Institute of Environmental Engineering, University of Kaiserslautern, Paul-Ehrlich-Str. 14, 67663. Kaiserslautern, Germany. Abstract While conventional rule ...
K. Klepiszewski and T.G. Schmitt Institute of Environmental Engineering, University of Kaiserslautern, Paul-Ehrlich-Str. 14, 67663 Kaiserslautern, Germany Abstract While conventional rule based, real time flow control of sewer systems is in common use, control systems based on fuzzy logic have been used only rarely, but successfully. The intention of this study is to compare a conventional rule based control of a combined sewer system with a fuzzy logic control by using hydrodynamic simulation. The objective of both control strategies is to reduce the combined sewer overflow volume by an optimization of the utilized storage capacities of four combined sewer overflow tanks. The control systems affect the outflow of four combined sewer overflow tanks depending on the water levels inside the structures. Both systems use an identical rule base. The developed control systems are tested and optimized for a single storm event which affects heterogeneously hydraulic load conditions and local discharge. Finally the efficiencies of the two different control systems are compared for two more storm events. The results indicate that the conventional rule based control and the fuzzy control similarly reach the objective of the control strategy. In spite of the higher expense to design the fuzzy control system its use provides no advantages in this case. Keywords Combined sewer overflow; flow control; fuzzy control; rule based control
Introduction
Conventional rule based control (RBC) for real time flow control in urban drainage systems is in common use (Schmitt, 1996; Khelil et al., 1994). The effluent of a combined sewer overflow tank (CSOT), for example, can be adjusted as a function of the water level in the storage tank. Additionally, the hydraulic conditions at other significant points in a sewer system or at the waste water treatment plant should be considered. Therefore, control systems are based on a large number of rules. Instead of conventional control systems it is possible to use control strategies based on fuzzy logic. Fuzzy logic control (FLC) combines the simple rules of an expert system with a flexible specification of output parameters. Especially for the control of complex sewer systems, demanding an extensive matrix of different rules, it can be favorable to use fuzzy control. FLC enables the integration of available operating experiences in a comprehensible rule base and avoids abrupt changes of controlled parameters. In waste water treatment FLC was successfully implemented to improve treatment processes during operation. The possibility to integrate operating experiences of technical staff into the rule base of a FLC, and the flexible reaction of fuzzy logic to different combinations of input parameters, led to positive results (Hansen, 1997). So far, FLC has only been rarely used for flow control in sewer systems. The application of FLC was tested for two differently structured combined sewer systems in order to minimize the storm water overflow volume (Fuchs et al., 1996; Fuchs et al., 1999). The comparison in the studies was solely based on the simulation of uncontrolled and fuzzy – controlled sewer systems for single storm events. In both cases the overflow volume could be reduced significantly by the use of fuzzy control. The studies were focusing on the comparison of the initial state with the state affected by fuzzy control.
Water Science and Technology Vol 46 No 6–7 pp 77–84 © IWA Publishing 2002
Comparison of conventional rule based flow control with control processes based on fuzzy logic in a combined sewer system
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The objective of the investigation reported here, is the comparison of a conventional rule based flow control with a fuzzy based flow control. Methods
K. Klepiszewski and T.G. Schmitt
The control processes of RBC and FLC are different in many respects. Even the use of an identical rule base for both systems leads to different inference values. An example of the operating conditions for the two different control procedures is illustrated in Figure 1. It refers to regulation of a storage tank outflow depending on the water level. A water level of 0.5 m in the storage tank leads to an outflow of 10 l/s using conventional RBC and to an outflow of 12.5 l/s using FLC. A water level of 1.01 m results in an outflow of 20 l/s using RBC, while FLC leads to an outflow of 17.6 l/s. In spite of an identical rule base FLC obviously enables a more flexible sizing of the outflow. A control system depending on the interaction of water levels in several storage tanks requires modified rules and an extended rule base, compared to the control scheme in Figure 1. The use of fuzzy logic to control several basins in a complex sewer system helps to avoid sudden and intense changes of the controlled effluents. The investigated combined sewer system is illustrated in Figure 2. The flow to the waste water treatment plant (WWTP) which consists of the CSOTs 2, 3 and 4 effluents, is limited to 83 l/s. The sewer system has a total storage volume of 2,000 m3. Both the RBC and the FLC system are generated to control