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Mode transition control of large-size tiltrotor aircraft

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Tiltrotors are an aircraft concept with the ability to rotate their rotors freely, achieving vertical take-off and fast forward flight. The combination of helicopter and fixed-wing flight into one aircraft provides versatility in mission selection, yet challenges persist in their construction and control. Tiltrotor aircraft can operate in three primary modes: helicopter, fixed-wing, and transition, with the transition mode facilitating the shift between helicopter and fixed-wing flight. However, control within this transition region is inherently challenging due to its non-linear nature, hence tiltrotors have been predominantly limited to military applications. Thus, this paper aims to explore transition mode control for a large-size tiltrotor aircraft, tailored to civil applications. A novel, large-sized, tiltrotor concept is presented, accompanied by a derived mathematical model describing the aircrafts behaviours. A PID control method has been used to control the height, pitch, and velocity variations within the transition mode with secondary control loop developed to control the tilt angle during transition. The derived model and control are then implemented within a MATLAB simulation, where the control method was iterated to improve performance. The results show a full transition was achieved in under 14 seconds, where altitude variations were kept below 10 metres. Though the transition mode control was successful, a collective look at the data showcases issues with assumptions as well as thrust discontinuities. The implications of these results are discussed, with suggested improvements proposed for future work.
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1
Mode transition control of large-size tiltrotor aircraft
George Kirst, Xinhua Wang
Aerospace Engineering,
University of Nottingham, UK
Email: wangxinhua04@gmail.com
ABSTRACT
Tiltrotors are an aircraft concept with the ability to rotate their rotors freely, achieving vertical take-off and fast
forward flight. The combination of helicopter and fixed-wing flight into one aircraft provides versatility in mission
selection, yet challenges persist in their construction and control. Tiltrotor aircraft can operate in three primary
modes: helicopter, fixed-wing, and transition, with the transition mode facilitating the shift between helicopter and
fixed-wing flight. However, control within this transition region is inherently challenging due to its non-linear nature,
hence tiltrotors have been predominantly limited to military applications. Thus, this paper aims to explore transition
mode control for a large-size tiltrotor aircraft, tailored to civil applications.
A novel, large-sized, tiltrotor concept is presented, accompanied by a derived mathematical model describing the
aircrafts behaviours. A PID control method has been used to control the height, pitch, and velocity variations within
the transition mode with secondary control loop developed to control the tilt angle during transition. The derived
model and control are then implemented within a MATLAB simulation, where the control method was iterated to
improve performance. The results show a full transition was achieved in under 14 seconds, where altitude variations
were kept below 10 metres. Though the transition mode control was successful, a collective look at the data
showcases issues with assumptions as well as thrust discontinuities. The implications of these results are discussed,
with suggested improvements proposed for future work.
1. INTRODUCTION
This paper considers the transition control for
a large-sized tiltrotor aircraft. For this problem,
an autonomous control solution is proposed for
a novel, tiltrotor aircraft configuration.
Through the methods proposed, this paper
aims to produce a robust control solution that
can stabilize the aircraft through transition,
with the goal to improve the adoption of
tiltrotor aircraft in wider industry.
1.1 Tiltrotor Aircraft
Sustained flight in civil and military aviation is
dominated by helicopters and fixed-wing
aircraft, with more novel concepts often being
overlooked due to technological limitations [1].
Several underlying restrictions of these
aircraft, has pushed attention to more novel
configurations, with the aim of removing these
limitations on future air travel.
Tilt Rotors in the same way are an aircraft
concept with the primary ability to direct their
rotors at varying angles to achieve both
forward and vertical thrust. This allows the
benefits of vertical take-off and landing (VTOL)
with fast forward flight, [2, 3, 4] effectively
combining fixed-wing and helicopter concepts
into one aircraft. Given their benefits, the
concept has attracted attention from the
military sector, notably the Osprey-V22 and
the AW609. Yet despite the benefits of the
concept, the high development costs due to
several challenges in design and control [1, 5],
have resulted in lacking success in the civil
aviation sector.
