Jeffrey T. Csank and Thomas J. Stueber

Glenn Research Center, Cleveland, Ohio

Shock Position Control for Mode Transition in a 

Turbine Based Combined Cycle Engine Inlet Model

NASA/TM—2013-217824

January 2013
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Jeffrey T. Csank and Thomas J. Stueber

Glenn Research Center, Cleveland, Ohio

Shock Position Control for Mode Transition in a 

Turbine Based Combined Cycle Engine Inlet Model

NASA/TM—2013-217824

January 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

45th Combustion/33rd Airbreathing Propulsion/33rd Exhaust Plume and Signatures/27th Propulsion 

Hazards Joint Subcommittee Meeting

sponsored by the Joint Army-Navy-NASA-Air Force (JANNAF)

Monterey, California, December 3–7, 2012
Acknowledgments

The authors would like to thank the Fundamental Aeronautics Program’s Hypersonics project for funding this work.

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Trade names and trademarks are used in this report for identification 

only. Their usage does not constitute an official endorsement, 

either expressed or implied, by the National Aeronautics and 

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This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2013-217824 1 

Shock Position Control for Mode Transition in a Turbine Based 

Combined Cycle Engine Inlet Model

Jeffrey T. Csank and Thomas J. Stueber 

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135 

Abstract

A dual flow-path inlet for a turbine based combined cycle (TBCC) propulsion system is to be tested 

in order to evaluate methodologies for performing a controlled inlet mode transition. Prior to 

experimental testing, simulation models are used to test, debug, and validate potential control algorithms

which are designed to maintain shock position during inlet disturbances. One simulation package being 

used for testing is the High Mach Transient Engine Cycle Code simulation, known as HiTECC. This 

paper discusses the development of a mode transition schedule for the HiTECC simulation that is 

analogous to the development of inlet performance maps. Inlet performance maps, derived through 

experimental means, describe the performance and operability of the inlet as the splitter closes, switching 

power production from the turbine engine to the Dual Mode Scram Jet. With knowledge of the operability 

and performance tradeoffs, a closed loop system can be designed to optimize the performance of the inlet.

This paper demonstrates the design of the closed loop control system and benefit with the implementation 

of a Proportional-Integral controller, an H-Infinity based controller, and a disturbance observer based 

controller; all of which avoid inlet unstart during a mode transition with a simulated disturbance that 

would lead to inlet unstart without closed loop control. 

Nomenclature

ADRC Active Disturbance Rejection Control 

AIP Aerodynamic Interface Plane

CCE Combined Cycle Engine 

CCE-LIMX Combined Cycle Engine Large Scale Inlet for Mode Transition Experiments 

DMSJ Dual Mode Scramjet

HiTECC High Mach Transient Engine Cycle Code

HSFP High Speed Flow Path 

LSFP Low Speed Flow Path 

MS Mixed Synthesis 

PI Proportional–Integral controller

SWT Supersonic Wind Tunnel

TBCC Turbine Based Combined Cycle 

Pressure recovery Diffuser total exit pressure divided by free stream atmospheric pressure

Pressure ratio Diffuser static pressure divided by free-stream pressure atmospheric pressure

Mass flow ratio Mass-flow rate through the inlet divided by inlet capture mass-flow rate

Introduction

The National Aeronautics and Space Administration (NASA) is exploring the use of reliable 

airbreathing launch vehicles for hypersonic flight through Earth’s atmosphere and to provide routine 

airline-type access to space. To accomplish these objectives, the Fundamental Aeronautics Program’s

Hypersonics project is investigating a Turbine Based Combined Cycle (TBCC) propulsion system, 
NASA/TM—2013-217824 2 

consisting of a turbine and a dual-mode scramjet (DMSJ) combustor, for horizontal take-off and 

acceleration to hypersonic speeds. 

The TBCC propulsion system features a split-flow inlet that is capable of directing airflow to either or 

both of the engines—a turbine engine and a DMSJ combustor. The technical challenge being addressed in 

this research is the transitioning of airflow from the turbine engine to the DMSJ with minimal loss of net 

thrust. This activity is referred to as inlet mode transition. A concern is that during this transition, the inlet 

may unstart due to a rapid change in the subsonic diffuser static pressure. The static pressure change can 

be due to noise in the system from unsteady flow or a system disturbance. The challenge is to maintain 

sufficient operability and performance of the propulsion system throughout the inlet mode transition 

event. Operability is defined as the margin of diffuser static pressure that does not result in an inlet 

unstart, also known as the stability margin, while performance is defined as a pressure recovery goal and 

tolerance of flow distortion. These objectives led the NASA Hypersonic team to design, develop, and 

fabricate an inlet system suitable for experimental testing in the GRC 10- by 10-ft supersonic wind tunnel 

(SWT) to study inlet mode transition. 

The experimental system is an integrated dual flowpath inlet known as the Combined Cycle Engine 

Large-scale Inlet for Mode transition eXperiments (CCE-LIMX) (Ref. 1). The design is such that one 

flow path can direct airflow to a turbine and the other can direct airflow to a DMSJ. The work addressed 

in this paper considers the dynamic operability and performance of the flow path designed to serve the 

turbine engine. 

