Jonathan A. DeCastro

QSS Group, Inc., Cleveland, Ohio

Rate-Based Model Predictive Control of Turbofan

Engine Clearance

NASA/CR—2006-214419

November 2006
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Jonathan A. DeCastro

QSS Group, Inc., Cleveland, Ohio

Rate-Based Model Predictive Control of Turbofan

Engine Clearance

NASA/CR—2006-214419

November 2006
Acknowledgments

This work was supported by the Propulsion 21 program at the NASA Glenn Research Center. The Jonathan A. DeCastro

gratefully acknowledges the insight and input provided by Kevin Melcher.

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An innovative model predictive control strategy is developed for control of nonlinear 

aircraft propulsion systems and sub-systems. At the heart of the controller is a rate-based 

linear parameter-varying model that propagates the state derivatives across the prediction 

horizon, extending prediction fidelity to transient regimes where conventional models begin 

to lose validity. The new control law is applied to a demanding active clearance control 

application, where the objectives are to tightly regulate blade tip clearances and also 

anticipate and avoid detrimental blade-shroud rub occurrences by optimally maintaining a 

predefined minimum clearance. Simulation results verify that the rate-based controller is 

capable of satisfying the objectives during realistic flight scenarios where both a 

conventional Jacobian-based model predictive control law and an unconstrained linearquadratic optimal controller are incapable of doing so. The controller is evaluated using a 

variety of different actuators, illustrating the efficacy and versatility of the control approach. 

It is concluded that the new strategy has promise for this and other nonlinear aerospace 

applications that place high importance on the attainment of control objectives during 

transient regimes. 

I. Introduction 

LTHOUGH model predictive control (MPC) has been used for decades in some form or another in industrial 

processes, it is gaining ever more acceptance in aircraft propulsion applications due to advances in computing 

power of modern on-board control platforms.1,2 Fast computation is necessary because the controller must generate 

current and future actuator commands based on open-loop receding horizon trajectories at each time instant.3

 The 

trajectory information allows the controller to optimize over the horizon while avoiding a pre-determined set of 

constraints, such as saturation limits of an actuator or operational limits that define the safety margins of a particular 

plant or process. In specific propulsion applications such as aircraft engine control or active turbine tip clearance 

control, this control strategy offers a wide range of utility. 

Figure 1 shows a general conceptual sketch of an active clearance control system, where the actuated shroud is 

depicted as responding to changes in clearance measured by a clearance probe. It is envisaged that replacement of 

open-loop clearance control systems aboard modern aircraft engines with faster actively-controlled systems will 

result in ultra tight clearances in the high-pressure turbine, permitting lower emissions and higher fuel savings by 

decreasing specific fuel consumption (SFC) as well as longer life through decreased exhaust gas temperatures 

(EGT).4

 Due to the wide variations in component deformations that occur during flight, if the clearance gap is not 

large enough, the turbine blades may rub against the shroud and permanently damage the blade tips. These 

variations arise due to the mismatch in thermal deformations and deformation rates of the rotor and stator assemblies 

along with centrifugal expansion and contraction of the rotor itself. However, on the basis that every 0.01-inch 

reduction in clearance results in nearly 1% improvement in efficiency and 10oC reduction in peak EGT during 

transients,5

 the need to control clearance as tightly as possible becomes abundantly apparent. Certainly, advances in 

actuation and sensing hardware for active clearance control will allow for fast and accurate positioning of the shroud 

relative to the blades,6,7 but at these tight clearances, detrimental blade rubs may still arise due to the fact that there 

is no way of imposing mechanical limits on the clearance. The advantage of applying MPC to this application is 

that an inherent degree of robustness against blade rubs may enable operation with the tightest clearances that the 

hardware will allow, enabling the maximum operational benefits to be extracted. 

A 

NASA/CR—2006-214419 1

Rate-Based Model Predictive Control of Turbofan 

Engine Clearance 

Jonathan A. DeCastro 

QSS Group, Inc. 

Cleveland, Ohio 44135 

Abstract 
Because MPC is heavily reliant on an open-loop plant model, the model itself should be an accurate 

representation of the plant; in this case, a turbofan engine. In numerous cases, the pitfall in applying successful 

computationally-intense model-based control strategies is in the complexity of the model, as is the case with 

nonlinear models with a high degree of parameterization (e.g. neural nets). On the other hand, lack of fidelity can 

result in poor performance or robustness. In this paper, a gain-scheduled, linear parameter varying (LPV) MPC law 

is considered that retains both computational efficiency and prediction fidelity. In the past, gain-scheduling has 

often been applied under the assumption that analytical models of the plant exist and are at the disposal of the 

control engineer, as in Heise and Maciejowski8

 and Shamma and Cloutier.9 Unfortunately, because high-fidelity 

numerical engine models often used in gain scheduling applications are highly complex, it is nearly impossible to 

arrive at representative closed-form analytical models. A smaller group of papers, such as Mehra et al,

10 treat the 

use of Jacobian linearized LPV models for MPC, but the limitation of traditional LPV models is in the loss in 

prediction quality when transients cause the models to move away from quasi-equilibrium. Over the horizon, these 

models may substantially depart from the near-equilibrium regions of the parameter space where model validity 

holds and substantially compromise optimality. Leveraged by a rate-based linearization method introduced by Leith 

and Leithead,11 an alternate framework conducive to rapidly-varying plants is explored in this work, which operates 

upon the state derivatives instead of the states themselves. A virtue of this transformation is that fidelity during 

transients is preserved, enhancing the prediction and global performance of the MPC. To the author’s knowledge, 

this is the first attempt at developing a rate-based LPV modeling technique (hereafter abbreviated as R-LPV) for 

MPC. The results of the assessment in this paper are useful as further guidelines from which to build MPC 

controllers for other aerospace applications (e.g. engine control), in addition to the application described here. 

This paper is organized as follows. To lay the groundwork for the new MPC, a description of both conventional 

and rate-based linearization methods for LPV representations as applied to a numerical turbofan engine model are 

presented. Next, a description of an LPV model predictive controller is given, along with the proposed disturbance 

model estimation structures. Aspects of applying the MPC to a fast active clearance control device are then 

described, and details of the actuators used and the high fidelity engine model are given. Finally, results of active 

clearance control simulations are presented, demonstrating the comparative advantages of the proposed controller 

over the conventional approach. In that section, both servohydraulic and thermal deformation-based actuators are 

investigated to illustrate the versatility and robustness of this control approach. 

II. LPV Models of Nonlinear Processes 

The purpose of this section is to introduce concepts relating to linearization of numerical models in the LPV 

framework, as motivated by the highly nonlinear nature of the turbofan engine. Once these methods are established, 

germane properties of the two methods are described, as they apply to model predictive control. 

General nonlinear systems of the form x& = f (x,u, v) , y = g(x,u, v) can be placed in the following standard LPV 

form: 

( ) ( ) ( )

y C() () () x D u D v

x A x B u B v

ρ ρ ρ

ρ ρ ρ

1 2

1 2

= + +

& = + +

 (1) 

shroud

turbine 

blade

clearance gap 

(sensed)

Clearance reduction 

mechanisms:

• rotor accel

• rotor heating

• case cooling

• aero loads

Clearance increase 

mechanisms:

• rotor decel

• rotor cooling

• case heating

• aero loads

Active clearance 

control

shroud

turbine 

blade

clearance gap 

(sensed)

Clearance reduction 

mechanisms:

• rotor accel

• rotor heating

• case cooling

• aero loads

Clearance increase 

mechanisms:

• rotor decel

• rotor cooling

• case heating

• aero loads

Active clearance 

control

Figure 1. Active turbine clearance control concept (cutaway view of turbine blade tip and shroud). 

NASA/CR—2006-214419 2
The state vector, control input, disturbance input, and output vector are n x ∈ R , nu u ∈ R , nv v ∈ R , and ny y ∈ R , 

respectively. The scheduling parameter vector is denoted by ρ and can be either exogenous, an input external to 

the plant, or endogenous, a state of the system. In the latter case, the system is said to be quasi-LPV. 

Two Perspectives on Linearization 

Jacobian linearization12 is often considered the default method for attaining representations of nonlinear 

processes, especially those for which analytical expressions do not exist. Although it is possible in theory to 

linearize away from equilibrium, practical considerations often limit perturbation of the model or actual system to 

steady-state operating points. This procedure, when conducted at several distinct operating points, produces a 

family of linear models 

( ) ( ) ( )

y C() () () x D u D v

x A x B u B v

δ ρ δ ρ δ ρ δ

δ ρ δ ρ δ ρ δ

1 2

1 2

= + +

& = + +

 (2) 

where the perturbation values 0 δx = x − x , δu = u − u0 , 0 δv = v − v , and 0 δy = y − y are functions of the steady-state 

trim values, 0 x , u0 , 0 v , and 0 y . Although this family can be quite large when adequate coverage of the entire 

operating envelope is needed, the result is by no means global as the state derivative trim value 0 x& must still be 

assumed to remain zero everywhere. This implies that LPV trajectories are limited to a subset of actual trajectories 

of the nonlinear system exactly at equilibrium, but this restriction is often relaxed by permitting transitions between 

points so long as variations in ρ are sufficiently slow. Within the neighborhood of a single linearization point, the 

LPV input/output relationship is accurate to within first-order of the actual system. 

Practically speaking, the family of state-space models is scheduled by either a nearest neighbor or interpolation 

approach. Since the LPV system in Eq. (2) is actually a nonlinear affine system, trim value updates must be 

included along with the system matrix updates, as depicted in Fig. 2. If the nonlinearity is particularly dominant, i.e. 

highly sensitive to minor variations in ρ , then quasi-LPV representations may be rendered invalid even with slow 

variations due to the fact that the trim values are only approximations as the trajectory progresses between operating 

points. Moreover, the recursive nature of the quasi-LPV parameter update causes any error to accumulate without 

bound, possibly leading to significant model/plant disparities even within small time frames. 

In an alternate linearization perspective known as rate-based linearization,11 the nonlinear system is 

approximated to first order by an affine Taylor series expansion as before, but the states are transformed by simply 

taking their derivatives. In so doing, the assumed static first-order terms disappear, leaving the actual system state 

derivatives as the LPV states. Perturbation values now become unnecessary, and the system of equations takes on 

the following form: 

( ) ( ) ( )

y C() () () x D u D v

x A x B u B v

& & & &

&& & & &

ρ ρ ρ

ρ ρ ρ

1 2

1 2

= + +

= + +

 (3) 

In this representation, the state vector is now represented by [ ]

T T T ξ = x& y and the state matrices are augmented 

appropriately. To complete the R-LPV model, initial states must be specified if the model is to start at points other 

than the origin. Figure 3 shows an input/output signal diagram for this type of model. If the trim values are, in fact, 

obtained at steady-state, it may be observed that the perturbation states δx in Eq. (2) are first-order approximations 

Gain-Scheduled

Model

(ρ) 0 y

δy y

ρ

+

−

+

+

( )

( )⎥

⎦

⎤ ⎢

⎣

⎡

ρ

ρ

0

0

v

u

⎥

⎦

⎤ ⎢

⎣

⎡

v

u

δ

δ

⎥

⎦

⎤ ⎢

⎣

⎡

v

u

(δx)

Gain-Scheduled

Model

(ρ) 0 y

δy y

ρ

+

−

+

+

( )

( )⎥

⎦

⎤ ⎢

⎣

⎡

ρ

ρ

0

0

v

u

⎥

⎦

⎤ ⎢

⎣

⎡

v

u

δ

δ

⎥

⎦

⎤ ⎢

⎣

⎡

v

u

(δx)

Figure 2. Jacobian LPV models. 

NASA/CR—2006-214419 3
to the derivatives of the actual states x& in the limit sense. The family of Jacobians obtained in Eq. (2) may thus be 

substituted into Eq. (3) and scheduled identically. In contrast to Eq. (2), however, all trim values including the state 

derivative trim 0 x& become implicit to the model. To elaborate, if ρ is sufficiently slow during a particular 

transient, then the nonhomogeneous terms in Eq. (2), a linear combination of trim values obtained at equilibrium 

that are dependent upon ρ , will be close enough to reality that the resulting trajectory will closely correspond to the 

actual. If the system were excited by another transient where ρ is now fast, the nonhomogeneous terms will be 

incorrectly computed from the subset of trim values at equilibrium, causing inconsistencies between the model and 

actual trajectories. In the R-LPV setting, these nonhomogeneous terms are assumed constant, resulting in Eq. (3) 

being linear. No restrictions are therefore imposed on these terms being constructed from equilibrium trim values. 

 R-LPV models have improved fidelity at all neighboring points in the parameter space, including nonequilibrium conditions, implying that the slow variation condition may be relaxed to some extent. Furthermore, by 

removing the state derivative trim and all remaining trim values from the formulation, these quantities no longer 

need to be approximated. This does not solve the problem of obtaining new Jacobians away from equilibrium, but 

the reduced parameterization and interpolation thereof lessens propagation of error across the trajectory existent in 

quasi-LPV formulations. In the context of receding horizon control, improved fidelity means that global optimality 

is more closely preserved. Because the open-loop model is effectively a quasi-LPV model that recursively executes 

several samples into the future, reduced error propagation becomes equally important in realizing global optimality 

as maintaining fidelity in non-equilibrium regimes. 

The penalty for the improved model is that the state vector dimension is now expanded to n + ny and that the 

computed control signal is the integral of the actual controller output, ∫ u = u′ , due to the rate-dependency of the 

controller structure. Conversely, the measured disturbance inputs to the LPV models are brought in as a derivative, 

i.e. v′ = dv dt . It should be cautioned that introduction of uncertainties may certainly have a deleterious effect due 

to this derivative expression if these inputs are susceptible to noise or biasing, especially in plants with high inputoutput sensitivities. In practice, this disturbance is often manifested as a demand-related event that is subject to little 

noise or other types of uncertainty. Moreover, estimation structures that operate upon separate disturbance states 

decouple the estimation loop from these effects. 

III. Model Predictive Controller in Rate-Based LPV Form 

In this section, the practical problem setup for MPC is given. First, the disturbance model structure for output 

estimation in rate-based form is presented with treatment given to consolidating the estimator states with the 

expanded R-LPV states. Then, with this complete plant/estimator model, the R-LPV formulation of MPC is 

provided. 

Disturbance Models in the Rate-Based Paradigm 

In receding horizon control, input/output disturbance models are necessary to reduce the effects of any plantmodel mismatch and to absorb exogenous disturbances affecting the plant but unknown to the model. Due to lack of 

information regarding most disturbances, such models are often chosen to be pure integrators so that any constant 

disturbance may be asymptotically rejected and output tracking may theoretically occur without error. It is well 

known that, if the augmented system is detectable and the number of disturbance states equals the number of 

outputs, then all output channels will have zero steady-state error.13,14 Normally, the state vector is expanded to 

incorporate these new disturbance states, ny d ∈ R . However, this approach can be improved to avoid undue 

computational complexity arising from incorporating an additional ny integrator states (a total of 2ny more than the 

original model). Recognizing that the output integration is decoupled from the plant dynamics, the disturbance 

Gain-Scheduled

Model

y

ρ

s s

1

⎥

⎦

⎤

⎢

⎣

⎡

v

u

(x&)

y& ⎥

⎦

⎤

⎢

⎣

⎡

v

u

&

&

Gain-Scheduled

Model

y

ρ

s s

1

⎥

⎦

⎤

⎢

⎣

⎡

v

u

(x&)

y& ⎥

⎦

⎤

⎢

⎣

⎡

v

u

&

&

Figure 3. R-LPV models. 

NASA/CR—2006-214419 4
model inputs are simply added to y& in Fig. 3 and the state sub-vector y in Eq. (3) now becomes y + d . The state 

space equations are then 

m

p

y C w

A B u B v B w

= +

= + ′ + ′ +

ξ

ξ ξ 1 2 3 &

 (4) 

with the augmented matrices 

( )

( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

Λ =

y

C n

A

A

ρ

ρ 0 , ( )

( )⎥

⎦

⎤ ⎢

⎣

⎡ = ρ

ρ

1

1

1 D

B

B , ( )

( )⎥

⎦

⎤ ⎢

⎣

⎡ = ρ

ρ

2

2

2 D

B

B , ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ =

y n I B

0

3 , [ ] ny

C = 0 I

As in Eq. (3), the augmented state vector ξ is composed of the state derivative vector and the output vector. 

Uncorrelated additive process and measurement noise intensities, ny wp ∈ R and ny wm ∈ R , enter the disturbance 

model input channels and measurement channels, respectively. The diagonal filter matrix y Λn is included to avoid 

pure integration at the outputs. Note that the R-LPV realization augmented with disturbance models will have the 

same number of augmented states as conventional LPV realizations with disturbance models. 

Model Predictive Control Law 

Given the R-LPV plant/estimator model, optimal control actions are found by minimization of a finite-horizon 

linear quadratic objective function with respect to the controls and the outputs.3

 Converting to discrete time, the 

linear-quadratic cost function for the MPC law may be written as 

∑[ ] ( )( ) =

= + − + + − + + + +

p

i

k i

T

k i r k i k i

T Jk yk i yr k i Q y y u Ru

1

, , (5) 

subject to the discretized version of the plant model of Eq. (4) and constraints on the manipulated controls and 

measured outputs at time k. The subscript r denotes the reference setting and p represents the prediction horizon. 

The symmetric, positive-definite weight matrices Q and R are to-be-determined design parameters, and the usual 

requirement holds that the pairs ( ) 1 A,B and ( ) 1/ 2 A,Q are stabilizable. A Kalman filter state estimator is designed 

on the condition that (C, is detectable, assuming the proces A) s and measurement noise covariances W and V, 

defined by the intensities wp and wm, respectively. It is important to note that, in order to impose any weighting or 

constraints on the actual controls in the rate-based MPC framework, the output vector must be augmented with those 

control inputs. 

The LPV MPC formulation is achieved by computing state prediction equations recursively at each time step. 

Using the same state space notation from continuous time for the discrete time system equations, the state 

predictions are computed by 

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

′

′

+

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

∆ ′

∆ ′

= + ′ +

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

+ + −

∆

−

+

+

1

1 1 1 2

1

ˆ

ˆ

ˆ

k p

k

k p

k

k k

k p

k

v

v

u

u

M Aξ B u B M B M

ξ

ξ

 (6) 

where ξ k

ˆ are the estimated R-LPV states. The prediction matrices are 

( )

( )⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

+

=

∏=

p

i

A k i

A k

0

A M , 

( )

( ) ( )⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

+ + + −

=

∑

−

=

, 1 1

1

1

1

1

1

F j k p B k p

B k

p

j

B M , 

NASA/CR—2006-214419 5
( )

( ) ( )() ( ) ( )⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

+ + + − + + + − + −

=

∑ ∑

−

=

−

=

∆

, 1 , 1 1

0 0

1 1

2

1

1 1

1

1

1

1

1

F j k p B k p F j k p B k p B k p

B k

p

j

p

j

L

M M O L

L

B , 

( )

( )( ) ( )⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

− + − + +

=

F p k p F p k p F k p

B k

1, 2, 1,

0 0

2 2 2

2

2

L

M M O L

L

B , 

where 

( ) , ( ) ( ) 1

1

⎥ − −

⎦

⎤ ⎢

⎣

⎡ = − ∗

=

F∗ j ∏A i B j

j

i

l l l

In this representation, the control inputs are split into the present value of the control derivative uk

′ and a vector of 

future control derivative moves. 

The trajectory of predicted outputs is 

( ) ( ) k i k i k i y C k i D k i v + + + = + + + ′ 2 ˆ ξ (7) 

for each i =1,K, p . The dependence of the Jacobians on ρ is implied by their discrete-time dependence on k. 

From the above equations, it is readily apparent that the internal models assume quasi-LPV formulations (an 

internally-computed scheduler) in forming the predictions, but may use an external scheduler for state estimation as 

long as state continuity between each realization is guaranteed. Because the internal model must be strictly proper; 

i.e. zero gain at infinite frequency, it is necessary to formulate Jacobian LPV systems without the D1 term. In 

contrast, the fundamental model in R-LPV systems may be of any type because the R-LPV transformation is, by 

definition, one that maps any arbitrary system to a strictly proper system because the original D matrices become 

part of the B matrices. 

Standard quadratic programming (QP) approaches are available to efficiently solve this convex constrained 

optimization problem; the approach employed here uses an “active set” method that optimizes on a subset of 

inequality constraints that are active at the current step. Common ways of making the control law computation more 

efficient are to limit the control horizon m to some m < p or to update only intermittently (known as blocking). To 

expand the feasible set of the QP problem, the constraints are not posed as hard limits but instead are softened by 

incorporating a slack variable on the cost function that introduces an expensive penalty should any constraint 

violations occur. Computation is further streamlined by generating the Jacobians, estimator gains, and prediction 

matrices in an offline batch mode as a set of parsed arrays so that the on-line algorithm only needs to perform linear 

interpolation on these arrays at each time step. 

IV. Active Tip Clearance Control in a Commercial Turbofan Engine 

As depicted in Fig. 1, the clearance control actuator is designed to move a segmented shroud structure toward 

and away from the turbine blades. The concept, as referred to in Lattime, et al15 consists of several identical 

actuators that are placed at locations around the shroud circumference with each effecting movement in one shroud 

segment. It is assumed that each actuation point has a collocated clearance measurement at the shroud’s frame of 

reference. In this configuration, the detected clearance is the difference between the combined deformation of 

turbine components (referred to as the un-actuated clearance) and the actuator displacement, where a positive 

displacement results in smaller clearance. The active clearance control system can operate either upon a minimum 

detected clearance and single command signal, or upon several local clearance signals and multiple actuator 

commands. The MPC is adaptable to both configurations, but only the single-output case is considered here. 

NASA/CR—2006-214419 6
Two actuator platforms were used to demonstrate predictive control behavior across different realistic hardware 

design scenarios: one representing a servohydraulic actuator and the other representing a thermal deformation-based 

actuator. A detailed nonlinear model of the servohydraulic actuator described in DeCastro and Melcher16 is 

implemented as the truth model and a parsimonious reduced order model is used in the MPC. The dynamics of the 

actuator are primarily driven by the servo control loop and are approximated here by the following third-order 

system with corner frequency of approximately 0.2 Hz: 

( )( )( ) 223.2 4.035 1.424

1283

+ + + = s s s

G (8) 

The actuator stroke is measured by a transducer for servo-control and is therefore accessible to the engine control 

unit as a measured state of the system. The second actuator, a thermal-deformation based device, is similar to 

current thermal actuation systems that utilize secondary engine air to regulate the flange attachment to the shroud 

structure by way of a proportional air valve.4

 This device is represented by the first order system 

1

1

+ = s

G

τ

 (9) 

Because the intent of this case is purely illustrative, the thermal actuator internal model and truth model are taken to 

be identical. For both actuator types, constraints were placed on the minimum and maximum allowable control 

input settings, corresponding to zero and 0.1-inch displacements, respectively. 

For this tip clearance application, a commercial engine simulation (CES) representative of a large, high-bypass 

turbofan engine coupled with the actuator model was used as the baseline truth model for closed-loop evaluation. 

The simulation features a detailed model of the turbine section component deflection to accurately represent 

demand-related clearance effects. On the basis that the MPC is to be implemented as an isolated control loop from 

the engine controller, a simplified closed-loop engine fan speed compensator was incorporated. The compensator is 

a linear, second order system with a free integrator at the output, designed to obtain a slightly overdamped nominal 

closed-loop bandwidth of approximately 0.6 Hz. The requested fan speed is actually a mapping function consisting 

of power lever angle (PLA) and three environmental parameters (altitude, Mach number, ambient temperature). 

Multi-mode controllers that typically deal with limits normally encountered with large transients have not been 

incorporated, but the MPC structure can be viably altered in practice to accommodate this additional level of 

sophistication. Alternately, if the tip clearance MPC is implemented in a unified engine MPC, separate models of 

the controller are unnecessary because the MPC generates these engine commands. 

Nine linear models were generated of the closed-loop engine at equispaced PLAs between ground idle and 

maximum power at sea-level static conditions, constructed with several sensed output channels and two input 

channels: delta clearance (provided by the actuator) and fuel flow. Jacobians at these points were found by 

perturbing these inputs, nine engine states (fan and core shaft velocities and seven internal metal temperatures), and 

the three fan speed controller states. The turbine component states are numerous and were omitted from the 

linearization. Because the operating conditions considered here are limited to constant altitude and airspeed, the 

scheduler is taken simply as the measured fan speed, XN2. 

With the hydraulic actuator model, the LPV model has a total of two inputs, fifteen states, and six outputs; these 

I/O’s are listed in Table 1. The total number of R-LPV internal model states is 22 ( y u n + n + n ), only one state 

greater than the Jacobian LPV counterpart. Figure 4 shows the interconnection of the rate-based active clearance 

control MPC and the turbofan engine plant. The exogenous disturbance (δ k ) is brought in only to the engine, while 

the demand-induced measured disturbance ( k v ) input, PLA, is brought in to the engine and MPC. This may be 

extended to capture other sensed inputs (ambient temperature, Mach number, altitude) if needed. As mentioned 

earlier, differentiation of input variables is necessary in the rate-based internal model framework. Such a 

transformation can amplify any noise or biasing on the input channels, but since this application calls for a 

disturbance that is a function of throttle position, it may be argued that the signal is mostly free of noise and other 

sources of uncertainty. Nonetheless, examining the effect that these uncertainties have on transient performance is 

warranted to ensure that optimality is not compromised. 

NASA/CR—2006-214419 7
Design Considerations 

In this tip clearance implementation, minimization of SFC and EGT is indirectly achieved by penalizing 

clearance excursions away from a small-valued set point. Hence, the objective function and loop transfer function 

reduce to single-input, single-output (SISO), with the actuator command as the control input and clearance as the 

regulated output. The unconstrained SISO control input is then used exclusively for design: 

uk Kξ k

ˆ ′ = − (10) 

where K is the full-state feedback gain matrix. 

The tuning procedure selected in this paper follows Doyle and Stein,17 where the objective is to first specify a 

desired loop transfer function (closed or open), then apply a quasi-deadbeat estimator to the loop to asymptotically 

achieve the specification. With the ratio R Q set to 0.001, the controller attains fast response but avoids highfrequency gain/phase distortions in the control loop return ratio ( ) 1

1

K zI A B−− due to discretization effects. In so 

doing, the return ratio more closely resembles its continuous-time counterpart, which has the property of providing 

infinite gain margin against gain increases and 60o of phase margin. 

V. Demonstrative Simulations 

In this section, simulated results of the active clearance control MPC application are given and comparisons 

made between controllers derived using conventional internal modeling methods and the rate-based method 

explained in this paper. Additionally, ties are made to the practicality of this MPC implementation in active 

clearance control using the two actuation methods described earlier. For all reported results, a 50-Hz sample rate 

was used. The minimum clearance constraint and clearance set point were set to identical values, which presents the 

QP solver

(quasi-LPV)

Engine

Selector

Estimator

(LPV) Selector

ρ k

k y

uk

′

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

′

′

k+ p

k

u

u

M

∫

k v′

k v

uk

MPC

δ k

ξ k

ˆ

k v′

QP solver

(quasi-LPV)

Engine

Selector

Estimator

(LPV) Selector

ρ k

k y

uk

′

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

′

′

k+ p

k

u

u

M

∫

k v′

k v

uk

MPC

δ k

ξ k

ˆ

k v′

Figure 4. Block diagram of MPC with R-LPV models. 

Table 1. Inputs and outputs for R-LPV tip clearance controller. 

Inputs Outputs 

Actuator command, UACT Fan speed, XN2 

Power lever angle, PLA Fuel flow, WF

 Exhaust gas temperature, T5 

 Stage 1 clearance, CLR 

 Actuator position, XACT 

 Actuator command, UACT 

NASA/CR—2006-214419 8
most demanding scenario for the controller since maintenance of the clearance set point and avoiding blade rubs are 

now invoked as competing objectives. 

Distinctions between Rate-Based and Jacobian MPC 

Clearance responses with the Jacobian-MPC law for the servohydraulic actuator given a large-magnitude PLA

transient are shown in Fig. 5. For this assessment, the prediction horizon p was set to 20 samples and the control 

horizon m to 2 samples, with both these settings chosen to obtain an unconstrained response that resembles the 

infinite-horizon response. In the figure, fan speed and adjusted clearance (top and bottom traces, respectively) 

represent measured outputs. While not a physical output, the un-actuated clearance shown in the middle trace 

represents the combined deformation of the turbine section components, a demand-related effect from the engine 

essential for predicting the evolution of clearance through time. This quantity is computed as the sum of the 

controlled clearance and the actuator displacement (not shown), which is a valid estimate only since the feedback 

effects of clearance on the engine’s gas path dynamics are considered to be minor. 

In the bottom trace of Fig. 5, it is clear that the transient causes the adjusted clearance to fall below the constraint 

(dashed line) at about 1.8 seconds, which is in violation of the objective that the adjusted clearance must be kept 

positive to avoid the possibility of blade rubs. The open-loop prediction trajectory overlays reveal that the model 

incorrectly predicts the evolution of fan speed and un-actuated clearance outputs, especially during the time interval 

between 1.8 and 2.2 seconds, which correlates to the time when the constraint violation begins. The output 

trajectory plot in Fig. 6 is helpful for visualizing gradient information in the output space, containing the same 

prediction trajectories as Fig. 5 plus one additional trajectory at the 1.8-second mark. As expected, the 1.8-second 

prediction has the largest initial gradient error of the four trajectories, as shown by the large migration away from 

the actual trajectory early on in the horizon. 

The improvements that the R-LPV models afford the optimization are shown in Fig. 7, given the same PLA

transient and an identically-tuned controller (i.e., one with the same design parameters). In comparison with the 

previous case, the adjusted clearance (bottom trace) stays at or above the constraint, satisfying the blade rub 

objective. The prediction traces in Fig. 7 and associated output trajectory plot in Fig. 8 show that the sharp, erratic 

responses disappear, with initial gradients following much closer to the actual. Note that the 1.5-second prediction 

traces settle out at constant rates-of-change. The reason for this is because the measured disturbance derivative, not 

the measured disturbance itself, is held constant throughout the horizon in the R-LPV setting. For all simulations 

0 1 2 3 4 5 0.2

0.4

0.6

0.8

1

XN2 (normalized)

0 1 2 3 4 5 0.05

0.06

0.07

0.08

0.09

0.1

CLR w/o actuator (in)

0 1 2 3 4 5

-5

0

5

x 10-3

CLR - CLRsetpoint (in)

time (sec)

Figure 5. Jacobian LPV responses, showing actual 

(red) and predicted outputs (black dots). 

0.4 0.5 0.6 0.7 0.8 0.9 1 0.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

0.09

0.095

0.1

XN2 (normalized)

CLR w/o actuator (in)

3.0 secs

2.0 secs

1.8 secs

1.5 secs

Figure 6. Jacobian LPV output trajectories, 

showing actual (red) and predicted outputs (black 

dots). 

NASA/CR—2006-214419 9
executed, this does not negatively impact the convergence of the controller. At 3.0 seconds, all internal model 

transients die out, with any subsequent error being a result of the slow neglected clearance dynamics. The closer 

agreement between the R-LPV models and the nonlinear plant throughout the transient is owed to the fact that the 

non-homogeneous terms in the R-LPV models are no longer explicitly parameterized and therefore not subject to the 

associated limitations. 

Practical Assessment of the Rate-Based MPC 

Where the previous evaluation was only concerned with utilizing the feedforward attributes of the MPC in 

optimizing control actions based on demand-induced clearance events, actual in-flight situations require the need to 

reject exogenous disturbances and maintain performance with changing parameters, an exercise that is largely a 

question of feedback compensation. In the active clearance control application, clearance changes induced by flight 

loads acting on the engine are considered, whose effects become more problematic as clearance set points decrease 

because of the decreased margins against blade rubs. As alluded to in Olsson and Martin,18 there are multitudes of 

engine transients that occur during flight that are of interest in active clearance control; a sampling of which includes 

takeoff, re-burst, thrust reversal, hard turns, and aircraft stall. Each event contributes a demand-induced component 

on clearance due to PLA, etc., and a presumed unknown flight load-induced component as a result of turbulence, 

maneuvering of the aircraft, and asymmetric thrust loads that cause the engine to bend. Because of their large, 

rapidly-acting contributions on clearance, the takeoff, thrust reversal, and aircraft stall events are employed to 

exercise the MPC laws given realistic clearance events that occur during normal operation; the magnitudes and 

rates-of-change of each event were reproduced approximately from actual flight data reported in Ref 18. Since 

takeoff and re-burst are essentially identical in nature aside from the thermal state of the turbine at the start of the 

event, examining the transient MPC response with a takeoff event effectively serves the dual purpose. 

To compare the MPC strategy with a controller very similar to a linear quadratic Gaussian (LQG) control law, 

the clearance constraint was removed from the MPC computations, rendering the new controller to be similar by 

nature to a gain-scheduled LQ controller with anti-windup protection. The purpose of this comparison is to justify 

the benefit of MPC in the face of the additional computational burden. Note that the unconstrained, LQG-like 

controller is still globally valid in the sense of Eq. (3). If a truly gain-scheduled LQG controller were used, this 

would be optimal only in the vicinity of the linearization points. Figure 9 shows the MPC response given the three 

event scenarios at nominal conditions for a thermal actuator with 1.6-second time constant (τ =1.6 ). This case 

represents an actuator whose response rate roughly matches the maximum deformation rate of the rotor during a 

0 1 2 3 4 5 0.2

0.4

0.6

0.8

1

XN2 (normalized)

0 1 2 3 4 5 0.05

0.06

0.07

0.08

0.09

0.1

CLR w/o actuator (in)

0 1 2 3 4 5

-5

0

5

x 10-3

CLR - CLRsetpoint (in)

time (sec)

Figure 7. R-LPV responses, showing actual (red) 

and predicted outputs (black dots). 

0.4 0.5 0.6 0.7 0.8 0.9 1 0.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

0.09

0.095

0.1

XN2 (normalized)

CLR w/o actuator (in)

3.0 secs

2.0 secs

1.8 secs

1.5 secs

Figure 8. R-LPV output trajectories, showing 

actual (red) and predicted outputs (black dots). 

NASA/CR—2006-214419 10
power-increase event. To extend the anticipation capability, the prediction horizon p was increased to 50 samples 

and control horizon m to 5 samples. From the figure, the MPC response to a thrust reversal transient produces the 

most benefit over an unconstrained controller, eliminating the 2-mil excursion below the constraint. It is 

encouraging that enforcement of the clearance constraint is a result of very smooth actuator command signals rather 

than abrupt or highly oscillatory control actions. Although unconstrained responses in the remaining two events 

have milder constraint violations, it is important to note that the constrained controller satisfies the blade rub 

objective in both cases. One may interpret these results from a systems point-of-view. If the clearance setpoint 

using this LQG-like controller must be 2 mils greater than the MPC setpoint to accommodate the possibility of the 

worst-case event, then this would detract from exploiting the benefits of a tip clearance control system. Based upon 

past studies,5

 the penalty on efficiency would be 0.2% and the penalty on EGT overshoot would be 2oC. 

Figure 10 shows the response with a thermal actuator with τ = 5.3 , a rate 60% slower than the previous case. 

0 2 4 6 8 0.2

0.4

0.6

0.8

1

XN2

(normalized to max pwr)

0 2 4 6 8 0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 -0.015

-0.01

-0.005

0

flight load input (in)

0 2 4 6 8 -0.015

-0.01

-0.005

0

0 2 4 6 8 -0.02

-0.015

-0.01

-0.005

0

0 2 4 6 8 0.2

0.4

0.6

0.8

1

UACT (normalized)

0 2 4 6 8 0

0.5

1

0 2 4 6 8 0

0.2

0.4

0.6

0.8

0 2 4 6 8 -5

0

5

10 x 10-4

time (sec)

CLR - CLRsetpoint (in)

0 2 4 6 8 -2

-1

0

1 x 10-3

time (sec)

0 2 4 6 8 -10

-5

0

5 x 10-4

time (sec)

0 2 4 6 8 0.8

0.85

0.9

constraint inactive

constraint active

Figure 9. R-LPV responses for fast thermal actuator. 

Thrust reversal Aircraft stall 

0 2 4 6 8 -0.015

fligh

0 2 4 6 8 -0.015 0 2 4 6 8 -0.02

0 2 4 6 8 0

0.5

1

UACT (normalized)

0 2 4 6 8 0

0.5

1

0 2 4 6 8 0

0.2

0.4

0.6

0.8

0 2 4 6 8 -6

-4

-2

0

2 x 10-3

time (sec)

CLR - CLRsetpoint (in)

0 2 4 6 8 -15

-10

-5

0

5 x 10-3

time (sec)

0 2 4 6 8 -10

-5

0

5 x 10-3

time (sec)

constraint inactive

constraint active

Figure 10. R-LPV responses for slow thermal actuator. 

Takeoff Thrust reversal Aircraft stall 

Takeoff 

NASA/CR—2006-214419 11
This case is included to illustrate the consequences of applying MPC to an actuator that is slower than the rate of 

mechanical rotor growth, similar to state-of-the-art actuators. In the figure, the range of the control signal lies 

between one and zero and saturates beyond those values. For both controllers, the control signal saturates at zero in 

attempt to move the shroud away from the blades. With the constrained controller, anticipation of the event in the 

takeoff and thrust reverse events results in a slight increase in adjusted clearance before becoming altogether 

negative upon loss of authority. Although no anticipation is possible in the purely exogenous stall event, the 

adjusted clearance stays at zero longer than for the unconstrained case, a result of the more rapid compensation of 

the constrained MPC when riding the clearance constraint. It may be suggested that MPC performance can be 

further improved with anticipation of the exogenous events, perhaps either by direct estimation of the flight load 

event or by correlating to other measurements (e.g. structural sensors). These effects may not be assumed uniform 

around the turbine circumference.

Table 2 summarizes the MPC benefits for the three actuators and also presents a case of tip clearance control 

amidst off-nominal engine conditions. Note that any violations of the constraint are a result of the slack tuning 

parameter described earlier. Comparing the fast thermal actuator with the nominal hydraulic device, both the 

unconstrained and constrained clearance values are quite different, which is directly related to sub-optimality 

introduced with plant/model mismatch. Recall that the nonlinear hydraulic actuator is adopted as the truth model, 

while the thermal actuator only uses the linear model. With the exception of the slow thermal device, enforcement 

of the constraint results in commensurate amounts of clearance improvements for each. As echoed in Fig. 10, the 

MPC applied to the slow actuator offers some improvement, albeit less than a full-authority actuator does. The 

degraded engine case is implemented as a shift in engine parameters to roughly represent 6000 cycles of engine 

service life degradation, as described in Sallee,19 coupled with a shift in fuel flow sensitivity of -5%. In a gross 

dynamical sense, any engine degradation is not expected to significantly impact the behavior of the engine, and 

much less the behavior of clearance dynamics. This important attribute is exemplified by the results. 

To address the aforementioned issue concerning the integrity of the internal model amidst uncertainties in the 

measured disturbance signal, simulation cases were generated where the PLA measured disturbance input was fouled 

by uncertainties. The results are shown in Fig. 11, where two cases show the effects of the MPC receiving PLA

commands corrupted by a ±5% shift in sensitivity and a third where the PLA has additive white noise with variance 

of approximately 6% of full scale. The traces show that the introduction of noise causes excitation of higherfrequency controller modes, but no adverse effects in control performance. Although the controller sees a PLA

derivative that differs greatly from the actual value entering the engine, the deadbeat estimator is quick to reject 

these disparities and the prediction is largely unaffected during the comparatively short span of the horizon. 

Naturally, longer horizons will exacerbate the effects of noise on the input channel, possibly producing an erratic or 

Table 2. Minimum clearance for constrained and unconstrained R-LPV MPC. Values are in mils 

( 3 1 10− × in). 

 Unconstrained Constrained Delta 

Thermal Actuator, τ = 1.6, nominal engine 

Takeoff -0.28 -0.01 0.27 

Thrust reverse -1.93 -0.01 1.92 

Aircraft stall -1.00 -0.04 0.96 

Thermal Actuator, τ = 5.3, nominal engine 

Takeoff -5.01 -4.69 0.32 

Thrust reverse -10.5 -9.80 0.70 

Aircraft stall -8.71 -8.02 0.69 

Hydraulic Actuator, nominal engine 

Takeoff -0.80 -0.18 0.62 

Thrust reverse -2.29 -0.50 1.79 

Aircraft stall -3.26 -0.71 2.55 

Hydraulic Actuator, off-nominal engine 

Takeoff -0.60 -0.13 0.47 

Thrust reverse -2.15 -0.50 1.65 

Aircraft stall -3.26 -0.70 2.56 

NASA/CR—2006-214419 12
even divergent control signal. Nevertheless, these results are important in confirming that R-LPV models are indeed 

viable for use in MPC even in the presence of noise. 

VI. Conclusions 

In this paper, an innovative model predictive control (MPC) strategy using rate-based linear parameter varying 

(R-LPV) models is introduced. The virtues of the rate-based framework permit state derivatives to be directly 

specified, resulting in the implicit inclusion of state derivative trim values in the family of trajectories within the 

neighborhood of linearization equilibrium points. This enhances transient performance by widening the model’s 

valid applicable range without introducing additional linearization points, especially at non-equilibrium. Removal 

of the explicit trim value information furthermore results in models that exhibit less approximation error, an 

important attribute of any recursive modeling technique, such as quasi-LPV. 

The new MPC strategy is applied to an active clearance control system, where it is highly important to minimize 

clearance but avoid violating the minimum clearance constraint that protects against detrimental turbine blade rubs. 

In this work, the active clearance control optimization problem consists only of maintaining a minimal clearance set 

point, however directly optimizing against performance metrics such as exhaust gas temperature (T5) and fuel flow 

(WF) is a straightforward extension using this framework. The R-LPV strategy was demonstrated to maintain 

prediction fidelity and control optimality in transient regimes where the conventional Jacobian LPV method does 

not. Additionally, the controller was proven to be advantageous for tip clearance control when comparing against an 

analogous unconstrained, gain-scheduled controller similar to LQG. 

With regard to computational complexity, although the R-LPV transformation produces models with state 

dimensions greater than conventional LPV by the number of controlled inputs and outputs, it is shown that the 

integrated output states may be merged with the disturbance model states. As such, the internal model states are 

greater by only the number of inputs, which is usually small in propulsion system applications. Although the new 

MPC strategy was applied to the rather demanding active clearance control problem with competing objectives, the 

theoretical groundwork presented here provides sufficient generality to carry over to MPC applications in other 

nonlinear control problems; among the possibilities being turbofan engine control. Because of the demonstrated 

advantages this method has over conventional methods, it has great potential for control of aerospace applications 

where maintaining control optimality during transients is especially critical. 

0 1 2 3 4 5 6 7 8 0

0.5

1

UACT (normalized)

0 1 2 3 4 5 6 7 8 -2

0

2

4

6

8

10 x 10-4

time (sec)

CLR - CLRsetpoint (in)

-5% sensitivity

+5% sensitivity

additive noise

Figure 11. Constrained R-LPV responses for a thrust reverse transient with corrupted measured 

disturbance. 

NASA/CR—2006-214419 13
References 1 Brunell, B.J., Bitmead, R.R., and Connolloy, A.J., “Nonlinear model predictive control of an aircraft gas turbine engine,” 

Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, 2002, pp. 4649-4651. 2 Fuller, J.W., Kumar, A., and Millar, R.C., “Adaptive model based control of aircraft propulsion systems: status and outlook for

naval aviation applications,” ASME Paper GT2006-90241, May 2006. 3 Maciejowski, J.M., Predictive Control with Constraints, Prentice Hall, Harlow, England, 2002. 4 Lattime, S.B. and Steinetz, B.M., “High-pressure turbine clearance control systems: current practices and future directions,” 

Journal of Propulsion and Power, Vol. 20, No. 2, 2004, pp. 302-311. 5 Wiseman, M.W. and Guo, T.-H., “An investigation of life extending control technologies for gas turbine engines,” 

Proceedings of the American Control Conference, Arlington, VA, 2001, pp. 3706-3707. 6 Geisheimer, J.L., Billington, S.A., Holst, T., and Burgess, D.W., “Performance testing of a microwave tip clearance sensor,” 

AIAA Paper 2005-3987, July 2005. 

7 DeCastro, J.A., Melcher, K.J., and Noebe, R.D., “System-level design of a shape memory alloy actuator for active clearance 

control in the high-pressure turbine,” AIAA Paper 2005-3988, July 2005. 8 Heise, S.A. and Maciejowski, J.M., “Model predictive control of a supermaneuverable aircraft,” AIAA Paper 96-3768, July 

1996. 

9 Shamma, J.S. and Cloutier, J.R., “Gain-scheduled missile autopilot design using linear parameter varying transformations,” 

Journal of Guidance, Control, and Dynamics, Vol. 16, No. 2, 1993, pp. 256-263. 10 Mehra, R.K., Prasanth, R.K., Bennett, R.L., Neckels, D., and Wasikowski, M., “Model predictive control design for XV-15 tilt 

rotor flight control,” AIAA Paper 2001-4331, Aug. 2001. 11 Leith, D.J. and Leithead, W.E., “Input-output linearization by velocity-based gain-scheduling,” International Journal of 

Control, Vol. 72, No. 3, 1999, pp. 229-246. 12 Stengel, R.F., Optimal Control and Estimation, Dover, New York, 1994. 13 Pannocchia, G. and Rawlings, J.B., “Disturbance models for offset-free model-predictive control,” AIChE Journal, Vol. 49, 

No. 2, 2003, pp. 426-437. 

14 Badgwell, T.A. and Muske, K.R., “Disturbance model design for linear model predictive control,” Proceedings of the 

American Control Conference, Anchorage AK, 2002, pp. 1621-1626. 15 Lattime, S.B., Steinetz, B.M., and Robbie, M.G., “Test rig for evaluating active turbine blade tip clearance control concepts,”

Journal of Propulsion and Power, Vol. 21, No. 3, 2005, pp. 552-563. 16 DeCastro, J.A. and Melcher, K.J., “A study on the requirements for fast active turbine tip clearance control systems,” NASA 

TM-2004-213121, July 2004. 

17 Doyle, J.C. and Stein G., “Robustness with observers,” IEEE Transactions on Automatic Control, Vol. AC-24, No. 4, 1979, 

pp. 607-611. 

18 Olsson, W.J. and Martin R.L., “B747/JT9D flight loads and their effect on engine running clearance and performance 

deterioration; nacelle aerodynamic and inertial loads (NAIL)/ JT9D jet engine diagnostics programs,” NASA CR-165573, Feb. 

1982. 

19 Sallee, G.P., “Performance deterioration based on existing (historical) data; JT9D jet engine diagnostics program,” NASA CR135448, April 1978. 

NASA/CR—2006-214419 14
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E–15692

WBS 561581.02.01.03.07

NAS3–00145

20

Rate-Based Model Predictive Control of Turbofan Engine Clearance

Jonathan A. DeCastro

Optimal control; Adaptive control; Clearances

Unclassified -Unlimited

Subject Category: 07

QSS Group, Inc.

21000 Brookpark Road

Cleveland, Ohio 44135

An innovative model predictive control strategy is developed for control of nonlinear aircraft propulsion systems and

sub-systems. At the heart of the controller is a rate-based linear parameter-varying model that propagates the state

derivatives across the prediction horizon, extending prediction fidelity to transient regimes where conventional models

begin to lose validity. The new control law is applied to a demanding active clearance control application, where the

objectives are to tightly regulate blade tip clearances and also anticipate and avoid detrimental blade-shroud rub occurrences by optimally maintaining a predefined minimum clearance. Simulation results verify that the rate-based controller

is capable of satisfying the objectives during realistic flight scenarios where both a conventional Jacobian-based model

predictive control law and an unconstrained linear-quadratic optimal controller are incapable of doing so. The controller

is evaluated using a variety of different actuators, illustrating the efficacy and versatility of the control approach. It is

concluded that the new strategy has promise for this and other nonlinear aerospace applications that place high importance on the attainment of control objectives during transient regimes.

Prepared for the 42nd Joint Propulsion Conference and Exhibit cosponsored by the AIAA, ASME, SAE, and ASEE,

Sacramento, California, July 9–12, 2006. Project manager, Ten-Huei Guo, Instrumentation and Controls Division,

NASA Glenn Research Center, organization code RIC, 216–433–3734.