THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS Three Park Avenue, New York, N.Y

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1 THE AMERCAN SOCETY OF MECHANCAL ENGNEERS Three Park Avenue, New York, N.Y GT-63 The Socety shall not be responsble for statements or opnons advanced n papers or dscusson at meetngs of the Socety or of es Dvsons or Sectons, or prnted n ts publcatons. Dlecusson s prnted only lthe paper s publshed n an ASME Journal. Authorzaton to photocopy for nternal or personal use s granted to lbrares and other users regstered wth the Copyrght Clearance Center (CCC) provded 33/artcle s pad to CCC, 222 Rosewood Dr., Danvers, MA Requests for specal permsson or bulk reproducton should be addressed to the ASME Techncal Publshng Department. Copyrght by ASME An Rghts Reserved Prnted n U.SA HYDROMECHANCAL CONTROL FOR A VARABLE DELVERY, POSTVE DSPLACEMENT FUEL PUMP El gupplotn Tmothy J. Gaudet Prncpal Engneer Hamlton Standard Dvson of Unted Technologes ABSTRACT Fuel pumps for gas turbne engnes have tradtonally been fxed delvery, postve dsplacement type pumps. The crtcal pump szng crtera are typcally the fuel flow and pressure needed for engne lghtoff at crankng speeds (approxmately 0% of full speed). However, these pump szng crtera result n excess fuel delvery at hgher engne speeds and alttudes. Ths excess fuel s typcally bypassed back to the pump nlet, resultng n sgnfcant fuel heatng. n contrast, a varable delvery, postve dsplacement fuel pump has the ablty to vary delvery flow, to thereby match engne demands for a wde range of engne speeds and alttudes. Ths elmnates the excessve fuel delvery and resultng heat generaton nherent n fxed delvery pumps. An approach to controllng fuel flow delvered to the engne s presented n whch the dfferental pressure across a fuel meterng valve s regulated by smultameouslyvaryng the pump dsplacement and a small amount of bypass flow. Ths approach results n mproved transent response and Steady State accuracy at all operatng condtons, as compared wth alternate methods. NOMENCLATURE A_pcv Pump control valve spool end area Fuel bulk modulus Pump control valve dampng constant FADEC Full authorty dgtal engne control Fnet_pcv Net force on pump control valve spool F_press Net pressure force on pump control valve spool F_sprng Pump control valve sprng force G ntegral path gan from pump control valve poston to rate of change of pump flcnv 02 Proportonal path gan from pump control valve poston to bypass flow, at constant pump dscharge pressure 03 Common gan from pump control valve poston to meterng valve dfferental pressure Pump control valve mass MA Mllarnps mvpos Meterng valve poston, MATRDot OLTF Pb Pd Pfl Pf2 Pf3 PRV q_byp q_mv q_or q-pump Wf WFMD X_act Xdot_pcv X_pc-v AP AP_mv AP_or td Regstered trademark of ntegrated Systems, nc. Open loop transfer functon Engne burner pressure Pump nterstage (dran) pressure Man pump dscharge pressure Pressure downstream of meterng valve Pressure upstream of engne nozzles Pressure regulatng valve Volumetrc flow bypassed to pump nterstage Meterng valve volumetrc flow Pump control valve dampng orfce volumetrc flow Man pump volumetrc flow Man pump dscharge volume Fuel weght flow delvered to the engne Meterng valve weght flow Pump actuator poston Pump control valve velocty Pump control valve poston Dfferental pressure Fuel meterng valve dfferental pressure Pump control valve dampng orfce dfferental pressure Pump control valve mass tme constant Pump dscharge pressure volume tme constant CONTROL TECHNQUES FOR POSTVE DSPLACEMENT PUMPS Postve dsplacement pumps have been overwhelmngly selected as the man fuel pump for gas turbne engne control systems, partcularly when hgh flows and pressures are requred over a wde range of drve speeds (Petro, 972). Two of the most wdely used types of postve dsplacement pumps are gear pumps and vane pumps. Presented at the nternatonal Gas Turbne & Aeroengne Congress & Exhbton ndanapols, ndana June 7-June 0, 999 Downloaded From: on 05/07/208 Terms of Use:

2 Hstorcally, the control of desred engne flow from a postve dsplacement pump has been obtaned by three technques: Varable pump dsplacement - Requres precse control of pump geometry. Control of drve shaft speed Requres precse control of accessory drve speed. Bypassng of excess flow - Requres an overszed pump and addtonal valvng. FXED DSPLACEMENT PUMP CONTROL DESGN TRADMONAL APPROACH - BYPASS OF EXCESS PUMP FLOW Of the three control technques, the overwhelmng choce has been to bypass excess flow from a fxed dsplacement gear pump. Ths approach reduces techncal rsk and captalzes on components wth very hgh mechancal relablty (Petro, 972). A block dagram representaton of ths approach s llustrated n Fgure. Fuel flow output from the pump enters a fuel meterng unt. A full authorty dgtal engne control (FADEC) determnes the desred engne flow, and controls the poston of a fuel meterng valve wth a varyng flow wndow usng a feedback sgnal from a poston transducer on the meterng valve. The heart of the fuel meterng system s the pressure regulatng valve (PRV). The PRV senses the dfferental pressure (AP) across the meterng valve, and bypasses flow back to the nlet of the pump as requred to mantan a constant, regulated pressure drop across the meterng valve. n ths way, desred fuel flow s drectly plow, clonal DD meterng valve poston. POP H. [ [ RAG, [.0: t kletzla: a At SLOW WL.Y! FGURE. FXED DSPLACEMENT PUMP WTH BYPASS REGULATOR n ths approach, the crtcal pump szng crtera are typcally the fuel flow and pressure requred for engne lghtoff at crankng speeds, whch s approxmately 0% of full speed. However, these pump szng crtera result n excessve fuel delvery at hgher engne spenle and alttudes. whch represents the majorty of normal engne operaton. As a result, actual pump delvery flow n excess of requred engne flow s bypassed back to the pump nlet. The rato of bypass flow to engne flow can be 20 or hgher for arcraft gas turbne engnes (Gbson and Fox, 970). A major problem wth ths result s that bypass and recrculaton of fuel results n sgnfcant fuel heatng due to the pressurzng of the fuel by the pump and the subsequent pressure drop of the fuel n the bypass lne upstream of the pump. The hgh fuel temperature s a problem snce the fuel s typcally used as a heat exchanger medum n the engne. ra YE bra Wth the latest fuel effcent engne desgns, excessve fuel heatng becomes a serous problem. Reduced engne fuel consumpton s accompaned by ncreased engne and ol lubrcaton system temperatures. Excess ol lubrcaton system heat s normally managed wth a combnaton of fuel/al and ar/ol heat exchangers. However, heat exchangers are undesrable n ths stuaton because of ther assocated sze, weght, and cost. Ar/ol coolers are problematc berm:se of the drag penalty they ncur on the arcraft. Yet, the coolng burden on an ar/ol cooler s decreased wth lower fuel temperatures. Ths s bermee the. lower fuel temperatures permt more lubrcaton system heat to be drected to the fuel system through the fuel/ol heat exchanger. Ths can result n a sgnfcant reducton n heat exchanger system sze, weght, and cost, as well as a reducton n the drag penaltes assocated wth ar/ol coolers (Reuter and Gaudet, 998). VARABLE DSPLACEMENT PUMP n contrast to fxed delvery pumps, varable delvery, postve dsplacement fuel pumps have the ablty to vary delvery flow, to thereby match engne