Robust Optimal Control of a Natural Gas-Fired Burner for the Control of Oxides of Nitrogen(NOx)

Tightening requirements on indus1rial boilers and furnaces will require hands-rree techniques to (I) assure peak performance with respect to emission, and (2) assure an ability to achieve peak performance throughout a load duty cycle. In the present paper, robust optimal control of a model industrial, swirl-stabilized, natural gas-tired burner is explored as a strategy to attain and main1ain low flue-gas nitrogen oxide concentration ([NOx]l concomitant with high combustion efficiency (I/,). A performance index, J, is defined such that the maximization of J correlates to optimal burner performance, with respect to (NOxJ and 'le- Two parameters, swirl intensity (S') and excess air(C:A), are made amenable to control and incorporated as variable burner inputs. For a given load, the settings of EA and S' arc automatically adjusted by a specialized search algorithm in order 10 maximize the performance index, thereby optimizing 'I, and (NO,). The robustness of the approach is demonstrated and evaluated by initiating a change in load and observing the reaction of the modified control system. The control scheme is shown 10 effectively increase and maintain overall burner performance. Implementation of robusl optimal control to practical systems is discussed in terms of chullengesoutstandingand opportunities to integrate with overall system performance.


INTRODUCTION
While combustion of fossil fuels provides most of the world's energy, it also produces most of the world's air pollution. One straightforward technique to reduce these emissions from stationary combustion systems is to switch the fuel being burned, substituting a cleaner-burning fuel where a more poll uting type is being used (i.e., switching from coal to oil or from oil to natural gas).
Although natural gas combustion generates significantly lower emissions of sulfur oxides and soot than coal or oil, reducing the emission of oxides of nitrogen (NO and N0 2 , collectively referred to as NOx), a major contributor to photochemical oxidant ("smog"), remains a challenge.
Many techniques are employed in the task of controlling NOx emissions from stationary combustion applications. Some controls seek to prevent NO x formation during combustion, such as staged combustion, flue gas recirculation, catalytic combustion, etc. Other control processes destroy NOx in a post-combustion reaction; these include selective catalytic reduction (SCR), selective non-catalytic reduction (SNCR), and non-selective catalytic reduction (NSCR) (U.S.E.P. A., 1992).
In any of these processes, a set of static input parameters (fuel load, equivalence ratio, etc.) will correspond to particular values for each of a set of output parameters (NOx emission, heat loading, combustion efficiency, etc.). For a given combustion process there will be at least one set of input parameters that produces an optimum set of output parameters. Identifying the input parameters that produce this optimum condition is not trivial. Furthermore, these optimum input parameters will change as boundary conditions vary due to changes in load, fuel type, inlet air properties, or even subtle changes due to equipment degradation.
Using a natural gas-fired, I 00,000 Btu/ hr, model industrial burner, research at the University of California, r rvine, has shown that certain values of swirl intensity and excess air (equivalence ratio) can significantly reduce the NOx concentration in the exhaust gases without reducing combustion efficiency (St. John and Samuelsen, 1994).
Previous research in the a rea of combustion control has dealt with the problem of reducing pressure oscillation (McManus et al. , 1993). The present work explores the potential of applying a robust, on-line, active optimization scheme to a combustion process for the control of the emission of nitrogen oxides, over a range of conditions. A specialized optimization algorithm, static by operation, is applied to control the fuel-air mixing process via swirl intensity and excess air in order to optimize burner performance, which is defined in terms of combustion efficiency and NO" concentration, measured in the exhaust gas.
An active control scheme has been postulated in order to continuously monitor NOx concentration ( [NO,.]) and combustion efficiency (I'/,). and adjust the fuel-air mixing process to maintain optimum performance of the burner as boundary conditions vary. Given a constant burner geometry, and a set of variable input parameters (in this case swirl intensity, S', and excess air, EA), the active control system should be able to find some combination of those parameters such that a desired performance, the optimum condition, is attained and maintained.

APPROACH
The approach adopted implements the active control hypothesis in fo ur seeps: (I) development of the experiment; (2) definition of performance in quantitative terms; (3) achievement of a "proof-of-concept" phase demonstrating the viability of the active control scheme; and (4) exploration of a more advanced control algorithm and of the control scheme's reaction to a large scale change in boundary conditions (in this case, fuel load).

