Brief Paper Fuzzy wide-range control of fossil power

Automatica 36 (2000) 69}82

Brief Paper

Fuzzy wide-range control of fossil power plants for life extension androbust performanceq

P. Kallappa, Asok Ray*Mechanical Engineering Department, The Pennsylvania State University, University Park, PA 16802, USA

Received 5 June 1998; revised 11 January 1999; received in "nal form 12 April 1999

Abstract

This paper presents a fuzzy-logic-based methodology of life extending control (LEC) for robust wide-range operation of fossilpower plants including load-following, scheduled shutdown, and hot startup. The objectives of the LEC are performance enhance-ment and structural durability of both aging and new fossil power plants. The proposed control system has a two-tier architecture,which explores and optimizes the plant performance and structural durability trade-o!. The lower tier consists of a feedforwardcontrol policy and a family of linear multivariable robust feedback controllers, which are gain-scheduled for wide-range operation.The sampled-data feedback control laws are synthesized based on an induced ¸

2-norm technique that minimizes the worst-case gain

between the energy of the exogenous inputs and the energy of the regulated outputs. The supervisory controller at the upper tiermakes decisions on plant operations with due consideration to structural durability of critical plant components (e.g., steamgenerators, steam headers, and turbines). The supervisory controller is synthesized based on approximate reasoning embedded withrule-based expert knowledge of the power plant and analytical models of structural damage. Using the fuzzy logic, the plant operationstrategy is modi"ed on-line for trade-o! between plant performance and structural damage in critical components. The fuzzyalgorithm facilitates bumpless controller switching for gain scheduling under wide-range operation and control. It also addsrobustness to the control system especially if the lower tier of gain-scheduled controllers is not able to maintain stability under plantperturbations. ( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Power plant control; Life extending control; Robust control; Gain scheduling; Fuzzy control

1. Introduction

Life extending control (LEC) is a "eld of researchinvolving the integration of two distinct disciplines: SystemSciences and Mechanics of Materials. The objectives ofLEC are performance enhancement and structural dura-bility of both aging and new plants. Ray, Wu, Carpinoand Lorenzo (1994) have shown that, using optimalopen-loop feedforward control sequences, it is possible tosubstantially reduce the damage in an explicit mannerwithout any signi"cant reduction of dynamic perfor-mance. The concept of LEC has been later extended byseveral researchers including Kallappa, Holmes and Ray

qThis paper was not presented at any IFAC meeting. This paperwas recommended for publication in revised form by Associate EditorM. Araki under the direction of Editor K. Furuta.

*Corresponding author. Tel: #1-814-865-6377; fax: #1 814-863-4848.

E-mail address: [email protected] (A. Ray)

(1997), Tangirala, Holmes, Ray and Carpino (1998), andHolmes and Ray (1998) for robust feedforward-feedbackcontrol. This paper is a sequel to the earlier publication(Kallappa et al., 1997) where feedforward control policiesare generated via extensive o!-line optimization toachieve high performance and life extension of fossilpower plants. Each feedforward policy is synthesized asa "nite sequence of open-loop control inputs via con-strained optimization under transient operations. Theoptimization process uses plant and damage models(which are complex and often computationally intensive)and the cost functional consists of performance and dam-age criteria. This control methodology is tested for lifeextension of a single plant component, namely, the mainsteam header, because inclusion of other critical compo-nents into the optimization process signi"cantly in-creases the computation time to achieve convergence.The present paper develops a procedure for synthesisof output feedback laws for life extending control inwhich reduction of structural damage to several plant

0005-1098/00/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 5 - 1 0 9 8 ( 9 9 ) 0 0 1 0 3 - X

Table 1List of plant input and output variables

d Input variables Symbol Unit Output variables Symbol Unit

1 Governor valve area AGV * Throttle steam temperature TTS 3F(3C)2 Feedpump turbine valve area APT * Hot reheat steam temperature THR 3F(3C)3 Fuel/air valve area AFA * Throttle steam pressure PTS psi (MPa)4 Attemperator valve area AAT * Electrical power JGN MW

components is implicitly considered. It focuses onlife extension of steam generator tubes, main steamheader, and hot reheat header that are the most criticalcomponents in a fossil power plant (Electric PowerResearch Institute, 1988). The major contributions ofthe present paper beyond what is reported in the pre-vious publication (Kallappa et al., 1997) are summarizedbelow:

f The plant operating range under load maneuvering isextended down to 25% rated power in the presentcontrol system in contrast to 40% rated power in theearlier one. Since the plant dynamics are relativelymuch more nonlinear in the 40}25% range, a bank ofrobust linear feedback controllers is introduced in-stead of a single controller. This, in turn, requires gainscheduling leading to on-line controller recon"gura-tion. The fuzzy supervisory controller allows bumplessswitching of controllers to ensure both dynamic per-formance and structural durability as well as providesstability under gain scheduling.

f The present control system follows a two-tier architec-ture where the supervisory control law makes intelli-gent decisions for wide-range load maneuvering witha trade-o! between plant performance and structuraldurability of several critical components. The conceptof a fuzzy control law for controller switching andstructural durability in power plants has not beenreported elsewhere to the best of the authors' knowl-edge. A typical example of the reported work in fuzzycontrol of power systems stability is to maintain thegenerated load frequency and voltage constant in thepresence of varying demand (Jamshidi, Vadiee & Ross,1993).

f The present control system is more #exible thanthe earlier one in the sense that operational maneuversare not assumed to be known a priori. Therefore,load regulation can be remotely exercised withoutan explicit knowledge of the initial and targetstates.

f The present control system simultaneously regulatesstructural damage in several plant components in con-trast to the earlier one, which is limited to a singleplant component due to complexity of optimization ofthe feedforward signal.