demands for a wde range of engne speeds and alttudes. Thus, the varable delvery pump elmnates the excessve fuel delvery and resultng heat generaton nherent n fxed delvery pumps. An actuator s typcally used to alter the pump dsplacement. n the followng dscusson, three approaches to control flow by modulatng a varable dsplacement pump actuator represented. VARABLE DSPLACEMENT PUMP CONTROL DESGN APPROACH # - REGULATE METERNG WNDOW DFFERENTAL PRESSURE BY VARYNG PUMP DSPLACEMENT Fundamentally, ths approach s smlar to the tradtonal control method that has been used wth fxed dsplacement pumps. A FADEC controls the poston of a varable meterng wndow n the pump flow path, wth hydromechancal regulaton of the AP across the meterng wndow. The dfference here s that nstead of bypassng flow to regulate AP, pump dsplacement s vared. n ths type of control scheme, llustrated n Fgure 2, pump dsplacement s typcally altered by an actuator drven by a plot valve. The sprng based plot valve senses pressure both upstream and downstream of the meterng wndow. As pump flow condtons change, a dfferent meterng valve pressure drop s sensed by the plot valve. n response, the plot valve translates and moves the plot valve wndows from ther null poston. Ths causes the pump actuator to stroke, thereby varyng pump dsplacement untl the desred and constant meterng valve AP s restored. However, a problem wth ths control scheme s ts nablty to quckly and adequately respond to sudden external dsturbances r flow. These dsturbances occur f the fuel pump also provdes flow to slew an actuator whch s used to poston engne components such as a stator vane or bleed valve. The bandwdth of ths pressure drop control s lmted by the ntegratng nature of the pump actuator servo system. f the servo system response could be mproved, the control 2 Downloaded From: on 05/07/208 Terms of Use:

3 system bandwdth could ncrease. However, the ncrease n control system bandwdth s lmted by the requrements for control stablty at all operatng condtons. addton, control gans as well as engne flow schedules can easly be altered electroncally through software, rather by hardware mplementaton. Ortatn q ll. scrueo t t WTPs0 Wn.07/44 P However, meetng control system dynamc response requrements can be a problem wth the closed loop on flow approach. The bandwdth of the flow control loop s lmted by both flow sensor dynamc response and FADEC dgtal samplng delays. To acheve the necessary flow control loop bandwdth, dgtal samplng rates much hgher than 00 Hz are requred, whch results n ncreased FADEC cost and complexty. The selecton of a flow sensor requres a tradeoff between sensor dynamc response and accuracy. n addton, the electronc control scheme exhbts the same senstvty to pump servo frcton as the pressure drop regulaton scheme. FGURE 2. REGULATE METERNG WNDOW AP BY VARYNG PUMP DSPLACEMENT A second nherent drawback n the pressure drop control scheme s ts senstvty to pump servo frcton. A pump control actuator nherently has a large amount of frcton, whch causes a flow schedulng deadband, whch can lead D3 naccuraces and nstablty. VARABLE DSPLACEMENT PUMP CONTROL DESGN APPROACH #2 - DGTAL CLOSED LOOP CONTROL USNG FLOW SENSOR FEEDBACK A flow control for a varable dsplacement, fxed delvery pump may be carred out wth a loop closure through the FADEC. The FADEC detects pump fuel flow to the engne va a flow sensor located n the engne fuel flow delvery lne. The FADEC software compares actual flow wth desred flow, and based an the dfference, vares pump dsplacement by postonng a pump servo system va an electromechancal nterface devce, such as an electrohydraulc servovalve. untl commanded flow matches delvered flow. A