Experiment
T he burner facili ty and associated control hardware are shown schematically in Figure 1. Given a fixed fuel flow (load), the two inlet parameters (EA and S') are varied by adjusting the amount of air flowing through the axial and swirl air streams. First, the sum of the two air streams (m~ + m 0 ) determines the overall excess air (EA) provided for combustion. Second, the percentage of flow through the swirl air stream with respect to the total amount of air flow uniquely defines the swirl intensity (S') for this burner. · To facilitate computer control of the air and fuel flow, sensor/valve packages were installed in the fuel line, the axial air line, and the swirl air line. Each sensor and valve is referred to collectively as a mass flow controller (MFC). Figure 2 is a block diagram representing the general control scheme employed in this study. The burner is the plant, or object under control. The sensor is composed of a bank of gas analyzers, similar to continuous emissions monitoring systems installed in many industrialjcommercial burner operations today. A continuous sample is extraced and pulled through five analyzers which measure [CO], [C0 2 ], [HC], [0 2 ] and [NOxl The controller consists of a 486-based computer which reads emissions signals from the analyzers and calculates NO x concentration (corrected to 3 % 0 2 ), and combustion efficiency. Using a specialized optimization algorithm, the controller determines new values of S' and E_A , and sets the air How accordingly.

Performance Definition
For a given burner, optimum performance can be qualitatively defined as the value of swirl intensity, S', and excess air, EA, where [NO~] is rela tively low and combustion efficiency remains relatively high. In order to make an 'CONTROL OF NO, 5 objective evaluation, performance is quantified by a weighted sum called a performance index, which is denoted as .I. This performance index is a function of [NO,.] and l'/c· The performance index is defined such that an increase in combustion efficiency and a decrease in NO, concentration both lead lo an increase in J. That is, performance of the burner is considered optimized when J is maximized. The performance index, J , can be defined in terms of any measurable parameters of interest. For the purposes of active control demonstration, the performance index is defined as where [NO"Jm .. and "le.min are set according to the ranges expected for a particular burner geometry. The definition of the effici_ ency function term is such that an increasing reward (i.e., an increase in J) is applied as combustion efficiency increases. The purpose of the piece-wise definition of/([NO,..]) is to impose a high penalty on J above (NOxJiimii and a rapidly decreasing penalty (increasing reward) for measurements below this limit. In other words, the contribution from f([NOxJ) to J is high as long as the measured NO,.. concentration is below the specified limit. The value of [NOJ 1 imil can have practical significance, such as the permitted NO x emission limit for a particular burner application. Hence, a burner with perfect performance would yield a va,ue of J equal to 1.0 (l'/c = 100%, [NO"]= 0 ppm).
The intention of this performance index is to provide a single variable (a function of the two variables of interest) that may be evaluated and searched in real-time by a computer, using specialized optimization techniques. The way in which the performance index is defined is specific lo the particular burner configuration, and its emission character, under study. It should not, in the form presented above, be used as a universal parameter for comparing the performance of different burners, but it may be useful in comparing the performance of different configurations of the same burner.
This performance index, applied to [NOxJ and' '1c measurements taken across the stability limits of one particular nozzle configuration at 100% load, is plotted in Figure 3. The region of optimum performance (maximum J) is indicated by the white band in Figure 3. ·

Proof-of-Concept
As a demonsrrarion of the viability of the active control approach, a relatively simple problem was considered: Optimize the performance of the burner for a given geomet ry, a t a static load (100%), using a relatively simple and wellunderstood search algorithm. T hat is, determine if the active control system can find the optimum of the surface shown in Figure 3, without having knowledge of the shape of that surface, other than the location of the stability limits. The burner geometry incorporates a nozzle that injects the fuel in the same sense as the flow of the swirling air (co-swirl). This problem was presented in a previous work (St. John and Samuelsen, 1994) and is summarized here for completeness.
The optimization technique employed in this demonstration is known as a d irection-set technique. Any technique which works from an initial point in a given search space and then optimizes along each of a set of directions within that space can be classified as a direction-set technique. What distinguishes individual techniques within this classification is the process by which those directions are chosen. The method of steepest descent is one popular direction-set technique. This method is considered a first order technique because it involves calculating or measuring the local gradient and then optimizing along the line in the direction of steepest descent (or ascent). Upon optimization in one direction, the gradient is again determined and optimization proceeds in the new direction. Although powerful, the time-consuming process of measuring the gradient at each turning point prevented exploration of this method in the current research.
