Evolutionary Design and Optimization of Aircraft Engine Controllers

Transkript

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IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 35, NO. 4, NOVEMBER 2005
Evolutionary Design and Optimization of
Aircraft Engine Controllers
Raj Subbu, Senior Member, IEEE, Kai Goebel, and Dean K. Frederick, Life Member, IEEE
Abstract—We present methods to automatically identify and
optimize controllers for large-scale complex dynamic systems;
in particular, aircraft gas turbine engines. We show how the
optimization of different elements within the overall controller
can be addressed in an efficient fashion. These elements include
local actuator gains, control modifiers, and control schedules. An
evolutionary algorithm (EA) is utilized to realize multiobjective
optimization on a local as well as a global level, depending on
the optimization task at hand. The fitness function comprises
performance metrics that incorporate stall margins, exhaust gas
temperature, fan-speed tracking error, and local tracking errors.
Less attention has been given in the literature to the application of
optimization techniques to aircraft engine control systems design,
where the controls design and optimization is performed using
a full-order engine model and full control systems structures
that do not oversimplify the inherent complexities in these highly
complex nonlinear dynamic systems. This paper attempts to close
that gap.
Index Terms—Aircraft engine, automated control, control
design, design optimization, evolutionary algorithm (EA), gas
turbine.
I. INTRODUCTION
C
ONTROLLERS for modern jet engines have evolved into
very complex systems that are difficult to design and require a considerable expenditure of time by many experienced
design engineers. Some of the reasons for this situation are the
following:
• inherent complexity of the engine;
• necessity of always protecting the engine and keeping it
operating;
• importance of efficiency for commercial engines and high
performance for military engines.
The fact that modern engines are controlled by digital computers allows the designers to implement the high level of
complexity necessary to achieve the many and varied operating
objectives. However, the combination of a complex engine,
varied performance objectives and constraints, and a computer sufficiently powerful for real-time operation of extensive
amounts of code results in a formidable design challenge.
Manuscript received December 21, 2003; revised August 10, 2004. This work
was supported in part by the General Electric Global Research Center under the
Automated Controller Design Project. This paper was recommended by Associate Editor Z. Wang.
R. Subbu and K. Goebel are with the General Electric Global Research
Center, Niskayuna, NY 12309 USA (e-mail: [email protected]; [email protected]).
D. K. Frederick is with Saratoga Control Systems, Inc., Saratoga Springs, NY
12866 USA (e-mail: [email protected]).
Digital Object Identifier 10.1109/TSMCC.2004.843250
Although current practice makes extensive use of computation for simulation, design calculations, analysis of test results,
and verification and validation of performance, the process is
very labor intensive and probably falls short of achieving the
best possible performance in many cases. Also, the designers
who create the final control system as computer software to
be executed in real-time on the engine’s electronic control unit
(ECU) must be very skilled and have considerable experience
in jet-engine control system design. Furthermore, much of their
work is done under tight time constraints.
Throughout the design process, people are required to make
decisions about the organization and structure of the control
system and about the numerical values of the many parameters
that constitute the thresholds, limits, additive, and multiplicative adjustments, and the tables that implement the many functions of one or two variables that are known as schedules. In
current practice, the designers, based on prior experience, computer simulation, satisfaction of constraints, and driven to find
the best solution with the resources available, select the parameter values. To achieve this objective, numerous computer simulations are run in an attempt to cover the range of important
operating cases. However, the set of cases to be considered is
substantial when one accounts for a realistic range of altitudes,
Mach numbers, ambient temperatures, different levels of bleeds
and power extraction, fuel properties, engine-to-engine quality
variations, and deterioration effects. Another consideration is
that design work as described previously is best done by engineers with experience, rather than people with a good general
controls background but with limited practical experience in the
operation and control of jet engines.
To deal with these problems, the authors undertook a project
to apply computer-optimization tools to some selected aspects of
the design of control systems for an in-service high performance
commercial engine designed and manufactured by General
Electric Aircraft Engines (GEAE). For this example, we assume
that the structure of the controller has been determined, including
the logic and at least a rudimentary set of schedules that will
allow the dynamic response of the engine to be simulated.
Furthermore, we assume that the structure of the individual
actuator loops has been defined, but that the best values of
the gains, as a function of operating conditions, are unknown.
