SPECIAL FEATURE ADVANCED CONTROL

Control configuration design for the aircraft

gas turbine engine

by A. 6. Shutler

UK research into the design of multivariable controllers for gas turbines has been under way for several years. The results of simulation and

engine test evaluations have been reported by Sutton6, and Shutler and Betteridge.7 This article focuses on one aspect of multivariable controller

design which is that of selecting outputs for closed-loop feedback control; this process is often referred to as control configuration design.

complex system can be characterised in part by the relatively large number of control variables required to influence the behaviour A of the plant in accordance with the

performance and safety specifications. The selection of a satisfactory control strategy for such a plant is known to present problems which cannot normally be tackled solely by simple or intuitive reasoning. The main reason for this is the large number of options for controlling any particular plant output which arise partly from the number of input variables, partly from the availability of alternative measurements to define performance or safety limits, and largely from the likelihood that a high degree of interaction may exist between the various inputs and outputs.

The problem has been highlighted over recent years because of the trends which are impacting heavily on all modern engineering systems: first, the systems requiring control are becoming even more complex in the sense defined above and, secondly. increasingly stringent accuracy and response requirements are being imposed. These trends lead naturally to concern regarding system cost, reliability and maintainability and, in particular, to questions regarding the system robustness to environ- mental uncertainty. So the prime motivations facing modern control theories should include both robustness and system complexity. Robustness in control system design has been vigorously researched, but the issue of system design to minimise complexity has claimed less

than adequate attention. Major exceptions to this observation are the work on the use of the relative gain array (RGA) for input-output pairing selection in multi- loop systems by Bristol' and McAvoy? and a powerful theory for control configuration design by Reeves, Nett and Arkun.3

Control configuration design may be viewed as the process of identifying a control structure which allows a satisfactory trade-off between the conflicting require- ments of system performance (favouring a more complex system with multiple inputs, outputs and closed loops) and system reliability and maintainability (favouring a system with a minimal number of measurements and closed loops).

In general, control configuration design covers two stages of the total design process. First, it allows for the selection of the most appropriate set of measurements and manipulations and the choice of particular open-loop or closed-loop control modes. Secondly, control configura- tion design covers the partitioning of the total number of closed-loop controls into subsections of single and multiple closed-loops.

In the next section, some aspects of control system configuration typical of current in-service aircraft gas turbine engines are summarised in order to explain and emphasise the necessity for the development of a formal methodology to solve the engine parameter and control mode selection problem for the more complex, variable cycle, engines now being projected. Finally, two methods

COMPUTING & CONTROL ENGINEERING JOURNAL FEBRUARY 1995

ADVANCED CONTROL

used by Rolls-Royce plc at Bristol in research and feasibility studies on advanced powerplant systems, are described and supported by examples. The first method is based on a steady-state sensitivity matrix relating all engine performance and safety parameters of interest to all engine input variables. The method allows parameter choice and open-loop versus closed-loop options to be compared. A second method is based on dynamic relationships between engine inputs and outputs and allows selected closed-loop options to be compared in terms of achievable bandwidth and robustness criteria.

Control of gas turbine aero-engines The mechanical layout of a typical gas turbine engine

is shown in Fig. 1. Two spools, each comprising a number of compressor and turbine stages, rotate on concentric shafts. There is only aero-thermodynamic coupling between the spools. Air is drawn into the low-pressure compressor (LP or fan) and compressed. A portion of the fan exit air flow may be allowed to pass down a bypass duct whilst the remainder is compressed further by the high-pressure compressor (HP). The high-pressure air is mixed with fuel and combusted before being expelled through the HP and LP turbines. Power is absorbed by the turbines to drive the compressors and the turbine exit flow is mixed with the bypass air flow and ejected through the jet pipe and final nozzle to generate thrust.

Conventional propulsion system control The majority of current in-service civil and military

powerplants use closed-loop control of a selected thrust- linked parameter such as low-pressure spool speed (NL

or NF) or engine pressure-ratio (EPR) to set engine fuel flow (WFE). Commands to the thrust control loop are scheduled against the pilot's lever position with corrections applied for intake conditions of temperature and pressure to achieve maximum thrust over the operational range of altitude and flight llach number. The basic requirements for the thrust control loop specifl- accuracy, stability and robustness to engine and fuel system degradation due to ageing or manufacturing tolerances. Physical protection for the engine is provided by automatic selection of closed-loop limiter controls which are designed to override the thrust control loop to limit fuel flow increases. Variable geometry in this generation of engine is limited to variable compressor inlet airflow guide vanes which are used to assist engine starting rather than to provide control of engine efficiency. The guide vanes are set by open-loop schedules.