The direction-set technique used in the proof-of-concept stage is known as Powell's method, a zero order technique, because it does not require calculation of a gradient. The approach and results of the proof-of-concept demonstration are included in the Appendix.
Following success of this initial demonstration, more practical studies were undertaken. First, a more advanced optimization method, known as the genetic algorithm, was incorporated and applied to the same problem, and same burner geometry, addressed in the proof-of-concept. The results from this study appear in a previous work (St. John and Samuelsen, 1994) and are presented here in the Appendix.
Genetic algorithms represent a radical departure from traditional forms of optimization, such as the direction-set class of search methods. Based on natural selection mechanics, the description of this method requires language borrowed from that field of study. The process starts with a population of individuals. The fit11ess of each individual is evaluated and individuals are selected for reproduction according to each one's fitness: individuals with higher fitness have a better chance of reproduction. Each individual selected for reproduction can be represented by a character string and functions as a chromosome. Each chromosome may undergo crossover with its mate based on a finite probability that crossover will occur. In addition, each allele-represented by a single character in an individual's chromosome (string) -has a small probability of mutating (Goldberg, 1989).
In the present context, a population of individuals is comprised of twelve discrete points in EA and S' search space, either randomly or uniformly distributed, initially. An individual's fitness is that individual's scaled perform· ance index value. Individuals are presented as chromosomes, undergoing crossover and mutation, by coding each point as a ten bit unsigned integer string (ten ones or zeros). The next step involves application of both search techniques to a single burner geometry, incorporating a step change in load into the experiment, so 8 D. ST. JOHN AND S. SAMUELSEN tha t the control system's response to such a change may be evaluated. A second burner geometry was used in this study due to the observatio n of a more pronounced change in the location of the peak region following a change in load. The geometry of the second burner differs from previous work only in the fuel nozzle; the second nozzle injects fuel against the flow of the swirling air (and is referred to as the counter-swirl nozzle).
A change in load is incorporated into the control trials simply by starting at one load and a llowing the system to reach an optimum at that load, then returning the operation of the burner to it's initial operating point, initiating a change in load, and a llowing the controller to relocate the new region of optimum performance.

RESULTS
Results are submitted in several graphical forms, which merit discussion. First of all is the most basic presentation, absolute performance index value versus iteration. This type of graph is sjmply a line-plot of performance index evaluations as a function of sequential algorithm iterations. Graphs of this type are generated for both the direction-set and the genetic algorithm techniq ues. They answer the fundamental question for a particular run: Over time, was performance of the buner improved? These graphs are individually helpful in addressing the ideas of efficacy, o r whether or not the control system completed its objective. Two or more of these graphs can be helpful in comparing the efficiency of one technique to another: Did one technique reach a high performance condition sooner than another? This type of graph is referred to as an absolute performance history curve.
Another graph type is similar to the first but displays a running average performa nce rather than a n instanta neous performance, versus iteration. This gives an indication of the burner's o verall performance for a particular run, and can be used to compare the efficiency of competing optimization techniques. This type of graph is called an average perf ormance history c~rve.
The third type of result pcrscnted here is also useful in evaluating the efficacy of a particular direction-set trial. T his graph is a contour plot of the performance map, overlaid by the path that a particular direction-set trial run produced. It shows where operation of the burner started, and if the region of measured high performance was indeed a ttained by the direction-set technique. This plot type is known as a direction hisLOry graph.