the four CSOTs in this system. The control processes enable a better utilization of storage capacities in order to reduce the overflow volume. The hydraulic behavior of the sewer system is simulated by the hydrodynamic model KOSMO in conjunction with control tools implemented under MATLAB/SIMULINK. The control strategies are based on the results of a hydraulic long term simulation of the initial sewer system. The developed control systems are tested and optimized for a single storm event, which affects heterogeneously hydraulic load conditions and local discharge. Finally the efficiencies of the two different control systems are tested and compared for two more storm events. Both control systems consist of two different control units. The first unit contains a rule base of 9 rules and controls the outflow of CSOT 1, depending on the water levels in CSOTs 1 and 2. The effluents of CSOTs 2, 3 and 4 depend on the water levels in these structures and are effected by the second control unit, containing a rule base of 27 rules. For each control system and all CSOTs water levels are divided into the categories low, medium and high. In
Input processing
Rule base
Inference
Rule based control If W < 1m
then Q = 10l/s
If W > 1m and < 2m then Q = 20l/s If W > 2m Water level
0 0.5
1
W
then Q = 30l/s
2 3 Water level [m]
0
10
20
30 Outflow[l/s]
Fuzzy logic control If W is low low
1.0
medium
high
If W is high
0.6 0.5
then Q is low
If W is medium then Q is medium
Center of gravity of the area low medium large
then Q is large
0.2 0 0.5 1
78
2 3 Water level [m]
0
10 12.5 20
Figure 1 Scheme of the operating conditions for the compared control systems
30 Outflow [l/s]
Storage outflow
Qout
Catchment 3
Catchment 4
CSOT 4
CSOT 3
Qout = 5 l/s V = 160 m³
Qout = 14 l/s V = 240 m³
Catchment 2
Catchment 1
CSOT 2
CSOT 1
Qout = 64 l/s V = 1300 m³
Qout = 20 l/s V = 300 m³
Flow time at full discharge capacity: 50 min
Figure 2 Scheme of the initial sewer system
1.0
medium
low
high
0.5
0.0 0.0
0.5
2.5 2.0 1.5 Water level CSOT 1 [m]
1.0
Membership function [ - ]
Membership function [ - ]
the RBC these categories are explicitly dedicated to a fixed range of water levels. Water levels leading to a storage utilization of less than 34% are classified as low. All water levels effecting a storage utilization of more than 67% are considered as high, water levels in between are medium. Such an explicit attribution of a water level to a single category is not implemented in FLC. In FLC a single water level can be dedicated to several categories, which are differently weighted by membership functions. The membership functions are represented by triangular and trapezoid functions. These two kinds of functions are approved in several FLC systems (Kahlert et al., 1993). The classification realized in FLC to control the outflow of CSOT 1 is pictured in Figure 3. The effluents of the CSOTs are divided into the categories low, medium and large. The RBC assigns a category to an explicit flow value. The outflow category medium represents the state of the uncontrolled system. In the first control unit, effecting the effluent of CSOT 1, the three categories are dedicated to flow values of 10 l/s, 20 l/s and 30 l/s. In the FLC the outflow categories are attributed to membership functions, as illustrated in Figure 4. In the control process of FLC the outflow of CSOTs results from the x-coordinate of the center of gravity of the area (centroid method) bordered by the membership function of the
1.0
low
K. Klepiszewski and T.G. Schmitt
WWTP
high
medium
0.5
0.0 0.0
0.5
1.0
1.5
3.0 2.0 2.5 Water level CSOT 2 [m]
Membership function [ - ]
Figure 3 Weighted dedication of water levels to categories by FLC in the first control unit
medium
low
1.0
large
0.5
0.0 5
10
15
20
30 35 40 25 Outflow CSOT 1 [l/s]
Figure 4 Membership functions for inference of flow categories to flow values by FLC in the first control unit
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K. Klepiszewski and T.G. Schmitt
dedicated flow category, the weight of the flow category and the x-axis (minimum-method) (see Figure 1). The weight of flow category is equivalent to the weight of the associated water level category, which is dedicated by the active rule of the rule base. Table 1 shows the complete rule base of the first control unit of RBC and FLC. Contrary to RBC, in the control process of FLC more than one rule of the rule base can become effective for an explicit combination of input water levels. This can lead to several executed categories of outflow as well as one category of outflow to become activated several times during the process of inference. If several rules apply to the same flow category the largest of the dedicated areas is decisive (maximum method). The decisive area for the evaluation of center of gravity of area is fixed as the sum of all resulting areas of the different active categories. An example for the control process of FLC for the first unit is given in Figure 5. On one hand the procedure of FLC is obviously more complex and more expensive to establish than the procedure of RBC. On the other hand FLC enables a more flexible sizing and avoids both the sudden as well as the intense changes of the controlled effluents. This is
Table 1 Rule base of the first control unit of RBC and FLC No.