2. Wide range life extending control system

The life extending control (LEC) system is designed forwide range (i.e., 25}100% rated power) operations offossil-fuel steam power plants via damage mitigation inthe critical power plant components whose failure mayforce unscheduled plant shutdown. This paper focuses onstructural durability of radiant superheater tubes of thesteam generator, and main steam header, and hot reheatsteam header as they together constitute the largestsource of failures (due to creep-fatigue interaction) infossil-fuel power plants (Electronic Power ResearchInstitute, 1988).

The LEC system synthesis is carried out based on thedynamic models of: the power plant under control andstructural damage in critical components. The details ofplant dynamic model are reported by Weng, Ray and Dai(1996). The plant model is a "nite-dimensional state-space representation having 27 states, 4 inputs and 4 out-puts. The plant inputs that are actuator commands, andthe plant outputs that are sensor signals for the feedbackcontrol system, are listed in Table 1. Some of the plantoutputs in Table 1 along with additional sensor signalsare inputs to the component structural model that gener-ates the necessary information for the damage predictionmodel. The output of the damage model is the damagevector that consists of changes in shape, size, cracklengths and geometry of components. For example, forsuperheater tubes, reduction in tube thickness due tocreep #ow is an element in the damage vector. Thedamage models for the main steam header and hot reheatheader have been derived by Kallappa et al. (1997) andthe damage model for the superheater tubes by Lele, Rayand Kallappa (1996).

The onus of damage mitigation is on feedback, butfeedback alone is not capable of sustaining the plantstability and performance for the nonlinear plant forwide range operation. Since the role of linear feedbackcontrollers is to reduce deviations from nominal trajecto-ries, a family of controllers is designed to locally regulatethe plant at a series of operating points. It is thereforelogical to use a static feedforward sequence that is for-mulated based on steady-state plant conditions and in-crement with robust feedback control. In contrast to(optimized) dynamic feedforward control reported earlier

70 P. Kallappa, A. Ray / Automatica 36 (2000) 69}82

Fig. 1. Wide range life extending control system.

by Kallappa et al. (1997), this static feedforward controlpolicy is obtained as an algebraic function of certainmeasured plant outputs.

In the wide range of operation from 25 to 100% of fullload, a single linear feedback controller may not yield therequired robustness for performance and stability espe-cially in the range below 40% where the power plantdynamics are increasingly nonlinear (Weng et al., 1996).Speci"cally, a single controller, designed on a given lin-earized plant model, may not meet the stability andperformance requirements while operating away fromthe equilibrium point of linearization. Furthermore,structural damage in plant critical components willsigni"cantly increase due to large oscillations in theplant states. Analogous to plant stability and perfor-mance, the damage mitigation quality of a control systemmay not be e!ective away from the postulated region ofplant operation. Therefore, a viable option for LEC isgain scheduling that is commonly used for wide rangecontrol of complex dynamical processes such as powerplants and tactical aircraft (Nichols, Reichart & Rugh,1993).

We propose a new approach to supervisory control inwhich gain scheduling is supplemented with fuzzy con-trol to ensure robust stability while achieving high dy-namic performance and extended life over a wide range ofpower plant operations. Wang et al. (1996) use fuzzy logicto gain schedule a series of linear controllers for verysmall order systems by interpolating the outputs of linearcontrollers. This technique may not ensure stability forlarge-order dynamical systems. Due to the use of staticfeedforward, the combined role of supervisory controland robust feedback control reduces to locally regulatingthe plant at a series of operating points and mitigatingstructural damage in the critical components. The familyof linear robust feedback controllers, under considera-tion, is synthesized based on induced ¸

2-norm tech-

niques (Bamieh & Pearson, 1992) as reported earlier(Kallappa et al., 1997). Fig. 1 gives an overview of thewide-range control system and the control strategy issummarized as follows:

f The (static) feedforward control u&& is calculated andstored, based on steady-state operating conditions

from 25 to 100% plant load. In the present design,u&& is calculated at 5% intervals that yields a smoothcurve-"t to the data points for each element of u&& withthe plant load as the independent variable.

f The linear robust feedback controllers are designed atdi!erent levels of plant load to cover the entire range ofplant dynamics. The supervisory controller is used togain schedule these linear controllers based on theplant load. The concept of an observer-based bi-direc-tional switching technique (Astrom & Wittenmark,1984; Graebe & Ahlen, 1996) is used to switch fromone controller to the other. The supervisor also usesa fuzzy-logic-based algorithm to calculate the refer-ence trajectory y3%& in order to maintain stability andperformance as well as to keep the damage rates low.

2.1. Supervisory controller

The hierarchically structured supervisory controllerplays a central role in the robust wide-range operation ofpower plants for high performance and life extension. Itutilizes mathematical models of plant and damage dy-namics, heuristics of plant operations, and behavior ofmaterial degradation based on the knowledge derivedfrom human experience. The supervisory functions areachieved in part, through approximate reasoning, asa fuzzy-logic-based control law (i.e., the fuzzy controller),and in part through gain scheduling of a family of linearrobust controllers. The supervisor is critical for perfor-mance and life extension during transient operations(e.g., during load ramp up and down). The crucial perfor-mance goal is to track the load-following schedule asclosely as possible and maintain plant stability, while thelife extension goal is to keep damage rates in plantcomponents low. To achieve these goals, the supervisorycontroller makes use of the available sensory informationto relax or tighten the load-following schedule based onthe current stability and damage-rate indicators. If these(time-dependent) indicators suggest high damage rates orinstability, the load-following accuracy is compromised.Another role of the supervisor is to achieve smoothdynamic transfer between the individual controllers byusing observer-based switching and the fuzzy controller.Smooth dynamic transfer is required for plant stabilityand damage reduction.

2.2. Linear feedback controller design

As discussed earlier the feedback control system con-sists of a family of linear gain scheduled controllers.Major issues in gain scheduling include the number oflinear controllers, the algorithm for switching from onecontroller to another, the choice of the scheduling vari-able, and constraints on the scheduling variable. Theheuristic used for maintaining stability during gainscheduling is that the scheduling variables must vary

P. Kallappa, A. Ray / Automatica 36 (2000) 69}82 71

slowly and capture the nonlinearities of plant dynamics(Shamma & Athans, 1991). For control of the powerplant under consideration, a scheduling variable thate!ectively captures the plant nonlinearities is the gener-ated power output (i.e., the generated load in MW).Intuitively, slow variations in plant load also reducestructural damage in the critical plant components andmeet the requirements for plant stability during gainscheduling.

