Compressor Surge: A Limit Detection and Avoidance

Problem

Manuj Dhingra∗, James Armor†, Yedidia Neumeier‡, and J.V.R. Prasad§

School of Aerospace Engineering,

Georgia Institute of Technology,

Atlanta, GA 30332

Compressor surge control is an important part of intelligent engines. A new perspectiveon this problem is presented. The problem is cast as a limit avoidance control. A singlepressure sensor is used to monitor the uncertain surge limit, via an innovative methodusing the so called correlation measure. The stochastic nature of this measure has beenanalyzed and a model for the same has been developed. The model is incorporated into adigital simulation of a turbo-shaft engine. A Monte-Carlo simulation has been carried outto investigate the impact of parameters associated with the stochastic model. The limitavoidance formulation is demonstrated on a laboratory axial compressor facility.

I. Introduction

Limit detection when employed in the context of aerospace systems typically refers to the flight envelopelimits. However, flight envelope limits are not the only limits of concern to the aerospace engineer. Thoughnot always modeled as such, compressor surge and rotating stall impose limits on gas turbine operation.On the compressor map (see Figure 1), this limit is represented by the “surge line” or the “surge limit”.The surge line demarcates the regions between stable and unstable operation of the compressor. To date,numerous efforts,1–6 have been undertaken to analyze, understand, control and/or mitigate the impact ofthese phenomena. However, to the best of our knowledge, the solution adopted for production engines,remains open loop avoidance of the limit in question. This is accomplished by establishing the operatingline well below the surge limit, where the distance between the two is designated as the stall margin. Theopen-loop nature of this avoidance, the uncertain nature of the boundary, and the detrimental effect on theengine on crossing the surge line all necessitate an overly conservative margin. Inlet distortions, e.g. duringan aggressive maneuver, lower the stall line. This effectively brings the operating point closer to the stallpoint and thus contributes to a large margin requirement.

The various studies in stall control, despite not resulting in an industry adopted solution, have contributedgreatly towards our understanding of the flow phenomena involved.

The need to reduce the stall margin is two-fold. First, for many designs the point of maximal efficiencylies within the buffer zone. Thus from a steady continuous operation perspective, it could be beneficialto move the design point into the currently unavailable region. Secondly, the conservative stall marginnegatively impacts the emergency response of the engine. As an example, aborted carrier landings of fixed-wing planes, or auto-rotation recovery for helicopters both demand a sharp increase in thrust or power fromthe gas turbine. The open-loop scheduling while keeping the engine safe even in the worst case scenario,significantly increases the engine response time.

In most cases a reactive control action, executed after the surge line has been crossed is unacceptable.Any occurrence of such an event raises safety concerns and adds to the maintenance costs. The guidelinesusually require dismantling of the engine and at least a visual inspection after any reported event.

∗Graduate Student†Graduate Student‡Member AIAA, Senior Research Engineer§Associate Fellow AIAA, Professor

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AIAA Guidance, Navigation, and Control Conference and Exhibit15 - 18 August 2005, San Francisco, California

AIAA 2005-6449

Copyright © 2005 by Manuj Dhingra. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

(with Active Control)Expanded Limit

EfficiencyContours of Constant

Lines of ConstantRotational Speed

Surge

Limit

Pre

ssur

era

tio

Mass Flow Rate

Current Limit

Figure 1. Expected performance en-hancement with active control.

The problem of compressor surge control is thus that of ”prox-imity to the limit” detection and its subsequent avoidance. A modelfor the compressor system is available since the mid 1980s.7, 8 Thismodel while illustrating the qualitative behavior of the system, isunable to capture with significant accuracy, the quantitative as-pects of compressor surge and rotating stall. Moreover, experimentalwork9, 10 in compressor stall has revealed a non-modal, “spike-like”route to stall which is not captured by the model at all. Furtherexperimental work11, 12 has suggested that under certain conditions,this spike-like stall initiation may be the dominant route in manymodern high-speed compressors.

In the present work, it is shown that limit detection, at least withregards to the compressor surge and stall, does not necessarily needa deterministic model of the system. This is done by developing astochastic model of a previously developed stall margin indicator.This indicator, hereafter referred to as the correlation measure isbriefly described. The statistical properties of correlation measureare explored in order to obtain a stochastic model. This model isthen incorporated into a digital simulation of a small turbo-shaft engine. The simulation is used to identifythe trade-offs involved in the choice of a threshold value of the measure, associated with the control actuation.The correlation measure based scheme is experimentally verified on the GT-Axial Rig. Typical results forboth “ride the limit”, as well as “limit avoidance under fast transient” cases are presented.