1 2 3 4 5 6 7 8 9
Rules
If water level CSOT 1 is If water level CSOT 1 is If water level CSOT 1 is If water level CSOT 1 is If water level CSOT 1 is If water level CSOT 1 is If water level CSOT 1 is If water level CSOT 1 is If water level CSOT 1 is
low low low medium medium medium high high high
and water level CSOT 2 is and water level CSOT 2 is and water level CSOT 2 is and water level CSOT 2 is and water level CSOT 2 is and water level CSOT 2 is and water level CSOT 2 is and water level CSOT 2 is and water level CSOT 2 is
Water level CSOT 1: 0.5 m
low medium high low medium high low medium high
Water level CSOT 2: 1.5 m
then outflow CSOT 1 is then outflow CSOT 1 is then outflow CSOT 1 is then outflow CSOT 1 is then outflow CSOT 1 is then outflow CSOT 1 is then outflow CSOT 1 is then outflow CSOT 1 is then outflow CSOT 1 is
medium low low large medium low large medium medium
Outflow CSOT 1: 16 l/s
1 2
Rule number
3 4 5 6 7 8 9 0.0 m
2.5 m
0.0 m
3.0 m 5 l/s
80
Figure 5 Example of FLC procedure in the first control unit
40 l/s
Fuzzy logic control
Wat er
Outflow CSOT 1 [l/s] leve l
CSO T1
v er le Wat
[m]
SOT el C
2 [m
] W ater leve lC
SOT 1
[m]
ve l C er le Wat
2 SOT
[m]
Figure 6 Connection of the water levels in CSOT 1 and 2 with the outflow of CSOT 1 for RBC and FLC in the first control unit
proved by Figure 6. It illustrates the connection of the water levels in CSOT 1 and 2 with the outflow of CSOT 1 for RBC and FLC in the first control unit.
K. Klepiszewski and T.G. Schmitt
Outflow CSOT 1 [l/s]
Rule based control
Results and discussion
The previously presented differences in the effect of RBC and FLC processes are illustrated for the outflow of CSOT 1 during storm event 1. The simulation results for the outflow of CSOT 1 during this event is shown in Figure 7 for all systems. In the uncontrolled system the effluent ranges between a dry weather flow of 5 l/s and a maximum of 20 l/s during rainfall events. RBC and FLC regulate the outflow of CSOT 1 depending upon the water levels in CSOT 1 and CSOT 2 which is positioned downstream (see Figure 2). RBC regulates the outflow of CSOT 1 four times abruptly down to 10 l/s during the storage of combined sewage to reduce the flow to CSOT 2 (see Figure 7). This is equivalent to eight interventions by RBC including the regulation back to an outflow of 20 l/s. In contrast to the effluent of CSOT 1 effected by RBC, the effluent gradient effected by FLC is continuous. This is caused by the variety of interpolated effluent values effected by different water level combinations in FLC (see Figure 6) and leads to an increase of necessary control interventions compared to RBC. Additionally, a vernier control for the operation of outflow gate valve is required for FLC. Furthermore, the requirements for mechanical and electronic equipment of a FLC system are very high. The temporary flow reduction caused by both control systems leads to an extension of storage utilization in CSOT 1. This is illustrated by a delayed achievement of dry weather flow conditions of the controlled systems compared with the uncontrolled system in Figure 7. An advantage of FLC over RBC is the faster emptying of the CSOT 1. Outflow CSOT 1 [l/s]
25 20 15 10 5 0 0
200
400
600
Uncontrolled system
800
1000
1200
RBC
1400
1600 Time [min] FLC
Figure 7 Outflow of CSOT 1 for the uncontrolled system, RBC and FLC during storm event 1
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The distribution of rainfall intensity and the utilization of the CSOTs’ capacities of the uncontrolled, rule based and fuzzy logic controlled systems during storm event 1 are shown in Figure 8. A utilized CSOT capacity of 100% is equivalent to a water level reaching at least the top of the overflow weir. The duration of 100% capacity utilization (in general equivalent to discharge time) and the emptying time of the CSOTs is almost the same for the controlled systems.