Packard et al. (1997) have proposed the linear para-meter varying (LPV) control technique where the linearplant dynamics are assumed to be a function of a time-varying parameter vector o. However, since the LPVtechnique solves linear matrix inequalities (LMI), a con-vergent solution is often di$cult to "nd for high-orderplants such as the power plant under consideration. Thenext best step would be to use a series of linear control-lers. In choosing the number of controllers two factors(that are mutually con#icting) need to be taken intoaccount: (i) robust stability and performance in the entireoperating range for which larger the number of control-lers better is the performance; and (ii) occurrence ofswitching transients or interpolation of control signals onthe plant performance, which is reduced with a smallernumber of controllers. Based on the results of extensivesimulation experiments a set of three controllers isdeemed appropriate for gain scheduling over the entireoperating range of 25}100% plant load. The threecontrollers, designed for linearized plants at 25, 35 and60% load, are found to yield the best performance anddamage mitigation. The reason for using a larger numberof controllers at lower operating range is increased non-linearity of plant dynamics at lower load (Weng et al.,1996).

The controllers are designed using the sampled-datacon"guration similar to what is reported in the earlierpublication (Kallappa et al., 1997). The three design para-meters to be chosen are the input multiplicative modelinguncertainty function =

$%-, the disturbance weighting

function =$*45

, and the performance weighting function=

1. The (frequency-dependent) input multiplicative

weighting function =$%-

and the disturbance weightingfunction =

$*45are the same for the three controllers as

given below:

=$%-

(s)"2As#0.05

s#1 B, (1)

=$*45

(s)"0.1

s#0.1. (2)

Eq. (1) implies that the magnitude of plant uncertainty isbeing estimated as 10% at low frequencies and increasingto the limit of 200% at very high frequencies. Eq. (2) isbased on the assumptions that exogenous disturbanceshave a maximum gain of 0.1 tapering o! at frequenciesover 0.1 rad/s. The performance weights are chosen to be

di!erent for each of the three controllers and are basedon several criteria as discussed below.

It is observed that large oscillations of steam temper-ature and pressure are the major sources of damage inpower plant components. Large oscillations in steamtemperature are also detrimental for turbine blades whilepressure oscillations are much less damaging. The struc-tural damage in steam headers is caused primarily bycreep #ow at high temperatures and by fatigue crackslargely due to thermal stresses. The creep phenomenon isan exponential function of temperature and rapid tem-perature oscillations cause high thermal stresses andstress oscillations. On the other hand, unlike an exponen-tial function, mechanical stress cycling induced by pres-sure oscillations is governed by a relatively mildnonlinear relationship. Therefore, the weight on steampressure is relaxed to enhance the quality of load-follow-ing performance. Since the dominant modes of thermal-hydraulic oscillations in a power plant are expected to bebelow 10 rad/s (Weng et al., 1996), the amplitude ofhigh-frequency oscillations (e.g., in the order of 102 rad/sor higher) of any output variables is likely to be insigni"c-ant. Therefore, larger penalty is imposed on lower fre-quencies of each performance weighting function.However, due to unmodeled dynamics, the risk ofcompletely ignoring high-frequency oscillations isnonnegligible because, rare as they might be, these transi-ents can cause instability leading to catastrophic failuresor unscheduled plant shutdown. Based on the aboveobservations, each performance weight is formulated asa linear combination of a low-pass "lter and an all-pass"lter.

The main steam generator is the major source ofthermal-hydraulic instability in sub-critical power plantswhere rapid variations in the length of the evaporator(e.g., two-phase water/steam region under subcriticalconditions) section may occur due to #uctuations insteam/water #ow and rates of heat absorption. Any vari-ations in the evaporator length are re#ected in thethrottle steam temperature (TTS) that is most signi"cantof the damage-causing variables. Therefore, the penaltyimposed on TTS is the largest. The performance weightsof the output variables, listed in Table 1, for the control-ler at 60% plant load are selected as follows:

=p1

(s)"20#100

s#5for TTS,

=p2

(s)"20#2

s#0.1for THR,

=p3

(s)"10#1

s#0.1for PTS,

=p4

(s)"20#2

s#0.1for JGN. (3)


The performance weights for the controllers at 25 and35% load impose a larger penalty on temperature oscilla-tions because larger temperature variations are observedat lower load levels. This quality of dynamic performanceis traded o! for better damage mitigation and stability.The performance weights for the controllers at 35 and25% load are made identical as follows:

=p1

(s)"30#150

s#5for TTS,

=p2

(s)"30#3

s#0.1for THR,

=p3

(s)"10#1

s#0.1for PTS,

=p4

(s)"20#2

s#0.1for JGN. (4)

The induced ¸2

synthesis is performed throughD}K iteration (Balas, Doyle, Glover, Packard & Smith,1995; Zhou, Doyle & Glover, 1996). Initially, the control-ler at 60% had 71 states and each of the two controllersat 35 and 25% load had 79 states. Since many of thecontroller states were only lightly controllable, it waspossible to perform Hankel model order reduction sothat the order of each controller is reduced to 26 statesat the "nal stage of design. There is no noticeable increasein the structured singular value (k) for performance ro-bustness that still remains below 0.8 after model orderreduction.