Experiments in the SWT are segmented into three phases. To date, the testing for Phase 1 and 2 has 

been completed and the analysis work is ongoing. The first phase studied the CCE-LIMX operability and 

performance at steady-state conditions. One of the Phase 1 products was a steady-state inlet mode 

transition schedule that discretely identified inlet operating conditions that must be passed through while 

performing an inlet mode transition. Characteristics of acceptable operating points are those with 

maximum performance, specifically pressure recovery, while maintaining operability with clean airflow–

low flow distortion to the engine. When defining the operating points, objectives which maximize inlet 

performance are sacrificed to reach an acceptable stability margin while avoiding excessive distortion. 

The second phase of testing was to perform system identification experiments at the defined inlet mode 

transition operating points. Data from the Phase 2 experiments are reduced to control design models to 

support controls research at each operating point. The controls research is to design a closed loop control 

algorithm that can reject inlet disturbances and afford the opportunity to operate the inlet at more 

aggressive conditions or with a reduced stability margin. The third phase will be to test candidate control 

algorithms. 

The illustration in Figure 1 is a computer aided design replication of the CCE-LIMX as mounted in 

the Glenn Research Center’s supersonic wind tunnel—airflow is from left to right. The CCE-LIMX has 

an over-mounted low speed flow path (LSFP) and an under-mounted high speed flow path (HSFP). 

During inlet mode transition, the splitter will rotate clockwise towards LSFP close-off. The variable ramp

can be raised, or lowered, to change the cross sectional area of the LSFP throat. The desired throat area is 

scheduled based upon free stream conditions. At the aft end of the LSFP subsonic diffuser, the 

aerodynamic interface plane (AIP) is where the turbine engine is normally mounted; however, the CCELIMX configuration has a cold pipe and mass-flow plug system in lieu of the turbine engine. Also at the 

aft end of the diffuser are overboard bypass doors that can be opened to vent and reduce the air pressure 

in the diffuser. The diagram of the CCE-LIMX inlet shown in Figure 1 is configured for supersonic 

operation, vehicle speed of Mach 4.0, prior to and during mode transition. For this state, most of the 

captured air is directed through the LSFP to the turbine engine. 
NASA/TM—2013-217824 3 

Figure 1.—Diagram of the CCE-LIMX inlet shown in its designed Mach 4.0 configuration.

The main function of the LSFP is to convert the kinetic energy of the incoming air into a static 

pressure rise and provide a uniform flow at the AIP. In general, the ratio of total pressure measured at the 

AIP relative to free stream, known as the pressure recovery, increases and flow distortion decreases as the 

terminal shock moves upstream towards the throat, making it desirable to operate the shock as close as 

possible to the throat. An airflow disturbance upstream of the inlet due to an atmospheric pressure drop or 

a downstream pressure rise from the turbine engine may cause the normal shock to move upstream from 

the throat and be expelled from the flow path. This is known as inlet unstart. 

The use of bypass doors as an actuator to regulate pressure ratio, the ratio of diffuser static pressure 

relative to free stream, has been successful for keeping supersonic inlets started (Refs. 2, 3,and 4). For an

axisymmetric, mixed compression inlet designed for Mach 2.5, a control system was implemented using a 

110 Hz bypass door system and 250 Hz diffuser pressure measurement as the feedback variable. The 

control system was shown to reduce the normal shock movement due to a disturbance up to a frequency 

of 40 Hz, just below the inlet’s resonant frequency of 55 Hz. 

In parallel to the first two phases of wind tunnel testing, NASA is designing controllers based on 

computational simulations with the High Mach Transient Engine Cycle Code (HiTECC); which is the 

topic of this paper. HiTECC (Ref. 5) is a combined cycle engine (CCE) simulation tool featuring a 

turbine engine and a DMSJ propulsion system model, nozzle models, a heat transfer model, fuel flow 

models, hydraulics models, etc. The HiTECC tools consist of the following four building blocks, a 

propulsion system(Ref. 6), a thermal management and fuel system model (Ref. 7), hydraulics and 

kinematics model (Ref. 8), and finally a control system. The HiTECC inlet model and propulsion system 

has been modified to be representative of the CCE-LIMX (Ref. 9). The modifications included replacing 

the propulsion system engine models with a cold pipe and mass-flow plug system, as done with the 

experimental system and adding a simulated bypass door at the aft end of the diffuser. The bypass door is 

opened and closed via a 2.36 in. linear actuator with a maximum exit area of 3.57 in.2

. The bypass door is 

capable of operating up to 77 Hz and is modeled as an under damped unity gain transfer function with a 

damping factor of 0.6266 and includes saturation limits. The actuator model does not include rate limits. 

This configuration, referred to as the HiTECC wind tunnel model, is used in this paper for proposing, 

designing, testing, and evaluating potential control algorithms before implementation on the CCE-LIMX. 

This paper focuses on the design process for a closed loop controller to ensure operability of the inlet 

during mode transition even in the presence of an external disturbance using the HiTECC simulation. The 

next section of this paper will discuss the development of a mode transition schedule and simulation of a 

mode transition without active feedback control. Linear models of the diffuser will be discussed followed 

by the closed loop controller design and results. 
NASA/TM—2013-217824 4 

Mode Transition

As part of the CCE-LIMX Phase 1 experiments, data is collected to plot the total pressure recovery 

with respect to the engine flow ratio. These plots are called total pressure characteristic curves or the 

“cane” curve due to its shape like a cane. This map is created by plotting the steady-state pressure ratio 

measurements (diffuser exit pressure divided by free stream atmospheric pressure) against the mass-flow 

ratio (mass-flow rate through the inlet divided by inlet capture mass-flow rate) for varying splitter angles 

and LSFP mass-flow plug positions. This is standard practice for characterizing supersonic inlets in a 

wind tunnel using a cold-pipe and mass flow plug in lieu of a turbine, because the data to report total 

pressure recovery requires pressure sensor rakes at the AIP (Ref. 10). A rake of sensors at the AIP is not 

expected to be available when a turbine is installed. Since a control system is intended to be useful for 

tests with or without the turbine, this work assumes the pressure rakes at the AIP are not available. The 

control system is designed using the diffuser static pressure; therefore, instead of plotting the pressure

recovery, the pressure ratio (ratio of diffuser static pressure measurements to free-stream) will be plotted 

against the mass-flow ratio. The relationship between the diffuser pressure ratio and mass-flow ratio at a 

splitter angle results in a cane shaped curve as shown in Figure 2. 

The curve in Figure 2 contains the following three segments: a vertical section, a horizontal section, 

and a transition region also referred to as the “knee”. The vertical section of the cane-curve occurs when 

the normal shock is located aft of the stability bleed region. This placement of the shock occurs when the 

diffuser static pressure is low. Because inlets operating in this region will have supersonic flow over the 

bleeds, slightly perturbing the position of the mass-flow plug, or bypass door, will change the pressure 

ratio but will have little to no change in the mass-flow ratio. Inlets operating at the top end of this region 

have the desired high performance. Operating points on the lower part of the vertical segment of the cane 

curve typically have higher distortion measurements that may exceed turbine engine tolerance. 

The knee of the cane-curve occurs when the normal shock is close to or partially covers the passive 

stability bleeds. The knee forms because mass flow losses will increase as the shock progresses upstream 

into the bleed region. Small perturbations in the diffuser pressure ratio will results in a change in mass 

flow ratio. An inlet operating in this region can be moved back to the vertical region by opening the 

Figure 2.—Example cane-curve. The red box is the last steadystate point recorded before the inlet unstarts and the green 

box is the desired operating point.

0.65 0.7 0.75 0.8 0.85

0

0.1

0.2

0.3

0.4

0.5

0.6

Mass-Flow Ratio

Pressure Ratio

Unstart

Desired 

Operating Point
NASA/TM—2013-217824 5 

bypass doors to decrease the pressure ratio. Multiple cane-curves can be created and plotted on the same 

chart at various discrete splitter positions. Finally, the selected operating points of each cane curve can be 

connected to create a mode transition schedule as the splitter rotates towards LSFP close-off as shown in 

Figure 3. Mode transition is continuous, but the schedule is created from limited test data at specific 

splitter angles.

The HiTECC simulation does not contain detailed computational fluid dynamics (CFD) code and will 

not accurately simulate the effect of the normal shock passing over the stability bleeds; therefore, an inlet 

performance map cannot be created as done in the hardware experimentations. To create a mode 

transition schedule using HiTECC, an alternative method is employed where the mass-flow plug is 

inserted towards cold pipe close-off and the steady-state diffuser static pressure ratio and shock locations 

are recorded at varying splitter angles as shown in Figure 4. The shock locations, indicated by the 

abscissa on the Figure 4 chart, are measurements from the bow tip of the vehicle. Therefore, as shock 

location increases the shock is located further downstream; whereas, a shock that moves upstream will 

have decreasing shock location values. The inlet will unstart if the shock location moves upstream of the 

162 in. mark. For this process, the mode transition schedule is found by specifying the desired normal 

shock location. The empirical approach does not have a shock location sensor and therefore uses the cane 

curves to estimate the shock location; whereas, the HiTECC approach actually calculates the shock 

location as part of its process. Figure 4 shows the mode transition schedule for a desired shock location of 

167 in. This method reveals desired pressure ratios for maintaining the normal shock at specific locations 

for various splitter positions. Even though there are small differences in the mechanics, the resulting 

mode transition schedule is a collection of desired pressure ratios as a function of the splitter angle. 

During mode transition the turbine engine power level is decreased. This in turn decreases the turbine 

mass flow which will increase the LSFP diffuser static pressure. The event can be simulated with the 

CCE-LIMX by further inserting the mass-flow plug toward cold-pipe close-off. Increasing the diffuser 

pressure at the LSFP AIP will also move the normal shock upstream and decrease the operability of the 

inlet—more susceptible to unstart. Furthermore, closing off the splitter will also decrease the captured 

mass flow and the static pressure upstream of the normal shock, also allowing the normal shock to move 

towards the front of the inlet. An open loop controller can be designed using a bypass door located in the 

diffuser which is opened as a function of splitter angle and decrease the back pressure at the LSFP AIP.

This results in a HiTECC based open loop control method. 

Figure 3.—Example mode transition curve created by plotting canecurves at several splitter locations. 

0.4 0.5 0.6 0.7 0.8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Mass-Flow Ratio

Pressure Ratio

Mode Transition 

Schedule

Decreasing Splitter Angle 

(Splitter Closing)
NASA/TM—2013-217824 6 

For the mode transition simulations, the splitter will be closed from an angle of 0 to -7.5° between 0.5 

and 2.0 s and the mass flow plug moves an additional 0.25 in. linearly towards cold-pipe close-off. 

Beyond a splitter angle of -7.5°, the bypass doors are fully opened to maintain supersonic airflow through 

the throat. The simulation results using the open loop control method are shown in Figure 5 with the 

pressure ratio (middle plot) and shock location (bottom plot) graphed with respect to time. In the bottom 

plot of Figure 5, the location of the throat where inlet unstart will occur is identified with a black dotted 

line. Figure 5 indicates that the inlet remained started during the mode transition. 

A disturbance is added to the system (shown in Figure 6) to determine if the inlet will remain started 

while performing a mode transition. The disturbance input magnitude for the design process was chosen 

to be approximately the same size as the control actuator, bypass door, with a frequency of 20 Hz. The 

disturbance is added to the system by modifying the exit area of the diffuser, or adding an additional 

disturbance door as will be done in the wind tunnel experiments. Decreasing the disturbance increases the 

pressure while increasing the disturbance input decreases the pressure. At the beginning of the simulation, 

the disturbance increases the exit area by 3.49 in.2

 and the mass flow plug is positioned to provide the 

desired pressure ratio. At a time of 0.7 s into the simulation, the disturbance is decreased to zero, 

increased at a time of 1.25 s, and decreased to zero again at 2.3 s. Only the first 0.8 s of the simulation 

with the disturbance added to the mode transition is illustrated in Figure 7 because the inlet unstarts 

shortly after the initial step disturbance input. The drop in shock location below the unstart dotted line 

illustrated in the lower chart in Figure 7 shows that the inlet does indeed unstart when the disturbance is 

initially decreased at a time of 0.7 s. Simply scheduling the bypass door input during mode transition in 

an open-loop fashion is unable to decrease the back pressure in response to the disturbance and unstart 

occurs. To mitigate the effect of the disturbance on shock position, closed loop control solutions will be 

studied. 

Figure 4.—Diffuser pressure ratio versus shock position location at 

various splitter angles (degrees).

160 165 170 175 180 185 190 195 200

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Pressure Ratio

Shock Position, in

0°

-2°

-4°

-6°

-8°
NASA/TM—2013-217824 7 

Figure 5.—Open loop results showing the splitter angle command (top), the 

diffuser pressure ratio (middle) and shock location (bottom). 

Figure 6.—Disturbance input profile.

0 0.5 1 1.5 2 2.5 3

-8

-6

-4

-2

0

Time,s

Splitter, degrees

0 0.5 1 1.5 2 2.5 3

0

0.2

0.4

0.6

0.8

Time, s

Pressure Ratio

Output

Setpoint

0 0.5 1 1.5 2 2.5 3

160

165

170

175

180

Time, s

Shock Position, in

0 0.5 1 1.5 2 2.5 3

0

1

2

3

4

Area, sq. in

Time, s
NASA/TM—2013-217824 8 

Figure 7.—Open loop mode transition results showing the diffuser 

pressure ratio (top) and shock location (bottom) with the disturbance 

input added.

Linear Model

Linear models are developed to aid in the control design process. The linear models will be developed

empirically using the HiTECC tool. This approach applies a sine-sweep perturbation pattern, starting 

from a frequency of 0.01 to 50 Hz. This signal is applied to the bypass door exit area of the diffuser and 

includes the unity gain dynamics of the bypass door actuator. In addition, a step change command will be 

applied with the same magnitude of the sine sweep. Using sine sweep results, linear models can be 

obtained using the MATLAB (The MathWorks, Inc.) arx command (provided in the MATLAB System 

Identification Toolbox). The step response of the linear model is then compared to the recorded step 

response test from the HiTECC simulation using the MATLAB compare function to determine the 

accuracy of the linear model. The resultant linear system is a single input single output system (SISO) 

process, with the input being the open exit area in the diffuser and output being the diffuser pressure ratio, 

with the bypass gate dynamics included. Using the arx command, the linear model (exit area to pressure 

ratio) at Mach 3.75 flight condition, with a steady-state initial shock location of 173 in., is described with 

the following continuous time transfer function:

02.13( )( 1.234 )( )7208083.77

6.768(4929.13 )( 1238 )778600 )( 2

2

++ ++

− + ++ = sssssss tf s (1)

This linear model is only valid at the Mach 3.75 flight condition, with the splitter fully open, and a 

steady state shock location of 173 in. A Bode plot comparison of the linear models at the Mach 3.75 flight 

condition and at various steady state shock locations are shown in Figure 8. As the linearization point 

moves downstream, the subsonic volume decreases. This is represented in the linear model as a loss in 

system gain and can be seen in Figure 8 by the decrease in gain near steady-state as the shock moves 

further downstream. In addition to this change, the natural frequency increases as the shock moves 

downstream. Bode plots can also be developed at a consistent shock location, 173 in., and with a varying

splitter angle as shown in Figure 9. This Bode plot shows that the system losses gain as the splitter rotates 

towards LSFP close-off and the natural frequency of the resonant poles increase. Since the dynamics of 

the diffuser inside the desired control bandwidth, max 20 Hz, do not greatly change based on the splitter 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.5

0.6

0.7

0.8

0.9

Time, s

Pressure Ratio

Output

Setpoint

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

160

165

170

175

180

Time, s

Shock Position, in
NASA/TM—2013-217824 9 

location and steady state shock location, as shown in Figure 8 and Figure 9, the plant model of 

Equation (1) will be the only model used for control design purposes. 

Figure 8.—Bode plot for varying shock location.

Figure 9.—Bode plot for varying splitter angle.

-60

-40

-20

0

20

40

Magnitude (dB)

10-1 100 101 102

-90

0

90

180

Phase (deg)

Frequency (Hz)

173

176

180

187

-60

-40

-20

0

20

40

Magnitude (dB)

10-1 100 101 102

-90

0

90

180

Phase (deg)

Frequency (Hz)

-8.5°

-10.5°

-12.5°
NASA/TM—2013-217824 10

Figure 10.—Closed Loop Control System with an error (e) signal applied to the controller (K), which produces a 

bypass command signal (u) applied to the plant (G). The measured diffuser static pressure (y) is fed back and 

subtracted from the setpoint (r). 

Shock Location Control Design

With the relationships between the normal shock location and pressure ratio based on splitter angle 

defined in Figure 4, a closed loop control system is designed to reject disturbances and increase the 

operability of the TBCC inlet. The closed loop control system, shown in Figure 10, consists of a setpoint 

function to calculate the desired pressure ratio, r, based on the splitter angle, a controller, K, and the plant, 

G, which consists of a bypass door and diffuser which produce the pressure ratio output, y. In this control 

system the error, e, and the desired control action, u, are inversely related. This means that a decreased 

command signal results in an increased pressure ratio. Therefore, the error is multiplied by –1. If the 

feedback is greater than the setpoint, the control command is increased to further open the bypass door to 

further reduce the pressure ratio. 

Proportional-Integral Control

Using the closed loop control system shown in Figure 10, a Proportional-Integral (PI) controller is 

designed and implemented. The PI control law is:

∫ −−= ip )()()( dttektektu (2) 

where e(t) is the error (r(t) – y(t)), and kp and ki are the PI controller gains. The PI controller gains were

set to provide the quickest response time with no overshoot, using trial and error PI tuning methods 

(Ref. 11). The PI controller was selected to serve as a baseline because it is the most widely used closedloop controller due to its simplistic control law and ease of tuning. This algorithm does not require 

extensive knowledge of the process that is being controlled, adding to its popularity. 

H-Infinity Mixed Sensitivity Control 

The PI controller can be replaced with an optimal controller using the MATLAB mixsyn command 

from the robust toolbox. The mixsyn command computes a controller that minimizes the H-Infinity norm 

for the weighted mixed sensitivity control problem:





















=

TW

RW

SW

Tyu

3

2

1

 (3) 
NASA/TM—2013-217824 11

where W1, W2, and W3 are user defined weighting functions, S is the sensitivity function, R is the closed 

loop transfer function, and T is the complimentary sensitivity function. For tuning, each weight 

determines the importance of the associated term. General rules for tuning are that the gain of W1 is 

usually small inside the desired control bandwidth and is greater outside the control bandwidth to achieve 

good disturbance attenuation. W2 defines the shape of the control input, and can be defined as a filter to 

reduce high frequency spikes from the controller. The weighting function W3 is typically chosen to be of 

small magnitude outside the control bandwidth and large inside the control bandwidth to ensure good 

stability margin. 

One method for choosing W1 is:

( )

Aws

w W

B

M B s

+

+

1 = (4) 

where M is the value of W1 at very high frequencies (infinity), A is the value of W1 at steady state, and wB

is the desired or approximate bandwidth. These values can be modified to provide the desired 

performance. Increasing WB will increase the overall gain of the system and make the response more 

aggressive. M was chosen to be greater than 1 to ensure that S is smaller at high frequency and A is 

chosen to be small to amplify S at frequencies less than WB. Usually W2 is chosen as a gain, however W2

can also be a filter to amplify the control signal at low frequencies and filter the control signals at high 

frequencies. 

Active Disturbance Rejection Control

During mode transition, the inlet will be transitioning through operating points that are off the Mach 4 

design geometry; therefore, the inlet will be more susceptible to inlet unstart. Pressure disturbances, either 

negative pressure disturbances from the atmosphere or positive pressure disturbances from the turbine 

engine will result in increased diffuser pressure ratio, and the normal shock will move upstream. The task 

to prevent an unstart is to reject the disturbance before the inlet unstarts. To provide better disturbance 

rejection, a disturbance observer type controller can be implemented. In this paper the active disturbance 

rejection controller (ADRC) has been chosen due to success in previous disturbance rejection applications 

(Refs. 12, 13, and 14). 

The ADRC controller has three parameters: the DC plant gain (b0), the controller bandwidth (ωc), and 

the observer bandwidth (ωo). The DC plant gain is found from the transfer function. The controller and 

observer bandwidths are tuned to provide the best performance, quickest response time with smallest 

overshoot. Increasing the controller bandwidth makes the control system response more aggressive while 

increasing the observer bandwidth tends to increase disturbance rejection; however, increasing the 

observer bandwidth too much can destabilize the system. It has been noted that in most applications, the 

observer bandwidth is set to 10 times the controller bandwidth (Ref. 14). 

Transient Stability Index

A generic approach to analyze and compare the effectiveness of using closed-loop feedback control to 

maintain stability is to evaluate the system with a transient stability index (TSI) analysis (Ref. 15). For 

this case, the TSI determines the frequency and percentage of the total airflow that when forced to exit the 

cold pipe instead of the bypass door causes the inlet to unstart. The TSI evaluation process first 

determines a stability index (SI). The SI is determined by opening the bypass door to a specified area and 

decreasing the cold pipe exit area to obtain a desired steady-state pressure ratio. The stability index is the 

percentage of airflow through the bypass door with respect to the total airflow captured—captured airflow 

is the sum of the airflow through the bypass door and past the cold-pipe mass flow plug, or
NASA/TM—2013-217824 12















 = Wcp

W

SI doorbypass 100

 

 (5)

After calculating the SI, the bypass door will be closed and reopened at a frequency, f. At a given time, t1, 

the negative half of a sine wave is applied to the bypass door to close and then reopen the bypass door to 

the starting area at t2 determined based on the frequency of the input signal. 

An example input curve is shown in Figure 11. If the inlet remains started, the frequency is reduced 

and the test is once again applied until a frequency is found that results in an inlet unstart. Once the 

frequency which results in unstart is found, the bypass door area is changed and the SI evaluation process 

is repeated for the new open area. This process is repeated for multiple bypass door open area settings. 

Control Design Results

The proposed control algorithms of the control design section have been implemented in HiTECC.

All results are simulated using the same disturbance profile as appeared in the Shock Position Control 

Design section (Figure 6).

Proportional-Integral Control

A computational simulation of the PI controller proposed has been implemented and tuned. The 

system response to a PI controlled mode transition with controller gains of kp = 9.9 and ki = 21.84 is 

shown in Figure 12. The PI controller was tuned to maximize the disturbance rejection response time 

while minimizing overshoot. The top plot of Figure 12 shows the bypass door open area (control effector) 

for the experiment. Not illustrated is the disturbance door position which is the same as used in the 

previous simulation. Without closed-loop feedback control, the disturbance input step change would have 

increased the diffuser pressure ratio to a level that would surely unstart the inlet as shown in Figure 7. The 

bottom plot in Figure 12 compares the shock location against the setpoint, desired, shock location 

throughout the experiment. Figure 12 shows that the PI controller successfully rejected the disturbance, 

thus increasing the operability of the LSFP even though the shock did move forward of the setpoint, but 

remained downstream from the throat, as the splitter closes. 

Figure 11.—Bypass door command for creating the transient stability index plot.
NASA/TM—2013-217824 13

Figure 12.—Control input (top), pressure ratio (middle), and shock 

position location (bottom) for a PI controlled mode transition with a 

disturbance step added to the system.

H-Infinity Mixed Sensitivity Control 

To design a mixed synthesis controller using MATLAB, the mixsyn command requires a plant 

transfer function, G, with a linear gain from the linear actuator command to actuator door open area, and 

the user-defined weights from Equation (3). The plant model from Equation (1) is used for the mixsyn

command. The weighting functions used for finding K are:

( )

( )

0)(

1

1 )(

1948.0

8319.62 )(

3

4956.188

2

10

1

=

+ =

+

+ =

sW

sW

s

sW

s

s

(6) 

The closed loop simulation with the mixed synthesis controller through mode transition is shown in

Figure 13. Again, the same disturbance was applied to the process at time 0.7 s as explained in the PI 

discussion. This controller has the ability to keep the shock downstream of the setpoint as the splitter 

closes. This simulation only temporarily had the shock move upstream of the setpoint and, as desired, no 

unstart occurred. Notice that with the mixed sensitivity controller there is some overshoot when 

recovering from the disturbance 

0 0.5 1 1.5 2 2.5 3

-10

-5

0

5

10

Time, s

Bypass Area, sq in

0 0.5 1 1.5 2 2.5 3

0

0.2

0.4

0.6

0.8

Time, s

Pressure Ratio

Output

Setpoint

0 0.5 1 1.5 2 2.5 3

160

165

170

Time, s

Shock Position, in
NASA/TM—2013-217824 14

Figure 13.—Control input (top), and shock location (bottom) for the mixed 

synthesis (H-Infinity) controlled mode transition with a disturbance step 

added to the system at t = 0.7 s.

Active Disturbance Rejection Control

The active disturbance rejection control has been implemented as discussed in the Shock Position 

Control Design section. With the plant gain and tuning parameters of b0 = 1659, ωc = 502.6548 rad/s, and 

ωo = 3141.6 rad/s, the system response with an ADRC controlled mode transition is shown in Figure 14. 

This is the only controller that does not allow the shock position to move forward of the shock position 

setpoint during the entire simulation, and does not place the shock aft of 169 in. This controller performs 

the best in terms of disturbance rejection, disturbance affects shock position the least, and it also has the 

smallest error between the desired shock position and actual shock location. The ADRC command does 

have a high frequency control effort which is revealed in the door area plot of Figure 14. 

Transient Stability Index Results

The transient stability index created for the scheduled mode transition system, with the open loop 

method (No), the PI controlled, H-Infinity mixed synthesis (MS) controlled, and ADRC systems at the 

desired pressure ratio of 0.784 is shown in Figure 15. For a given method, all stability indexes below the 

line will not unstart the inlet. In addition, any SI value below the lowest SI value shown on the plot will 

not unstart the inlet for any frequency between 1 and 80 Hz. Figure 15 shows a clear advantage in 

increased operability with the addition of a closed loop control system, while there are only small 

differences comparing the effectiveness of each closed loop controller. This plot indicates that the system 

is capable of avoiding inlet unstarts for much larger magnitude disturbances than the open loop controlled 

method. 

0 0.5 1 1.5 2 2.5 3

-10

-5

0

5

10

Time, s

Bypass Area, sq in

0 0.5 1 1.5 2 2.5 3

0.2

0.4

0.6

0.8

Time, s

Pressure Ratio

Output

Setpoint

0 0.5 1 1.5 2 2.5 3

160

165

170

Time, s

Shock Position, in
NASA/TM—2013-217824 15

Figure 14.—The control input(top), pressure ratio(middle), and shock 

location(bottom) for a mode transition with the Active Disturbance 

Rejection Controller and a disturbance step added to the system.

Figure 15.—Transient Stability Index for the scheduled mode 

transition with the open loop method (No) with a proportionalintegral (PI) controller, with a Mixed-Synthesis (MS) controller 

and with an active disturbance rejection control (ADRC). 

0 0.5 1 1.5 2 2.5 3

-10

0

10

Time, s

Bypass Area, sq in

0 0.5 1 1.5 2 2.5 3

0.2

0.4

0.6

0.8

Time, s

Pressure Ratio

Output

Setpoint

0 0.5 1 1.5 2 2.5 3

160

165

170

Time, s

Shock Position, in

0 10 20 30 40 50 60 70 80 90

0

10

20

30

40

50

60

70

80

90

100

Stability Index, SI

Frequency, Hz

No

PI

MS

ADRC
NASA/TM—2013-217824 16

Summary and Conclusions

This paper discussed the simulated design and testing of controllers to increase the stability and 

disturbance rejection capability for a closed-loop mode transition in the Combined Cycle Engine Largescale Inlet for Mode transition eXperiments (CCE-LIMX). A turbine based combined cycle (TBCC) 

simulation, known as the High Mach Transient Engine Cycle Code (HiTECC), has been redesigned to 

replicate the CCE-LIMX. The new simulation replaces the full TBCC propulsion system which included 

a turbine model, with one which simulated cold pipes and mass flow plugs in place of the turbine, as done 

with the CCE-LIMX. In order to simulate mode transition, the relationship between the shock position 

location and pressure ratio at varying splitter angles is determined to create a mode transition schedule, 

which is also used as the setpoint for the closed loop control system. An open loop control method was 

used in the mode transition simulation where a bypass door, a control actuator intended to decrease the 

diffuser exit pressure, was opened as a function of the splitter location. However, when a disturbance was 

added to this simulation, the inlet unstarted. Three closed loop controllers were designed to reject the 

disturbances and improve the operability of the inlet. A proportional-integral controller, an H-Infinity 

mixed synthesis controller, and an active disturbance rejection controller were added to the mode 

transition simulation. These closed loop controllers were shown to reject the disturbances and avoid 

unstart. A transient stability index (TSI) plot was created to further compare these closed loop control 

methods. The transient stability index plot shows the frequency and percent of total airflow (disturbance) 

that when diverted from a bypass door to the cold pipe resulted in inlet unstart. The closed loop control 

systems were shown to provide significantly better performance than the inlet without control. In terms of 

smallest error and disturbance rejection, the best performance was obtained by using the active 

disturbance rejection controller, which was also shown to have the highest bandwidth and gain. The 

proportional-integral controller has slightly larger error but a much smoother control signal.

References

1. Sanders, B.W., and Weir, L.J., Aerodynamic Design of a Dual-Flow Mach 7 Hypersonic Inlet System 

for a Turbine-Based Combined-Cycle Hypersonic Propulsion System, NASA/CR— 2008-215215 

(June 2008). 

2. Neiner, G.H., Crosby, M.J., Cole, G.L., Experimental and Analytical Investigation of Fast Normal 

Shock Position Controls for a Mach 2.5 Mixed-Compression Inlet, NASA TN D–6382( July 1971).

3. Cole, G.L., Neiner, G.H., Crosby, M.J., Design and Performance of A Digital Electronic Normal 

Shock Position Sensor for Mixed-Compression Inlets, NASA TN D–5606 (December 1969).

4. Baumbick, R.J., Neiner, G.H., Cole, G.L., Experimental Dynamic Response of a Two-Dimensional, 

Mach 2.7 Mixed-Compression Inlet, NASA TN D-6957 (September 1972). 

5. Haid, D.A., and Gamble, E.J., Integrated Turbine-Based Combined Cycle Dynamic Simulation 

Model, 58th Joint Army-Navy-NASA-Air-Force (JANNAF) Interagency Propulsion, Arlington, VA 

(April 18-22, 2011). 

6. Gamble, E.J., Haid, D., D’Alessandro, S., and DeFrancesco, R., Dual-Mode Scramjet Performance 

Model for TBCC Simulation, AIAA–2009–5298 (August 2009). 

7. Gamble, E.J. and Haid, D., Thermal Management and Fuel System Model for TBCC Dynamic 

Simulation, AIAA 2010-6642, 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and 

Exhibit, Nashville, TN (July 25-28, 2010). 

8. Gamble, E.J. and Haid, D., Hydraulic and Kinematic System Model for TBCC Dynamic Simulation, 

AIAA 2010-6641, 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 

Nashville, TN, July 25–28, 2010.

9. Csank, J.T., and Stueber, T.J., A Turbine Based Combined Cycle Engine Inlet Model and Mode 

Transition Simulation Based on HiTECC Tool, AIAA 2012-4149, 48th AIAA/ASME/SAE/ASEE 

Join Propulsion Conference and Exhibit, Atlanta, GA (July 31–August 1, 2012). 
NASA/TM—2013-217824 17

10. Slater, J., Design and Analysis Tool for External-Compression Supersonic Inlets, AIAA-2012-16, 

Nashville, TN (January 2012). 

11. Åström, K. and Hägglund T., PID Controllers: Theory, Design, and Tuning, 2nd Edition, Instrument 

Society of America, Research Triangle Park, NC (1995).

12. Gao, Z., Active Disturbance Rejection Control: a Paradigm Shift in Feedback Control System Design, 

American Control Conference, Minneapolis, Minnesota (June 14–16, 2006).

13. Gao, Z., Huang, Y., and Han, J., An Alternative Paradigm for Control System Design, IEEE 

Conference on Decision and Control (2001).

14. Gao, Z., Scaling and Bandwidth-Parameterization Based Controller Tuning, American Control 

Conference, Denver, CO (June 2003). 

15. Sanders, B.W. and Mitchel, G.A., Throat-Bypass Bleed Systems for Increasing the Stable Airflow 

Range of a Mach 2.5 Axisymmetric Inlet with 40-Percent Internal Contraction, NASA TM–X–2779 

(May 1973). 
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Shock Position Control for Mode Transition in a Turbine Based Combined Cycle Engine Inlet 

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14. ABSTRACT

A dual flow-path inlet for a turbine based combined cycle (TBCC) propulsion system is to be tested in order to evaluate methodologies for 

performing a controlled inlet mode transition. Prior to experimental testing, simulation models are used to test, debug, and validate potential 

control algorithms which are designed to maintain shock position during inlet disturbances. One simulation package being used for testing is 

the High Mach Transient Engine Cycle Code simulation, known as HiTECC. This paper discusses the development of a mode transition 

schedule for the HiTECC simulation that is analogous to the development of inlet performance maps. Inlet performance maps, derived 

through experimental means, describe the performance and operability of the inlet as the splitter closes, switching power production from 

the turbine engine to the Dual Mode Scram Jet. With knowledge of the operability and performance tradeoffs, a closed loop system can be 

designed to optimize the performance of the inlet. This paper demonstrates the design of the closed loop control system and benefit with the 

implementation of a Proportional-Integral controller, an H-Infinity based controller, and a disturbance observer based controller; all of 

which avoid inlet unstart during a mode transition with a simulated disturbance that would lead to inlet unstart without closed loop control. 

15. SUBJECT TERMS

Propulsion control; Shock wave control; Feedback control 

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