block dagram representaton of ths approach s llustrated n Fgure 3. car re ACUTCO %sat Jae m.o. sew. aoonswouc MSSOte ao -0= = ages VARABLE DSPLACEMENT PUMP CONTROL DESGN APPROACH #3 REGULATE METERNG VALVE DFFERENTAL PRESSURE BY SMULTANEOUS VARMON OF PUMP DSPLACEMENT AND BYPASS FLOW A preferred method of controllng flow usng a varable dsplacement pump s to regulate the Al' across a meterng wndow usng a pump control valve whch combnes two prevously dscussed technques. The pump control valve vares pump dsplacement as n approach #. n addton, the pump control valve smultaneously vares the amount of bypass flow, n a manner smlar to de tradtonal fxed dsplacement pump approach. One major dfference of ths approach s that only a small amount of flow s bypassed, and thus the resultant fuel heatng s nsgnfcant. The addton of ths bypass flow path results n mprovements n dynamc response, stablty, and steady state accuracy. A schematc of ths approach s llustrated n fgure 4. Fuel flow =put from the pump enters a fuel meterng unt and ntally encounters a meterng valve wth a varable flow wndow. The meterng valve poston s controlled by the FADEC as n other approaches, usng LVDT poston feedback. sma, _ ,,,..... J j L Trj-L.., 'Mc Pt N MEMO, Pa.-. &Wm FGURE 3. CLOSED LOOP ON FLOW BY VARYNG PUMP DSPLACEMENT - 0:Pa R an A beneft of the flow sensor and FADEC approach s that a varable meterng wndow wth a fxed regulated pressure drop s not requred. Elmnaton of ths pressure drop across the meterng wndow reduces the total system pressure drop. Ths reduces the maxmum workng pressures at maxmum fuel flow condtons, as well as reduces the requred pump head at startng condtons. n FGURE 4. REGULATE METERNG VALVE AP BY, VARYNG BOTH PUMP DSPLACEMENT AND BYPASS FLOW The pressures at two dfferent postons across the meterng wndow are transmtted to the correspondng ends of a spool of the pump control valve. The sprng load on the pump control valve spool 3 Downloaded From: on 05/07/208 Terms of Use:

4 equals the dfference of the spool pressures multpled by the pston area. The pump control valve spool has 4-way plot valve lands to provde flow caftan both sdes of the pump control actuator. An addtonal land s used to bypass flow from pump dscharge back to pump nlet. As the meterng valve wndow area changes, due to external changes n pump flow demand, the pump control valve spool senses the changed AP across the meterng valve wndow, and moves n a drecton to restore AP back to ts regulated value. For example, an ncrease n flow demand results n an ntal drop n meterng valve AP. n response, the pump control valve spool moves to command an ncrease n pump actuator dsplacement, whle smultaneously bypassng less pump output flow. As meterng valve AP returns to ts regulated value, the pump control valve spool returns to ts null poston. At ths null poston, whch s always the same, the pump actuator velocty s zero, the pump actuator s n steady-state, and a small amount of flow s bypassed. Snce the pump control valve null poston does not vary, the steadystate bypass flow area s constant, and the amount of steady-state bypass flow vares as a functon of the square root of pump Al'. Pump AP typcally vares by a factor of 4:, resultng n a 2: varaton n bypass flow from mn-to-max engne flow. DYNAMC ANALYSS OF PUMP CONTROL VALVE AP REGULATOR The dynamc analyss of the pump control valve AP regulator ncludes a lnearzed representaton of the AP control loop, shown n Fgure 5. The state varables assocated wth the AP control loop are pump control valve poston (X_pcv) and velocty (Xdot_pcv), pump actuator poston (X_act), and pump dscharge pressure ('ll). Startng at the left sde of the block dagram, the summaton