Fuzzy Supervisory control of a steam power plantduring load rejection

HABBI AHCENE, ZELMAT MIMOUNApplied Automation Laboratory, F.H.C

University of Boumerdès, 35000 Boumerdès, AlgeriaPhone/Fax: +213-24816905

Abstract–In this paper, an intelligent coordinatedcontrol scheme for a fossil-fuelled drum boiler-turbineplant is presented. It consists of a two-levelhierarchical control strategy. At the supervisory level,a fuzzy reference governor generates the water levelset-point deviations during load rejections accordingto a fuzzy rule-based policy. At the control level, arobust control system via LQG/LTR is implemented.The performance of the proposed fuzzy supervisorycontrol system is demonstrated by simulations undervarious conditions and results are compared to thoseobtained by only considering the robust controllerwithout the supervisory reference governor.

Keywords: Fuzzy supervisory control; Robustcontrol; Reference governor; Boiler-turbine.

1. Introduction

An optimal power plant operation depends on theperformance of the individual components: boiler,turbine and generator. Drum boiler system is anenergy conversion device which transforms the inputchemical energy of fuel into the mechanical energyacting on the turbine and the generator. For aneffective participation of a power plant unit in load-following duties, stringent requirements on controlperformance and life extension of major equipmenthave to be fulfilled. Hence, the implemented controlstrategies need to efficiently orchestrate all energytransformations taking place in the steam power unitand to undertake large steam and power demands aswell as random fluctuations about their patterns.Therefore, the performance of a drum boiler-turbinecontrolled system can be addressed for tracking loadchanging commands of power output and drumpressure, and regulating deviations of drum waterlevel. Since the drum boiler-turbine system isnonlinear with many complicated physicalphenomena, a great deal of attention has been devotedto the control of its strongly interacting variables[5,7,8,9]. In [7], a linear quadratic gaussian (LQG)with loop transfer recovery (LTR) approach isconducted for a linear time invariant boiler model withthe emphasis on the robustness against uncertaintiesand modeling errors. On the issue of the optimalcontrol theory, Chen and Shamma proposed in [9] again-scheduled 1! -optimal control approach for

boiler-turbine controller design. In their designprocedure, state constraints and control saturations areexplicitly addressed. Coordinated control schemes forboiler systems were also investigated in many papers.In [8], Ben-Abdennour and Lee proposed a fuzzysupervisory scheme to improve the performance of aboiler system. The controller is synthesized using theboiler model without taking into account the electricalpart of the plant i.e., the turbine and the generator.These approaches were successful to a large extent inproviding robustness to variations in the operatingpoints. This paper presents yet another alternative tothe classical approach for boiler-turbine control. Here,a mixed fuzzy logic and robust control strategy is usedto improve the control performance of a drum boiler-turbine system, especially during severe disturbancessuch as load rejections. The effectiveness of the fuzzyknowledge based representation is exploited at thesupervisory level by considering a fuzzy logic basedset-point generator to monitor the set-point deviationsduring plant operations in order to enhance theperformance of the implemented robust controller.

2. Boiler-turbine dynamics

For this study, a 160MW oil-fired boiler-turbinenonlinear model is used. It was developed by Bell andÅström for a P16/G16 power plant [1,2]. The model isbased on the basic conservation laws which govern theboiler operation while maintaining an emphasis onsimpler structure. The inclusion of the extraevaporation equation and fluid dynamics delivered areasonable depiction of the drum water leveldynamics. The model is obtained through both

Fuel flow

boiler

Air

drum

Feedwater flow

Steam flow

Power

Turbine

Fig.1. Schematic of the drum boiler-turbine system.

Proceedings of the 6th WSEAS Int. Conf. on FUZZY SYSTEMS, Lisbon, Portugal, June 16-18, 2005 (pp89-93)

physical and empirical methods and compared wellagainst actual plant data. The plant dynamics aredescribed by the following nonlinear equations:

)19.01.1141(851

1.0)016.0073.0(

15.09.00018.0

11233

28 9

122

318 9

121

xxuux

xxux

uuxux

−−=

−−=

−+−=

"

"

"

(1)

where x1 denotes the drum pressure (kg/cm²), x2denotes the electrical output (MW), and x3 denotes thefluid density in the system (kg/cm3). The inputs to thesystem are the valve positions for fuel flow, u1, steamcontrol, u2, and feedwater flow, u3. The control inputsare subject to magnitude and rate saturations asfollows:

1,,0 321 ≤≤ uuu (2)

007.0007.0 1 ≤≤− u" (3)02.02 2 ≤≤− u" (4)

05.005.0 3 ≤≤− u" (5)

Another quantity of interest is the water leveldeviation which is given by:

)975.67910013073.0(05.0 3 −++= ss qxL α (6)

where the quality factor of steam, αs, and theevaporation mass flow rate, qs, are expressed by:

)0012304.00394.1()6.258.0)(001583.01(

13

13

xxxx

s −−−=α (7)

096.2514.259.45)147.0854.0( 3112 −−+−= uuxuqs(8)

By taking a Taylor’s series approximation of thenonlinear model at half load, we derive a state spacerepresentation defined by constant matrices A, B, Cand D.