Due to the highly nonlinear nature of the engine controller
and the fact that it is implemented as a large collection of computer modules (typically over 100) that employ a variety of
one- and two-input tables, switching variables, logical elements,
limiters, priority-select logic, etc., the control design space is
high-dimensional, highly nonlinear, multimodal, and discontinuous. Traditional optimization methods based on nonlinear programming are not likely to be successful in finding an optimal,
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SUBBU et al.: EVOLUTIONARY DESIGN AND OPTIMIZATION OF AIRCRAFT ENGINE CONTROLLERS
or near-optimal solution for such a design problem.1 Another
complicating factor governing the selection of an optimization
scheme is that a closed-form functional approximation of the
performance metric is nontrivial and often impossible. In addition, it is important to define the performance metric in a flexible
manner since it is necessary to properly account for such diverse
requirements as maintaining stall margins above certain limits,
minimizing both peak temperatures and the time spent above a
certain temperature, and obtaining short rise times in response to
changes in demand values. Furthermore, the minimization must
be done over a wide range of flight conditions and disturbance
inputs.
To accomplish these challenging objectives, we employ evolutionary algorithms (EAs) [1], [15], a class of global stochastic
search techniques. Such algorithms execute utilizing principles
of natural evolution and are robust adaptive search schemes suitable for searching nonlinear, discontinuous, and high-dimensional spaces. This optimization approach does not require an
explicit mathematical description of the objective function over
the multidimensional search space, and instead relies solely on
an objective function that is capable of producing a relative
evaluation of alternative solutions. These features make EAs
good candidates for the design of modern jet-engine control systems. The EA in our application is implemented in MATLAB and
launches simulation runs of General Electric Aircraft Engine’s
controller and engine simulation program, FSIM.
II. BACKGROUND
Only a very small portion of an overall engine control system
is designed to operate in a linear fashion, and even then, the controller gains are often scheduled as functions of the operating
conditions (altitude, Mach number, and ambient temperature deviation from standard day). Although much is known about the
behavior and design of linear control systems, this information
is not relevant to the problems under consideration here. Rather,
one must be prepared to work in the nonlinear domain, where
theories and analytical results are much more scarce than for the
linear domain. Also, the literature on nonlinear control systems,
of necessity, tends to deal with specific situations, such as the
area of integrator-windup protection (IWP).
As indicated in the Introduction, it is not to be expected
that conventional optimization methods and those that depend
on gradient evaluations, should work. Rather, an evolutionary
search algorithm is used which has features and characteristics
that make it particularly well suited to the problem at hand. In
this section, we present background information on EAs and
their application to aircraft engine control systems design.
A. EAs
EAs include genetic algorithms [11], [13], evolutionary programming [6], [7], evolution strategies [1], and genetic programming [14]. The principles of these related techniques
define a general paradigm that is based on a simulation of
1During the initial stages of this technical investigation, we applied a variety
of traditional, well-known optimization techniques based on mathematical programming. The performance of these solvers was consistently unsatisfactory,
and this was principally because they were ill-suited to the class of problems of
our interest. This was a principal factor in pursuing the use of EAs as a robust
search methodology.
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natural evolution. EAs perform their search by maintaining at
of
any time a population
individuals. “Genetic’ operators that model simplified rules of
biological evolution are applied to create the new and more
. This process continues until a
superior population
sufficiently good population is achieved, or some other termi, represents via
nation condition is satisfied. Each
an internal data structure, a potential solution to the original
problem. The choice of an appropriate data structure for representing solutions is very much an “art” than “science” due
to the plurality of data structures suitable for a given problem.
However, the choice of an appropriate representation is often
a critical step in a successful application of EAs, and effort is
required to select a data structure that is compact, minimally
superfluous, and avoids creation of infeasible individuals [15].
For instance, if the problem domain requires finding an optimal
real vector from the space defined by dissimilarly bounded
real coordinates, it is more appropriate to choose as a representation a real-set-array2 instead of a representation capable
of generating bit strings.3
Closely linked to the choice of representation of solutions,
, that assigns
is the choice of a fitness function
credit to candidate solutions. Individuals in a population are
assigned fitness values according to some evaluation criterion.
Fitness values measure how well individuals represent solutions to the problem. Highly fit individuals are more likely
to create offspring by recombination or mutation operations.
Weak individuals are less likely to be picked for reproduction, and so they eventually die out. A mutation operator
introduces genetic variations in the population by randomly
modifying some of the building blocks of individuals. EAs
are essentially parallel by design, and at each evolutionary
step a breadth search of increasingly optimal subregions of the
options space is performed. Evolutionary search is a powerful
technique of solving problems, and is applicable to a wide
variety of practical problems that are nearly intractable with
other conventional optimization techniques. Practical evolutionary search schemes do not guarantee convergence to the
global optimum in a predetermined finite time, but they are
often capable of finding very good and consistent approximate
solutions. However, they are shown (theoretically and practically) to asymptotically converge under mild conditions [16].
