Abstract—A decentralized PI controller tuning method is presented and is applied to a two input two output model of a Rolls-Royce jet engine. Using a zero assignment technique, the process is firstly decoupled through a stable decoupler matrix to attain the benefits of decentralized control techniques. Next, a model reduction method is introduced to reduce the resulting high order diagonal matrix to a diagonal matrix which has first order plus dead time elements. Finally, a single input single output PI controller tuning method which has been optimally obtained for first order plus dead time processes is used to determine optimal PI controllers for each loop.

I. INTRODUCTION

EEDBACK control has always been an essential part of jet engines, because they operate at near their

mechanical or aero thermal limitations [1]. The primary engine variable is the engine thrust. Other variables such as compressor surge margin(s) are important for safety. The main strategy in jet engine control is to use fuel flow to control the thrust. Open loop scheduling is often used for other control signals [2].

Modern jet engines, which are more complex and have more control variables, are able to improve engine performance and safety. Reducing fuel consumption and increasing engine life can also be considered as objectives in jet engine design. Proposing advanced control strategies for modern civil or military jet engines in order to improve performance and safety is currently an important subject for research at companies including General Electric, NASA, Volvo and Rolls-Royce. Research projects focusing on multivariable engine control have been undertaken since 1970. A multivariable controller for a jet engine using Nyquist array methods was designed in [3]. Another multivariable frequency domain method proposed in [4] has been frequently used by General Electric. In [5], this method was also applied to the GE16 experimental engine. In 1974, the US Air Force and NASA initiated a major research program to evaluate the applicability of LQ design methods to jet engine control. The works carried out in [6, 7] are examples originating from this program. LQG and LQG/LTR techniques were applied to jet engines in [8, 9]. In 1990s, H control design techniques have been applied to jet engines in many research projects. One example is given in [10], where an H controller was designed for a

Manuscript received February 28, 2005. This work was supported in part by Rolls-Royce.

S. Tavakoli (phone: +44-114-2225686; fax: +44-114-2225138; e-mail: s.tavakoli@sheffield.ac.uk), I. Griffin (i.griffin@sheffield.ac.uk) and P. J. Fleming (p.fleming@sheffield.ac.uk) are with Rolls-Royce UTC, Department of Automatic Control & Systems Engineering, University of Sheffield, Sheffield, S1 3JD UK.

Rolls-Royce Spey engine. Another application of Hcontrol to a General Electric engine was described in [11]. A comparison between LQG/LTR and H multivariable design techniques for application to a linear model of a jet engine was carried out in [12]. H methodology has also been used in integrated flight and propulsion control (IFPC) system design methods [13, 14]. In [15], a robust integrated flight and propulsion controller was designed for an experimental V/STOL aircraft configuration, using Hloop shaping method. In [16], a multivariable PID controller was applied to the linear and nonlinear NARMAX and neural network models of Rolls-Royce Spey MK202 aircraft gas turbine. This research work showed that gain scheduling is necessary because the system dynamics change significantly when considering all operating conditions.

This paper aims to investigate decentralized PI control for the Rolls-Royce ANTLE (Affordable Near-Term Low Emissions) jet engine. The paper is organized as follows. Section 2 discusses compressor instabilities which limit the performance and effectiveness of jet engines. A brief description of the jet engine model is given in Section 3. Also, use of a multivariable controller is suggested to improve engine performance and efficiency through extending the stable operating range of the compressor system. In Section 4, the two input two output (TITO) engine model is decoupled through a decoupler. Section 5 discusses a simple technique to deal with TITO models resulting in unstable decouplers. Simulation results are given in Section 6. At the end, the concluding remarks are drawn.