3. The intelligent coordinated control scheme

The performance of a boiler-turbine controlledsystem can be addressed for tracking load changingcommands of power output and steam generation,keeping the drum water level around a small deviationin order to avoid the shrink-and-swell effect associatedwith the water dynamics, satisfying the physicalconstraints imposed on control efforts and achievingwide range control. For this purpose, a robustcontroller based on the linear quadratic Gaussian withloop transfer recovery approach (LQG/LTR) isdesigned for the drum boiler-turbine plant. Thisapproach guarantees an adequate degree of robustness

and performance for a wide range of operatingconditions and system disturbances. These featurescan be complemented with the capabilities of fuzzylogic in knowledge representation to get improvedperformance even further as will be shown bysimulations. The fuzzy reasoning is introduced at thesupervisory level in order to monitor the systemoutputs and to generate the set-points deviations to therobust controller. Qualitatively speaking, the fuzzyreference governor specifies and coordinates thedesired responses of the boiler, steam turbine andelectric generator so that better performance can beachieved with a particular emphasis on the drum waterlevel control which is a critical variable of the plant. Itwas stated that about 30% of emergency shutdowns inthermal power plants are caused by the poor control ofwater level [1].

3.1 Robust LQG/LTR controller

The LQG/LTR approach uses two design steps torealize a robust controller. The first step consists of anoptimal control design problem. The second stepconsists of a Kalman filter design where uncertaintiesin the system are modeled as process andmeasurement noises. Since the boiler-turbine systemhas a non-minimum phase behavior, dynamicsaugmentation is introduced, first, to meet the designspecifications. The state space representation of theaugmented system is given by:

vtxCtywtuBtxAtx

aa

aaaaa

+=++=

)()()()()(

δ" (9)

where w and v are zero-mean Gaussian white noiseprocesses with covariances Qf and Rf, respectively,and

T

aaaa DC

CH

BBA

Aux

x

=

=

=

= and

0,

00,

δδ

The control variable ua satisfies the followingequation:

)()( tHutu a=δ" (10)

LQG/LTRController

Boiler -turbineSystem

FuzzySupervisor

Set-PointGenerator

Fig.2. Block diagram of the coordinated control scheme

Proceedings of the 6th WSEAS Int. Conf. on FUZZY SYSTEMS, Lisbon, Portugal, June 16-18, 2005 (pp89-93)

where H is obtained by using the pseudo-diagonalization method and a column scaling diagonalmatrix [10]. The introduction of this constant matrixinto the state equations plays the role of achievingweak interactions between the system variables andforcing the local dynamics to meet the desiredspecifications in the control design procedure. Thefirst step of the design process is to select theparameters of the optimal state feedback regulator Qcand Rc to construct a target frequency response loop.In the second step, the Kalman filter parameters areadjusted so that the target loop is recovered. Thefrequency domain specifications imposed on the targetloop are: high gain at low frequency with minimum 20dB roll-off, low gain at high frequency, and a cut-offfrequency in the order of 0.01 rad/sec.

3.2 Fuzzy set-point generator

In order to enhance the performance of the drumboiler-turbine plant operation in general and the waterlevel control in particular, a fuzzy logic basedsupervisor is incorporated to the control scheme. Sinceour main concern is to improve the level performanceduring disturbance rejections, we focused on the levelset-point modifications while designing the fuzzy set-point generator. This mixed approach of fuzzy logicand optimal control theory combines the advantages ofboth schemes to form a hybrid controller capable ofimproving the boiler-turbine response. The blockdiagram of the intelligent coordinated control schemeis shown in Fig.2.

The inputs to the fuzzy supervisor are the waterlevel deviation (L) and its rate of change L∆ . For

each variable, triangular/trapezoidal shapemembership functions are constructed based on thespecifications of the level performance. The followinglinguistic terms are used: NB (Negative Big), NM(Negative Medium), ZE (Zero), and PB (Positive Big),PM (Positive Medium). The high drum level alarm isknown to be around 0.25m and normal level deviationis around 0m. These fuzzy partitions are depicted inFig. 3. Using an approximate reasoning, a fuzzy rulebase including twenty five fuzzy rules is determinedfor the fuzzy supervisor which can be completelydefined by the fuzzy set-point generation surfaceshown in Fig. 4. Defuzzification of the fuzzy output isdone using the center of gravity (COG) method.

4. Simulation results

In order to demonstrate the effectiveness of theproposed coordinated control scheme, disturbancerejection test is carried out with the assumption thatthat a step change in drum pressure has occurred at t =50 seconds. The performances of the two controlschemes (LQG/LTR, and coordinated control) appliedto the nonlinear boiler-turbine model are compared inFig. 5. The main objective of level control is tomaintain the drum water level around small deviationsto guarantee the equipment safety.