The induced-¸2

method for multivariable robust con-troller design introduces a state-space structure that maylimit the application of gain-scheduling because of theneed to interpolate between di!erent controllers forsmooth scheduling. Parametric controllers (Nichols etal., 1993) and other smooth scheduling (pole-zero inter-polation) techniques have been tested only for low-ordersystems. The wide range of the high-order nonlinearplant in the present design implies that the controllersmay not be structurally similar in terms of the proximityof the poles and zeros. This makes it di$cult to parametr-ize controllers. As explained earlier, the plant perfor-mance gains at di!erent operating points are weighteddi!erently, leading to dissimilar, high order linear con-trollers (e.g., 26 states after order reduction). Therefore,gain scheduling based on switched scheduling has beenadopted that involves binary bi-directional switchingfrom one controller to another with no intermediatestage. Successful implementation of the switching sched-uling requires a bumpless, antiwindup transfer (Graebe& Ahlen, 1996) between controllers. Given that the con-troller is observable (because it is minimally realized), anobserver-based policy (Graebe & Ahlen, 1996) is used forcontroller switching.

2.3. Fuzzy controller design

Since the role of the supervisory controller is, in part,to emulate some of the decision-making capabilities of ahuman supervisor, it must be embedded with the knowl-edge and intuitions of human operators. For this pur-pose, a knowledge-based system in the setting of approx-imate reasoning is a viable option. Yen, Langari andZadeh (1995) have demonstrated, through various indus-trial applications, the ability and versatility of fuzzy logicto emulate human supervisors for decision and control.In this application, the fuzzy control algorithm serves toachieve three interrelated goals:

f Damage rate reduction in the critical components whilesatisfying the plant performance requirements: Sinceslow dynamics of the tracking signal (i.e., the load-following rate) may lead to loss in dynamic perfor-mance, the fuzzy control law is designed to makea trade-o! between plant performance and structuraldamage during these transients, while taking into con-sideration the required plant load.

f Robust stability of the gain-scheduled control system:Slow variations in the scheduling variable (i.e., theplant load) facilitates stability during gain scheduling.The fuzzy controller limits the plant load variations tomaintain stability without any signi"cant deviationsfrom the load demand.

f Avoidance of large abrupt dynamic changes in plantvariables during controller switching: Large abruptchanges, even if they do not result in instability, maycause considerable structural damage to critical plantcomponents. The fuzzy controller enhances smoothswitching to avoid these large abrupt changes.

Holmes and Ray (1998) have proposed the basic con-"guration of a damage-mitigating fuzzy controller. Itconsists of: a fuzzi"er that takes crisp inputs, an inferencemechanism with a rule base and a defuzzi"er that con-verts the fuzzy outputs in the crisp form. The nonfuzzyinput to the fuzzy control system is the sensor data vectory(t) that is readily available. Based on the fuzzy inputs,a course of action is adopted, via an if}then rule base thatpartially captures the expertise of human operators. Thenonfuzzy output of the fuzzy system is the load ramp rateand the actual load (i.e., the generated power) is the gainscheduling variable. This choice provides a convenientmeans for achieving "rst goal of damage reduction. Theremaining two goals can also be achieved through fuzzylogic by judicious choice of the membership functions.For example, if the goal is to achieve a smooth loadincrease from 30 to 60% at an average rate of 10% fullload per minute, the fuzzy controller may decrease theramp rate below 10% at certain points to maintainstability or reduce damage. On the other hand, if thesensor-based information indicates a low damage rate


Fig. 2. Membership functions for temperature rate of change.

Fig. 3. Membership functions for temperature error.

Fig. 4. Membership function for load ramp rate.

and stable operation, the load ramp rate can be safelyincreased.

The inputs to the fuzzy controller have to be measur-able quantities that are available as sensor outputs.Keeping the goals of the fuzzy system in mind, the criticalplant states and outputs that a!ect stability and struc-tural damage need to be identi"ed as inputs. We havediscussed the e!ects of throttle steam temperature (TTS)and hot reheat temperature (THR) in terms of damageand their ability to re#ect overall plant stability. In con-trast, stability is not very sensitive to the other two plantoutputs, Throttle steam pressure (PTS) and generatedpower (JGN). Therefore, two temperature outputs, TTSand THR, are used to derive the fuzzy controller. Bothabsolute temperature error and rate of temperature vari-ation are critical to plant stability and structural damage.Thus the four fuzzy inputs are the two output temper-ature errors and their respective rates of variations. Inthis respect the fuzzy controller is analogous to a classicalProportional-derivative (PD) controller.

Similarly, the outputs of the supervisory controllermust be quantities that a human operator should be ableto manipulate to achieve the mission goals. The patternsand behavior of the outputs that lead to appreciabledamage and instability need to be identi"ed, observed,and incorporated into the membership functions and rulebases. The output of the fuzzy controller is the magnitudeof the load ramp rate, which is the derivative of thereference signal, y3%& (4). During transient operations,such as ramp-up or ramp-down, the two temperaturesTTS and THR are major indicators of the damage rates.In order to obtain a better control of the damage-causingvariables, slowing down of the process dynamics is themost natural action of the supervisory controller. Thisimplies a reduction in the load ramp rate. On the otherhand, a good temperature performance can leave su$-cient margins to increase the ramp rate, which a supervi-sor might choose to do. This justi"es the choice ofabsolute value of the ramp rate as the fuzzy controlleroutput. A unique feature of the output membership func-tions that are expressed in terms of the rate of change ofload demand (i.e., the required load ramp rate) is their#exible nature. The membership functions are shown inFigs. 2}4.

For the two temperature errors, the same universe ofdiscourse and membership functions are used becausethe process variables, TTS and THR are functionallysimilar. The same argument holds for the rates of changeof these two temperatures. A third membership functionis required for the output. Unlike the other two member-ship functions of temperature rate and temperature errorin Figs. 2 and 3, the membership function of load ramprate in Fig. 4 is not uniformly spaced. The spacings in Fig.4 are obtained by trial and error over extensive simula-tion runs, similar to what a human operator would liketo do to obtain an understanding of the physical process.