1.2 Transition
Unique to tiltrotor aircraft is the transition
mode, wherein the aircraft shifts between
helicopter and fixed-wing flight configurations.
During this phase, the rotor angle changes
from 90-0 degrees, which vectors the thrust
forward, accelerating the aircraft and
increasing its forward flight velocity.
While helicopter and fixed-wing flight modes
are widely recognized, the transition mode
presents a unique set of challenges with
limited examples of successful
implementations. The complexity and non-
trivial nature of transitioning from helicopter to
fixed-wing mode underscores the importance
of accurately capturing the behaviour’s
exhibited within this mode.
1.3 Challenge of Control
Transitioning between helicopter and fixed-
wing flight modes poses a significant challenge
for control, primarily due to the highly coupled
flight dynamics [3, 4] and nonlinearities
inherent with the transition phase.
As the aircraft changes from vertical to
horizontal flight, altitude and pitch dynamics
exhibit rapid change. Notably, the transition
involves replacing the lift generated with the
rotors, by the lift generated by the fixed-wing,
leading to significant variation in the systems
aerodynamic characteristics [3]. The control
system must adequately manage these
dynamic shifts, particularly as thrust levels
fluctuate prominently throughout the
transition process.
2
To complicate the issue further, the large
propellers, required for lift during helicopter
mode, induces complex flow patterns around
the wing [6]. These flow dynamics, which
contribute to system instabilities, are then
exacerbated by external disturbances like wind
gusts, thereby diminishing overall stability.
The inherently non-linear nature of this control
problem highlights the imperative for a
comprehensive understanding of the
aerodynamics and the dynamic behaviour
throughout transition. Addressing this control
challenge therefore requires sophisticated
control strategies to implement a successful
control method.
1.4 PID & Gain Scheduling
While (proportional, integral, differential) PID
control methods are widely used, they struggle
to adapt to the changing aircraft dynamics
during mode transition. With varied flight
conditions, a single set of controller gains lacks
consistent responsiveness across the entire
flight envelope [2, 7]. Scheduling the control
gains based on the current flight condition
(Gain Scheduling) can be used to tune the
responsiveness at each flight conditions, thus
providing stable and responsiveness control
throughout the flight envelope.
1.5 Conversion Corridor
To ascertain aircraft stability, a conversion
corridor can be established. This corridor
describes a range of forward flight velocities
and tilt angles within which the aircraft can
maintain stability during transitioning.
Adhering to this corridor is critical, as deviating
from it implies an inability to sustain stability
[8]. By constructing a conversion corridor
outlined in section 5, we effectively define the
stability region, as the aircraft tilts [6],
enabling the determination of a stable desired
tilt angle for every forward flight velocity.
However, this only describes the points at
which stability is feasible, not points of
stability, hence this tool must be used in
conjunction with control methods such as gain
scheduling, to build a suitable controller.
1.6 Large-Size
For small sized tiltrotor aircraft, the act of
transition control is simple [9]. Due to their
small size, the aircraft can produce enough
thrust to both counteract weight, as well as
accelerate forward. However, for large aircraft
the maximum thrust to weight ratio becomes
a significant factor, as an increase in thrust
necessitates an increase in engine and
propeller size, which negatively impacts the
efficiency of forward flight.
Thus, given our project aims we have selected
a large-scale aircraft, such that control
becomes non-trivial.
1.7 Aims & Objectives
Our project aims to develop a robust control
method, facilitating stable transition between
vertical and horizontal flight modes. This
endeavour seeks to deepen our understanding
of the transition mode, enhancing the
applicability of tiltrotor technology in future
aircraft designs.
Objectives include designing a technically
feasible aircraft, developing a complete
mathematical model to describe dynamic
behaviour, implementing a control method,
and conducting simulations for performance
evaluation. Through completion of these
objectives, we will have assessed the viability
of our derived control method, and thus
satisfied our overall project aims.