B. Evolutionary Design and Optimization of Aircraft Engine
Control Systems
Evolutionary design and optimization of aircraft engine control systems is a novel applications domain, and therefore there
are relatively few reported results in the literature. Multiobjective evolutionary optimization of parameters in simplified
engine controllers for simplified Rolls-Royce engine models
are reported by Chipperfield and Fleming, and Fonseca and
Fleming [3], [4], [8]. Thompson et al. [18] report the selection
of components of the controller architecture to meet a range
of performance criteria including performance and cost. The
choice of architecture is shown to have a large impact on the
achievable engine performance. Gremling and Passino [12]
2A
real-set-array is an array of bounded sets of reals.
representation that generates bit strings can create many infeasible
individuals, and is certainly longer than a more compact sequence of reals.
3A
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report the design of an online adaptive state estimator for a
jet engine compressor whose model is evolved by a genetic
algorithm.
Less attention has been given in general to the application of
EAs to aircraft engine control systems design, where the controls design and optimization is performed using a full-order
engine model and full control systems structures4 that do not
oversimplify the inherent complexities in these highly complex
nonlinear dynamic systems. This paper, based on an industrial
case-study, attempts to close that gap.
III. AUTOMATING CONTROLLER DESIGN
Typically, aircraft engine controller design is an iterative
process. Initially, a linear engine model is built by extracting
partial derivatives from models based on first-principles [5].
Then, local controllers are designed and optimized using
first-principles as well as derivatives from previous engine
designs. Next, schedules are designed using performance
requirements. Finally, the control logic is established which
integrates the individual components and takes overall stability
and performance requirements into account.
The performance of the overall control system is tested on increasingly more complex systems starting with the local model,
the bare component level model (CLM), the CLM with the full
controller integrated, a dry rig test, wet rig test, test cell runs,
and test flight. Each test cycle might necessitate a revision of
some controller components with renewed validation and verification. This is a labor-intensive process that will benefit from
some level of automation. In particular, design and optimization
of the following is beneficial:
• local actuator gains, either constant or scheduled;
• logic thresholds;
• adders and multipliers for gains and schedules;
• schedule entries;
• control logic structure.
This paper describes the optimization for select control variables in the first four categories. Design changes in the control
logic structure have not yet been considered.
The design and optimization of the controller is decomposed
into several complementary subtasks. These subtasks include:
1) optimization of the actuator gains; 2) optimization of the control modifiers (adjustables); and 3) design and optimization of
the control schedules. This task decomposition is necessitated
by the fact that local gain modifications often do not result in
any significant variation at the global performance level. In addition, the potential for crosstalk, i.e., the difficulty to track correlations of several simultaneously manipulated variables on the
overall controller, supports the strategy of dividing the optimization endeavor into smaller optimization tasks. Depending on the
impact the particular control variable under consideration has
on the overall and local performance criteria, we maximize the
observability from an optimization standpoint. This means that
4The simulation models we use for the experiments reported in this paper
are the very same entities General Electric aircraft engine designers use on a
day-to-day basis for actual design and verification prior to embarking on physical module-level verification and validation. Such models are a complex aggregate of a large number of coupled, highly realistic, and field tested simulation
entities.
Fig. 1. Overall architecture.
for some control variables only local performance criteria (local
tracking errors) are considered while other control variables are
considered from a global level (stall margins, exhaust gas temperature, fan-speed tracking error). Fig. 1 gives an overview of
this strategy.
The optimization takes advantage of the FSIM simulator that
can simulate the dynamic behavior of a production engine and
its controller with a high degree of fidelity. The simulation modules comprise the CLM and an emulation of the fully automated
digital engine controller (FADEC). The user may specify control settings and flight scenarios, and execute FSIM to obtain
the engine response given a high-level (pilot5) command such
as demanded fan speed, which is a good measure of thrust.
A. Actuator Gains
A combination of domain knowledge and several trial runs of
FSIM was utilized to isolate and identify the gain candidates to
be optimized. Based on the principal consideration of the impact a particular actuator has on engine performance, the fuel
metering valve (FMV) proportional gain (FMV-Kp), and the
variable stator vane (VSV) proportional gain (VSV-Kp) were
selected as parameters to be optimized. While VSV-Kp is a constant, FMV-Kp is a function of the FMV actuator position and
the corrected core speed, where a higher core speed results in
a higher gain. A simplified view of the proportional path in the
VSV actuator control system is shown in Fig. 2, and a simplified view of the proportional path in the FMV actuator control
system is shown in Fig. 3.
In these actuator loops, d is the demanded actuator position,
and p is the achieved actuator position. The optimization
problem then is to select that gain value that minimizes the
time integral of the square of the position tracking error e of
the actuator loop
5The pilot’s thrust specification is via the position of the throttle resolver angle
(TRA) measured in degrees, where a lower TRA setting corresponds to a lower
thrust demand.
Fig. 2.
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Proportional path for the VSV actuator.
