BENEFITS OF INVERSE MODEL CONTROL OF ROLLS-ROYCE CIVIL GAS TURBINES
Cerith Davies, Jonathan E Holt, Ian A Griffin
Rolls-Royce plc, Derby England
Rolls-Royce plc, Derby, England
Department of ACSE, University of Sheffield, England
Abstract: Rolls-Royce Civil Aerospace has historically used linear, gain-scheduled
proportional-integral (PI) compensation for control of gas turbine fuel flow. Engine
dynamics vary with flight and power conditions, and a lengthy design and
verification process is required to meet the specification for all conditions. This
paper reports a feasibility study that has allowed the core linear PI compensation to
be replaced with non-linear inverse model control. The inverse model controller
minimises dependence against engine power level, removes the dependence against
altitude, and reduces the cost of downstream software verification. The controller
will run for the first time in February 2006 on the Rolls-Royce Trent 1000 engine.
Copyright © 2006 Rolls-Royce plc.
Keywords: inverse modelling, gas turbines
1. INTRODUCTION
The modern gas turbine is a complex item of
machinery requiring an advanced digital control
system to guarantee safety and performance. Digital
control enables complex safety functions to monitor
engine performance and identify the onset of risk or
performance degradation to the pilot and maintenance
staff alike. It allows accurate and repeatable engine
performance with attendant fuel burn and operability
benefit.
The flexibility of digital control has enabled RollsRoyce (R-R) to continually evolve its gas turbine
control strategy. To a simple approximation the
dynamics of a modern three shaft engine are first
order, and the required bandwidth and steady state
performance can be achieved using a classical
proportional and integral control function. Section 2
of this paper outlines such a control strategy
employed in all Trent family engines to date. The
advent of inverse modelling techniques and the ease
with which it can be introduced within the core
control architecture has provided an opportunity for
change at considerable benefit to the company.
Section 3 will outline the Rolls-Royce Inverse
Modelling (RRIM) (Shutler, 1989; Mahmood, et al.,
2005) technique and the change in the core
architecture required for implementation. Side by side
comparisons of the traditional versus RRIM approach
are reported in section 4.
The successful feasibility tests were a major factor in
the subsequent introduction of the RRIM at the heart
of future Rolls-Royce gas turbine (GT) control
systems.
The paper concludes with a summary of the major
benefits afforded by this change. At the time of
submission, Rolls-Royce is preparing for the first
civil engine demonstration of RRIM control on the
Trent 1000, due to run for the first time in February
2006.
2. TRADITIONAL ARCHITECTURE
The traditional control of the three shaft GT employs
a number of independent closed loop control loops all
vying for control of the engine fuel flow (FF) through
the loop selection logic, which is a series of highest
and lowest wins gates.
The functions are split into three main areas:
a)
Steady-state control of engine performance used to maintain engine thrust to a set level
indicated by the pilot’s throttle lever position.
The primary indication of thrust used on RollsRoyce three shaft engines is the Turbofan Power
Ratio (TPR) (Rowe and Kurz, 2001), which
provides an accurate indication of thrust for
engines with very large bypass ratios.
b) Transient control of engine performance – used
to accelerate or decelerate the engine. Typically
these are loops which control to shaft
acceleration i.e. rate of change of spool speeds
(Ndot), the rates of which are maximised to meet
contractual engine acceleration and deceleration
times but without compromising surge margins
within the compressor.
c)
Limiter control - to ensure minimum engine
conditions are maintained to e.g. prevent
generator dropout or ice build up on the fan; and
to ensure maximum limiter control to prevent
shaft spool over speed or excessive combustor
pressure.
The architecture of each loop is essentially the same
and is shown schematically in Figure 2: a feedback
parameter compared against a reference setpoint
demand. The generated error is then compensated as
appropriate by a first order lead/lag compensator and
forward loop gain. (Note the transient loops control to
an Ndot (acceleration) schedule to maintain adequate
compressor working lines, and therefore require a
second integrator to maintain a zero steady state error
response).
Table 1 Loop Identification and Fuel Index
Name
Type
Fuel
Index
TPR
Steady
State
4
Primary Thrust Control
ACU
Transient
11
Ndot Acceleration Control Unit
DCU
Transient
13
Ndot Deceleration Control Unit
Description
Table 1 identifies the main loops and provides a brief
description of their role under normal operation. Also
identified in Table 1 is the (legacy based) fuel loop
index assigned to the loop in order to give an
indication when the loop gains authority after
winning through the loop selection logic.
Figure 1 Loop Selection & Integrator Arrangement
Figure 1 shows the arrangement where the output of
each loop (by architectural definition in units of rate
of change of fuel flow) is continually fed to the lowest
wins/highest wins gates which form the loop selection
logic. This logic arrangement and the order of
precedence protect the engine from requesting
abnormally large changes in fuel flow. For example,
during a step change in throttle position the steady
state TPR loop (fuel index 4) will attempt to follow
this transient and ask for a sudden and severe step in
the fuel flow. The use of the selection logic
automatically de-selects this loop at the final lowest
wins gate and selects in its place the smaller loop
demand from the Acceleration Control Unit (ACU)
loop. A sensible step in fuel flow results, and the
engine is protected against surge.
The integrator in Figure 1 integrates the selected loop
output (in units of rate of change of fuel flow (FFdot))
to a final fuel flow (FF) signal for onward passage to
the engine’s fuel pump and metering system. The
stand alone integrator also smoothes out any
discrepancy as a result of changing from one loop to
another at the loop selection stage.
Figure 2 Basic Loop Architecture
Gas turbine aero-thermal properties are such that the
engine response changes with flight conditions and
power levels. The gains and time constants applied to
each loop must be tuned in order to provide the
required bandwidth and stability margins across the
flight envelope. The gains/time constants are typically
recorded as a series of look up tables against the two
main flight parameters - altitude and shaft speed. This
immediately imposes an onerous task on the designer,
that of having to optimally tune the controller against
a model operating at a series of altitudes and repeated
for a series of power conditions. This is time
consuming, a burden on computational storage and
requires additional downstream software verification
of the chosen matrix of parameters – each entry
having to be tested individually.
3. R-R INVERSE MODEL ARCHITECTURE
A departure from the traditional architecture is
employed in the Rolls-Royce Inverse Model
technique. The basic system architecture at a
functional requirement level remains unchanged: a
series of independent loops (14 for the Trent 1000) all
vie for control of the engine fuel flow. The primary
difference comes from the removal of the FFdot
integrator used in the traditional approach and its
replacement with a self-referencing proportional and
integral term. With respect to Figure 2, the final loop
output changes from an FFdot demand to a high
pressure shaft acceleration (NHdot) demand.
3.1 Description
The inverse modelling technique works by identifying
the response of a dominant engine state variable (in
the RRIM’s case HP shaft speed (NH)) to known
changes of fuel. By arrangement, this model of the
engine’s highly non-linear behaviour can be inverted
(within the controller) such that the required fuel flow
can be established for a given flight condition.
Figure 3 shows the basic RRIM layout.
to the proportional arm in the classical PI control in
Figure 5 (see area labelled section A in both figures).
The integral action (highlighted as section B)
provides the necessary steady state fuel flow (FFss)
for the given spool speed. The elements of Fs are in
units of fuel flow (pounds per hour).
Figure 3 RRIM Architecture
Mathematically, it can be shown that the architecture
in Figure 3 is exactly that of a classical PI controller
with additional features such as automatic altitude
compensation and self-referencing dynamics.
Schematically, the similarity to a classical PI
controller is shown by noting PI control can be
implemented by placing a first order lag in positive
feedback as shown in Figure 4.
Together the two tables define the proportional and
integral gain of the system and therefore form the
pole-zero characteristics (or time constant) of the
controller to match engine dynamics. The controller
zero (which varies with condition) is therefore
tracking and cancelling the (condition dependent)
pole part of the plant dynamics. The total fuel flow
FF is the summation of both terms.
FF = FFss + ∆FF
Two important differences from the classical PI
control are noted:
a)
Figure 4 PI as a Lag in Positive Feedback
This lag can further be split into constituent
components as shown in Figure 5.
(1)
In order to control the non-linear plant the
RRIM’s steady state and dynamic tables use the
integrator output as the reference parameter. This
means an extra connection is required between
the dynamic table (Fd) and the RIMM’s
integrator (see connection on Figure 3). This is a
connection not normally seen in the classical
structure.
b) In order that the RRIM’s integrator can be used
as the scheduling parameter, it must be fed with
an engine parameter. Noting that the negative
feedback term in the RRIM already calculates the
transient fuel flow change (∆FF), this is
multiplied by the transient table (Fd) to calculate
the modelled NHdot input for the integrator.
3.2 Self Referencing Against Power
Figure 5 Lag split as an Integrator in Negative
Feedback
The RRIM has two basic tables that capture the nonlinear engine behaviour – a steady state table (Fs) and
a dynamic over-fuelling table (Fd). Comparison of
Figure 3 (RRIM) and Figure 5 (classic PI control)
show the basic equivalence:
The dynamic table (Fd) defines the rate of change of
shaft speed (and therefore bandwidth) in response to a
given change in fuel (∆FF) i.e. units of (NHdot/∆FF).
The table output is inverted such that when multiplied
by the chosen loop demand (in units of NHdot rather
than FFdot in traditional control) the correct transient
change in fuel (∆FF) is established. This is analogous
The RRIM automatically compensates for the
inherent non-linear properties of the GT. The use of
the integrator output as the reference parameter
allows the model to self-regulate and follow engine
power level. Contrast this with the traditional
approach where the loop compensators must be tuned
at every power condition.
In theory, because the PI control contains an inverse
model of the plant, only simple outer loop
compensation is required for the loop in control,
typically in the form of a gain term.
In practice, a small degree of trim scheduling against
engine power level is performed. This can be
attributed to the limitations of the RRIM tables,
which cannot accurately reflect the dynamics of the
plant at all frequencies – such a model being
impossible. Indeed, the nature of the method
employed to populate the RRIM’s tables means the
inverse model is accurate at two frequencies only:
•
DC. By measuring the steady-state spool speeds
in response to a given steady-state fuel flow, and
•
High frequency. By measuring the instantaneous
peak shaft acceleration (NHdot|max) in response to
a transient step change in fuel (∆FF).
Both RRIM and traditional architecture are tested
against two different types of throttle movement: a
staircase (small step) throttle movement, and a slam
(larger step) acceleration/deceleration. The results of
additional noise rejection tests are also noted.
4.1 Staircase Tests
SLS, MN=0 : Response to Step Changes in Throttle Position
70
Traditional
RRIM
60
3.3 Self Referencing Against Altitude
50
40
TPR
In contrast to the traditional approach, the RRIM is
invariant against changes in altitude. This is achieved
by the use of referred parameters (Walsh and
Fletcher, 2004) in the RRIM steady state and transient
tables.
30
20
GT referred parameters are defined as:
Referred NHdot:
Referred NH:
Referred Fuel Flow:
10
NHdotr = NHdot/δ
NHr = NH/√ϑ
FFr = FF/(δ.√ϑ)
Where δ and ϑ are computed from the fan input
pressure P20 and temperature T20 as defined by
δ = P20/14.696
ϑ = T20/288.15
All calibration data is collected at sea level static
(SLS) and zero Mach Number (MN), and all input to
the tables must be referred to their SLS condition.
Similarly, on exit from the RRIM tables, all data is
un-referred back to the prevailing flight conditions.
(For clarity, this referral and un-referral of engine
parameters is not shown explicitly in Figure 3).
This use of referred data means that the designer is
presented with a much-simplified problem because
the degree of dependence associated with altitude has
been removed.
0
10
20
30
40
50
60
time [sec]
70
80
90
100
Figure 7 Comparison of Staircase Plots at Sea Level
Static, MN=0
Figure 7 compares the response of both controllers to
step changes in the primary thrust setting parameter
(TPR). Also shown on this (and subsequent) plot(s) is
the relevant fuel index identifying the loop in control.
In both cases, the initial transient is on the ACU
(index 11) (or occasionally the secondary thrust
setting loop (index 19)), followed quickly by the
majority of time on the primary thrust setting TPR
loop (index 4). Clearly, the RRIM has been able to
duplicate the results from the standard controller, but
with a much simplified set of tuning parameters.
Figure 8 repeats this test but at 30,000 feet and
MN=0.9. Once again, the RRIM architecture is able
to match that of the classical control strategy.
30,000 feet MN=0.9 : Response to Step Changes in Throttle Position
60
Traditional
RRIM
4. COMPARISON OF TRADITIONAL VERSUS
RRIM APPROACH
50
40
TPR
As part of the feasibility study to identify the benefits
of the RRIM approach, both architectures were used
to control the fuel flow to a model of a typical Trent
engine. The test layout is shown schematically in
Figure 6.
0
30
20
10
0
0
10
20
30
40
50
60
time [sec]
70
80
90
Figure 8 Comparison of Staircase Plots at 30000 feet,
MN=0.9
Figure 6 Engine and Controller Test Harness
100
Inspection of Figure 8 reveals the same response is
obtained, but for significantly less design effort in the
case of the RRIM architecture. Table 2 compares the
number of gain and time constant scheduling points
employed in the TPR loop in each case.
SLS, MN=0 : Response to slam Acceleration and Deceleration from High Idle
80
Traditional
RRIM
70
60
50
TPR
Table 2 Number of Tuning Parameters for TPR Loop
Traditional
RRIM
Engine Power
27
5
Altitude
27
0
TOTAL
54
5
40
30
20
Clearly, the RRIM wins in terms of a reduced number
of parameters for tuning against engine power level,
and the complete absence of the need for any tuning
parameters for altitude compensation.
10
0
0
10
20
30
40
50
60
time [sec]
70
80
90
Figure 10 Comparison of Slam Accel/Decels from
High Idle (SLS, MN=0)
4.2 Slam Acceleration/Deceleration Tests
Figures 9 and 10 compare the response to a slam
acceleration and deceleration of the engine, starting
from a low and high engine idle condition
respectively. Both tests are completed at SLS, MN=0.
Finally, the ability to remain on the ACU for as long
as possible will accelerate the engine more quickly.
This could in future be traded as benefit elsewhere in
the engine design. To achieve this the TPR loop must
lose out in selection against the protection afforded by
the ACU loop. To do this the NHdot demand from the
TPR loop must be larger than the ACU demand at the
top end of the transient, thereby losing out in
selection at the loop selection stage. A larger loop
demand will be obtained if the TPR loop gain is
increased.
Naturally,
without
any
further
compensation the thrust overshoot is likely to be
prohibitive.
In each case the behaviour near the idle setting is
slightly different. This is a typical behaviour of
systems configured in a multi-loop selection logic
scheme. Small changes in loop gain can cause the
loops to come in and out of authority. The important
point is the ability to maintain an overall smooth
profile in the engine fuel flow and thrust setting
parameter. Deviations from this are allowed in and
around the vicinity of a bleed valve closure/opening
(to protect engine surge margins). Such a feature is
seen clearly on Figure 10 at the top of the take off
profile. The prominence of the effect is easily
removed by a de-tuning of the TPR loop gain.
An inspection of Figure 11 shows the classic PI
controller applied to Trent engines requires the lead
term in the lead/lag compensator to be non-zero to
implicitly form the proportional plus integral control
by coupling with the central integrator. (The lag term
removes high frequency noise).
Figures 9 and 10 again show comparable performance
in the RRIM versus traditional approaches, but with
the former resulting in a much reduced tuning effort.
SLS, MN=0 : Response to slam Acceleration and Deceleration from Low Idle
80
Traditional
RRIM
70
60
TPR
50
40
Figure 11 Explicit and Impicit Formation of the PI
pole-zero term
30
20
10
0
0
10
20
30
40
50
60
time [sec]
70
80
Figure 9 Comparison of Slam Accel/Decels from
Low Idle (SLS, MN=0)
90
100
The RRIM however has an explicit PI control as it’s
based on a lag in positive feedback (see section 3.1,
Figure 4). The lead/lag compensator is therefore free
to be used to provide phase advance around the
crossover frequency i.e. provide system damping. The
TPR bandwidth can therefore be increased, allowing
the ACU to remain in authority and accelerate the
engine at a faster rate.
100
4.3 Additional RRIM Tests
Additional tests have been conducted to evaluate the
robustness of the RRIM against disturbance rejection
and systematic errors in the RRIM tables.
The RRIM proved effective at rejecting an applied
disturbance in the form of noise on the engine input
data, and also changes in the electrical load off-take
from the shaft coupled generator. For the noise
disturbance, the loop gain served to attenuate the
noise and keep within an allowed tolerance. For
rejection of power off-take variations, the RRIM
control allowed sufficient forward gain to prevent the
shaft spool speed from dropping below the allowed
minimum level.
The accommodation of systematic errors in the model
of the plant dynamics (tables Fs and Fd) were tested
by calibrating the RRIM tables as per normal and
then deliberately changing the engine dynamics so
that the RRIM tables are no longer a perfect inverse
of the plant behaviour. The mismatch was achieved
by incorporating errors into the dynamics of the
engine model. The RRIM architecture proved
effective at rejecting this mismatch. In effect the polezero cancellation applied by the RRIM is no longer
optimal, but the external loop gains accommodate this
and increase or decrease the scheduled fuel flow
accordingly.
In summary, the side-by-side comparisons have
established that the RRIM at least matches the
performance of the traditional architecture, and has
the potential to improve in cases. It has been shown to
be a viable replacement for the existing architecture.
5. SUMMARY OF BENEFITS
The successful feasibility tests have proven the
concept of the RRIM as a viable architecture. The
benefits of RRIM versus traditional PI control are
summarised below.
d) The use of referred parameters means that a total
invariance against altitude dependency is
achieved.
e)
The core of the traditional architecture is a FFdot
integrator. The core of the RRIM is an NHdot
integrator plus proportional term. The extra
proportional term allows the RRIM designer to
use the external loop lead terms as an extra
degree of freedom to apply additional phase
advance (damping).
f)
The RRIM has proven robust against mismatch
to the engine dynamics, with the outer loops
being used to compensate in this case.
g) The RRIM has proven robust against disturbance
rejection in the form of noise and load addition.
6. CONCLUSIONS
A series of feasibility tests have shown the RRIM
performance to be equivalent to, and with the
potential to be better than, the existing PI control
scheme. The RRIM has been shown to introduce
significant benefits in terms of the design effort and
verification testing of the control system. The RRIM
architecture has been shown to be an equivalent of the
basic PI scheme currently used to control GT fuel
flow and, with minimal effort, has replaced the
traditional core PI compensation with the change
remaining transparent at a higher functional level.
ACKNOWLEDGEMENTS
The
authors
acknowledge
the
help
and
encouragement of many colleagues within Control
Systems Engineering and elsewhere at Rolls-Royce
and at the Rolls-Royce University Technology Centre
in Control and Systems Engineering, Department of
Automatic Control and Systems Engineering,
University of Sheffield.
REFERENCES
a)
Correction against power level and altitude vastly
simplify the degree of tuning. The downstream
costs associated with software verification and
testing of the parameter set therefore provides a
cost saving to the company.
b) The RRIM is essentially a self-referencing PI
controller, and can be accommodated with
minimal change to the existing system
architecture. The use of a loop selection logic
hierarchy to authorise the most appropriate
closed loop control can still be employed and
with minimal change.
c)
The RRIM encapsulates the highly non-linear
engine dynamics within its steady-state and
transient tables, and therefore self-regulates
against changes in engine power level.
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Patent No. 5083277)
Mahmood S., Griffin I.A., Fleming P.J. (2005).
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Expo 2005: Power for Land, Sea and Air.
Rowe, A.L. and Kurz, N. (2001). A Method of
Obtaining an Indication of the Power Output of a
Turbine. European Patent EP 1 069 296 A3.
Walsh P.P. and Fletcher P. (2004). Gas Turbine
Performance. 2nd edition. Chapter 4. Blackwell,
Oxford.