The triangular shape (i.e., piecewise linearity) of eachmembership function is chosen for mathematical simpli-city and produces su$ciently good results, as will be seenin the next section. Each membership function set hascardinality of "ve. An interpretation of these membershipfunctions from the perspectives of the supervisory con-troller is as follows:

f r1" very low rate of change of temperature; r

2" low

rate of change of temperature; r3" moderate rate of

change of temperature; r4" high rate of change of

temperature; r5" very high of change of temperature.

Similar labels can be assigned to temperature error andload ramp rate.

The output membership functions are themselvesa function of the required load ramp rate that is derived


Fig. 5. Parallel processing of the fuzzy control algorithm.

Table 2If}then rules for temperature rate of change (fuzzy controller S1)

rTHR1

rTHR2

rTHR3

rTHR4

rTHR5

rTTS1

RR5

RR4

RR3

RR2

RR1

rTTS2

RR4

RR4

RR3

RR2

RR1

rTTS3

RR3

RR3

RR3

RR2

RR1

rTTS4

RR2

RR2

RR2

RR2

RR1

rTTS5

RR1

RR1

RR1

RR1

RR1

Table 3If}then rules for temperature error (fuzzy controller S2)

ETHR1

ETHR2

ETHR3

ETHR4

ETHR5

ETTS1

RR5

RR4

RR3

RR2

RR1

ETTS2

RR4

RR4

RR3

RR2

RR1

ETTS3

RR3

RR3

RR3

RR2

RR1

ETTS4

RR2

RR2

RR2

RR2

RR1

ETTS5

RR1

RR1

RR1

RR1

RR1

from the operation strategy, which in turn is obtainedfrom the rate of change of load, i.e., required ramp ratedenoted by RR

REQ. The actual values of the mean of each

of the "ve output membership functions (see Fig. 4) are:

RR1"0.06 RR

REQ,RR

2"0.3 RR

REQ,RR

3"0.6 RR

REQ,

RR4"0.9 RR

REQ,RR

5"1.1 MW/s.

These values are arrived at through trial and error andare based on human experience. They are speci"c to thepower plant under consideration and can be easily modi-"ed on-line to achieve a di!erent level of performance-damage trade o!. For this speci"c plant, the highest valueof ramp rate is 1.1 MW/s that can be achieved onlyduring near &perfect' stability and very low damage rates.

The membership functions are now combined intoa set of fuzzy rules constituting a four input}single outputfuzzy control system with each input having cardinalityof "ve. This implies that there can be 54 ("625) combi-nations of inputs and an if}then rule is required for eachcombination. To simplify this situation, the fuzzy controlsystem is partitioned into two parallel processing systemsS1 and S2 as shown in Fig. 5. The inputs to S1 aretemperature rates and the output is the load ramp rate,while the inputs to S2 are the temperature errors andoutput is also the load ramp rate. The junction &(' inFig. 5 represents an operation which picks the minimumof the two outputs, i.e., the slower ramp rate. The advan-tage of this simpli"cation is that, instead of 625 rules,two sets of 25 if}then rules are now needed as listed inTables 2 and 3.. For example, a rule If rTTS

1and rTHR

1, then

RR5 represents: If the rate of change of Throttle SteamTemperature is very low and the rate of change of HotReheat Temperature is very low, then ramp rate should bemade very high.

The membership functions fuzzify the nonfuzzy inputs.In the inference mechanism, the parameter j

ijis used to

express the applicability of each of the 25 rules to thepresent situation. It takes a value in the interval [0,1]representing a measure of the amount the inputs satisfythe if part of the respective rule. The subscripts i andj represent the row and column of the rule matrices. Forexample, j

ij"minMrTTS

i, rTHR

jN referring to Table 2 where

the rows (i.e., subscript i) and columns (i.e., subscript j)indicate the membership values of functions involving

TTS and THR, respectively. The defuzzi"er calculatesa unique output in the form of ramp rate. The output iscalculated as a weighted average of the outcome of eachrule, RR

k, k"1, 2, 3, 4, 5, with the respective j

ij's as the

weights. The outcome of each rule is represented as rrij

where a unique value of rrij

is determined as the outcomeof each if}then rule. The three middle membership func-tions, RR

2, RR

3, and RR

4, in Fig. 4 are symmetric. For

these three functions, each outcome rrij

is concentratedon its respective geometric mean (i.e., center of gravity).For the two remaining membership functions, RR

1and

RR5, the outcome rr

ijis, respectively, equal to the largest

and smallest ramp rates with membership value of one.The defuzzi"ed ramp rate is given by

ramp rate" +i, j/1, 2, 5

jijrr

ijN +i, j/1, 2, 5

jij

(5)

which is the weighted average of the geometric means ofthe output membership functions.

2.4. Control system implementation

The implementation strategy of the supervisory con-trol system, shown in Fig. 6, has three main functionalmodules where the discrete-time and continuous-timesignals are denoted by &k' and &t', respectively, in parenth-esis. The supervisory controller module consists of thegain scheduler and the fuzzy controller. The gain sched-uling of controllers is carried out based on the measuredplant outputs y(k), speci"cally the fourth element of y(k),which is the generated load JGN in MW. Given a powerplant operating strategy, the fuzzy-logic-based controlmodule in the supervisory controller serves the role of


Fig. 6. Implementation of supervisory control system.

generating y3%&(k). The feedforward signal is generated viaequilibrium steady-state calculations. The robust feed-back module is realized by three linear controllers whoseranges of operation are as follows:

f controller synthesized at 25% plant load: used forrange [25%, 32%] plant load;

f controller synthesized at 35% plant load: used forrange (32%, 50%] plant load;

f controller synthesized at 60% plant load: used forrange (50%, 100%] plant load.

All three controllers are synthesized closer to the lowerend of their operating range. The rationale is that theextent of nonlinearity is much more severe as the load isdiminished.