II. Stochastic analysis

A correlation measure which quantifies, in a way, the distance to the surge line has been previouslydeveloped.13 The measure is defined on the basis of the repeatability of the pressure time-trace, as observedby a sensor located over the rotor. The pressure time-trace is mostly periodic when the compressor isoperating away from the surge line. However, as the boundary of stable operation is approached, thisperiodicity is progressively disrupted. The loss of periodicity is quantified via a modified form of auto-correlation. Mathematically, the correlation measure can be expressed as

C[n] =

∑ni=n−Nwnd

P [i]P [i − Nshaft]√∑ni=n−Nwnd

P 2[i]∑n

i=n−NwndP 2[i − Nshaft]

where n is the index of current sample, P [i] is the digitized pressure, Nwnd is the size of the correlationwindow and Nshaft is the number of samples in one shaft rotation.

A. Stochastic Model

0 0.2 0.4 0.6 0.8 10

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rrel

atio

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easu

re

Time (s)

CorrelationThreshold (0.70)

Time Between Events

Figure 2. Random occurrence ofevents. An event is defined as down-wards crossing of a threshold.

So far it has been shown that the average value of the correlationmeasure decreases monotonically with stall margin.13 Although im-portant in its own right, average value is not a good basis for activeavoidance control. An average value is slow to respond by definition,and would be unreliable during transients with rapid variations install margin.

An inspection of the experimentally obtained correlation measureshows that along with a change in the average value, the correlationmeasure exhibits a tendency to dip from time to time. These dipsincrease in frequency and magnitude as the compressor approachesits limit of stable operation. The appropriate approach, then, is tomonitor the dips in the correlation measure and generate an alarmevent whenever the measure falls below a specified level. This idea isillustrated in Figure 2, which shows the time trace of the correlationmeasure. The apparent randomness of the dips in the correlation

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measure leads to the alarm events that are randomly distributed in time. In a possible implementation, acontroller would react to these alarm events by initiating suitable preventive actuation. Consequently, thetime between two consecutive events (TBE), as identified in Figure 2, is an important metric. A stochasticmodel is then sought which captures the distribution of the events and its relationship to the stall margin.

Motivated by the Poisson process, along with experimental observations, it is proposed that TBE isexponentially distributed, and its distribution function is given by,

F (τ) = 1 − e−µτ

with the parameter µ defined as,

µ = limT→∞

N(0, T )T

where τ is the time between consecutive events, and N is the total number of events in time period (0, T ).

B. Model Validation

In this section, the validity of the proposed stochastic model is evaluated via analysis of sets of data acquiredon the GT-Axial Rig, a laboratory axial compressor facility. As part of each set, data is acquired for differentsteady operating conditions characterized by their stall margins.

As a first step, Figure 3 shows the distribution function of the correlation measure for different stallmargins, under steady state operating conditions. The results show that the mean value of the correlationmeasure decreases while the variance about the mean increases as the stall margin is decreased. Further, itmay be noted that the different distribution curves appear to be of the same family. However, the existenceor form of this family has not been identified to-date. To illustrate the uniqueness of the underlying process

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

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Cu

mu

lati

veD

istr

ibu

tio

n

SM 14.0%SM 13.1%SM 11.5%SM 8.5%SM 5.2%SM 1.9%SM 1.1%

Figure 3. The cumulative distribution of the Cor-relation Measure.

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lati

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istr

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SM 14.0%SM 13.1%SM 11.5%SM 8.5%SM 5.2%SM 1.9%SM 1.1%

Figure 4. The cumulative distribution of TBE.The threshold is set at the average correlationmeasure for each case.

that characterizes the correlation measure, and its independence of the compressor steady state, the statisticsof the time between events has been analyzed. As mentioned earlier, an event is defined as the downwardcrossing of a given level, CTh by the correlation measure C(t). An specific example of the distributionfunction of time between events (TBE) is presented in Figure 4. Each curve corresponds to steady stateoperation of the compressor at a different stall margin. For each stall margin, the threshold level CTh isset equal to the mean value of the corresponding C(t), and is thus a function of the stall margin. For thisspecial choice of threshold, all the TBE distributions collapse to a common function, irrespective of the stallmargins. Consequently it may be concluded that the variation of C(t) about its mean value, under steadystate conditions, is driven by an invariant process.