II. COMPRESSOR INSTABILITIES

In recent years, the study of airflow through jet engines has attracted the attention of a large number of academic and industrial researchers. The main reason for this interest is because of the fact that when the jet engine operates close to its optimal operating point, the flow may become unstable. A survey of basic concepts and control methods of the compressor instabilities can be found in [17]. Typically, a surge avoidance line is drawn at a specified distance from the surge line to ensure that the operating point does not cross the surge line under any conditions. This stability margin is usually considered very conservatively, as it may be reduced by many influences on the engine. As shown in Figure 1, the transient trajectory of the high pressure compressor working line during engine acceleration from idle to full power or from a specific spool speed to a faster one moves toward the surge line. Another significant factor in the reduction of the stability margin is inlet distortion.

Decentralized PI Control of a Rolls-Royce Jet EngineSaeed Tavakoli, Member, IEEE , Ian Griffin, and Peter J. Fleming

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Proceedings of the2005 IEEE Conference on Control ApplicationsToronto, Canada, August 28-31, 2005

MB6.4

0-7803-9354-6/05/$20.00 ©2005 IEEE 370

Fig. 1. Transient trajectory in high pressure compressors while accelerating.

Moreover, many jet engine variables cannot be measured when flying or can only be measured with complex instrumentation systems. This includes variables that are important for the safe operation of the engine such as the surge margin of the compressors or those related to the engine life, such as temperature of the high-pressure turbine blades. As a result, current control systems have to transform limits on these variables into limits on other variables that can be measured by the engine’s sensors. This leads to increased safety margins and more conservatism.

Furthermore, because of the engine build tolerances, the compressor working and surge line may be different from one engine to another. These lines may also be changed due to aging and engine deterioration. Finally, combinations of the above effects must also be handled. The result is that during engine design a significant portion of the pressure rise capability of the compressor is given over to “surge margin”, resulting in decreasing the engine efficiency.

In order to improve engine performance and efficiency and to extend the stable operating range of the compressor system, multivariable control can be employed to suppress compressor instabilities and therefore to reduce the safety margin.

III. JET ENGINE DESCRIPTION

A jet engine is composed of four main parts. First, there is a fan that sucks and accelerates the air into the front of the engine. In commercial jet engines the fan generates most of the thrust that the engine produces. Then, incoming air is compressed by the compressors. The third main part is the combustion chamber, where the air is mixed with fuel and then this compressed mixture is ignited. As a result, the pressure increases dramatically and the air rushes to the back of the engine after passing through the turbines. The turbines extract energy from the flow to drive the fan and compressors.

The highly cross-coupled linear models of the Rolls-Royce ANTLE jet engine derived from the nonlinear model have 4 inputs, 147 outputs and 35 states. It was shown in [18] that for a given stationary point, the higher order nonlinear thermodynamic models derived from the engine physics could be reduced to linear models of the same order

as the number of engine shafts. ANTLE is a three-spool jet engine with low power (LP), intermediate power (IP) and high power (HP) shafts. Therefore, the linear models of ANTLE can be reduced to 3 states.

In order to satisfy performance requirements and safety issues, the jet engine should have at least two outputs. For engines with two shafts the safety issue relating to surge should often be considered during acceleration only, while for three-spool jet engines surge during both acceleration and deceleration should be dealt with. Considering a TITO jet engine model, the first output shows the thrust whilst the second one represents the safety. In this research work, these outputs are turbine pressure ratio (TPR ) and SM . The second output is representative of the overall surge risk to the engine during any given engine transient. The first input that manipulates the thrust is the engine fuel flow rate (WFE ). Another input should contribute to dealing with compressor instabilities. A capable second input is variable inlet guide vanes (VIGV ). These vanes, which are situated in the front stages of the IP compressor, are adjusted according to the compressor speed and flight conditions to deflect the air flow into the IP compressor at an appropriate angle of incidence. In order to use a decentralized control strategy to simplify the control design procedure, the TITO jet engine should first be decoupled by a decoupler matrix. The resulting decoupled process can then be controlled through a decentralized controller. One great advantage of this method is that it allows the use of well-understood single-input single-output (SISO) controller design methods. Moreover, compared to a full matrix controller, a decentralized controller has less parameters to be tuned. In addition, in the case of actuator or sensor failure, it is relatively easy to stabilize the loop manually in a decentralized control strategy, because only one loop is directly affected by the failure [19]. However, for a full matrix controller, cross coupling of the process channels make it difficult to design each loop independently.