Fig. 5 shows the input and output time responsesof the boiler-turbine plant under the two controlschemes. These responses are noticeably different.The improvement provided by the fuzzy coordinatedcontrol system is significant. It can be seen that thedrum water level performance is substantiallyimproved in terms of the magnitude of the fluctuation.In addition, we can see that the LQG/LTR controllerhas a slow rising time and large overshoot. In theLQG/LTR case, the maximum magnitude of waterlevel is around 0.15m while the fuzzy supervisorenhances such performance even further by keeping itto well below 0.1m. Also, better handling of thecontrol inputs saturations is obtained especially for thefeedwater valve and the steam valve. Variations in thesteam valve are considered to be as one of the major

Fig. 4. Fuzzy level set-point generation surface

L∆L

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.20

0.2

0.4

0.6

0.8

1

(a)

-4 -3 -2 -1 0 1 2 3 4

x 10-3

0

0.2

0.4

0.6

0.8

1

(b)

Fig. 3. Fuzzy partitions: (a) water level deviation, (b)rate of change of water level deviation

NB NM ZE PM PB

NB NM ZE PM PB

Proceedings of the 6th WSEAS Int. Conf. on FUZZY SYSTEMS, Lisbon, Portugal, June 16-18, 2005 (pp89-93)

sources of uncertainties. The proposed coordinatedcontrol scheme has considerably reduced thesevariations by dumping out the oscillation modes muchmore quickly than the LQG/LTR controller.

5. Conclusion

In this paper, a coordinated control scheme isproposed for the nonlinear oil-fired boiler-turbinesystem. A fuzzy logic based set-point generator and anLQG/LTR controller are combined together in order toenhance the performance of the nonlinear plantoperation and to improve the drum water level control.As can be noticed, adding a fuzzy logic basedsupervisory loop to monitor the level deviation cansignificantly improve the robustness and theperformance of the existing robust controller.Additionally, control constraints on control inputsmagnitude are handled better by the proposed hybridscheme and fluctuations of the plant controlledvariables about their patterns are considerablyreduced.

References

[1] Åström K. J., & Bell R. D. (2000). Drum-boilerdynamics. Automatica, No. 36, pages 363-378.

[2] Bell R. B., & Åström K. J. (1987). Dynamicmodels for boiler-turbine-alternator units. LundInstitute of Technology, Sweden.

[3] Driankov D., Hellendoorn H., & Reinfrank M.(1996) An introduction to fuzzy control (Secondedition). Springer.

[4] Habbi H., Zelmat M., & B. Ould Bouamama(2003). A dynamaic fuzzy model for a drumboiler-turbine system. Automatica, Vol. 29, Issue7, pages 1213-1219.

[5] Habbi H. & M. Zelmat (2004). Design of a fuzzymodel-based controller for a drum boiler-turbinesystem. Proceeding of the 6th International FlinsConference on Applied ComputationalIntelligence, pages 659-664.

[6] Jang R., & Sun C. (1995). Neuro-fuzzy modelingand control. Proceeding of the IEEE, Vol. 83, n°.3, pages 378-406.

[7] Kwon W. H., Kim S. W., & Park P. G. (1989). Onthe multivariable robust control of a boiler-

0 50 100 150 200 250 300 350 400102

104

106

108

110

112

114

116

118

120Steam Pressure (Kg/cm²)

Time (s)

0 50 100 150 200 250 300 350 40066.4

66.5

66.6

66.7

66.8

66.9

67

67.1

67.2Electrical Output (MW)

Time (s)

0 50 100 150 200 250 300 350 400-0.1

-0.05

0

0.05

0.1

0.15Water Level (m)

Time (s)

0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

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1Fuel Valve Position

Time (s)

0 50 100 150 200 250 300 350 4000.64

0.66

0.68

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0.72

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0.78

0.8Steam Valve Position

Time (s)

0 50 100 150 200 250 300 350 400

0

0.2

0.4

0.6

0.8

1

Water Valve Position

Time (s)

Fig.5. Boiler-turbine input and output time responses during disturbance rejection (solid : intelligent coordinatedcontrol system, dashed : LQG/LTR controller).

Proceedings of the 6th WSEAS Int. Conf. on FUZZY SYSTEMS, Lisbon, Portugal, June 16-18, 2005 (pp89-93)

turbine system. Proceeding of the IFAC PowerSystems and Power Plant Control, pages 219-223.

[8] Ben-Abdennour A, & Lee K. Y. (1996). Improvingboiler performance during partial load rejectionsusing a mixed fuzzy logic and LQG/LTRapproach. Proceeding of the American ControlConference, pages 304-308.

[9] Chen P., & Shamma J. S. (2004). Gain-scheduled1! -optimal control for boiler-turbine dynamics

with actuator saturation. Journal of ProcessControl (14), pages 263-277.

[10] Rosenbrock H. H. (1974). Computer-aidedcontrol system design. Academic press Inc.

Proceedings of the 6th WSEAS Int. Conf. on FUZZY SYSTEMS, Lisbon, Portugal, June 16-18, 2005 (pp89-93)