of fates on the pump control valve (Fnet_pcv) s calculated based on the pressure force (F_press) and the sprng force (F_sprng). The pressure force conssts of the meterng valve AP plus the AP across the pump control valve dampng orfce. Pump control valve acceleraton s the net force dvded by the mass: acceleraton s ntegrated to calculate velocty (Xdot_pcv), whch s ntegrated to calculate poston (X_pcv). There are two parallel paths downstream of pump control valve poston. One path represents the effect pmp control valve poston on pump flow (q_pump), whle the other path represents the effect on bypass flow (q_byp). t should be noted that the pump flow path s an ntegral path, whle the bypass flow path s proportonal. The rato of these ntegral and proportonal gans are crtcal D AP control loop stablty. The net flow at pump dscharge s represented by the summng juncton whch adds pump flow (q_pump) comng nto the volume, and subtracts bypass flow (q_byp) and meterng valve flow (q_mv) whch ext the volume. Rate of change of pressure s calculated by multplyng the net flow by the fuel bulk modulus (B). and dvdng by the volume (V). Ths rate of change of pressure s ntegrated to calculate pump dscharge pressure (P). Feedback paths represent the effect of Pfl on bypass flow and meterng valve flow. A change n N affects the AP aaoss the meterng valve (AP_mv). nsght nto the effect of ndvdual terms on the AP control loop stablty can be ganed through maluaton of the open loop transfer functon usng block dagram reducton. The result of ths reducton s llustrated n Fgure 6 Ths block dagram reducton s accomplshed by combnng terms as follows. D= A _pcv d(lp - or) (pump control valve dampng) d(q _or) d= (pump control valve mass tme constant) d d(xdot _act) d(q _pump) G = (ntegral path gan) d(x _pcv) d(x _act) G - d(q -byp) 2 d(x _pcv) G 3 A _pcv* d(ap _mv) d(pl) [a (q_byp) d(q _mv)] a(pfl ) ± a(pfl ) (common path gan) V B 2 Q - (volume tme const.) [ a(q_byp) + d(q _my)] a(t) a() P There are 2 paths from pump control valve poston to the pump control valve net force, a mechancal path va the sprng, and a flud path va pump control valve AP. The mechancal path s small relatve to the flud path, and wll be gnored n the subsequent analyss. The open Al' control loop transfer functon can be expressed as: (G +G 2 s)g 3 D ' S 2 0-dS+ D('r ws +) (proportonal path gan) Usng ths open loop transfer functon, the stablty and response of the Al' control loop can be evaluated. Typcal fuel control AP regulators have a bandwdth n the range of 50 rad/sec (0.020 sec equvalent tme constant), whch cceresponds to an open loop crossover frequency of approxmately 50 ral/sec. For the pump control valve Al' regulator to acheve ths response whle mantanng adequate stablty margn, the secondary tme constants d and S. must be substantally smaller than sec, and the rato of ntegral gan to proportonal gan, 0 / 02. must be less than 50 ral/sec. 4 Downloaded From: on 05/07/208 Terms of Use:

5 For the tradtonal bypass type AP regulator wth a fxed dsplacement pump, G =0, and stablty margn s acceptable as long as G2G3/D s not excessvely large. Gan 02 s a functon of the bypass wndow gan, and D s determned by the dampng orfce dameter. That parameters can be szed to yeld good stablty and response. For varable dsplacement pump control desgn approach #, whch has no bypass flow, 02= 0. resultng n an unstable AP control loop f the pump plot valve sprng rate s gnored. However, ths confguraton can be made to be stable by ncorporatng a sprng wth a rate much hgher than that used on conventonal bypass regulatng valves. Based on ths analyss, stablty margn s mproved as the proportonal path gan Gl, from pump control