Fig. 2 shows a typical fan performance characteristic relating pressure ratio to air flow at a given rotational speed. The working line is a definition of the steady-state operating conditions of the fan. The surge line is an aerodynamic stability boundary. Acceleration of the engine from idle to maximum thrust requires movement away from the steady-state working line. In a simple, fixed geometry engine, movement towards surge can be controlled only by limiting acceleration rate, i.e. by limiting the rate of increase of engine fuel flow.

From the foregoing it can be seen that control configuration for a conventional propulsion system poses few problems. Parameter selection is no more than finding a parameter which is sufficiently related to thrust

fan pressure ratio (PRFANO)

HP compressor speed

(") bypass duct Mach No (DPQPl3)

turbine blade temperature fan speed (NF)

1 $ 1(

fan HPC

t - fan inlet guide vane fuel flow bypass area final nozzle area

(VCIGVP) (WFE) (A16) (AB)

Fig. 1 Gas turbine layout

COMPUTING & CONTROL ENGINEERING JOURNAL FEBRUARY 1995

to satisfy the thrust rating requirements and to be measurable, accurate and reliable. Similarly, parameters appropriate to the various structural and aerodynamic safety parameters, with the same controllability characteristics, have to be sought.

Variable cycle engine control The demands on projected flight propulsion systems

for improved fuel economy and wide flight envelope and mission capabilities may be met by engine designs which incorporate more active internal variable geometry devices. This type of engine, known as the variable cycle engine (VCE), and its dependence on the control system for achievement of predicted performance, have been discussed by Ganvood and Baldwin.4 It is foreseen that between five and eight variable geometry devices might be included in a variable cycle engine designed to meet future military operational requirements."

Efficient operation of the VCE is dependent on accurate control of the variable geometry to ensure that the compressors and turbines run at the design conditions of pressure ratio and airflow. Since the design conditions vary with the operational mode (loiter, combat etc.), it is unlikely that the control philosophy adopted for current engine types can be simply extended to the VCE'

1 There is a limit to the accuracy with which engine variable geometry can be positioned-improvements can only be achieved by increasing system mechanical and electronic complexity.

2 The critical relationships between pressure ratios and air flows and geometry positions are inconsistent, both from engine to engine and due to engine ageing effects.

3 There exist alternative, measurable parameters which

Fig. 2 Typical LP compressor operating

characteristics

may be used to define the key efficiency and safety parameters. For example, fan surge proximity can be sensed using either fan pressure ratio or bypass duct airflow Mach number @add and Porte?).

For these reasons, it is certain that the VCE will require additional closed-loop controls to provide accuracy and robustness and that there will be options as to which engine parameters should be included in the closed loops and which variables can be positioned by open-loop schedules. This is the control configuration problem defined in the earlier part of this article.

We now discuss the value of two computer-based methods which are considered to provide the sort of information the control system designer needs in order to reduce the number of options prior to making a final decision on the control configuration solution.

Static sensitivity analysis Closed-loop control configurations can be defined in

terms of those selected engine output parameters (performance and safety parameters) which are to be used to control the positions of a corresponding selection of actuators. These selections are indicated by the vectors Y, and U,i in Fig. 3. The remaining engine outputs (Yo, in Fig. 3) are set under the influence of the open-loop scheduled actuator settings (UOl in Fig. 3). Uncertainty in the engine control accuracy can therefore arise from a variety of sources, including:

0 inaccuracy in the measured engine outputs (sensor

0 inaccuracy in the position control of the open-loop

0 engine degradation through age which means that the

errors) in the closed loops

actuators

/ maximumthrun I

COMPUTING & CONTROL ENGINEERING JOURNAL FEBRUARY 1995

open-loop actuator aduator

commands

gain terms relating engine outputs and inputs. Each element in the sensitivity matrix is scaled to represent 'percentages of useful range' variations in the input and output variables.