If the threshold level CTh is kept fixed across all runs, a more pertinent choice, the situation is slightlydifferent. The results in Figure 5 correspond to a fixed threshold level of 0.72. No event is observed for stallmargins higher than 5.2%. As the compressor is moved closer to its surge limit, the margin reduces from5.2% to 1.1%, the probability of an event occuring in a given time increases. As an example, for a 100ms time

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interval, it increases from close to zero to about 0.8. This is a consequence of an increased number of events ina given time period. Recall that the proposed stochastic model contains the single parameter µ, which is the

10−3

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Cu

mu

lati

veD

istr

ibu

tio

n

SM 5.2%SM 1.9%SM 1.1%SM 5.2%model predictionSM 1.1%model prediction

Figure 5. The cumulative distribution of TBEwith CTh of 0.72. A comparison with the proposedmodel is shown.

0 2 4 6 8 10 12 140

50

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450

Stall Margin (%)

Ave

rag

eN

o.O

fE

ven

ts(µ

)

0.60 − Threshold Level0.650.700.750.800.85

Figure 6. Variation of the average number ofevents with stall margin. The threshold valueplays a dominant role in this relationship.

average number of events per unit time. The fairly close agreement of the predicted and the experimentallyobtained curves, as observed in Figure 5, suggests that the proposed model is valid for the problem at hand.

01.0 01.7 04.8 08.10

100

200

300

400

500

600

700

Stall Margin (%)

Ave

rag

eN

o.O

fE

ven

ts(µ

)

Set 1Set 2Set 3Set 4

Figure 7. The day to day variation ofthe observed average number of events.

Similar analysis for different threshold levels in this as well as othersets of data shows that TBE distribution for lower stall margins isconsistently captured by the model. On the other hand, for the largerstall margins some discrepancy between the two has been observed.

The parameter µ is central to the model, and its relationshipwith stall margin as well as threshold level CTh has been analyzed.The results presented in Figure 6 summarize this relationship. Eachcurve corresponds to a different threshold level. As this level CTh

is decreased, fewer events are observed, with the first appearance ofan event shifting to lower stall margins.

In order to investigate the repeatability of these results, averagenumber of events for different stall margins have been calculated us-ing four different sets of data. These data sets were acquired on dif-ferent days with varying ambient conditions, spread over two weeks.The results are presented in Figure 7 and exhibit good consistencyfor the cases studied.

III. Simulation Studies

The simulation studies conducted as part of the present work have been performed via a digital simu-lation of a turbo-shaft gas turbine engine. This simulation has been developed on the basis of a non-linearcomponent-type model of the T700-GE-700 turbo-shaft engine. The relevant model is described in detail byBallin,14 and formed the basis for real-time simulation studies in the cited work.

The model has been extended for use in surge avoidance studies.15 It has been made surge-capable byincluding a dynamic equation for the mass-flow rate through the compressor. Moreover, the compressormaps used in the model have been extended beyond the stall/surge line. This extension of the compressormaps is believed to be reasonable for a narrow region in the proximity of the surge line. Essentially, thesimulation is not able to capture the in-surge dynamics of the system, and its results are meaningful onlyfor a “surges” or “does not surge” type of analysis.

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A. Available Improvements

A helicopter rotor is designed to be run over a narrow range of RPM for its entire operational regime. Forthe rotor RPM to remain nearly constant, any variation in aerodynamic loads has to be matched by theengine. The aerodynamic torque loading is a function of flight conditions and pilot controls. If an increasein torque required, e.g. due to increased collective, is not met by the engine, the rotor RPM would go down.This decrease is often referred to as the RPM droop. The transient performance of a helicopter propulsionsystem can thus be benchmarked in terms of its ability to minimize RPM droop.

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500

Time (s)

To

rqu

e(l

b f−ft)

,ref

.to

eng

ine

shaf

t

Qdmd

Qpt

Figure 8. Variations of demanded and availabletorque with time for the nominal case.

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Mass Flow (lbm

/s)

Pre

ssu

reR

atio

Comp. Char.TrajectoryStart Pt.End Pt.

Figure 9. The trajectory for the nominal enginewith acceleration scheduler.