The sequence u&&(k) of the feedforward signal is up-dated every 1 s by the fuzzy controller, based on y3%&(k),and is stored in the control computer a priori. Thefeedback control law u&"(k) is generated on a 0.1 s sam-pling time. At each sampling instant, the feedforward andfeedback signals are added together and are convertedinto a continuous-time signal using the zero-order hold(ZOH) logic. Since the feedforward sequence is based ona 1 s sampling time while the feedback control is based ona 0.1 s sampling time, each element in the feedforwardsequence is applied for 10 consecutive sampling intervals.The error signal, y%3303(k) is obtained by subtracting thereference signal y3%&(k) from the plant output y(k).

The "rst three elements, namely reference signals forTTS, THR and PTS, of y3%&(k) are functions of the fourthelement (i.e., the reference signal for JGN). Once thevector My3%&(k)N is determined, it can be used to generatefeedforward input for the next sample. At any instant,only one linear controller provides the feedback signal.While a single speci"c controller is on-line, the trackersfor the remaining two controllers, which are o!-line, arefunctioning to ensure that the controllers are ready toswitch smoothly under a sudden change in the plant loaddemand. As soon as the active controller goes o!-line, itstracker is switched on. While the main role of the super-visory controller is life extension without any signi"cantloss of performance, it ensures stability and augments theoperating range of the power plant. It is shown in thesimulation section, that at times when the feedback con-trollers fail, the supervisory controller can maintain ro-bust stability.

3. Results and discussion of simulation experiments

Simulation experiments are performed to demonstrateperformance, robustness and damage mitigating capabil-ities of the wide-range control system. This is accom-plished by comparison of the plant dynamic performanceunder the following three feedback control system con"g-urations:


Case 1: Single controller: A single induced ¸2

robustcontroller designed to operate over the entire range ofplant operation (i.e., 25}100%);

Case 2: Gain scheduled without fuzzy logic (denoted as&gain sch.'): A combination of three gain-scheduled con-trollers without fuzzy logic to operate over the entirerange of plant operation;

Case 3: Wide range control system/gain scheduled withfuzzy logic (denoted as &gain sch. with fuzzy'): A combina-tion of three gain-scheduled controllers along witha fuzzy logic to operate over the entire range of plantoperation.

Each of these feedback control con"gurations is usedin conjunction with the same feedforward policy. Thesethree cases are compared based on output performanceand structural damage. The plant performance requiresgenerated plant load (JGN) to follow a predeterminedtrajectory. The other three outputs, namely, throttlesteam temperature (TTS), hot reheat temperature (THR)and throttle steam pressure (PTS) follow trajectoriesbased on the current plant load and are maintainedwithin respective bounds. During these operations, dam-age accumulation in each of the main steam header, hotreheat header and superheater tubes is calculated usingthe damage models reported in the earlier publication(Kallappa et al., 1997). Simulation experiments are alsoperformed to test robustness of the control system underplant perturbations.

3.1. Simulation set up

For both nominal and perturbed plant conditions, theclosed-loop control system is evaluated by simulation oftwo operation scenarios: a power ramp up from 25 to100% The recommended ramp rate is 10% (of full load)per minute for both operations. This makes RR

REQto be

0.875 MW/s. The desired operating conditions for theTTS, THR and PTS at a given plant load (JGN) becomealgebraic functions of the JGN and are determined as thesteady state values of these outputs at the given plantload. At loads above 40% of the full power level, these setpoint values are maintained unchanged. However, atloads below the 40% power level, the set points need tobe decreased, especially the pressure PTS. The steampressure di!erence across the feedwater pump turbine isinsu$cient to generate adequate power to drive the feed-water pump at low loads. Since it becomes di$cult tomaintain pressure at 2415 psi (16.65 MPa) without ac-tuator saturation, the reference signal for PTS is loweredfor operations below the 40% load level. The operatingtemperatures are also lowered slightly to avoid actuatorsaturation.. The operating conditions for each load are asfollows:

f 25% load - [ TTS, THR, PTS]"[9353F (501.73C),9903F (532.23C), 2050 psi (14.13 MPa)];

f 30% load - [ TTS, THR, PTS]"[9483F (508.93C),9983F (536.73C), 2285 psi(15.75 MPa)];

f 40}100% load - [ TTS, THR, PTS]"[9503F(510.03C), 10003F (537.83C), 2415 psi (16.65 MPa)].

A brief description of the geometry, materials and typeof damage in the three components are given below:

Main steam header: It is made of 214% Chromium and

1% molybednum ferritic steel. It has an inner diameter of4.5 in (114.3 mm) and an outer diameter of 7.2 in.(182.9 mm). Damage in main steam header results fromfatigue cracking and, thickness reduction due to creep.Normalized creep is obtained as the reduction in headerthickness per unit original thickness and is designated&Creep Thinning'. Maximum fatigue crack growth occurson the outer surface of headers in the radial direction.

Hot reheat header: It is made of 214% chromium and

1% molybednum ferritic steel. It has an inner diameter of6.5 in (152.4 mm) and an outer diameter of 7.0 in(177.8 mm). Damage in the hot reheat header is predomi-nantly due to creep and is represented as &Creep Thinn-ing' in a fashion identical to the creep damage in the mainsteam header.

Superheater: Each superheater tube is made of 214%

chromium and 1% molybednum ferritic steel. It has aninner diameter of 1.0 in (25.4 mm) and an outer diameterof 1.75 in (44.45 mm). Structural damage in superheatertubes occurs mainly due to creep and is also representedas &Creep Thinning'.

The steam temperatures and pressure, TTS, THR andPTS, determine stress conditions in the main steam andhot reheat steam headers as well as in the steam gener-ator and reheater tubes and in the high-pressure andintermediate-pressure turbines. The next two sectionspresent simulation results for nominal and perturbedplant conditions. The plots in the "gures are marked withappropriate labels (e.g., &single controller', &gain sch.', and&gain sch. with fuzzy') to indicate di!erent controllercon"gurations under both ramp-up and ramp-downoperations. The term &Ref. Traj.' in the "gures denotes&Reference Trajectory'. Results from power ramp upoperation are reported for both nominal and perturbedplant, because each of these simulations highlights a dif-ferent aspect of the system. Since ramp-down operationsfor both nominal and perturbed plant yield similar re-sults, only the simulation results for the perturbed plantare reported here.

