heat transfer in the reject section. It also affects the temperature of the make up and thus of the recirculating brine. - Brine heater condensate level: This ensures that the heat exchanger tubes are not submerged in condensed steam, since that will adversely affect the heat exchange. Brine level in the last stage: This affects the level of the brine in the preceding
161
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stages, and helps to avoid drainage of the system. Distillate level in the last stage: This ensures that the distillate does not overflow the distillate tray. Of the control loops mentioned above, the one responsible for regulating the top brine temperature (TBT) is most important to control and automation problems. This is due the significant influence of TBT on the performance ratio of the plant. It is common practice in MSF plants that brine heaters are designed for minimum resistance time at the highest brine temperature. Furthermore, it is important to have a brine temperature sensor with a fast response in any evaporator working near the upper limit of brine temperature. Brine temperature control is exercised by using desuperheater where
1 62
A. l s m a i l / D e s a l i n a t i o n 116 (1998) 157-164 I
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temperature of the steam flowing into the heater is adjusted in accordance to the signals from the temperature sensor. Permissible TBT should be provided to avoid any harmful overheating consequences.
shown in Fig. 4. In this figure, the TBT input to the brine heater is controlled by the proposed adaptive fuzzy controller. A c o n t i n u o u s c o m p a r i s o n b e t w e e n the operating or actual top brine temperature (TBT) of the brine heater and a reference or desired TBT input is performed. The difference between the two values or the error is eliminated or minimized by the use of the fuzzy controller. The aim of the scheme is to automatically modify the control action into the brine heater by adjusting the parameters of the fuzzy logic controller through the
4. FMRLC of TBT loop Fig. 3 shows a schematic diagram of the system forming the FMRLC of TBT of the brine heater. Another illustrative view of the TBT control loop with FMRLC scheme is
163
A. Ismail / Desalination 116 (1998) 157-164
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learning mechanism. This will lead to an overall closed loop system with the required performance specifications.
5. Simulation results The simulation of the TBT is performed for two cases of reference model, a slow one and a relatively fast one. Furthermore, to test the capability of the learning mechanism, the F M R L C designed for the desired TBT of 95°C is applied to the 100°C and 105°C cases. Also, a final comparison of the proposed FMRLC system with the direct nonfuzzy case mentioned in [13] is performed. In Figs. 5 and 6, the responses of the system for a fast and a slow desired references along
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Fig. 12. Comparing the responses due to the FMRLC and the non-adaptive FLC at 105°C. Output of plant (solid line) and reference model (dashed line).
with an optimally tuned PID controlled one are shown. The performances of the closed loop system with FMRLC is quite satisfactory and superior to that of the PID controlled case. It is evident that F M R L C learns fast enough to adapt to the speed of the desired response. The PID controller was tuned for the best performance possible by using the Huang-Atherton criterion mentioned in [12]. Comparing the responses of the FMRLC system to the non-adaptive fuzzy controlled and the PID controlled systems in Figs. 7 and 8, it is evident that FMRLC is superior in both transient, overshoot and rise time, and steady state, settling time, responses. Being originally designed for the desired TBT operating point of 95°C, the FMRLC was able to adapt to the new desired TBT
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A. lsmail / Desalination 116 (1998) 157-164
operating points of 100°C and 105°C as evident from the responses shown in Figs. 9 and 10, respectively. The response rise time is small and the steady state response is smooth with negligible oscillations. To prove the superior adaptive performance of FMRLC over direct nonadaptive fuzzy logic control, the two controllers were subjected to the changing situations of TBT of 100°C and 105°C respectively. The performance responses of the two cases are shown in Figs. 11 and 12, respectively. It is evident that the FMRLC has performed much better than the FLC in attempting to match the desired reference model. 6. Conclusions In this work, we have presented the application of fuzzy model reference learning control (FMRLC) to top brine temperature loop of large multi-stage flash (MSF) desalination plants. We have illustrated the learning capability of FMRLC to adapt to the control requirements of MSF plants under varying operating points. The FMRLC clearly outperformed the direct non-adaptive fuzzy controller in providing the necessary control actions to regulate the TBT with regard to different reference points. Further work on using FMRLC to other relevant control loops in MSF plants is under investigation. The nature of MSF plant complexity and model uncertainty would certainly urge the use of adaptive control techniques such as FMRLC compared to the direct non-adaptive fuzzy control. Acknowledgements The author would like gratefully to thank the Department of Electrical Engineering at the Ohio State University, particularly Prof. Kevin Passino, for hosting during the fullbright scholarship period and for
supporting the outcome of this paper. Further thanks go to the Water and Electricity Department of Abu-Dhabi, and in particular to Dr. Darwish A1-Gobaisi, for providing the necessary information about MSF plants. References [1]
S. Spiegler, Principles of Desalination: Parts A & B, 2nd Ed., Academic Press, New York, 1980. [2] E. Howe, Fundamentals Of Water Desalination, Environmental Science & Technology Series, Vol. 1, Marcel Decker, 1970. [3] R. Bakish, Desalination Processes - A Bird's Eye View, Fairleigh Dickinson University Press, 1973. [4] J. Layne and K. Passino, Fuzzy model reference learning control, Proc. 1st IEEE Conference on Control Applications, Dayton, OH, 1992. [5] K. Passino and S. Yurkovich, Fuzzy control: Theory and applications, Addison Wesley, 1997. 16] T. Procyk and E. Mamdani, A linguistic selforganizing process controller, Automatica, 15 (1979). [7] T. Yamazaki, An improved algorithm for a selforganizing controller and its experimental analysis, Ph.D. Thesis, London University, 1982. [8] E. Scharf and N. Mandic, The application of a fuzzy controller to the control of a multi-degreeof-freedom robot arm, Industrial applications of fuzzy control, M. Sugeno, Amsterdam, The Netherlands, 1985. [9] S. Daley and K.F. Gill, A design study of a selforganizing fuzzy logic controller, Proc. I. Mech. E., 1986. [ 10] R. Tanscheit and E. Sharf, Experiments with the use of a rule-based self-organizing controller for robotics applications, Fuzzy Sets and Systems, 1988. l l l ] A. Isaka, A. Sebald, A. Karimi, N. Smith, and M. Quinn, On the design and performance evaluation of adaptive fuzzy controllers, Proc. 1988 Conference on Decision and Control, December 1988. [12] A. Woldai et al., Simulation aided design development of an adaptive scheme with optimally tuned PID controller for a large multistage flash desalination plant: part I, part II, and Part III, 5th IFAC Symp. on Adaptive System in Control and Signal Processing, June 1995. [13] A. Ismail and E. Abu-khousa, Fuzzy control of multistage flash (MSF) desalination plant, IDA World Congress on Desalination and Water Sciences, Vol. VII, November 1995.