The conventional stall prevention during acceleration transients takes the form of a scheduler. This accel-eration scheduler restricts the maximum allowable fuel flow, as a predetermined function of the compressorstate and its inlet conditions. In order to illustrate the impact of the acceleration scheduler, and implicitlycompressor stall, on engine transient response, an autorotation recovery maneuver has been analyzed. Thisspecific case has been chosen to illustrate both the need for the scheduler and the increased performancefor the ideal case when it is bypassed. The maneuver involves a stop-to-stop step command in collective,switching it from the lower to the upper stop. This collective command translates to a step change in thetorque demanded from the engine. The response of the nominal engine along with the torque demanded aregraphed in Figure 8. The corresponding variations in compressor pressure ratio and inlet mass flow rate areshown as a trajectory plot superimposed on the compressor map in Figure 9. As expected, the accelerationscheduler protects the system from surge. This protection, however, comes at the cost of a significant droopin power turbine RPM, and in turn a large droop in the rotor RPM, as seen in Figure 10 (nominal case).This RPM droop is attributed to the lag in the engine torque response. The undesirable consequences ofthe RPM droop are two fold. The loss in rotor RPM means a loss of thrust, which is especially undesirablegiven the requirements of the maneuver. Moreover, the loss of main rotor RPM is also accompanied bya proportional loss in tail rotor RPM. This reduces the pilot’s rudder authority, sometimes leading to theincorrect inference of a tail rotor failure. Together, or even individually, these factors seriously impact thesafety of flight.

If the acceleration scheduler is bypassed, there is a significant reduction in the RPM droop for the samepilot command. This can be seen in Figure 10, which compares the power turbine RPM for the two cases.Moreover, due to a sufficient available surge margin, the compressor remains free of surge for the entiretransient, as seen in Figure 11.

The results so far show an incomplete picture. This dramatic gain in engine performance is valid only fornominal inlet and compressor characteristics. Several factors, including inlet distortion, deterioration withage, and ambient conditions could degrade the compressor performance. To capture this deterioration, thecompressor characteristics have been scaled down. The pressure-ratio at a given mass-flow rate and speedis multiplied by a factor of 0.94. This roughly reduces the surge margin for a given operating point by 7%.This degree of degradation is normal, and by no means exaggerated.

If this slightly degraded engine is subjected to the same step change in torque demand, and the scheduler

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0 5 10 15 20 25 30 35 40 45 5050

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120

Time (s)

Po

wer

Tu

rbin

eR

PM

(%d

esig

n)

Nominal Engine: Passive ControlMaximum Performance

Figure 10. Power turbine RPM variation withtime.

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Mass Flow (lbm

/s)

Pre

ssu

reR

atio

Comp. Char.TrajectoryStart Pt.End Pt.

Figure 11. The trajectory for the nominal enginewithout acceleration scheduler.

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Mass Flow (lbm

/s)

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ssu

reR

atio

Comp. Char.TrajectoryStart Pt.End Pt.

Figure 12. Trajectory for the degraded enginewithout acceleration scheduler.

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Mass Flow (lbm

/s)

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ssu

reR

atio

Comp. Char.TrajectoryStart Pt.End Pt.

Figure 13. Trajectory for the degraded enginewith acceleration scheduler.

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is bypassed, the compressor enters a surge cycle. This can be seen in Figure 12, where the trajectory issuperimposed on the compressor map. On the other hand, when the acceleration scheduler is retained, aswith the nominal engine, the degraded engine is free of any compressor instability for the duration of thetransient (Figure 13).

Clearly some form of surge prevention is required as a part of the engine control system. A passive,predetermined scheduler severely impacts the engine transient response. An active stability managementalternative is hence sought, which can save the engine during a degraded scenario, while improving itstransient response.

B. Model Implementation

The proposed stochastic model for the time between events has been incorporated into the simulation. Thisimplementation is based on Random Number Generator (RNG) proposed by Marsaglia and Tsang,16 the socalled ziggurat algorithm. The stochastic nature of the correlation measure suggests a need for a Monte-Carlo simulation. In order to facilitate this, the RNG is seeded with a random number obtained via the unixfacility /dev/random at the start of each run. This ensures that the RNG generates a different sequence ofrandom numbers with every run of the simulation program.

Two parameters have been incorporated into this implementation: the threshold level CTh, and aninformation time delay Td. The threshold level CTh determines the functional relationship of µ to the stallmargin, via interpolation of the experimentally obtained data (Figure 6). This parameter is expected to beimportant for limit avoidance control.