Fig. 4. Control systems architecture.
Fig. 3. Proportional path for the FMV actuator.
The actuator position demand signal d is computed by the
FSIM simulation modules through a complex transformation of
the thrust demand profile (with respect to time) specified by the
pilot.
B. Control System Modifiers/Adjustables
The FMV and VSV control systems are large and complex entities with numerous interconnected subsystems. Each of these
control systems is provided with a suite of modifiers that consists of adders and multipliers for gains, adders and multipliers
for schedules, and logic thresholds (see Fig. 4). In current practice, these control modifiers are selected heuristically.
Within the FMV and VSV control systems, a set of over 70
modifiers was identified for optimization. Each adjustable is a
bounded real number, and the bounds are specified in FSIM.
The optimization problem is to identify a set of modifiers such
that global performance criteria are optimized. Ideally, the performance metric should be aggregated over a number of flight
conditions such as altitude, Mach number, and ambient temperature deviation from standard day and engine configurations
such as horsepower extraction, deterioration, and component
tolerances.
To adequately evaluate performance, a metric is necessary
that allows the quantification of all global performance requirements. Such an ideal global performance metric should include
the following relative measures:
• booster stall margin versus booster inlet flow;
• compressor stall margin versus compressor inlet flow;
• VSV demanded position versus corrected core speed;
• Variable bleed valve (VBV) demanded position versus
corrected fan speed;
• corrected Phi6 versus corrected core speed;
• combustor fuel/air ratio versus any related severity parameters;
• high-pressure turbine inlet temperature versus corrected
core speed;
• exhaust gas temperature versus corrected fan speed and
time.
To reduce the complexity of the global performance metric,
we focus on typical input variations and study the most critical
6Phi
is the ratio of the fuel flow and the corrected combustor static pressure.
parameters for aircraft engine control systems validation. In
particular, we require meeting all stall margin limits, good
tracking of a fan-speed demand profile, and reduction in the
peak exhaust gas temperature. Toward this, let EGT be the
the acceptable cruise
exhaust gas temperature profile, EGT
temperature, the exponent by which the distance to the limit is
penalized, a weight for the temperature component, a weight
the fan-speed
for the fan-speed tracking error component,
the fan-speed demand profile, the time, E the
profile,
exceedance profile comprising the EGT exceedance
, the
, the booster stall margin
fan stall margin exceedance
, and the compressor stall margin exceedance
exceedance
. Then the optimization problem has the form
,
where
EGT
EGT
and
if EGT EGT
otherwise
if SM
SM
otherwise
if SM
SM
otherwise
if SM
SM
otherwise
C. Schedules
The control logic in a typical aircraft engine controller utilizes a suite of schedules that are functions of one or two input
variables. Schedules are implemented as lookup tables and the
output values are computed via linear interpolation among the
closest neighbors. Schedule surfaces represent nonlinear transformations of the inputs to the output and are critical components of an aircraft engine’s control logic.
Based on a combination of domain knowledge, simulation,
and knowledge elicitation from domain experts, a particular
schedule in the FMV module was selected as a candidate for
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Fig. 5.
Optimization of VSV-Kp for burst-at-cruise.
evolutionary optimization. This schedule outputs a rate-gain
reduction given the ambient pressure (a physical function of
altitude) and compressor speed, and is active during the burst
phase for a specific maneuver called a Bodie, wherein at cruise
the pilot cuts thrust for a short time period and increases thrust
through a burst before the engine temperatures have achieved
steady state at the reduced power level. In the absence of a
rate-gain schedule, the fan-speed response during the burst
phase is extremely sluggish, which is highly undesirable. What
is desirable however, is a rapid return to the original fan speed.
The optimization problem is to identify a set of schedule
entries such that fan acceleration is maximized during the burst
phase of the Bodie, subject to maintaining all stall margins
above acceptable limits. Simulation-based evaluation reveals
that during this maneuver the EGT is always well within limits,
so it is not included in the global performance metric. Let
be the fan-speed profile,
the fan-speed demand profile
described as a step function with the step coinciding with the
burst phase of the Bodie, the time, E the exceedance profile
, the booster
comprising the fan stall margin exceedance
, and the compressor stall margin
stall margin exceedance
. Then the optimization problem has the
exceedance
, where
form
and
if SM
SM
otherwise
if SM
SM
otherwise
if SM
SM
otherwise
An evolutionary optimization of a schedule that is the function of two input variables corresponds to a systematic and joint
manipulation of the table entries. An important requirement in
the automatic design and optimization of these control surfaces
is the smoothness of these derived surfaces. Unless smoothness
is explicitly included as a design requirement, an evolutionary
optimization can result in noisy albeit optimal, schedules. To facilitate smoothness in derived schedule surfaces, the entries in
each test surface T are filtered using a specialized bi-directional
,
filtering algorithm that is applied to each derived row
and is shown in the following:
1)
0
Fig. 6.