3.2. Simulation under nominal conditions

Three di!erent con"gurations of feedback control areused as mentioned earlier. The single robust controller,adopted for simulation experiments, yields the best per-formance out of many single controllers that were de-signed and tested. This controller is designed based onthe plant model linearized at 40% full load. Fig. 7 shows


Fig. 7. Ramp-up performance of a single controller in the nominalplant model.

Fig. 8. Ramp-up performance of gain-scheduled controllers in thenominal plant model.

the performance of this controller for ramp-up opera-tions. The plots show that the respective initial steady-state load is held constant for the "rst 100 s to demon-strate absence of any initial (non-steady-state) transients.Similarly, the "nal steady states are held for an extendedperiod of time to exhibit stability. Throttle steam and hotreheat steam temperatures, TTS and THR, in Fig. 7 ab-ruptly increase at the onset of power ramp-up. Rapidtemperature changes of this nature may cause structuraldamage in the steam headers as well as in the steamturbines. The "nal steady state responses are also ex-tremely oscillatory. This is undesirable for the perspect-ives of both performance and structural damage. Thesingle controller is also found to be unstable for injectedplant perturbations. It is reiterated that this single con-troller has yielded the best performance out of a largegroup of single robust controllers that were designed.

Fig. 8 compares the outputs of the &gain sch.' (i.e.,without fuzzy logic) and &gain sch. with fuzzy' controllersunder ramp-up. Gain scheduling shows a marked im-provement over the &single controller' system in terms ofsteady-state behavior although the transient response isstill poor. In contrast, the &gain sch. with fuzzy' controller

shows excellent behavior of the steam temperature andpressure transients. Unlike the other two controllers,&gain sch. with fuzzy' signi"cantly diminishes the risk ofpotential damage to the steam turbines by reducing ther-mal stresses arising from large temperature oscillations.The &gain sch. with fuzzy' system in Fig. 8 takes 738 s forload ramp-up from 25 to 100% (i.e., an average ramp rateof 6.1% of full load per minute). This fuzzy controllerreduces the load ramp rate to ensure stability and lowdamage rate; it also increases the load ramp rate when itis safe to do so. A major goal of the &gain sch. with fuzzy'control system is to ensure that the generated powerJGN closely follows the reference trajectory where en-forcement of a very small tracking error may induce largeoscillations in steam temperature and pressure resultingin increased damage. There is thus a trade-o! involved.The load-following performance can be improved bychanging the frequency-dependent performance weights=

1in the robust feedback controller synthesis as well as

by updating the fuzzy membership functions (e.g., allow-ing larger ramp rates in the membership functions of theplant outputs). Each change involves a trade-o! and isthe designer's decision. In essence, the fuzzy controller


Fig. 9. Damage during ramp-up operation in the nominal plant model.Fig. 10. Ramp down performance of the perturbed plant model.

can be designed to improve the transient responseof JGN at the expense of structural damage or viceversa.

Fig. 9 compares the structural damage under a ramp-up operation that is preceded by 1000 s of steady-stateand followed by 2000 s of transients. This ensures thatany delayed dynamics in damage will show up duringsteady state operation. For each of the critical compo-nents, the &gain sch. with fuzzy' controller yields betterdamage mitigation. Maximum damage reduction takesplace in the main steam header because it is a thick pipeand is more prone to thermal stresses arising from largertemperature gradients across the wall. The hot reheatheader, on the other hand, is a thinner pipe and itsdamage is mainly due to the temperature; temperaturevariations have much less detrimental e!ects. A similarlogic applies to the superheater tubes that are not asthick as the main steam header. The main cause ofstructural damage in superheater tubes is the radiantheat #ux from the "reball in the furnace. The "reball sizeis controlled by the air}fuel valve. Under nominal plantoperations, the feedforward control input to this valve is

carefully designed to avoid any sudden change in "reballsize and the feedback signal is responsible for "ne-tuningonly. Therefore, the life extending qualities of the feed-back system for the superheater tubes are not as evidentin the nominal plant, compared to those in the perturbedplant. To summarize, it is concluded that &gain sch. withfuzzy' is the best amongst the three controllers for perfor-mance and damage mitigation.

3.3. Perturbed plant simulation

Simulation experiments have also been conducted onthe plant model with injected perturbations to examinerobustness of the control system. The following perturba-tions are introduced:

f 3% decrease in the e$ciencies of all turbines andpumps due to structural degradation of rotating com-ponents;

f 3% decrease in the heat transfer coe$cients in thesteam generator and reheater tubes due to scale forma-tion on the inside surface;


Fig. 11. Damage during ramp-down in the perturbed plant model. Fig. 12. Ramp up performance of the perturbed plant model.

f 25% increase in the time constants of the governor,feedpump turbine and fuel/air valves due to possibleactuator degradation.

The &single controller' is unstable under perturbed con-ditions for both ramp-up and ramp-down and the resultsare not presented here. A comparison of the &gain sch.'and &gain sch. with fuzzy' controllers in Fig. 10 showsimprovements in the throttle steam and hot reheat steamtemperatures, TTS and THR. The &gain sch. with fuzzy'controller yields superior performance in terms of over-shoot and oscillations, especially in the later part oftransients. The response of the throttle steam pressure,PTS, is good for both controllers. The generated power,JGN, exhibits the trade-o!s. Without the fuzzy control-ler, the transient response of JGN is modestly superior atthe expense of other variables and speci"cally structuraldamage in the main steam header as seen in Fig. 11. Thisalso demonstrates the basic features of the fuzzy control-ler. When the steam temperatures are well within speci-"ed limits, the &gain sch. with fuzzy' controller increasesthe ramp and when the temperatures begin to oscillate,it lowers the ramp rate as seen in the bottom plate of

Fig. 10. For both ramp-up and ramp-down operationsunder &gain sch. with fuzzy' control, reduction in damagein one component does not result in increased damage inanother component. There are no trade-o!s involved atthis level. All trade o!s are made among the plant out-puts where the power ramp-up or ramp-down rates un-der load-following operations may have to be slightlysacri"ced to prevent large oscillations in steam temper-ature and pressure. It is concluded that good control ofsteam temperature and pressure transients leads to miti-gation of structural damage in plant components.