IV. DECOUPLING

The model of jet engine is represented by the transfer matrix shown in Equation (1).

)()()()(

)(1)(

2221

1211

sgsg

sgsg

sdsG (1)

where )(sd has no RHP zero. This TITO process should be decoupled through a decoupler. Considering the decoupler in Equation (2), )(sQ shown in Equation (3) will be a diagonal matrix. )(sQ should be controlled through a decentralized PI controller, whose elements are )(1 sk and

)(2 sk . In other words, )(1 sq and )(2 sq which are two SISO plants are controlled through )(1 sk and )(2 skrespectively, while each diagonal element of the decentralized control matrix is a PI controller.

Mass flow

Shaft speed

Surge line Pressure

Constant efficiency regions

Efficiency

Transient trajectory

371

1)()(

)()(

1)(

22

21

11

12

sgsg

sgsg

sD (2)

)(),()()()( 21 sqsqdiagsDsGsQ (3)

It is worth noting that interactions are zero unless additional large poles are added to the decoupler matrix to make it proper. In order to have a stable decoupler, )(11 sg

and )(22 sg should not have RHP zeros. Alternatively, if the decoupler matrix is given by Equation (4), the stable decoupler is subject to having no RHP zeros in )(12 sg and

)(21 sg . Therefore, a stable decoupler is obtained if either diagonal or off-diagonal elements of )(sG have no RHP zeros.

)()(

1

1)()(

)(

12

11

21

22

sgsg

sgsg

sD (4)

Let the TITO ANTLE model be as shown in Equation (1), where its elements are as follows

))(()(

))()(()())(()(

))()(()())(()(

322

1

3212222

322

12121

3211212

322

11111

esesessd

dsdsdsksg

cscscsksg

bsbsbsksg

asasasksg

Considering )(12 sg and )(22 sg , both decouplers represented in Equations (2) and (4) are unstable. In the following section an easy solution is suggested to decouple such TITO processes using a stable decoupler.

V. ZERO ASSIGNMENT

Considering the TITO process in Equation (1), suppose at least one element of diagonal elements of )(sG and one element of off-diagonal elements of this matrix have RHP zeros. The problem is to find )(sG so that its diagonal or off-diagonal elements have no RHP zeros. This may be done through multiplying )(sG by A , which is a static matrix, as shown in Equation (5).

AsGsG )()( (5)

Taking the )(sG needs into account, the range of elements of A can analytically be determined. This is illustrated through the following example.

Example:

Consider the following TITO process

2211

)2)(1(1)(

ssss

sssG

Using decouplers mentioned in Equation (2) or (4), )(sGcannot be decoupled through a stable decoupler. However, a static matrix A can be used to assign zeros of elements of

)(sG to the appropriate region. The objective is to have no RHP zero in either diagonal or off-diagonal elements of

)(sG .

2221

1211

2211

)2)(1(1)(

aa

aa

ssss

sssG

It can easily be shown that )(sG satisfies the requirements if the following equations hold

0

0

2212

2212

2111

2111

aaaa

aaaa

VI. SIMULATION RESULTS

Applying the method described in section 5 to the TITO ANTLE model in Equation (1) results in the TITO process shown in Equation (6).

)()(

)()()(

1)(2221

1211

sgsg

sgsg

sdsG (6)

where

)0538.0)(8781.1)(1976.2(2690.0)(

)0493.40092.4)(2812.0(7951.0)(

)643.1)(0086.2)(1374.11(3401.0)(

)2996.0)(4803.0)(0002.2(0534.3)(

22

221

12

11

ssssg

ssssg

ssssg

ssssg

The decoupler is given by Equation (7).

1)()(1

)(21

12

sd

sdsD (7)

372

where )(12 sd and )(21 sd are as follows

)0538.0)(8781.1)(1976.2()0493.40092.4)(2812.0(9558.2)(

)2996.0)(4803.0)(0002.2()643.1)(0086.2)(1374.11(1114.0)(

2

21

12

ssssss

sd

ssssss

sd

Using Equation (3), )(1 sq and )(2 sq are determined as follows

)2616.0)(299.0)(4805.0)(2(2616.01804.0)(

)05383.0)(2616.0)(878.1)(198.2(2616.00469.2)(

2

1

sssss

sq

sssss

sq

It is a common and well accepted practice to approximate high order processes by first order plus dead time (FOPDT) models. Applying the suggested model reduction technique described in appendix to )(1 sq and )(2 sq results in the following approximate models

14953.56269.0)(

14883.202119.9)(

0755.8

2

7214.6

1

se

sq

se

sq

s

s

The optimal PI controllers for the first and second loops can be determined using Equations (8) and (9) [20].

141

2 dcp

Tkk (8)

)9,711min(

TTTT ddi (9)

where pk , T and d are process gain, time constant and dead time in the process shown in Equation (10).

1)(

Ts

eksG

sp

p

d

(10)

Using Equations (8) and (9), the PI controllers for the first and second loops are given by

)6480.6

11(6566.0

)4485.2111(1732.0

2

1

sG

sG

c

c

TPR and SM responses to unit steps in WFE and VIGV are shown in Figures 2-5.

Fig. 2. TPR response resulting from applying a unit step in WFE .

Fig. 3. SM response resulting from applying a unit step in WFE .

Fig. 4. TPR response resulting from applying a unit step in VIGV .

The decoupler matrix has effectively decoupled the TITO jet engine transfer matrix, as Figures 3 and 4 show that interactions are negligible.

Zeros of elements of the resulting open loop diagonal matrix, )()( sDsG , can be found from roots of 0)(sG .Considering the model of TITO ANTLE jet engine given in section IV, )(12 sg and )(22 sg have RHP zeros. Therefore,

373

0)(sG may have some RHP roots, which is the case in this example. As a result, Figures 2 and 5 have inverse responses at the beginning.

Fig 5. SM response resulting from applying a unit step in VIGV .

VII. CONCLUSION

This paper presents a decentralized PI controller tuning method applied to a TITO Rolls-Royce jet engine. The process is firstly decoupled through a stable decoupler matrix. Next, the resulting high order diagonal matrix is reduced to a diagonal matrix which has FOPDT elements. Finally, optimal decentralized PI controllers for each loop are determined. Simulation results show that TPR and SMare controlled well through WFE and VIGV , respectively. Moreover, interactions in the different channels of the closed loop system are negligible.

APPENDIX

Approximation of high order processes by low order plus dead time models is a common practice. Although a FOPDT model does not capture all the features of a high order process, it often reasonably describes the process gain, overall time constant and effective dead time of such a process [21]. In order to find an approximate FOPDT model for )(sh which is an element of )(sH , the three unknown parameters in Equation (11), pk , d and T , should be determined.

1)(

Ts

eksl

sp

d

(11)

Fitting Nyquist plots of high order and low order models at particular points was successfully used in [22]. In this paper, Equations (12)-(14) are suggested to calculate the values of pk , d and T . These equations indicate that the high order and FOPDT models have the same steady state gains, cross over frequencies and gain margins.

)0()0( hl (12)

)()( cc jhjl (13)

)()( cc jhjl (14)

where the cross over frequency of the original system, c ,is determined from Equation (15).

)( cjh (15)

As a result, the parameters of the FOPDT model can be calculated using Equations (16)-(18).

)0(hk p (16)

c

cjhh

T

1))(

)0(( 2

(17)

c

cd

Ttg )(1

(18)

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