Optimization of VSV-Kp for Bodie-at-cruise.
Fig. 7.
Optimization of FMV-Kp for burst-at-cruise.
2)
3)
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(line 3) for each row following the procedure outlined in lines 1, 2, and 3. This is an important step, since selection of a reliable starting point is critical. Next, the smoothed
are computed using the procedure outlined in
values
line 4.
IV. RESULTS
4)
In the previous algorithm, is a smoothing factor. The objective of the algorithm is to first identify a reliable starting value
This section describes the initial observations followed by
systematic experiments that led to the simulation-based optimization of actuator gains, controls modifiers, and schedules.
The ambient conditions (e.g., altitude) selected for these experiments correspond to typical operational regimes of interest
560
Fig. 8.
Optimization of FMV-Kp for Bodie-at-cruise.
Fig. 9.
Optimization of FMV control modifiers, response for burst-at-cruise.
to engine designers. While we explored a variety of ambient
conditions, due to space considerations, we only report a select
representative sample of these results.
A. Preliminary Observations
In selecting candidates to which the search algorithm was to
be applied, several considerations were taken into account. First,
it was decided to start in an area of constrained complexity and
about which enough knowledge was accessible. The first subject
was the code that handles the adjustments to the VSV positions.
This operation can be divided into two parts: 1) the determination of the demanded VSV position, based on current flight
conditions and 2) the gains and other parameters of the VSV
actuator loop itself.
Upon looking at the Beacon7 diagrams that describe the code
used in the ECU of the engine, it was concluded that the gains
of the actuator loop made a better starting point than the demand-value determination. For the latter, 12 control modules,
implemented by 12 different Beacon diagrams, are involved.
Also, without an intimate knowledge of how these 12 modules
operated, it would be difficult to pose and carry out a meaningful
optimization problem. Hence, it was decided to start by focusing
attention on the tuning of the VSV actuator loop. Specifically,
experiments were carried out with the proportional gain of that
loop, since the code had an adjustable adder defined which could
be set to any desired value at the start of a run, without having
to rebuild the FSIM code.
7Beacon is the computer program used by GE Aircraft Engines to represent
the controller in terms of block diagrams and computational flow diagrams from
which the actual computer code is generated. Applied Dynamics, Inc., Ann
Arbor, MI, markets it.
Fig. 10.
Optimization of FMV control modifiers, response for Bodie-at-cruise.
Fig. 11.
Optimization of VSV control modifiers, response for burst-at-cruise.
B. Actuator Gains
1) Runs With Preset Values of VSV-Kp: Several FSIM runs
were made for a combination of a burst (increase of TRA from
36–78 ), a constant TRA for 25 s, followed by a chop (decrease
in TRA from 78–36 ). For a given FSIM run, the value of the
proportional-gain adder was varied such that the actual proportional gain was a constant between the limits of 78 and 778.
The design value is a constant (not scheduled according to core
speed or any other variable). In terms of the key engine variables, such as fuel flow, fan speed, VSV angle, exhaust gas temperature (EGT), etc., there were virtually no differences over the
tenfold range of the proportional gain. The only variable that
was affected by the change in proportional-gain value was the
error in the VSV actuator loop. This observed behavior suggests
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that the proportional gain could be selected so as to minimize the
square of the actuator error.
2) Optimization of VSV-Kp: Optimization of the VSV-Kp
follows the procedure outlined in Section III-A. Engine operation was simulated subject to changes in throttle position while
cruising at 35 000 ft, Mach 0.8, and standard-day temperature.
A burst and Bodie are used to excite the overall system, and
gain optimization is performed independently for each of these
excitation profiles. Fig. 5 shows the results of optimization
of VSV-Kp for the burst, while Fig. 6 shows the results for
VSV-Kp optimization under a Bodie maneuver. In each of
these cases the optimized gain is substantially higher than
the default gain, and this results in a significant reduction of
the position tracking error over the space of the excitation.
However, while there is a noticeable impact due to optimization
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Fig. 12.
Optimization of VSV control modifiers, response for Bodie-at-cruise.
on the actuator level performance, there is no global impact
due to optimization. A key observation is that VSV-Kp being a
gain that is not scheduled has different optimal values for the
burst maneuver and the Bodie maneuver.
Although this was an interesting and useful first step, this
result is probably of only limited significance. No attempt was
made to determine optimized values for other gains in the loop,
such as the integral gain, or other parameter values, such as a
lead-time constant. However, it would certainly be possible to
do so.