The second parameter, Td, has been introduced to incorporate the practical aspects of control implemen-tation. The delay Td is in addition to an existing delay associated with fuel transport phenomena. Hence Td

reflects any pure time delay present in a control system due to inevitabilities like loop rates and data transferrates. The correlation measure is calculated via a fast algorithm, and can be carried out at rates upwardsof 1 kHz on moderately fast hardware. Consequently, this calculation is expected to have a negligible timedelay contribution.

C. Results

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/s)

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ssu

reR

atio

Comp. Char.TrajectoryStart Pt.End Pt.

Figure 14. The trajectory for the degraded enginewith active fuel control. The stochastic model pa-rameters are CTh = 0.82 and Td = 10ms.

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wer

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rbin

eR

PM

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esig

n)

Degraded Engine: Passive ControlDegraded Engine: Active Fuel ControlMaximum Performance

Figure 15. The comparison of RPM variations inthe degraded engine between the open-loop accel-eration scheduler and active fuel control for surgeavoidance.

In order to demonstrate the feasibility of surge limit avoidance, the results from a successful run arepresented. A simple control law has been used, which cuts back the fuel when an alarm is raised by thestochastic model. These results correspond to a threshold level CTh of 0.80 and an information time delay of10ms. A trace of the engine trajectory on the pressure rise, mass flow rate state-space is shown in Figure 14.When the compressor gets close to the surge line, active fuel control keeps it within the safe region. In

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Figure 15, a comparison of the RPM droop in active control case to the nominal, as well as the unrestrictedcases shows that the active control enables a nearly maximum level of performance.

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Su

cces

sR

ate

Critical Delay

0.700.720.750.770.800.820.85

Figure 16. Monte-Carlo Simulation results: Suc-cess rate as a function of information delay Td andthreshold CTh.

Once the performance benefits and the feasibility oflimit avoidance are established, further studies have fo-cused on the impact of the two parameters, namely, theinformation delay Td and the threshold CTh. As part ofthe Monte-Carlo simulation, a hundred runs have beenperformed for each pair of CTh and Td values. The re-sults of these studies are condensed in Figure 16, whichshows the success-rates as a function of information de-lay for different threshold levels. Recall that this infor-mation delay is in addition to the fuel transport delayof 15ms, already part of the simulation. In general, thesuccess-rates are fairly independent of the delay for thelower part of its range, up to about 30ms. This representsthe fact that for this range of delay, a successful outcomeis dependent on the probability distribution of the timebetween events. In the upper range of time delay, from40ms to 75ms, success-rates fall with an increase in de-lay. Moreover, there exists a critical information delayvalue, Td crit, beyond which surge limit avoidance maynot be reliably achieved via active control, irrespective ofthe chosen threshold.

It is important to note that this critical value is not only a function of the system in question, but alsothe particular transient in consideration. Specifically, “fast” transients would tolerate smaller critical values,while in “slow” transients one may be able to get away with larger time delays. Consequently, the results inFigure 16 show the generic features of the problem and are not indicative of actual absolute values.

IV. Experimental Evaluations

The axial compressor rig located in the School of Aerospace Engineering at Georgia Institute of Technol-ogy has been established to facilitate control-oriented studies in surge and rotating stall. It includes an inletduct, a single-stage axial fan, a compressor discharge duct, a plenum, exhaust duct and a throttle. The lowspeed ducted fan delivers a pressure ratio of about 1.1. It has 14 blades on the rotor and 11 blades on thestator. The design speed is about 11800 RPM at which the tip Mach number is about 0.3. The plenum is alarge metal chamber, capable of withstanding pressures up to 400psi. It incorporates a self-entraining burnerand is thus capable of simulating a combustor. The compressor load is varied by a butterfly valve down-stream of the plenum. The compressor is known to have a very abrupt characteristic near the stall inceptionpoint. The compressor is instrumented using six pressure sensors of high natural frequencies. The sensorsare mounted flush to the inside of the compressor casing in order to maintain a large overall bandwidth.Significantly, all the measurements obtained as part of the present work are from a single sensor.

A. Results

The GT-Axial compressor facility has been used to demonstrate correlation measure based surge avoidancescheme. In the results presented here, a very simple control scheme has been utilized. A common strategyis employed for two cases: Ride the limit, and surge line avoidance under fast transients. An alarm event isgenerated when the correlation measure C(t) crosses a selectable threshold level. An open-throttle controlaction is triggered by an alarm event. The controller waits for a fixed short interval of time, after whichthe throttle is closed at a fixed rate, up to its operator commanded value. This open-pause-close strategy isfollowed for each observed event.

The objective for the “ride the limit” case is to keep the plenum pressure close to the maximum deliverableby the compressor, without crossing the stall boundary. This simple control law performs adequately in thiscase and can hold the system close to the stall line indefinitely. However, for the sake of clarity, Figure 17 onlyshows results for a 245 second segment. The system is held at about 4 − 5% stall margin by the controller.

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ress

ure

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rott

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ntr

olP

aram

eter

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Threshold (0.70)

Figure 17. GT-Axial Rig Results. The sim-ple open-pause-close control law keeps the systemclose to its maximum pressure operation.

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CommandControlled

Figure 18. GT-Axial Rig Results. The open-pause-close controller is able to avoid surge underthrottle transients.

The operator commanded value is deliberately set deep into the stall region, ensuring that any deficiencyof the control method will be manifested as a surge in the system. Further, the intermittent nature of thealarms is evident in the lower chart of Figure 17. As noted, the threshold level for the correlation measurehas been set at 0.70 in this case.

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leP

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Figure 19. Importance of threshold parameterCTh for surge limit avoidance. A poor choice cou-pled with stochastic nature of alarms can lead tofailure of the controller.

The “fast transient” case is a ramp command whichcloses the throttle from its fully open position to one cor-responding to deep stall in two seconds. As a matterof fact, the system reaches the stall line in about a sec-ond into the transient. This case is intended to emulatetransients analogous to those studied via the simulation.Consequently, the objective is to prevent the system fromsurging while following the operator commanded value asclosely as possible. A typical run, with threshold levelset at 0.75 is shown in Figure 18. As can be observedin these results, the controller prevents the system fromcrossing the surge line. Similar to the “ride the limit”scenario, with continuous active adjustment of the throt-tle, the controller tries to achieve the maximum pressuredeliverable by the system.

In order to emphasize the stochastic nature of the cor-relation measure based alarms, a sequence of ramp tran-sients have been performed. The results are summarizedin Figure 19. Although the figure contains roughly tentransients, active surge avoidance failed in two out of thetwenty transients performed. This translates into a 90% success rate at the selected threshold level of 0.75.This value was deliberately selected to showcase the importance of the threshold level in active surgeavoidance. The success rate, as shown via the simulation studies, is a function of the threshold value andcan be improved by adjusting the said level.

V. Conclusions

The work to-date demonstrates the advantages of bringing the limit avoidance perspective to compressorstability management. The success of this approach is dependent upon the method used for limit detection.In particular, the compressor stability limits, unlike say the flight envelope limits, are uncertain and difficultto predict. In the present work, correlation measure is used to indicate proximity to the surge line. Of note is

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the fact that this measure is stochastic in nature and can be used to generate “alarm” events. These eventsare randomly distributed in time. This distribution is significant because the limit avoidance actuation istriggered by the “alarm” events. The highlights of the current work are,

• A stochastic model for the time between “alarm” events has been proposed and validated. It has beenfound that the events generated by thresholding the correlation measure are exponentially distributedin time.

• The stochastic model has been incorporated in a digital simulation of a turbo-shaft engine. The result-ing simulation has been used to study the impact of information time delay and the event distributionon limit avoidance.

• The choice of threshold value plays an important role in compressor stability limit detection andavoidance. An appropriate choice results in successful instability avoidance, which can translate intosignificant performance gains.

• The key ideas associated with the proposed approach to compressor control have been experimentallyverified. This validation is in the form of demonstration of closed-loop control on the GT-Axial Rig, alaboratory axial compressor facility.

The limit avoidance studies so far have used very simple control laws. The validity of “proximity to thelimit” detection method has been established. This enables the focus to be shifted to the development ofintegrated control laws.

VI. Acknowledgments

This study was conducted under the NASA URETI on Aeropropulsion and Power Technology (UAPT)and the GE Aircraft Engines University Strategic Alliance (GEUSA) program at the Georgia Institute ofTechnology. Discussions with Mr. Peter Szucs and Mr. Andrew Breeze-Stringfellow of GEAE are gratefullyacknowledged. Dr. Carlos J. Riviera provided invaluable help with numerical ODE solvers.

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