APPLICATION OF HYBRID AERO-ENGINE MODEL FOR INTEGRATED FLIGHT/PROPULSION OPTIMAL CONTROL

Wang Jiankang,Zhang Haibo,Sun Jianguo,Li Yongjin

(College of Energy and Power Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing,210016,P.R.China)

Nomenclature

A8m2Nozzle throat area

dGvf/(°) Fan inlet variable guide vaneangle

d Gvc/(°) Compressor inlet variable guidevane angle

F/N Net thrust

H/km Flight altitude

Ma Flight Mach number

P/Pa Total pressure at specified engine station number

Pla/(°) Power lever angle

PNF/% Fan rotor speed

PNC/% Core rotor speed

sfc/(kg◦ h-1◦ N-1) Specific fuel consumption

SMf Fan stall margin

SMc Compressor stall margin

T/K Total temperature at specified engine station num

ber

V/(m◦s-1) Flight velocity

Wfa/(kg◦s-1) Afterburner fuel flow rate

Wfb/(kg◦s-1) Fuel flow rate

WA22C/(kg◦s-1) Fan outlet corrected airflow

WA25C/(kg◦s-1) Compressor inlet corrected airflow

T/(°) Angle of attack

cTPressure ratio of turbine

Suf fixes(aero-engine station numbers)

0 Free stream

2 Fan inlet

25 Compressor inlet

4 Main combustion outlet

45 Low-pressure turbineinlet

46 Low-pressure turbine outlet

7 Afterburner inlet

75 Afterburner outlet

8 Nozzle throat area

INTRODUCTION

The integrated flight/propulsion optimal control(IFPOC)[1-2]is to control the integrated system by aero-engine performance seeking control(PSC)[2-4].As the heart of IFPOC,PSC contains the following optimization modes:maximum thrust mode,minimum fuel-consumption mode and minimum turbine temperature mode.PSC en-ables the aero-engine to achieve its full potential and improves aircraft flight performance. In 1990s,National Aeronautics and Space Administration and US Air Force conducted a large number of PSC flight tests[5-6].The results[6]proved that PSC could significantly improve aero-engine performance and the flexibility,mobility and economical efficiency of aircraft.

The conventional optimization adopts linear programming(LP)to optimize the integrated model based on nonlinear aero-engine model.In Ref.[7], sequential quadratic programming(SQP)is applied to PSC successfully for the first time with a better optimization accuracy.However,the real-time capability of optimization is about 6 s,which can not meet the requirement in practical application.

Considering the large time-cost of iterative calculations during optimization[7],it is necessary to simplify the nonlinear aero-engine model to improve real-time ability. Therefore,propulsion system matrix(PSM)is introduced based on similarity parameters.The simplified model has two merits:real-time capability enhancement through linearizing models for most aero-engine components,and accuracy improvement by nonlinear models for some engine components.The geometrical dissimilarities of several components including nozzle are also considered during optimizing aero-engine.In this way,a hybrid aero-engine model is built in the whole flight envelop.

Finally,the approach of IFPOC is presented based on the hybrid aero-engine model and SQP.Digital simulations are conducted for cruise and accelerating flight. Results demonstrate that flight performance is further improved with good real-time ability of optimization.

1 ONBOARD HYBRID AEROENGINE MODEL

1.1 Design of hybrid aero-engine model

The object of the study is a dual-spool afterburning turbofan engine with mixed exhaust.To simplify the nonlinear aero-engine model in the whole flight envelope,the ground and nonground state of aero-engine need to be set interconvertible based on similarity theory[8]. For this,aero-engine must satisfy the conditions of geometric,kinematic and dynamic similarity.But the number of linear engine models grows exponentially with the increase of similarity conditions.Because theenginehas many adjustable parameters,including inlet ramp angle,fan inlet variable guidevanes angle,compressor inlet variable guide vane angle,nozzle throat area,it is difficult to build the hybrid engine model in the full envelop. Reducing similarity conditions is therefore necessary.

Similarity conditions are reduced in three main aspects.First,after considering possible shift of inlet ramp during supersonic flight,the inlet is separated from the engine and calculated alone so that the similarity condition of inlet can be ignored. Second,dGvfand dGvcare always changed slightly during optimization.Thus the influences of d Gvf and d Gvc on similarity are little and can beignored.Third,the nozzle throat area needs to be adjusted during afterburning or optimizing.Consequently the engine can not meet the similarity condition.Segregating afterburner and nozzle components from the engine is adopted to solve this problem.

The hybrid aero-engine model is proposed by block partition of components based on the above analyses.On onehand,becausecomponents from fan to mixer can meet the similarity conditions under all flight conditions,the models of these components are established with linear method and extended to thewhole envelope based on similarity theory.Therefore real-time ability is improved markedly.On the other hand,components including inlet,afterburner and nozzle sometimes can not meet thesimilarity conditions.Their models are built by nonlinear method toimprove the model accuracy.

1.2 Linear steady-state aero-engine model

Linear aero-engine model is used for aerothermodynamics calculation from fan to mix-er.Using linearization within a linear rangeof every small flight envelope,the functional relation between the engine control variable and the state variable is determined and mathematically expressed as

Set the engine control variable u=[A8,Wfb,W fa,d Gvf,d Gvc]Tand the engine state variable y=[PNC,PNF,P25,P4,P7,T25,T45,T7,WA22C,WA25C]T.The hybrid model is built under non-afterburning condition as well as afterburning condition.

In non-afterburning condition,if combustor inlet corrected pressure P3cor and mixer inlet corrected pressure P6cor are established,the state of aero-engine will be determined.The steps of obtaining PSM are as follows:

(1)P3corand P6corare divided by two-dimensional average segmentation in the standard atmosphere.

(2)The number of the engine operation points for the computation of PSM is defined(66 operation points in all).

(3)Twin-variable augmented linear quadratic regulator(LQR)controller[9]is designed to get the inputs of engine model.

(4)PSM is computed with the above engine operation points.

(5)Linear engine sub-models are all established in non-afterburning condition on the ground.

In afterburning condition,if a change of W fa occurs,c T will be altered.In closed loop system,A8 is adjusted accordingly to keep c T unchanged by the afterburning controller.That is,A8 is fixed with the affirmation of Wfa.Thestate of engine can be decided by W fa only.The method of gaining PSM follows the steps as:

(1)W fa is divided by one-dimensional average segmentation on the ground.

(2)The number of engine operation points is ensured as 30 in all.

(3)After the closed-loop engine system running,the open-loop control is switched on to compute PSM with the above operation points.

(4)Linear engine sub-models are all built in afterburning condition on the ground.

That all of linear engine sub-models are built on theground can cover all operation points in the whole envelope using similarity transformation(Fig.1).In Fig.1,old engine operating point is calculated from nonlinear engine model,and new engine operating point is determined by PSM.

1.3 Nonlinear steady-state aero-engine model

Nonlinear steady-state model is to calculate the components and parameters not suitable for similarity theory,including inlet,afterburner,nozzle,fan stall margin and compressor stall margin.

The inlet nonlinear model is expressed as

whereθ=[H,Ma,T]Trepresents flight parameter,and PNFc the fan rotor corrected speed.

Fig.1 Realization of linear model in whole envelope

According to theoutputs of linear model,the afterburner nonlinear model is built by calculating component characteristics and equilibrium equations.The model is represented as

The nozzle nonlinear model is built as

Besides,SMf and SMc depend on engine′s characteristic lines and working spots on those lines[10].Because the change of fan and compressor variablevane angle will influence characteristic lines and operation point location,the control laws and total characteristic data of fan and compressor variable vane angle are ported to the hybrid engine model.SMf and SMc are expressed as

1.4 Hybrid aero-engine model

Based on theaboveanalysis,the hybrid aeroengine model is established by Eqs.(1-6).The thrust and specific fuel consumption of aeroengine are expressed as

that is

Summarily the hybrid aero-engine model is described as

where Yengine=[F,sf c,SMf,SMc,PNF,PNC,T46]Trepresents the engine model output,θ=[H,Ma,T]Tthe flight parameter,u=[A8,W fb,W fa,d Gvf,d Gvc]Tthe control variable,and y=[PNF,PNC,P2,P25,P3,P4,P6,P7,T25,T45,T7,WA22C,WA25C]Tthe input of linear model.The realization of the hybrid aero-engine model in the whole flight envelopeis shown in Fig.2.

In order to check theaccuracy of hybrid aeroengine model,a small steps are added to all control variables to carry out simulations separately.Table 1 lists the accuracy of cruise operation point,H=12 km,Ma=0.8,Pla=40°.The accuracy while A8and Wfabeing changed are listed in Tables 2-3,respectively.Tables 1-3 prove that the hybrid model has good accuracy.

In Tables 1-3,″a″ represents the nonlinear aero-engine model, ″b″ the hybrid aero-engine model,and ″A8(+ 1%)″adding 1% step to A8,which is similar to the expression of other variables.Besides,theerror e,thrust and specific fuel consumption are relative value and formulated as

where x a and x b represent the parameter values of nonlinear model and hybrid model,respectively,and the subscript 0 identifies that the state is not optimized.