Fig. 4(4 shows the open- loop engme sensitivity matnx partitioned in order to distinguish between changes in the engme outputs and inputs selected for closed-loop control (AYc,, A&) and those remaining (AYo1, ALL) The action of a selected closed-loop configuration will be to

VcL engine outputs selected lor

Ucr actuators selected for

Yo, other engine outputs UoL actuators to be scheduled

closed-loop control

closed-loop control

open-loop

been used by Rolls-Royce plc at Bristol to aid in the choice between control configuration options for a variety of engine types The example chosen for this article relates to a variable cycle engme which has variable inlet airflow guide vanes (VCIGVP) on the low- pressure compressor and a variable area bypass duct (A16) in addition to the more conventional variable area let pipe nozzle (A8) and engine fuel flow W E ) as the engine control inputs The objective of the control

(

&I [&I-' [&I - [&I [&I -' ""] E:]

Fig. 3 Gas turbine control layout

COMPUTING & CONTROL ENGINEERING JOURNAL FEBRUARY 1995

VANCED CONTROL

Table 1 COMIC output: open-loop case dWFE dA16 dAS dVCIGVP

NH 0.35 0.01 0.26 0.03 NF 0.60 4.03 079 0.16 PRFANO 0.62 4.13 4 8 1 4.09 PRHPC 017 0.05 0.22 0.01 DPQP13 4 2 2 0.10 1.49 4 .02 DPQP3 4.09 4.03 4.09 4.01 T41 0.72 0.03 0.47 0.07 XGMN 1.05 4.01 4.04 4 . 1 2 P3 1.00 4 .07 4.57 4.08 T3 0.50 4 0 1 0.27 0.05

Table 2 COMIC output: controlled output NF, maniuulated variable WFE

. .. PRFANO 1.04 4.10 -1.64 4 . 2 5 PRHPC 0.28 0.06 000 4.03 DPQPl3 4.36 0.09 1.77 0.04 DPQP3 4.16 4.03 0.03 0.01 T41 1.21 0.07 4.48 -0.12 XGMN 1.76 0.04 -1.44 4 3 9 P3 1.67 4 .02 -1.89 -0.34 T3 0.84 0.01 4.40 4.09 W E 1.68 0.05 -1.33 4.26

explore the feasibility of using closed-loop control of low- pressure (LP) compressor speed (NF) and a LP compressor performance characteristic (€'WAN0 or DPQP13) to provide accurate thrust response to pilot command over a wide range of operating conditions. The traditional method for comparing the several alternative control options would be to design the controllers and test over the necessary envelope. The multiple options available, even with this relatively simple example, make this impossible in this case.

Table 1 shows the sensitivity matrix for the VCE at a nominal design condition with no loops closed. It can be seen that, for example, a change of 1% in fuel flow (dWFE) gives rise to a 1.05% change in thrust ( X G W . Clearly, fuel flow has a major influence on all output parameters, which is of course the reason for its control within closed loops in all conventional engine systems. Other points of interest are the much greater sensitivity of LP compressor pressure ratio (PRFANO) to positional errors in jet pipe nozzle (dA8) than to the bypass area (dA16). Note also that thrust (XGMN) is relatively insensitive to changes in either A8 or A16 (404"a and

The value of COMIC lies in its use to make visible the change in input-output sensitivities when one or more system outputs and inputs are combined in closed loops. Table 2 shows that a single closed-loop control involving LP compressor speed (NF) and fuel flow (WFE) results in quite different sensitivities. It is now possible to make three types of judgment about this mode of control:

1 How precise must be the control of the open-loop (scheduled) variables dA8, dA16, or VCIGVP to meet

401°.b).

the specified accuracy of control of the key performance and safety outputs (XGMA, PRHPC, T41)? For example, thrust ( X G W is now very sensitive to A8 (-14%) while loa on A16 gives only 0.04'4 variation in XGMN.

2 What are the effects of the closed-loop sensor errors (dNF in this case) on the system outputs? In this case, we can see that thrust is extremely sensitive (1.76%) to errors of 1% in the NF measurement.

3 How much control action is required by the closed-loop input variables (WFE) to correct for disturbances in the corresponding engine output variables (NF)? Note that a change of 168% WFE is required to restore NF to its demanded value.

Tables 3 and 4 show the value of COMIC in comparing two or more control configurations. Two of the four options originally thought to be viable (using experience and performance data) are presented. In each case the engine parameters chosen for a closed-loop section are LP speed (NF) and bypass duct airflow Mach number (DPQP13). But a choice is to be made between the use of fuel flow (WFE) and bypass duct area (A16), and fuel flow W E ) and jet pipe nozzle area (A8) as the closed-loop input variables. Two of the more obvious conclusions are:

1 The effect of schedule position errors in A8 (with A16 selected for control) is greater (compare the sensitivities in the relevant 3rd columns) than that due to schedule position errors in A16 (with A8 selected for control). For example, 1 'ZO position error in A8 leads to -2,30°% thrust whilst 1 ob position error in A16 leads to 0,1106 error in selected thrust.

Table 3 COMIC output: controlled outputs NF and DPQP13, maniuulated variables WFE and A16

dNF dDFQP13 dA8 dVCIGVP NH 0.70 0.34 4.81 4.07 PiiFANO 0.62 -1.16 0.42 4 2 1

052 0.67 -1.18 4 0 5 p m 4.28 4 3 4 0.64 0.03

0.83 -1.96 4.15 1.51 1.94 0.49 -2.30 4.41 XGMN

P3 1.59 4 2 2 -1.49 4.33 0.89 015 4.66 4.09 T3

W E 1.90 0.61 -2.41 4.29 Alfi 4.15 11.43 -20.27 4.42

KY

Table 4 COMIC output: controlled outputs NF and DPQP13. maniuulated variables WFE and AS - . -

dNF dDPQP13 dA8 dVCIGVP NH 0.54 4.11 0.04 4.06 PRFANO 0.70 4.92 4.02 4.22

0.28 0.00 0.06 4.03 p m DF'OP3 -0.15 0.02 4.03 0.01 T4l- XGMN P3 T3 WFE A8

1.11 1.47 1.29 0.76 1.41 0.20

4.27 4 . 8 1 -1.07 4 . 2 2 4 7 5 0.56

0.10 0.11 0.07 0.03 0.12

4.05

411 4.36 4.30 4.08 4 .24 4 .02

COMPUTING & CONTROL ENGINEERING J O W A L FEBRUARY 1995

2 The control action required by A16 for given errors in NF and DPQ13 are greater (as a percentage of full travel) than that required from A8 (4.15% and 11.43% for A16 compared with 0.2% and 0.56% for A8, respectively).

The overall conclusion from COMIC at this operating point is that A8 with W E should be used for closed-loop control of NF and DPQP13. Note that, in practice, this exercise should be repeated at many points throughout the operating envelope of the engine.

COMIC has been used successfully to provide useful, reliable information in a relatively painless way However, the conclusions drawn are independent of dynamic relationships between the outputs and inputs. Conse- quently, the most viable of the control configurations considered in COMIC must be examined for their control suitability in terms of response and robustness.

Resilience analysis Having selected candidate control configurations

using the static analysis offered by COMIC, it is necessary to be able to assess the potential difficulty (in a dynamic sense) of completing successful closed-loop designs. The resilience factor S i s a measure which is easily computed from the engine and actuator linearised dynamic models. The magnitude of Sviewed as a function of frequency, relates through a simple algorithm to the maximum uncertainty of the engine model for which a stable closed-

ADVANCED CONTROL

loop control strategy should exist. The theory behind the resilience factor is not repeated here. A full explanation can be found in Reference 3.

The resilience factor is related to the relative gain array (RGA) which is a well established method for control configuration design. A good overview of the theory underlying the RGA is given in Reference 6. Given a transfer function matrix G(s) representing a square plant, the RGA is defined as

[ R((G)l(S) = GN.* 3 yhere .* represents the element-by-element product and C = G-'.

Much of the value of the RGA stems from the existence of heuristics, for example, that input and output variables should be paired in order to give diagonal elements of the RGA as close as possible to 1; and that large or negative elements in the RGA will lead to difficulties in controlling the plant.

Whilst a number of theoretical results do exist, unfortunately, many of them are only valid for [ &G)](0) and assume integral action in the controller. The inadequacy of this when dealing with the gas turbine is illustrated by a two-by-two example described in Reference 2 this shows a case where the recommended pairings were reversed at low and at high frequency; successful control was achieved using the high-frequency pairings. Consequently, although the RGA may provide

1 P 10-2 lo-' 1 00 10'

WFE, A16-NF, -DPQP13

1 P 1 o-? 1 0-1 1 00 I O '

WFE. AWNF, -DPQP13

COMPUTING & CONTROL ENGINEERING JOURNAL FEBRUARY 1995

Fig. 5 Resilience plots

27

VANCED CONTROL

valuable guidance in assessing a candidate control configuration, it does not by itself provide a quantitative indication of the viability of a particular control configuration,

The resilience factor $ which addresses these shortcomings of the RGA is defined as:

$= ~max{ll@(O Ill' IlC(O) I!-- I

where

I k 11, is defined as mtx $. L& I

k I k. is defined as m w Z b& I l b

The calculated value of the resilience factor can be related to the maximum plant uncertainty which any closed-loop controller will able to tolerate:

whereas is closed-loop 3dB bandwidth of the system, and is the relative additive plant uncertainty

The key properties of the resilience factor are summarised as follows:

1 It provides a quantitative measure of the robustness achievable for a given control configuration.

2 It provides a measure which allows alternative control configurations to be more readily compared than is possible using more well established relative gain array.

3 The calculated value of the relative gain array is independent of the scalings of inputs and outputs.

4 In practice it has been found that, for frequencies below the closed-loop bandwidth, values of $greater than 2 indicate that satisfactory closed-loop robustness will not be achievable.

The use of the resiliency criterion is illustrated by means of extending the example chosen for demonstrating the COMIC analysis. The resilience factors $corresponding to the input-output selections (WFE, A16 to NF, DPQP13) and W E , A8 to NF, DPQP13) are shown in Fig. 5. The plots show the variation in $against frequency at four different engine operating points. The conclusion which can be drawn from these traces is that the selection (WFE, A8 to NF, DPQP13) gives $very close to 1 indicating that the system would be easy to control. The traces for the set (WFE, A16 to NF, DPQP13) show $values increasing to 2.4 within the frequency range of interest-indicating that this system would be more difficult to control and that the achievable robustness margin against uncertainty would be correspondingly much lower.

Therefore, the conclusion to the example is that a control configuration in which NF and DPQP13 are coupled in a closed-loop with A8 and W E , and in which the VCIGW and A16 are scheduled open-loop input variables, is most likely to result in a satisfactory eventual control design.

Concluding remarks Control configuration design is a crucial stage in the

control system design process for complex plants. The two methods described are recommended as providing the type of information needed to enable the control system designer to eliminate potentially troublesome candidate control options at an early stage in the design process.

The sensitivity analysis method allows the designer to make choices regarding open-loop and closed-loop controls for specific outputs and inputs. It also indicates the magnitude of controller action required to achieve desired offsets in controlled outputs.

The resilience criterion provides an indication of the level of robustness which is achievable with an eventual closed-loop control design. Furthermore, if information about plant uncertainty is available, then this criterion provides a necessary condition for a control design specification to be met.

Acknowledgments The author wishes to acknowledge support of former

colleagues in the Advanced Controls Group at Rolls-Royce plc at Bristol for implementing the software methods and developing the engine models. The specialist advice of Cambridge Control Ltd. is recognised as having been of key importance to the application of the resilience criterion to the gas turbine control problem.

The views expressed are those of the author and do not reflect any commitment on the part of Rolls-Royce plc.

neterenc.. 1 BRISTOL, 1. E. H.: 'On a new measure of interaction for multivariable

process control', IEEE Transaction on Automuti Control, 1966 2 McAVOY, T. J.: 'Interaction analysis', Research Triangle Park, NC,

USA, Instrument Society of America 3 REEVES, D. E., NETT, C. N., and ARKUN, Y.: 'Control configuration

design for complex systems: a practical theory', IEEE Transactions on Automati Control, 1991

4 GARWOOD. K. R., and BALDWIN, D. R.: 'The emerging requirements for dual and variable cycle engines'. 10th International Symposium on Air Breathing Engines 1992. RAE-TMP-1220

5 DADD, G. J., and PORTER, M. J.: 'Surge recovery and compressor working line control using compressor exit mach number measurement', AeroTech '92; C428/331210

6 SUTTON, A. E.: 'Application of multivariable control to a turbofan engine', Contml'91 Conference. Vol2

7 SHUTLER, A. G., and BETTERUXE, H. C.: 'Definition. design, and implementation of mntrol laws for variable cycle gas turbine engines', RAeSopc Conference, 3rd November 1994, Bristol

8 MACIEJOWSKI, J. M.: 'Multivariable feedback design' (Addison Wesley, 1989)

0 IEE 1995

Sam Shutler was formerly with Rolls-Royce plc, Bristol. He is now a Consultant.

COMPUTING & CONTROL ENGINEERING JOURNAL FEBRUARY 1995

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