valve stroke to bypass flow, s ncreased. A decrease n the ntegral path gan Oh from pump control valve stroke to rate of change of pump flow, also mproves stablty. Hence, the mplementaton of the bypass path n approach #3 results n mproved AP control loop stablty, relatve to approach #, wth acceptable dynamc response. At a low engne flow condton, the AP regulator was calculated to have an equvalent tme constant of sec. Ths ncreases to 0.02 sec at a hgh engne flow condton, prmarly due to the fact that gan Gs s lower at hgher engne flows. SMULATON OF PUMP CONTROL VALVE AP REGULATOR A detaled, non-lnear MATRDCx smulaton was bult to demonstrate the predcted performance of the varable dsplacement vane pump wth the pump control valve based AP regulator. n addton to the pump and fuel meterng system, the smulaton also ncludes a FADEC whch ncorporates a meterng valve poston control loop wth an equvalent tme constant of 0.04 sec. Fgures 7 and 8 llustrate the predcted response to a 00 PPH step change n Wf demand at a low and hgh engne flow condton. At the 300 PPH low flow condton, the dynamcs of the 6? regulator are fast relatve to the dynamcs of the meterng valve poston control loop. Hence, the plot of W engne s dynamcally smlar to the plot of meterng valve poston. At ths condton, the steady state bypass, or spll, flow s approxmately 000 PPH, much less than that assocated wth a conventonal bypass regulator and fxed dsplacement pump. At the 24,000 PPH hgh flow =edton, the W engne response llustrates a slght overshoot, whch s related to the effect of pump actuator frcton. The bypass flow at ths condton s approxmately 800 PPH. Fgure 9 compares the step response at 24,000 PPH wth and wthout frcton, ndcatng that the response wthout frcton does not exhbt overshoot. An advantage of the hydromechartcal AP regulator approach (#3) over the closed loop on flow approach (#2) s mproved rejecton of flow dsturbances. These typcally occur when pump dscharge flow s suddenly dverted to move actuators whch are used to poston external components such as engne stator vanes and bleed valves. Wth the closed loop on flow approach, the response to these dsturbances s lmted by the FADEC samplng tme, whch s typcally 0.02 sec. More frequent samplng results n ncreased FADEC coe and complexty. Fgure 0 llustrates the response of the hydroanechancal AP regulator to a 4500 PPH flow dsturbance. The resultant Wf engne transent s settled out wthn 0.0 sec, whch would have a neglgble mpact on thrust. The hydromethancal AP regulator approach (#3) compares favorably aganst the closed loop on flow approach (#2) when the effects of pump actuator frcton are consdered. Wth the AP regulator approach, frcton has a mnor effect on steady state accuracy. Ths s because the pump actuator s only one of two paths used to regulate df. When the pump actuator s n ts frcton band, the bypass regulaton path s stll actve. For the closed loop on flow approach, a software ntegrator n the FADEC logc s requred to correct for steady-state errors whch would occur as the result of actuator frcton. Ths software ntegrator degrades W loop stablty. n order D acheve both stablty and dynamc response requrements, a pump actuator poston control loop, whch s nested wthn the Wf closed loop, wll most lkely be necessary. A MATtlXx smulaton of control desgn approach #2 wth ths FADEC control loop archtecture was created. Fgures and 2 llustrate the response of the closed loop on W approach, wth and wthout pump actuator frcton. n ths case, frcton results n a hysteress from commanded to actual pump actuator poston, whch has a de-stablzng effect on the Wf control loop. FUEL LAB BENCH TEST RESULTS FROM AP REGULATOR A fuel