Fig.2 Realization of hybrid model in whole flight envelope

Table 1 Accuracy at H=12 km,Ma=0.8,Pla=40°

Table 2 Accuracy while A8 being changed at curse point

Table 3 Accuracy while W fa being changed at H=12 km,Ma=1.5

2 APPLICATION OF HYBRID AERO-ENGINE MODEL AND SQP FOR IFPOC

2.1 Linear search SQP algorithm

The problem to be solved by SQP is expressed as

The main idea of SQPalgorithm[7]is to solve the following Lagrangian function with two-order approximation,a quadratic regulator(QP)subproblem

Firstly,at the iterative point xk,construct a QP sub-problem.Secondly,take the solution of the sub-problem as the direction d k of linear search.Finally,repeat xk+1=xk+ak d k(ak is the k th steplength obtained by linear search)until the optimal solution is achieved.In addition,two-order calibration steplength dck is adopted to overcome Marotos effect.

The realization of SQPalgorithm mainly consists of three steps:(1)To renew Hessian matrix of Lagrangian function by BFGS,i.e.B k,(2)To solve the QPsub-problem,(3)To linearly search and calculate the target value. Therefore,through linearizing nonlinear constraint problem,QPsub-problem is described as follows.

Objective function

Constraint function

where d=d k+dck.And then the problem is solved by QPalgorithm.

2.2 Optimization of IFPOC system

The optimization of IFPOCis shown in Fig 3 schematically.This system consists of two levels as host computer and slave computer.The host compute is to simulate the real system,and the slave computer is for real-time tracking and PSC.In Fig.3,″1″and″2″represent theinputs and outputs of the hybrid aero-engine model respectively, ″3″the correct value of aero-engine control variable after optimizing.

In the slave computer,instead of thecomplicated nonlinear aero-engine model,the hybrid model combined with SQP algorithm is used in optimal control to improve aircraft flight performance and real-time capability.

PSC contains the maximum thrust mode(max F)and the minimum fuel-consumption mode(min sf c).The former is designed to maximize thrust for climbing and accelerating flight.The latter is to minimize fuel flow whilemaintaining constant F during cruiseflight.The operation point of engineis optimized online by adjustingthe aero-engine control variables based on SQPalgorithm.Max F and min sfc are mathematically described as

Fig.3 Schematic diagram of optimal control

max F(min sf c)

3 SIMULATION AND ANALYSIS

The simulation consists of three parts.The first part is the cruise simulation with the minimum fuel mode,the second is the acceleration simulation with the maximum thrust mode,and the third is the optimization time comparison between hybrid aero-engine model and nonlinear aero-engine model.The simulation results are discussed in the following subsections.

3.1 Cruise with minimum fuel-consumption mode

By controlling A8,W fb,d Gvf and d Gvc,the minimum fuel mode minimizes total engine fuel flow while maintaining constant F during cruise flight.The minimum fuel mode is evaluated at a flight condition of 0.88 Mach and 12 km altitude.Fig.4 presents the simulation results at the cruise operation point.

According to Fig.4,the fuel reduction at constant thrust is achieved by opening fan and compressor variablevanes and adjusting A8.And with the minimum fuel mode,the steady-state value of sf c decreases by 0.65%.In addition,T46 decreases by 1.1%.PNF and PNC stays within 2% of the initial values after PSCis engaged.

3.2 Acceleration with maximum thrust mode

Aircraft acceleration performance is essential to accelerating flight.The maximum thrust mode is designed to maximize F and improveaircraft acceleration performance.Fig.5 shows the simulation results of accelerating at 10 km altitude and 0.7 Mach.

According to Fig.5,the thrust increases and the flight speed is improved markedly when PSC is applied.Compared with normal acceleration condition,IFPOC system can keep a faster flight speed with the maximum thrust mode and fullfill the flying mission better.In this example,flight speed is raised from 209.6 to 280m/s,which cost 89.82 s without PSCwhile 75.18 s with the maximum thrust mode. The acceleration time is shortened by 16.3%,and the average thrust increases by 9.3%.

Fig.4 Cruise at H=12 km,Ma=0.88 with the minimum fuel mode

3.3 Comparison of optimization time

Through the above simulations,flight performance is improved dramatically after combining the hybrid aero-engine model with SQP in PSC.Meanwhile,the aero-engine does not lead to over-speed,over-temperature and surge.In Table 4,the optimization time based on the hybrid aero-engine model is compared with that of the nonlinear aero-engine model.

According to Table 4,optimization time decreases a lot by using thehybrid aero-enginemodel in PSC.In IFPOC system,the real-timeability of optimization obtains a ten fold increase with the maximum thrust mode,and more than 20-fold with the minimum fuel mode.

Table 4 Comparison of optimization time

4 CONCLUSION

A steady-state hybrid aero-engine model is built in the whole flight envelope combined with SQP in IFPOC.This approach has two merits.Oneis to enhance real-time ability of optimization with thehybrid aero-engine model,and the other is to improve optimization accuracy with SQP algorithm.The simulation results shows that the optimal control based on onboard hybrid aero-engine model and SQPcan improve real-time capability considerably with satisfactory optimization effectiveness.The proposed method has a great potential in engineering application.

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