i [mm/min]
0
200
400
600
800
Time [min] 1000 1200 1400 1600 1800 2000 2200
0 0.01 0.02 0.03
Utilized CSOT capacity of the uncontrolled system 120 Utilized capacity [%]
K. Klepiszewski and T.G. Schmitt
Rainfall intensity i during storm event 1
100 80 60 40 20 0 0
200
400
600
800
1000 1200 1400 1600 1800 2000 2200 Time [min]
Utilized CSOT capacity of the rule base controlled system Utilized capacity [%]
120 100 80 60 40 20 0 0
200
400
600
800
1000 1200 1400 1600 1800 2000 2200 Time [min]
Utilized CSOT capacity of the fuzzy logic controlled system Utilized capacity [%]
120 100 80 60 40 20 0 0
200
400
CSOT 1
82
600
800
1000 1200
CSOT 2
1400 1600 1800 2000 2200 Time [min] CSOT 3
CSOT 4
Figure 8 Utililized storage capacity of the CSOTs for the uncontrolled system, RBC and FLC during storm event 1
Table 2 Combined sewer overflow volume of the CSOTs for the uncontrolled system, RBC and FLC during three storm events Combined sewer overflow volume [m3] Storm event 1
Storm event 2
Storm event 3
rainfall: 27.2 mm
rainfall: 6.7 mm
rainfall: 63.3 mm
rainfall duration: 1900 min
RBC 810
FLC 815
UC1 74
RBC 59
FLC 58
rainfall duration: 5350 min
UC1 RBC FLC 18,237 18,175 18081
1 UC: Uncontrolled system
The increased utilization of CSOTs 1 and 4 capacities illustrates the positive effects of both control systems compared to the uncontrolled conditions. Obviously the utilization and the emptying time of CSOT 4 increases disproportionately. This leads to homogenous load conditions in the CSOTs of the controlled sewer systems during storm event 1. The rainfall appearing after 1800 min has no influence on flow conditions in the sewer system. All the curves of utilized CSOT capacities are very similar for FLC and RBC. This is also verified by an almost identical combined sewer overflow volume during all simulated storm events shown in Table 2. Additionally, the results illustrated in Table 2 indicate that the positive effects of the control systems depend on the characteristics of the storm event. For long and intense rainfall periods the influence of the control systems on the combined sewer overflow volume decreases. The maximum overflow and duration of the overflow period show no significant differences compared with the uncontrolled system. The results finally indicate that RBC and FLC similarly meet the objective of the control strategy.
K. Klepiszewski and T.G. Schmitt
UC1 882
rainfall duration: 95 min
Conclusion
The objective of this study has been the comparison of two flow control systems, a rule based and a fuzzy logic control, using an identical rule base. The input and the inference processes of the control systems are completely different. This leads to different effects of both control processes on hydraulic load conditions of four CSOTs in a combined sewer system during three storm events. Nevertheless RBC and FLC similarly meet the objective of the preconditioned control strategy. Flexible sizing of the controlled effluents and avoiding of their sudden and intense change by FLC provide no operational advantages compared to RBC. The procedure of FLC is more complex and more expensive to establish than the procedure of RBC. But FLC provides more possibilities to optimize the control processes by modifications of the input and inference membership functions without a change of the rule base. Compared to FLC an improvement of RBC processes requires a change of single rules or adding of new rules to the rule base. Additionally it has to be investigated which of the two control systems reaches the objectives of fixed control strategies best, if they are optimized individually. In this study the functioning of RBC processes is more comprehensive, and effects of changes in the control system are more predictable for technical staff than in a FLC process. Due to these circumstances and its other advantages, RBC seems to be the more effective control system. References Fuchs, L., Beeneken, T., Scheffer, C. and Spönemann, P. (1996). Model based real-time control of sewer systems using fuzzy-logic. Wat. Sci. Tech. 36(8–9), 343–347. Fuchs, L., Günther, H. and Scheffer, C. (1999). Comparison of quantity and quality oriented real time control of a sewer system. Proc. 8th Intern. Conf. on Urban Storm Drainage, Sydney, Australia, pp. 432–440.
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Hansen, J. (1997). Der Einsatz von Fuzzy Control für Regelungsaufgaben im Bereich der Nährstoffelimination in kommunalen Kläranlagen. Schriftenreihe des Fachgebiets Siedlungswasserwirtschaft der Universität Kaiserslautern, Band 10. Kahlert, J. and Frank, H. (1993). Fuzzy-Logik und Fuzzy-Control – Eine anwendungsorientierte Einführung mit Begleitsoftware. Vieweg-Verlag, Braunschweig, Germany. Khelil, A., Garching, M. and Broll-Bickardt, J. (1994). Steuerung eines Entwässerungssystems mit Hilfe eines regelbasierten Systems. Korrespondenz Abwasser, Heft 5, pp. 744–748. Schmitt, T.G. (1996). Operational Flow Control of Combined Sewer Systems in Long Term Pollution Load Simulation. Proc. 7th Intern. Conf. on Urban Storm Drainage, SUG-Verlagsgesellschaft, Hannover, Germany, pp. 827–832.