control unt ncorporatng the AP regulator approach was bult and tested both n the fuel lab and on an engne. Frequency response testng of the frst unt ndcated that pump control valve dampng was greater than analytcally predcted, whch necesstated an teraton n the pump control valve wndows. Wth the modfed wndows, the unt exhbted stable dynamc response, as llustrated n Fgure 3 whch was recorded n the Hamlton Standard hot fuel lab. SUMMARY Three dfferent approaches to control engne fuel flow, usng a varable delvery, postve dsplacement vane pump, were consdered. Approach #, whch controls meterng valve AP by varyng pump dsplacement only, s bandwdth lmted n order to acheve acceptable stablty. Approach #2, whch s a closed loop on flow approach, has dsturbance rejecton lmtatons, and s susceptble to lmt cyclng due to pump actuator frcton. Approach #3, whch controls meterng valve AP by smultaneously varyng pump dsplacement and bypass flow, has superor dynamc response and stablty when compared wth the other approaches. The arnotmt of fuel temperature ncrease due to the bypass flow assocated wth ths approach s nsgnfcant. 5 Downloaded From: on 05/07/208 Terms of Use:

6 ACKNOWLEDGEMENT would lke to acknowledge Charles Reuter, a mechancal systems desgn engneer for the Hamlton Standard Dvson of Unted Technologes. Hs orgnal deas ntated the development of the pump control valve concept presented n ths paper. REFERENCES Gbson, W. H. and Fox, L, A New Development n Hgh Speed Varable Delvery Vane Pumps, SAE Paper No presented at the Natonal Aeronautc and Space Engneerng and Manufacturng Meetng, Los Angeles, CA, October 5-9, 970 Petro, Davd, Fuel Pump Desgn Consderatons for Arcraft Gas Turbne Engnes, presented at the Jont Gas Turbne Dvson / fluds Engneerng Dvson Conference of the ASME, San Francsco, CA, March 26-27, 972 Reuter, Charles and Gaudet, Tmothy, Hydrontechancal Control for a Varable Delvery, Postve Dsplacement Fuel Pump. Unted States Patent No. 5,75,674, February 0, Downloaded From: on 05/07/208 Terms of Use:

7 F_prned ror. dfrx Reg X n a(e_prp) sam Xstert-Pcv dx_fa) a kact) Novo) (lce) Fps's a afro) Pll a PsPnv) el) a P a PM FGURES. LNEARZED BLOCK DAGRAM OF AP REGULATOR F_prebacle+.3 Ksprng_pcv 4 F_spnng H Gs Q-Peme Fnet_pcv /0 Xdot_pcv X_pcv (TdS+ G 3 S SS- FGURE 6. REDUCED LNEARZED BLOCK DAGRAM OF ep REGULATOR Downloaded From: on 05/07/208 Terms of Use: 7

8 PPM Step n Metered Flow PPH a S V co c 350 da O rfft0 (see)..2 a.4 Tme (sec) C. dp me ter valve O ct lo s Tme (sec) O Tme (sea) FGURE 8. SMULATON OF AP REGULATOR BASED FUEL CONTROL STEP RESPONSE AT HGH NF 8 Downloaded From: on 05/07/208 Terms of Use:

9 2420 Etta= ot pump actuator frcton a oso dp mete r valve o '. : Control valve pos a ra ' Ard:Ceedwo. Reder Tme (see) FGURE 9. SMULATON OF AP REG. BASED FUEL CONTROL WTH AND WTHOUT PUMP ACTUATOR FRCTON O.2 Tme (sec).3.4 t PPN servo flow dsturbance d! a , : C z a ! T ln (sac)! /! 0. O. at !.!., -r O!. :.4 27me (sec).8. FGURE 0. SMULATON OF AP REGULATOR BASED FUEL CONTROL RESPONSE TO A 000 PPH SERVO FLOW DSTURBANCE 9 Downloaded From: on 05/07/208 Terms of Use:

10 2200 n060 Closed Loop on W, Pump Act. Macon f._... _.,...., - : - : ,... _ Tme (sec) A.6 Tme (sac) FGURE. SMULATON OF CLOSED LOOP ON WE APPROACH, WTH FRCTON as now Closed Loop on W, No Maron "---t---- t--, !. :. 2203o 2200 nose l, : t 2 O Tme (sec) Pump an delta-p O. a a _ r--- --,,, Tme (sec) FGURE 2. SMULATON OF CLOSED LOOP ON WE APPROACH, WTHOUT FRCTON 0 Downloaded From: on 05/07/208 Terms of Use:

11 pos $70 : :re! ct f ant.. tcr WPOS P FPD :.. th?:77.(:c P".59e C: 3L. FGURE 3. FUEL LAB TEST DATA OF AP REGULATOR BASED FUEL METERNG UNT Downloaded From: on 05/07/208 Terms of Use: