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6

Model Predictive Control of NonlinearRotorcraft Dynamics with Application to

the XV-15 Tilt RotorRaman K. Mehra and Ravi K. Prasanth

Scientific Systems Company Inc., Woburn, MA

Rotorcraft development presents unique control challenges related to noise, vibration, and

flight. Model Predictive Control (MPC) is proposed as a holistic approach to rotorcraft

flight control capable of explicitly accounting for operational constraints. The first part of

this chapter describes MPC design using linear parameter-varying (LPV) approximation

of nonlinear dynamics. This procedure has several advantages including known quality of

approximation and polynomial-time computability. Details of MPC problem formulation

and its implementation are presented. As a first application, we consider active control

of aeromechanical instability, which is a major hurdle in the development of soft-in-plane

rotorcraft. A simple nonlinear parameter-varying model that contains a Hopf bifurcation is

used to capture the essential features of this instability. The effectiveness of MPC in sup-

pressing nonlinear vibrations subject to control constraints is illustrated. As a second and

more involved application, we present the design of an MPC-based flight control system

(FCS) for the XV-15 tilt rotor. The FCS was implemented on a 6-DOF high-fidelity XV-15

real-time simulator. Test pilots flew several missions on the simulator with MPC in the loop

including a highly nonlinear conversion maneuver. They observed significant reductions in

work load, fast response to commands, and rated MPC performance from good to excellent

during these simulated maneuvers.

1 INTRODUCTION

NASA, DoD, and the aerospace industry have a very strong interest in the development of

advanced rotorcraft. Some unique challenges related to noise, vibration, and flight control

are present in their development. A good example comes from tilt rotors, which can hover

like helicopter and cruise like a turboprop. When the pilot presses the pedals while in

helicopter mode, the tip path plane of one rotor tilts forward and that of the other tilts aft

producing a yaw moment. The same pedal input produces a rudder deflection in airplane

mode. The flight control system must accommodate these requirements and provide a

smooth transition during the conversion process.

© 2004 by CRC Press LLC

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Rotorcraft flight control system (FCS) is currently designed in a point-by-point man-

ner using linear principles. Gain scheduling is used to phase-in and phase-out control

effects during flight. The flight control computer is also responsible for controlling struc-

tural loads on the aircraft. This is achieved, in the V-22 for example, by limiting control

surface commands (displacements and rates) produced by pilot stick inputs. Apart from

being a complex task, control rate and position limiting have serious effects on aircraft-

handling qualities. Pilots evaluating FCS with rate limiting usually mark them down. Infact, control rate limiting is a known trigger mechanism for aircraft-pilot coupling (APC)

or pilot-induced oscillation (PIO), which can cause fatalities.

Model Predictive Control (MPC) is a multiinput multioutput digital-control design

methodology [6, 7] that uses a highly intuitive principle. At any time step, the control

inputs to be applied depend on the current state, control objectives to be achieved, and

the current operational constraints. So, a rational procedure is to formulate a constrained

optimization problem at each time step and obtain control inputs by solving it. This has the

advantage of explicitly accounting for time domain control constraints such as rate limits

and state-dependent constraints such as limits on normal acceleration. Frequency domainspecifications can also be brought in through MPC design parameters discussed later. Since

the control objectives and operational constraints are always updated and accounted for,

MPC can provide a holistic approach to rotorcraft flight control. Our aim is to demonstrate

this using realistic control problems.

This chapter is organized as follows. The next section describes the MPC problem

and implementation in detail. For nonlinear systems, the online optimization problem for-

mulated by MPC is generally nonconvex and cannot be solved in real time, especially at

the rates required for flight control. We say that a problem is solvable if there is an anytime

algorithm [13] that terminates in polynomial time for a given accuracy. A procedure fordesigning real-time implementable MPC using linear-parameter varying (LPV) approxi-

mations of rotorcraft dynamics is presented in the next section. Section 3 gives a brief

description of active control of aeromechanical instability using MPC. Our results show

the effectiveness of MPC in suppressing vibrations in the presence of actuator saturation

limits. Section 4 presents the design of an MPC-based flight control system (FCS) for

the XV-15 tilt rotor. FCS design specifications include frequency-domain MIL-F-83300

and MIL-F-8785C requirements and time-domain safety and control limits. MPC-based

FCS was implemented at 50 Hz on a real-time 6-DOF XV-15 simulator at Bell Helicopter.

Results of piloted simulations and evaluations by test pilots are presented. The chapterconcludes with some recommendations for future work. Due to space limitations, some

details have been omitted; a complete version of this chapter can be obtained from the

authors.

2 MODEL PREDICTIVE CONTROL OF NONLINEAR SYSTEMS

This section begins with a description of the control problem and the MPC approach. We

then indicate the computational difficulties associated with MPC and present an algorithm

that can be readily implemented. The algorithm uses a linear parameter varying (LPV) ap-

proximation of the nonlinear system to reduce the computational requirements significantly

from those for nonconvex nonlinear programming to that of convex quadratic program-

ming (QP). Thus, our approach trades off optimality for polynomial-time computability.


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The MPC implementation is described in detail. Although the presentation is geared to-

ward rotorcraft applications, the algorithm can be applied to problems in other areas as

well.

2.1 Control Problem

Consider the nonlinear system:

xk+1 = f (xk, uk) (1a)

yk = g(xk) (1b)

zk = h(xk) (1c)

ulbd ≤ uk ≤ uubd, for all k (1d)

zlbd ≤ zk ≤ zubd, for all k (1e)

where xk ∈ IRnx is the state vector, uk ∈ IRnu is the control input, yk ∈ IRny is thesignal that must track a specified command, and zk ∈ IRnz is the vector of signals that

are constrained (the control inputs are not included in this vector). It is possible to make

the constraint bounds ulbd, zlbd, uubd and zubd depend on time, but for simplicity they are

taken as constants. As part of the control problem, we are also given a desired trajectory or

commanded trajectory ykcmd.

Control Problem: Generate a feedback control law so that yk tracks the desired

trajectory ykcmd subject to the system dynamics and constraints given in (1).

MPC solution to this problem is the following: At time k , define the performance

index J as follows:

J (xk, δuk, δuk+1, · · ·, δuk+N −1) = J i + J p + J u (2a)

J i =N −1l=0

l

j=0

yk+j+1cmd − yk+j+1

T Qi

yk+j+1cmd − yk+j+1

(2b)

J p =N −1i=0

yk+i+1cmd − yk+i+1

T Q

yk+i+1cmd − yk+i+1

(2c)

J u = δuT k Rδuk +

N −2

i=0

(δuk+i+1 − δuk+i)T

R (δuk+i+1 − δuk+i) (2d)

and minimize it over control moves subject to the system dynamics and constraints in (1).

Apply the control input uk so obtained, increment k , and repeat the procedure.

The terms J i and J p in (2b) and (2c) can be thought of as discrete versions of integral

error and tracking error penalties over the control horizon. These terms are expected to

yield a proportional-integral (PI) effect in the closed-loop system. Like in classical con-

trol, the weights Qi and Q appearing in (2b) and (2c) can be tuned to obtain satisfactory

steady state and transient tracking performances. The third term J u in (2d) is a penalty for

excessive control rate which smoothes out the control inputs. The control inputs are also

constrained to satisfy the saturation limits (1d).

Note that the performance index requires knowledge of the desired or commanded

trajectory ykcmd over the prediction horizon. When the application is rotorcraft stability


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and control augmentation, the commands are pilot stick inputs passed through a command

shaping filter. So, their future values yk+1cmd, · · ·, yk+N cmd needed in the performance index will

not be known at time k. Therefore, we have to make an assumption, and the simplest (in

terms of computations) assumption is that

ykcmd = yk+1cmd = · · · = yk+N cmd .

This may also be reasonable if the horizon length is chosen to be relatively small. For

example, when aircraft dynamics is discretized at 0.02 seconds (50 Hz), a horizon length

N = 10 corresponds to 0.2 seconds (5 Hz), which is comparable to the pilot’s bandwidth

so that changes in the command inputs from its current value of ykcmd during the horizon

of interest can be neglected. We may be able to extrapolate past pilot commands by fitting

polynomials to arrive at better estimates, but this will not be used here. In other applications

such as autopilot design, the trajectory is defined by the controller itself and, hence, will

be known over the prediction horizon. Both problems fit into the MPC framework and the

only difference is in the data used by MPC.

2.2 Linear Parameter-Varying Approximation

When the tracked and constrained variables are written in terms of the control inputs (which

are the unknowns), the optimization problem to be solved online becomes nonconvex and

corresponds to a general nonlinear programming problem. This difficulty is usually cir-

cumvented by linearizing about the current state. The linearized system leads to a convex

quadratic programming (QP) that can be readily solved. However, this procedure is flawedfor a number of reasons: (a) linearization is performed about a nonequilibrium state, but the

linearized system is treated as time-invariant, (b) the quality of approximation provided by

linearization is not known because it depends on the states and their derivatives, (c) plant

model and state estimates have uncertainties, and (d) linearization requires the solution of

nonlinear algebraic equations, which can be difficult.

Here, we use a linear parameter varying (LPV) approximation of the nonlinear sys-

tem:

δxk+1 = A(θk)δxk + B(θk)δuk (3a)δyk = C y(θk)δxk (3b)

δzk = C z(θk)δxk (3c)

xk = xtrim(θk) + δxk, uk = utrim(θk) + δuk (3d)

yk = ytrim(θk) + δyk, zk = ztrim(θk) + δzk (3e)

ulbd ≤ utrim(θk) + δuk ≤ uubd, k = 0, 1, · · ·, N − 1 (3f)

zlbd ≤ ztrim(θk) + δzk ≤ zubd, k = 1, 2, · · ·, N , (3g)

where θk ∈ IRnθ is the scheduling variable (time-varying parameter). This parameter

defines the flight condition, and the set of all its possible values defines the flight envelope.

There are several ways to obtain an LPV approximation, some of which depend on

the application. See [9, 10, 11, 12] for details on LPV systems. A procedure that confirms

to the current practice in aerospace is the following:


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1. Subdivide the flight envelope into L polytopic regions. Each polytope is made of m

vertices. Let the total number of vertices be M . Let us order the vertices from 1 to

M and denote by θk the kth vertex.

2. At each of the M vertices, trim the aircraft equations of motion (or the nonlinear sys-

tem’s dynamical equations) to obtain trim states, control settings, tracked variables

and constrained variables. Thus at θk

we obtain:

xtrimk, utrim

k, ytrimk and ztrim

k

by solving the algebraic equation obtained from the dynamical equations in (1).

3. At the trim point (θk, xtrimk, utrim

k, ytrimk, ztrim

k), linearize the system in (1). This

gives a linear system of the form:

δxk+1 = Akδxk + Bkδuk (4a)

δyk = C ykδxk (4b)

δzk = C zkδxk. (4c)

4. The collection θk, xtrim

k, utrimk, ytrim

k, ztrimk, Ak, Bk, C yk, C zk

M

k=1

forms the LPV data.

This is done off-line and the quality of approximation can be checked over admissible

trajectories of scheduling variables.

2.3 MPC Implementation

With the LPV approximation in hand, we are now ready to describe the MPC implementa-

tion. There are three sequential steps:

1. Interpolation: Interpolate system data to obtain a linear system model valid at the

current value of scheduling variable.

2. QP formulation: Perform computations using interpolated system data and MPC

design parameters to set up quadratic programming (QP) problem.

3. QP solution: Solve QP problem and obtain optimal control input.

The objective of the first step is to obtain a linear system model that is valid locally. This

model depends on the scheduling variable and corresponds to the linear approximation

about the trim point associated with the scheduling variable. Thus, we avoid linearization

about a nonequilibrium point. In general the interpolation is difficult to perform because

the flight envelope need not be a regular region. We shall describe an efficient algorithm to

approximately interpolate. The second step as stated uses the same state-space model over

the prediction horizon. It is possible to combine steps 1 and 2 so that we use an LPV model

over the prediction horizon. This will result in better performance. We have separated

these steps to keep coding simple. The last step of QP solution is the most computationally

intensive task. It takes over 99% of the total computing required in each step of MPC.


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2.3.1 Interpolation

The purpose of this task is to determine a linear model that is valid at the current value of

scheduling variable θk. We use the following approximate interpolator:

(a) Define an M × M diagonal matrix of weights W :

W ii = e−σ(V i−θk)T (V i−θk).

This weight gets larger for vertices close to the current point θk and smaller for those

further away.

(b) Define M × 1 vector α:

α = W

V T 1

V T 2

··

V T M

[V 1, V 2, · · ·, V M ] W

V T 1

V T 2

··

V T M

−1

θk.

This α satisfies [V 1, V 2, · · ·, V M ] α = θk.

(c) Set data at current point as: Datacurr = [Data1, Data2, · · ·, DataM ] α.

2.3.2 QP Problem Formulation

At the end of interpolation, we have a linear system of the form:

δxk+1 = Acurrδxk + Bcurrδuk (5a)

δyk = C ycurrδxk (5b)

δzk = C zcurrδxk (5c)

ulbd ≤ utrimcurr + δuk ≤ uubd, k = 0, 1, · · ·, N − 1 (5d)

zlbd ≤ ztrimcurr + δzk ≤ zubd, k = 1, 2, · · ·, N, (5e)

which is used in this task along with the performance index (2) to formulate a QP problem.

The computations involved are algebraic and easy. The QP problem has the form:

minv

vT Hv + vT g (6a)

subject to U l ≤ Av ≤ U u, (6b)

where H , g, U l, A and U u are computed from the LPV state-space model (5).

2.3.3 QP Solver

The optimization problem in (6) is always convex because of the positivity of the matrix H ,

which comes from the fact that the control rates are penalized. As a result, this problem can


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Figure 1 Block diagram for active control of aeromechanical instability using MPC.

be solved in polynomial time. That is, there are algorithms (e.g., ellipsoid method, primal-

dual interior point) whose computational cost is a polynomial function of the number of

variables, number of constraints, and the (inverse of) the accuracy required. Moreover,

there are algorithms that are anytime, i.e., they can be stopped at any time to get an answer,

the accuracy increases with computational effort, and can be restarted with little overhead.

We use a primal-dual interior point method for real-time implementation [8].

3 APPLICATION TO NONLINEAR VIBRATION CONTROL

Consider the nonlinear system:

x

y

=

f (RPM) −ω

ω f (RPM)

+

x

y

(x2 + y2) +

10

u,

where x and y are the states,

f (RPM) = −0.15 + 0.45e−5(RPM 900

−1)2

and RP M is the scheduling variable. The scalar control input u is bounded above and

below:

umin ≤ u ≤ umax

With u = 0, the system is in normal form and, by a Theorem of Hopf, has a Hopf bifurca-

tion at RPM = 900 leading to a stable limit cycle. We are interested in the system behavior

as RPM changes with time. As RPM increases from 0 to 900, due to the nature of f the

(linear) damping of the system decreases and the system amplifies displacements. Beyond

RPM = 900, the system damping increases and oscillations become smaller. This behav-

ior imitates a particularly severe vibration problem in rotorcraft known as aeromechanical

instability.

Aeromechanical instabilities, ground and air resonances, are major design issues and

limiting factors in the development of soft-in-plane rotorcraft. Ground resonance, observed

in multibladed (more than 2 blades) soft-in-plane rotorcraft, occurs as the rotor RPM is


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Figure 2 Open- and closed-loop behaviors of aeromechanical system as RPM changes linearly from 600 to 1200.

Limit cycling in open loop (left), vibration suppression with MPC (middle), and control inputs generated by MPC

(right).

changed from rest to its operational value and is manifested as large uncontrolled rotor

tip displacements. Tilt rotor aircraft in airplane mode can, in addition, encounter coupled

wing-rotor-pylon instabilities known as air resonance. These instabilities are parameter

dependent in that, as the operating conditions change, the rotorcraft changes from stable

to unstable behavior. The primary design tool currently in use is frequency placement

of vibrational modes by increasing stiffness. This passive approach invariably increases

structural weight and reduces aerodynamic performance. The resulting reduction in opera-

tional envelope has prompted the rotorcraft industry to vigorously pursue active control of

aeromechanical instabilities. See [3, 4, 5] for more details. Typical control objectives are

to maintain rotor tip displacements within safety limits (or completely cancel when there is

no noise or uncertainty) subject to saturation limits on swashplate motion along any smooth

scheduling variable trajectory.

To design MPC, we formulate the control problem as shown in Fig. 1. Since the

objective is to make x go to zero asymptotically along smooth RPM trajectories, we intro-

duce a desired trajectory, namely zero, and an integrator to generate tracking error and its

integral. The open-loop system augmented with these elements forms the plant for MPC.

The next task is to obtain an LPV approximation of the plant, which becomes the internal

model used by MPC. This approximation and weights in the performance index (2) form

the data read in by the MPC solver prior to closed-loop simulation. Figure 1 shows the com-

plete closed-loop system. Finally, MPC design parameters are tuned using the closed-loop

simulation.

Figure 2 shows open- and closed-loop responses. On the left is the open loop response

that is typical of aeromechanical instability. Closed-loop response is shown in the middle.

The effectiveness of MPC in canceling the instability is clear. The control input on the right

clearly indicates how MPC is working. These simulations are for a linearly varying RPM

trajectory typical of rotorcraft startup.



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Figure 3 Block diagram representation of MPC-based FCS. Shaded block is toggled by pilot for SCAS or autopi-

lot.

4 APPLICATION TO THE XV-15 TILT ROTOR FLIGHT CONTROL

This section presents the design, real-time implementation, and piloted simulations of an

MPC-based flight control system (FCS) for the XV-15 tilt rotor. Current FCS design prac-

tices are based on linear time-invariant single-input single-output ideas and do not account

for nonlinearities or time-domain constraints. We shall show that the MPC approach can

accommodate frequency-domain MIL specifications as well as time-domain requirements.

A high-fidelity XV-15 simulator developed at Bell Helicopter using the Generic Tilt Rotor

(GTR) model is used for evaluating MPC-based FCS. XV-15/V-22 test pilots flew several

missions evaluating various aspects of the design. This section concludes with their evalu-ation.

4.1 MPC Architectures for FCS

A block diagram of MPC-based FCS is shown in Fig. 3. It can be adapted for two cases that

we shall consider by placing a reference model or a guidance command generator in the

shaded block. In the first case, MPC interprets pilot stick inputs as desired rate commands

and computes the optimal control surface deflections needed to track these commands.

MPC can be seen as a Stability and Control Augmentation System (SCAS) in this case.

The second case corresponds to an autopilot wherein the pilot can enter desired terminal

conditions and MPC generates the guidance commands as well as the stick movements to

follow the guidance track.



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4.2 Design Procedure

The MPC design parameters for the structure in Fig. 3 are: reference model dynamics,

penalties on tracking errors, integrated tracking errors and actuator rates, and horizon

length. These parameters were selected as follows:

1. Selection of reference models: This involves the selection of simple low-order

dynamic systems that interpret pilot stick inputs and generate a desired rate response as

shown in Fig. 3. The frequency and time response of these reference models must satisfy

all relevant MIL specifications. Since MPC is a time-domain technique, time-domain spec-

ifications such as g-limits and control-surface deflection limits are stated as they are and

accounted for in the online optimization. Ideally (in the absence of disturbances, model

mismatch, and unbounded controls), MPC design will match the desired rate responses ex-

actly so that the pilot will in effect be flying the reference model. Our experience suggests

that decoupled reference models — one for each body angle rate — is better than coupled

models from the pilot’s perspective. This makes the selection somewhat easier.

2. Formulation of augmented plant and LPV data generation: After selecting the

reference models, we generate the tracking error and the integral of tracking error as shown

in Fig. 3 by adding integrators. The augmented plant for MPC is given by the system from

pilot stick inputs and control inputs to the measurements, tracking error, and its integral.

The augmented plant is approximated by an LPV model that forms the system data used

by MPC.

3. Selection of weighting matrices and horizon length: For the LPV system, assume

that there are no state and control constraints. Design LQG controllers that give good

performance by adjusting the weights in the performance index in (2). The LQG weights

form the initial set of weights for MPC design. The weights and horizon lengths can be

further tuned to balance closed-loop performance and computational requirements.

4.3 Maneuvers for Evaluation

Two maneuvers will be used to evaluate MPC-based FCS in terms of its ability to track

pilot commands and reduce pilot workload.

Coordinated Turns: The maneuver begins in airplane mode trimmed at 150 knots.

The pilot initiates turn by moving the lateral stick. MPC-based FCS interprets pilot stick

inputs as rate commands and provides fast tracking with zero steady-state error and no

overshoot for step inputs (we let the pilot fly in actual tests). Level 1 flying qualities re-

quirements for this maneuver can be found in MIL-F-8785C [1].

Conversion-Decel: The maneuver involves converting XV-15 from airplane mode at

150 knots to helicopter mode at zero knots. The maneuver starts at, say, 2500 ft, and during

the maneuver the aircraft descends at an acceptable rate to about 1800 ft. At the end of the

maneuver, the aircraft hovers at a constant altitude. This maneuver is highly nonlinear as

the aircraft dynamics undergo large changes. Controller design is also complicated by the

fact that there are three modes of operation — airplane mode, conversion, and hover —

that must be considered. Our objective is to design a controller that would allow the pilot

to conduct this maneuver with hands off the stick. In addition, we would like to provide the

pilot with the ability to regain control of the aircraft at any time. Level 1 flying qualities


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Figure 4 Piloted coordinated turn simulation: pilot stick inputs and angular rates. Mean-square value of baseline

(dashed line) stick inputs are much higher than that for MPC-based FCS (solid line) indicating higher workload.

requirements for this maneuver were developed from MIL-F-8785C [1] and MIL-F-83300

[2].

4.4 Piloted Simulations

MPC-based FCS was evaluated by V-22/XV-15 test pilots at Bell Helicopter. The pilots

flew simulations with and without MPC. A few initial runs with a digital SCAS were made

to familiarize the pilots with the XV-15 simulator cab. During these runs, the pilots noted

some differences between the GTR simulator model and actual aircraft. These include

higher pitch-power coupling and more delays in the simulation than in the aircraft. For

the evaluation maneuvers, the collective-power lever was released to the pilots on their re-

quest; MPC computed all four control inputs, but the computed collective stick was not fed

back.



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Figure 4 (Continued).

Figure 4 shows sample results from left and right turn simulations. The effectiveness

of MPC in reducing pilot work load is very clear. The pilot was happy with the way

MPC performed, especially in coordinating the pedal. He noted that very small/no-pedal

inputs were required, the aircraft responded well to commands, and rated the controller

performance as excellent.



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Figure 5 Piloted conversion/decel maneuver with MPC-based FCS in the loop. Note the large variations in

airspeed from airplane mode to helicopter mode.



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The conversion-decel maneuver began at approximately 145 knots, 2500 feet altitude

and 50% power. After bringing the aircraft closer to the landing area, the pilot began

converting at which time the MPC-controller was turned on. Sample results are shown in

Fig. 5. The pilot noted that the pitch axis control was tight and reasonably good, although

the pitch attitude excursions during the maneuver were at times about 4 degrees more than

what he would have liked. Over several runs, he rated MPC performance from good to

excellent.

5 CONCLUSIONS

We have described a model predictive control paradigm that uses a linear parameter-varying

approximation of nonlinear systems instead of on-line linearization. This method has sev-eral advantages, the most notable of which are its quality of approximation and polynomial-

time computability. These features are essential for successful flight control design. As a

demonstration, MPC was implemented on a real-time XV-15 tilt rotor flight simulator.

Even though the simulator math model is highly nonlinear, the implementation performed

very well in piloted simulations. A coordinated turn maneuver was used to evaluate the

multiaxis capability of MPC-based SCAS; while a highly nonlinear conversion maneuver

was used to evaluate the autopilot capabilities of MPC. Test pilots rated MPC performance

from good to excellent in both cases.

MPC-based flight control system design used several MIL-F-83300 andMIL-F-8785C requirements as well as time-domain saturation type constraints. However,

a number of issues such as verification of these requirements were not considered in this

study. We have identified the following areas for future research and development:

1. Further Piloted Simulations and Hardware-in-the-Loop (HIL) Testing of MPC-

based FCS — During the piloted simulations, the test pilots suggested that further simula-

tions are needed for a complete evaluation of MPC-based FCS. This is also the natural step

before HIL testing. Future work should include (a) piloted simulations, (b) implementation

of MPC-based FCS on a flight computer, and (c) piloted simulations with a flight computer

in the loop.

2. Applications of Virtual Tilt Rotor to Predictive Control1 — This is a nonlinear

dynamical model of a tilt rotor that resides in the flight computer and is executed at rates

faster than real time. A high-fidelity virtual tilt rotor model has been developed by Bell

Helicopter. This concept has many applications including predictive control. Future work

should consider (a) MPC implementations with the virtual tilt rotor as the internal model,

and (b) computational requirements for real-time implementation of MPC-based FCS.

3. Multivariable Control of Quad Tilt Rotor (QTR) — QTR is the next generation

of tilt rotors being developed by the rotorcraft industry. The QTR has more control in-puts than the number of equations/states and represents significant control challenges and

opportunities for reconfiguration under control failures.

1Proposed by Dr. Richard Bennett of Bell Helicopter.


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Acknowledgments

This work was funded by NASA Ames Research Center under contract NAS2-98022. We

are grateful to Mr. Stephen Jacklin of NASA Ames for support and encouragement dur-

ing the project. The real-time simulations were flown at Bell Helicopter Textron Inc. by

V-22/XV-15 test pilots Thomas Warren and Roy Hopkins. Their comments and insights

were of great help to us in evaluating the controller as well as in identifying future researchissues. Dr. Richard Bennett, David Neckels, and Dr. Mark Wasikowski of Bell Helicopter

also contributed to this project. We thank them for their efforts.

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