The fourth graph type is similar to the direction history graph but is used for display o~ the genetic algorithm results. One plot of the performance map is ('()('."flWl. or NO, l/ produced for each generation. with the location of each 111dl\ 1dual in :1 particular generation denoted by a data marker. This shows whether or not, O\'er time, the lncattons of the in<li\it.luals converged tt) the region nf high performance. It also shows. over se,cral generations. how less-fit indi,·iduals are less like!) to be selected for repwduction than more-fit creatures. This final graph ·ypc is referred to a::; a pop11lati1111 hfawry graph Results from the proof-of-concept phase.< nd the m1tial exploration l>f the geneuc algorithm, arc included in the \ppc11di\, and sho"" he ability of tlw genetic algorithm to find the optimum region of a search sp<tce Ill a practical com buslilrn application. The true test of the <1cti,·e control system. however. is the question of ro'.lustness: Can the system n:spond to a largt•-scalc change in boundary condittllns. such as a change in th\! fuel now rate·~ The absolute and a\craged performance hi·aory for a representative trial using the direction-set method is p1·cscnte<l in Figure 4. The shaJmg changC' in the plot corresponds to the change in load from 100% to 70°·0 dming. thC' trial. This phH -.hows that. as in the case of tho; single load. performance of thC' b.1rncr ss increased over time. Following tlw load change. the search hegins ancv .. and pcrfcYtmmce of the burner is again improved Note that the aholutc: diITercncc between th~ value of the pcrfomrnnce index al the starl and near I he end is not as great as 11 was tn the proof-of-concept result~ (rig. A2). This difference anses from the fact that the per ormancc of the "ccond geometry (counter-~mirll is better tWerall than that of the first geometry (co-swirl). There 1s not us much difference between a low pcrform-<rncc con<lition and a high perlormance condition for the bdter performing burner ge,1111ctry. This ditierencc in scale is also the reason why large excursions arc e' pl.!ricnccd (note. the line is not a~ llat as it is in Fig . .\2)  direction. reflects off or a stabilit) limit. and proceeds to another edge of stabilny. These plots arc vcr} telling. fM in blllh case~ 1hc global optimum Clm<lilJOll$ is nut reached. The system essentially get-; hung up on a local peak. llr can not find the din.:ction in which lo continue searching (which would be exactly along the stability limit linr:J. This <kmonstratcs two Wr) 1mportan weaknesses in lhc dircction--;ct technique: First. if the com roller reaches a local peak. 11 wi I remain there; second. if a path of 2.sccnt exists fror1 a po111t. but 1t 1s namm. the algorithm may lake a long time finding that path.
The pe1forma111.:c history results Cab~olutc and a\crage) for a typical genetic algorithm search with a change in load arc shown in Figure 6. Note tile Jagged nature, which is typica I of the gcm:tic algorithm's clrnractcr. Tl\ dillicull tll tell much from this plot. o ther than performance of the burner has h!.!en imprnYed O\'cr time. and this improvement is repeated following a change 111 load.
Figures 7a and 7b are the population histories for th1s same trial for 100% and ?o n,~. load. respectively. Some very inten~sting obserrnt10ns can be made fnim these figures. J-irst of all. J· igurc 7a shc.ll\s thl.! familiar genetic algorithm bcha\'ior: :-tarting from a random d1stnbutic•n of twelve indi\'iduals. more-li t individual" propagate and less-lit mdi\ 1duals die off. H) the fi'th generation. i11 fact. all but three individuals arc clustered about the rcgi1lll or the global optimum. where performance is at its peak for I his burner. The outlyin!! ind1\ 1duals are <lue to the mutatwn effect.
Looking now at Figure 7b. the load has changed (along with the stability limits) and the sixth generation is re-initialized in a random distribuuon . The sun ival of the fittest behavior of the gen1:tic alg<irithm can be follll\\'Cd through the genl'ralions again. and hy the 1enth generation. all of the indi\ iduals arc crowded ahout the region of peak performance. For a more in-depth c,nnparhon of the t\\ o techniques. 1cfer to the results summari1cd in the Appendix.

SUMMARY
The goal of de\ eloping an acti\c l'Ontrol approach that will :main operation of a hurncr at tb l1ptimum pcrft)mrnncc. and that will maintain peak operation ,gray numerals ind1ca1c clustering.
following a change in houndary <.:1.luditions. has been reali/cJ. The approach presented 1 1crcin has been shm\ n to adjust hurncr in kl parameters in order lo optimi/e 1\0, emission-. and combustion eflkicnc) . Thi-. \\,ls accomplished by dcfinmg a trade-off between c0mhustinn el'liciency and "i()_ concentration in the form of a performance index. The performance 111dc\ fun ctions as a single search criterion. to \\ hich two search techniques were applied in the current '' ork. compared to a zero-order direction-set method. The main advantage of the genetic algorithm seems to be its ability to locate a global optimum more reliably than a direction-set technique, without the tendency to settle on a local ridge. While these results are encouraging, care must be taken in applying them to the general problem of practical burner optimization. Certainly, each burner application will have peculiar characteristics that must be accounted for in the development of a control scheme. This research does not indicate that either the direction-set or the genetic algorithm search technique can be applied to the practical control of a burner. Rather, this study should be seen as a first step, providing guidance to future research into the development of a practical application of active control. The achievement of such a goal will benefit from a refined search mecha nism, and an improved emissions and stability sensor.
The system developed in the present work continuously searches for the optimum operating condition of a burner, and successfully achieves optimum performance even following a change in load. While the present system optimizes emissions, it does so without any knowledge of that burner's particular emissions character. The only requirement, in the present case, is knowledge oft he stability limits. The successful be ha vi or of the control scheme following a large-scale change in boundary conditions (fuel load) implies that the system would respond to smaller-scale changes in boundary conditions as well (fuel composition, equipment degradation, etc.).

APPENDIX: POWELL'S METHOD IN 2 DIMENSIONS
Powell's direction-set technique was first proposed as a method for minimizing a mathematical function (Powell, 1964). To explain Powell's method in two dimensions, first consider an objective function, F, which is a function of two variables, X 1 and X 2 , represented by the vector, X. Now consider a search direction, represented by the normalized vector, S. Thus, the direction along the X 1 coordinate would represented by S=(l,O), and a search in the direction 45° to the X 1 and X 2 directions would result if S = (I, I). Given an initial position, X;, and an initial search direction, S;, a new position, X 1 + 1 is found by maximizing (or minimizing) the objective function along the line defined by the search direction. Computationally, optimization is accomplished in an iterative fashion by finding the (scalar) value of a 1 that produces a value of X; + t> which maximizes the objective function, F, according to T his is, in fact, the general optimizing strategy for all direction-set methods. The direction-set method chosen for this research is a zero order technique, because it requires evaluation of the objective funct ion (performance index) only. This method is a modified version of a powerful, popular, and wellunderstood technique known as Powell's method. Figure  In discussions about search processes of this modified type, some clarification should be made regarding numbering convention. A position in the search space is still denoted by the vector, X = (X 1 , X 2 ) , where X 1 = S' and X 2 =EA. In the modified approach, each position in the search space has two numbers associated with it, Xij. The first index, i, corresponds to the search iteration, just as in the discussion of Powell's method. For the initia l position, i = 0. After maximization along the initial direction, a 0 , the new value of i is 1.
And so on. The second index,}, refers to steps within a search direction. Hence, the first position is denoted X 0 • 0 , and the first evaluation of performance is J o.o· Following the first step alonga 0 , the} index is incremented by one, but the i index does not change until the search direction changes. So, if it takes ten decrease (or a stability limit 1s encountered) thr<:e times. Thus, along. a unimodal linl.' this search will generate a \':llU<· of X that rl.'sults 111 a maximum 'alue 1lf J along that line.
This 11.~hnique has the undesirable clwractcristic of settling. on the first peak cncnuntcrcd. Howe,·er, the hill climbing technique is employed because c\aminatil"1 of the character of the J surface reveal-; an essential!) unimotl•tl surface with rcsrect to swirl intcn,,ity and excess air Hill dimbing on a u1111nodal surface ensures that the first maximum encountered ;dong any line is the globnl maximum on that line.
The direction history for lhe same trial displayed in Figurt~ A2 ~own in hgurc AJ. Keep in mind thal the control prngram ha~ no knowledge of the shape <'f the performance map {conlnurs) during its operation': the map 1s ,:;hown for refcn:ni;e only Operation of the burner starts nlT in a n:g1on of rclat1\ ely low performance. I nitiali.1cd along a dmxtton of JJJ . the search rrocecd.; umil a constrauu 1s encountered (1cro percent excess air. in Lh1s case). al which point the system changes dirccLion and hunts along a rath that is 90 to the fir.;t direction. Search along this second dm.:ct1on takes the opcraLion of the hurncr up to the region of peak performance. \\here performance i-; essentially optimzcd Search conltnucs. however. in difleren1 directions, until a slight increase 1s cncounrcred The tnal was halted after 83 itcrauons. Figure ·\4 1s the average performance history curve lor this same trial. indicating average performance of the burner up to a given point l-1gurc A5 shows both the absrilutc and the J\'Cragc performance h1s1orics or a typical application of the genetic algorithm. Nole lhe relativd) erratic tm:c oflhc absolute pl'rformance mdex as compared to Figure A2. This is due to lbc genetic algorithm's cvalu:uion d an entire population al once. The genetic ~lgonthm is not concerned with the order in \\.hich evaluations .ue made. Jt functions. rather. from the whole popula11on at once. taking all pe""formance \'alucs in parallel and generating a new population hased on the relative pcrfom1ance of 1 1 1C previous population. I Jenee. the separalton of the genetic algorithm's performance histor) curve into sections 1s demarcated by \·ertical lines in the figure. All hough probably of concern 1n a practical sense. the jagged nature of the absolute pcrfom1ancc line is not impnrtalll to the func•ion llf the genetic algorithm. \\hat 1s important 1s the average performance. after each entire populatton This average performance 1s shown to increase steadily. I-' 1gurc A6 is the population h1:aory for this same run. This figure is perhaps more illustrati\·e than Figure A5. The first generation is cssenually unifon'l <icross the search space. In the sccon<l generation. it is clear that some less-fit indh iduals ha\'c die<l off. By the third generation. there is a dear migra110·1 toward the reg.ion of peak performance and in the fourth generation all bu1 three of lhe twelve individuals have converged to the sume area of high performance.
The three outliers CHn be attrabuled to tw0 sources. One or lhc rogues, at EA= 17°/o and S' = 0.44. is simpl) u stubbt)rn mdtrn.lual. rhis parltcular point has been carried through all the Wa} from the initial generation. with little varianon. The reason thi!> indi\ldual persists rs becauc;e each in<lrvrdual. even a poorly fit one, has a finite prnbabilit) of being reproduced il simply got lucky. Ifs likely that it \\oukl die offrn subsequent generations, although ii is finitely rossihlc thal it would nc\"er dre off The other two outlier" were produ1.:c<l by a sepllrate mechanism: mutation Rccall 1hat after a populauon's fil'.1ess has been C\ialuatcd. individuals arc selected for reproduction. then they t:; ..: . are potentially crossed-over wilh their mates. and ea{·h hit al011g an indi' idual's coded binary string is subjected to potential mutation. These tv. o individuals arc the product of I his process. Thus, the genetic algorithm has hecn successful in demonstrating the fundamental rec uirement of an active contrnl system as \\.ell: performance llf !he burner. under a stat11.: fuel load and burner geometry. has been steadily increased lwer t me.
Figure,\ 7 is a plot of both a vcragc performance of the direction-set and 1 he genetic algorithm cases. Note that even after 48 iteration'\ the average per-fom1ance of the direction-set method has lllll surpassed and the overall performance of the genetic algorithm.
The behavio1 of the two t} pica) trials discussed so far deserve some "'what-if'' discussion From other allcmpls, the results of whil'h arc not presented herc.1t 1s clear that the genetic algorithm will perform essentially the same as in thb typical case: erratic start, converging after a few generations. but almost always wJth a fe,, outliers. The direction-set technique. however. could perform quite differently. It should be obvious that this method depends heavily on two initial parameters: the starting location and the starting scan:h Jirection. One can imagine the lrinal search that starts in the peak region. In this cas.:. the goal is achieved by default. e1ltaining and maintaining peak operations wilholll any search. Or. consider starting a search in a ""poor" performing region. but initializin!! the search d1rcction headed exactly for the region of peak performance. For this scenario. peak performance would be achieved much earlier than in the re~;ults pre~;ented. So, the apparent dominance of the genetic algorithm must be tempered with the stalcmcnt that there arc circumstances \\.here the direction-set could pc.:rform more cfficielllly than the genetic nlgornhm. but that bcha\ iour is not guaranteed The genetic algorithm. on the other hand.\\ ill provide relative!) consistent behavior. and has the added feat urc of locating the global optimum. steps along the initial search direction to maximize J, then the final position is denoted X 0 . 10 , and the final evaluation of J is J o.io· T he fina l position along a search direction becomes the initial position in the next search direction. For example, X1.o is given the value of X 0 . 10 , J 1.o is evaluated and the search continues in the next direction, a 1 • In Figure A I, ··maximizing J along the direction a;" can be accomplished through a variety of methods, including polynomial approximation or the golden section method (if the minimum is bracketed). For practical reasons, the method of line maximization used in this study is a simple hill climbing technique. Starting at a given Xi.O• the settings of EA and S' are stepped along the d irection, !X;. Search proceeds in finite steps as lo ng as the value of J continues to increase. If the performance index value decreases, or if a stability limit is encountered, the search d irection is reversed. A new d irection is determined and a new search initiated only after the value of J is found to