3) Runs With Constant Values of FMV-Kp: Next, this actuator design method was applied to the FMV actuator loop
proportional gain. Here, the actuator controller is slightly more
complicated than the VSV one in that the proportional gain is a
function of both the FMV actuator position and the core speed,
where a higher core speed results in a higher gain. As in the
VSV actuator study, it was found that changes in the FMV proportional gain had virtually no effect on the engine variables
(fan speed, fuel flow, temperatures, etc.). The scheduling of the
gain was removed by modifying the appropriate schedule table
and the burst and chop simulations were run over a wide range
of constant gains. As before, only the error in the actuator loop
was affected.
4) Optimization of FMV-Kp: Optimization of the FMV-Kp
follows the procedure outlined in Section III-A. Engine operation was simulated subject to changes in throttle position while
cruising at 35 000 ft, Mach 0.8, and standard-day temperature.
A burst and Bodie are used to excite the overall system, and
gain optimization is performed independently for each of these
excitation profiles. Fig. 7 shows the results of optimization
of FMV-Kp for the burst, while Fig. 8 shows the results for
FMV-Kp optimization under a Bodie. As observed from the
optimization of the VSV-Kp, in each of these cases, the optimized gain is substantially higher than the default gain, and this
results in a significant reduction of the position tracking error
over the space of the excitation.
In order to find critical parameters whose values will affect
global performance metrics (such as stall margins or exhaust
gas temperature), attention was focused on the extensive set of
ECU modules that are used to produce the incremental changes
in the demanded fuel flow. These incremental changes are continuously summed in order to produce the demand value for
the FMV actuator. The behavior during a burst operation, in
response to a sudden request from the pilot for an increase in
power, was examined. During such a situation, several different
regulators are active, depending on the various limits and constraints that must be satisfied in order to guarantee safe operation of the engine. By looking at which regulator was selected
as time evolved following the burst command, we determined
the sequence of active regulators.
The study of control logic charts (“Beacon diagrams”) for the
modules that are active during the flight maneuver of interest
gave understanding of their operation and the conditions that
cause a transition from one module to another. This allowed the
formulation of an optimization problem that did produce some
interesting results for a problem whose complexity is comparable to what would be required to do in a real design. The optimization task focused then on the modifiers and schedules as
described in the following.
C. Optimization of Control System Modifiers
Determining the values for the control modifiers in the FMV
and VSV control systems follows the procedure outlined in Section III-B. Engine operation was simulated subject to changes in
throttle position while cruising at 36 000 ft, Mach 0.8, and standard-day temperature.
Fig. 9 shows the results of optimization of the FMV control system modifiers under a burst-at-cruise excitation, and
Fig. 10 shows the result of optimization of the FMV control
system modifiers under a Bodie-at-cruise excitation. Unlike the
procedure followed for optimization of actuator gains, where
optimization was performed independently for each of the excitation profiles, the optimization of control modifiers for each
control system is performed jointly over the two excitation
profiles. Such an approach helps determine the best set of
control modifiers8 for the two excitation profiles combined.
In practice, such an approach could be extended to include
other excitation profiles corresponding to other flight scenarios
of interest. It is seen that the FMV control modifiers have a
significant impact on engine performance at the global level,
and optimization results in a solution set that significantly
8The normalized form of each modifier, default, and optimized, is presented
for purposes of comparison. For each normalized modifier, 0 represents its
minimum allowable value and 1 represents its maximum allowable value.
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reduces exhaust gas temperature transients albeit at the slight
expense of fan acceleration during a burst-at-cruise. However
for the Bodie-at-cruise, the exhaust gas temperature transients
are significantly reduced and fan acceleration is improved.
Moreover, the stall-margin limits are strictly followed.
Figs. 11 and 12 show corresponding results of optimization of
the VSV control system modifiers. While there is a slight reduction due to optimization in the exhaust gas temperature transient,
there is no perceivable impact on the fan acceleration, which is
directly related to engine thrust. This observation lends experimental evidence to the common knowledge that considered independently, certain control system modules can have a more
significant impact than others at the global performance level.
D. Optimization of Schedules
Optimization of the schedule rate-gain entries follows the
procedure outlined in Section III-C. Engine operation was simulated subject to changes in throttle position while cruising at
41 000 ft, Mach 0.8, and standard-day temperature.
Fig. 13 shows the default and optimized rate-gain schedule
surface, where the optimization elevates the rate gain over the
input space in order to improve fan acceleration. Fig. 14 shows
the performance metrics that exhibit differences due to the default and optimized schedules during the Bodie maneuver. The
key observations are that schedule optimization results in a substantial improvement in fan acceleration without sacrificing exhaust gas temperature limits and stall margin limits. Also, the
minimum stall margins with the optimized table are no lower
than those with the default table.
E. Discussion
In optimization applications involving EAs, a principal issue
is the execution speed of the underlying models and its impact
on the speed, and consequent quality of convergence achievable
given computational resources. Though we used highly realistic
and complex engine simulation modules, the time to execute
one complete run of the simulation modules was of the order
of a few seconds on typical desktop processors. Therefore, a
typical evolutionary search did not take more than a few hours
to complete. In realistic design scenarios, it would be highly
advantageous and attractive to designers if they were to get near
instantaneous feedback within a few minutes at most. For such
scenarios, it would be suitable to distribute the simulation-based
evaluation tasks to multiple processors to meet the optimization
response-time requirements.
Determining values of the controls modifiers so as to simultaneously track a reference fan-speed profile and reduce the
exhaust gas temperature, while adhering to stall margins and
temperature limits, is a multiobjective optimization problem.
The issue of the manner in which the individual terms in
the objective function are weighted is critical, because the
optimization method will try to satisfy the objective function
depending on the weights placed on individual criteria. If one
criterion is weighted heavily relative to the others, the optimization result will be skewed in favor of this particular
criterion. Therefore, a careful balance that reflects what is
really important needs to be found.
Fig. 13.
Default and optimized schedule surfaces.
Another issue is the design of the individual criteria. Although a general idea exists as to what the optimization ought
to accomplish, there are differences in the implementation of
the objectives. For example, the optimizer could be asked to
closely follow an ideal fan-speed profile. The question then
arises as to how such an ideal fan-speed profile should look. It
is necessary to draw upon domain knowledge to properly trade
off the different criteria and to properly set up the objective
function.
Finally, the results of a multiobjective optimization could be
expressed as a Pareto frontier [2], [3], [4], [8]. In other words,
there are a number of possible solutions that all meet the criteria that may result in different engine behavior. It is then necessary to express a preference for a particular solution from the
set of possible solutions. Ideally, the preference could be cast
within the objective function. However, the effects of the solutions are not always apparent until after the optimization results
are reviewed.
V. SUMMARY AND CONCLUSION
We have formulated a framework to the design of jet-engine
controllers by applying evolutionary search algorithms to actuators, multiplicative, and additive adjustments, and table generation and/or modification. To that end, we developed meaningful
performance functions whose minimization produces controller
parameters that result in desirable engine behavior. It incorporates stall margins, EGT, and tracking of changing throttle
positions. In addition, we employed a smoothing function that
in effect penalizes discontinuous table solutions. We then used
these techniques successfully to adjust over 70 parameters at a
time in the controller modules of a real commercial engine. In
addition, we demonstrated the ability to tune the proportional
gain of a regulator in the context of its operation in a nonlinear environment by minimizing the integral of the square of
the actuator error. Finally, we employed evolutionary search
algorithm methodology to generate a 3-D table of the form
to maintain rapid response to a demanded power
increase as a part of a Bodie maneuver.
564
Fig. 14.
Schedule optimization results.
There are a number of avenues for future work. One avenue is
the integration of the optimization for design assistance during
the various design and validation stages—cycle deck over CLM,
FSIM, dry rig, wet rig, test cell, and flight test. Moreover, this
optimization approach may be extended to adapt engine performance based on in-service data, and to adapt engine performance as an engine deteriorates. This assistance could range
from automated validation of design choices to suggestion of
parameters as shown in this paper. Another avenue leads to
scaling the optimization task. Of particular interest is ensuring
cross-communication of individual results from components in
a concurrent optimization scheme. Such a coevolutionary optimization [17] would allow concurrent module-specific exploration of the global design space, thus, responding to the need of
both domain-specific focus and adhering to global performance
metrics. This could be accomplished via agent-based multiobjective optimization. Also of interest is the integration of external information such as expert knowledge, historical runs,
information from pilots during test flights, etc. This task would
need the development of an information aggregation component
[9], [10] that can deal with the inherent uncertainties and the different format to more formally translate these observations into
an objective function and performance metric.
Another avenue could lead to a fault-tolerant controller that
would respond to a fault signature with appropriate changes
to the control structure. This could be an extension of the
compensatory optimal control using quality and deterioration
estimates. Similarly, one could perform individualized optimization of engines using modifiers by responding to specific
engine characteristics (as opposed to model wide baselines),
thus, further improving performance. In addition, one could
also explore performance-enhancing optimization through the
reduction of schedule size, thus, reducing FADEC memory
requirements and improving throughput. This could lead to
selection of optimal schedule sizes for a number of controllers
such as the FMV and power management, which typically deal
with large schedules. In addition, the overall FADEC architecture could be optimized by identifying obsolete elements
(schedules, etc.). Finally, we mentioned as one opportunity for
optimization the logic structure itself. This could be accomplished through genetic programming or inductive learning
such as experience based learning.
ACKNOWLEDGMENT
The authors would like to thank General Electric for helpful
cooperation during the preparation of this manuscript. They
would also like to thank the reviewers for their efforts, and for
their very helpful suggestions.
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335–348, Sep. 2001.
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for a jet engine compressor,” in Proc. 12th IEEE Int. Symp. Intelligent
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, “Network-based distributed planning using coevolutionary
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+
565
Kai Goebel received the Ph.D. degree in mechanical engineering from the University of California at
Berkeley.
He is a Senior Research Scientist in the Computing and Decision Sciences Group, General
Electric Global Research Center, Niskayuna, NY. He
is also an Adjunct Professor in the Computer Science
Department, Rensselaer Polytechnic Institute (RPI),
Troy, NY, since 1998, where he teaches classes in
soft computing. He has carried out applied research
in the areas of artificial intelligence, soft computing,
and information fusion. He has worked on using soft computing techniques for
real time monitoring, diagnosis, and prognosis of industrial equipment such
as aircraft engine, and power plants, and structures such as aircraft wiring.
He has also carried out research for both data fusion and decision fusion in
mechanical systems as well as financial applications. He has published more
than 50 articles, including two book chapters. He holds five patents.
=
Raj Subbu (M’00–SM’04) received the Ph.D. degree
in computer and systems engineering from Rensselaer Polytechnic Institute (RPI), Troy, NY, in 2000.
Since 2001, he has been a Senior Research Scientist in the Computing and Decision Sciences Group,
General Electric Global Research Center, Niskayuna,
NY. His research interests are in the areas of information systems, control systems, novel multiobjective
optimization methodologies, and soft computing. At
General Electric, he serves as a principal technologist
at the intersection of these areas for several high-business-impact projects. In addition, he served as Co-Principal Investigator in a
multiyear (2001–2004) National Science Foundation funded project in scalable
enterprise decision systems, in collaboration with RPI. He has authored over
25 publications and proceedings, has received one U.S. patent, and has 15 U.S.
patents pending. He is the principal coauthor of the book Network-Based Distributed Planning Using Coevolutionary Algorithms (Singapore: World Scientific).
Dr. Subbu received the Best Paper Award at the IEEE International Conference on Fuzzy Systems in 2003. He is an Associate Editor of the IEEE
TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS—PARTS A and C.
Dean K. Frederick (S’60–M’64–LM’00) received
the B.E. degree in mechanical engineering from
Yale University, New Haven, CT, the Sc.M. degree
in electrical engineering from Brown University,
Providence, RI, and the Ph.D. degree in electrical
engineering from Stanford University, Stanford, CA.
After teaching at Clarkson University, Potsdam,
NY, he spent 30 years as a Faculty Member in the
Electrical, Computer, and Systems Engineering
Department, Rensselaer Polytechnic Institute (RPI),
Troy, NY. During this period, he coauthored more
than 40 papers in the area of modeling, simulation, automatic control, and
computer-aided control system design. He also coauthored two text books
dealing with linear systems and the modeling and analysis of dynamic systems.
He had a number of visiting positions, including NASA’s Marshall Space Flight
Center, Huntsville, AL; the Exxon Corporation, Linden, NJ; General Electric’s
Corporate Research Center, Niskayuna, NY; The Control Systems Center,
UMIST, Manchester, U. K.; Lund Technical Institute, Lund, Sweden; and
Technical University of Delft, The Netherlands. He also consulted for General
Electric Company, Emhart Glass, Lawrence Livermore National Laboratory,
and The Applied Physics Laboratory of The Johns Hopkins University. After
retiring from Rensselaer in 1994, he spent six years as a senior engineer with
Unified Technologies, Troy, NY, where he did contract work related to the
control of jet engines for General Electric’s Aircraft Engines Division and
their Global Research Center. Areas of work included multivariable control,
simulation, fault detection, and the development of graphical-user-interface
(GUI) systems for the analysis and control of both military and commercial
jet engines. In June 2002, He established his own company, named Saratoga
Control Systems, in Saratoga Springs, NY. He continued performing contract
work for GE until September 2003, and also did an engine-related project for
RLW, Inc. of State College, PA. In December 2003, he began work for the
Glenn Research Center of NASA on a project to produce a Simulink dynamic
model of a commercial jet engine. At present, he is also working on advanced
power-plant controls with GE’s Global Research Center in Niskayuna, NY.
He is a coauthor of two MATLAB books, dealing with continuous-time and
discrete-time control systems.
Dr. Frederick is a member of the IEEE Control Systems Society. He received
a Centennial Certificate from the American Society of Engineering Education
for his work with computers in engineering education.

Evolutionary Design and Optimization of Aircraft Engine Controllers

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