Fig. 12 shows the ramp-up operation for the perturbedplant. The &gain sch. with fuzzy' controller performsreasonably well and the control system becomes unstablewithout the fuzzy controller. As the generated powerJGN starts to move away from its reference trajectory,the fuzzy controller slows down the load ramp rate andthereby the rate of change of the plant load is reducedand stability is maintained. This is in accordance with thestatement in Section 2 that slow variation of the gainscheduling variable, in this case the plant load, ensuresstability. This observation demonstrates the e!ectivenessof fuzzy logic in keeping the control system robust.


4. Summary and conclusions

This paper presents a methodology for synthesis of lifeextending control systems for wide range operations offossil-fuel steam power plants. The goal is to achievedamage mitigation in critical plant components and toenhance dynamic performance and robustness of thepower plant control system. Since the fuzzy controllermakes the decision of changing the load reference signalbased on damage predictions, it can react to unexpectedchanges in real time, which cannot be predicted a priori.A distinct feature of this approach is that the knowledgeof plant dynamics and mechanics of the structural mate-rials are synergistically applied to formulate a controllerdesign methodology which can be readily used by prac-ticing engineers with the aid of commercially availablesoftware.

A combination of three gain-scheduled controllers isused as the linear feedback system in the lower tier of thehierarchical control system. Since power plant dynamicsare more nonlinear at lower loads (because of reducedwater/steam #ow rate), the controllers are synthesized at25, 35 and 60% of full load. The (frequency-dependent)performance weighting functions for these controllers areselected after a careful study of the plant and damagedynamics to simultaneously achieve robust performanceand structural durability.

A supervisory control system in the upper tier is createdfor: (i) implementation of gain scheduling; (ii) enhancementof life extension capabilities; and (iii) increased stabilityrobustness. The supervisor consists of a fuzzy-rule-basedcontroller that captures the expert knowledge of plantdynamic stability and structural damage in the criticalcomponents. Implementation of these rules leads to dy-namically smooth switching between controllers undergain scheduling. It enhances robust stability of plant op-erations and simultaneously reduces structural damage.The fuzzy controller design does not require any direct useof the nonlinear plant model and damage models. Thefuzzy supervisor is designed based on a given trade-o!between tracking error under load-following and damagerate. Results of simulation experiments show that theramp rate is reduced from 10% to just over 6% to reducethe damage rate. The level of trade o! can be altered byusing a combination of the following strategies:

f Changing the mean values of the ramp rates: The meanvalues of the ramp rates are increased for better perfor-mance and they are reduced for improved stability andlife extension. This modi"cation can be executed on-line.

f Changing the input membership functions: The permis-sible errors and rates of change are reduced to main-tain the damage rates low and they are increased forbetter performance. This is a design modi"cation thatcan only be executed o!-line.

Based on the results of simulation experiments, it isapparent that reduction of damage in one componentdoes not lead to increase in damage in other components.It also establishes the overall superiority of gain schedul-ing with fuzzy control, especially for power ramp-upoperations. This concept of wide-range life extendingcontrol is of signi"cant engineering importance.

Acknowledgements

The work presented in this paper has been supportedby: National Science Foundation under Grant Nos.ECS-9216386, DMI-9424587, and CMS-9531835; Elec-tric Power Research Institute under Contract No. EPRIRP8030-05; National Academy of Sciences under aResearch Fellowship award to the second author.

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Asok Ray earned the Ph.D degree in Mechanical Engineering fromNortheastern University, Boston, MA in 1976, and also graduate de-grees in each discipline of Electrical Engineering, Mathematics, andComputer Science. Dr. Ray joined the Pennsylvania State University inJuly 1985, and is currently a Professor of Mechanical Engineering.Prior to joining Penn State, Dr. Ray held research and academicpositions at Massachusetts Institute of Technology and Carnegie-Mel-lon University as well as research and management positions at GTEStrategic Systems Division, Charles Stark Draper Laboratory, andMITRE Corporation. Dr. Ray was also a Senior Research Fellow atNASA Lewis Research Center under a National Academy of Sciencesaward. Dr. Ray's research experience and interests include: Fault-

accommodating and robust control systems, Modeling and analysis ofthermo-mechanical fatigue and creep in both deterministic and stochas-tic settings, Intelligent instrumentation for real-time distributed pro-cesses, and Control and optimization of continuously varying anddiscrete-event dynamic systems, as applied to Aeronautics and Astro-nautics, Undersea Vehicles and Surface Ships, Power and Processingplants, and Autonomous Manufacturing. Dr. Ray has authored orco-authored three hundred research publications including over onehundred and thirty scholarly articles in refereed journals such as trans-actions of ASME, IEEE and AIAA, and research monographs. Dr. Rayis a Fellow of ASME, and Associate Fellow of AIAA, and a SeniorMember of IEEE.

Pattada Kallappa was born in India. He received his undergraduatedegree in Mechanical Engineering, from the Indian Institute of Techno-logy, Kanpur in 1988. After working in the industry for a few years, hecame back to school to obtain a Masters degree in Mechanical Engin-eering from Tulane University, New Orleans in 1993. He received hisPh.D. in Mechanical Engineering in 1998, from the Pennsylvania StateUniversity. He is currently working at the Applied Research Laborat-ory (ARL) at Penn State. His research interest include, robust control oflarge order systems, modeling and control of structural damage inmechanical systems, load control in power plants, fuzzy logic basedcontrols, and hybrid controls and robotics.


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Brief Paper Fuzzy wide-range control of fossil power