2. AIRCRAFT CONFIGURATION
The following section highlights the selected
aircraft, for which control will be implemented.
It is important to consider the aircrafts
feasibility, as our conclusions on stability will
be negatively impacted.
2.1 General Configuration
A large 6 engine, 12 tonne cargo aircraft has
been developed with an outline of the model
shown in Figure 1. Four engines are located on
the aircraft wing whilst two are located on the
tail, providing a significant lever arm to
balance the aircraft.
Figure 1 Chosen Aircraft, Layout of
Key Components
The configuration was chosen from among
several designs based on several performance
criteria, notably a trade-off between
performance and design feasibility. Increasing
the number of rotors was seen to benefit the
stability and redundancy of the aircraft.
However, it was impractical in terms of design
implementation, thus a 6-engine design was
selected as a compromise between them.
3
2.2 Initial Sizing
The aircrafts maximum take-off weight
(MTOW) was based on a defined payload of 2
metric tonnes and a range based on historic
aircraft data. This MTOW was then used to
approximate the maximum required thrust for
each engine based on a safety factor of 1.5.
The design was then iterated to achieve a
reasonable aircraft configuration. Methods to
size the aircraft were taken from Raymer [10]
with a summary of aircraft parameters
displayed in Table 1.
Table 1: Key Aircraft Parameters
Parameter
Value
MTOW
12,000kg
Wingspan
26m
Rotor Diameter
5.4m
Design Range
500Nm
Design Altitude
25,000ft
Disk loading
130kgm
²
Cruise Velocity
125ms
¹
2.3 Wing Sizing
Aircraft data from similar-sized fixed-wing
aircraft were utilized to estimate a wing
planform. Subsequently, data from the MS317-
IL aerofoil, obtained from an aircraft with a
similar payload size, was employed to calculate
the required wing area based on cruise
requirements. Given the relatively low
designed flight velocity of the aircraft,
incorporating a taper into the wing design
would not significantly enhance aerodynamic
performance. Therefore, a square wing with an
aspect ratio of 12 was selected to finalize the
wing planform.
2.4 Rotor & Engine Sizing
The size of the rotors was determined by
comparison of a disk loading, taken from
historic data, and a blade element method
[11], developed using a flat plate aerofoil
assumption. These two methods were then
used to derive the power and thrust
requirements for each engine. For these
requirements, the engine (PT6C-67A) was
selected and used to estimate inertial data for
the aircraft mathematical model. This engine
was previously used in the AW609 tiltrotor
aircraft, and such is known to be suitable for
tiltrotor application.
Vortex ring generation [12] was assumed to be
negligible, with the spacing of the rotors
increased to mitigate their effect and ensure
the validity of this assumption. However, to
fully confirm this assumption, further analysis,
through physical and numerical testing would
be necessary, outside the scope of this paper.
2.5 Wing & Tail Placement
The wing and tail were placed along the
fuselage based on the two stability points for
helicopter and fixed-wing modes, where the
sum of forces and moments equal zero.
Helicopter mode constrained the tail mounted
engines to be 2 times the distance from the CG
position than the wing mounted engines due to
the wing having more thrust capability.
Whereas the fixed-wing mode constrained the
relative heights of each engine about the CG
position in the vertical direction in addition to
ensuring that a trim position for the aircraft
was attainable.
2.6 Sustainability
As the configuration is focused on civil
application, several design decisions have been
made with implications for current and
potential future sustainability initiatives within
the tiltrotor aircraft domain. For instance, the
decision to incorporate a greater number of
engines than typical tiltrotors aircraft was to
facilitate electrification. Increasing the number
of engines decreases their individual power
requirements, aligning with the trend towards
electrification in aviation. Tiltrotors, with their
VTOL capability and low infrastructure
requirements, are well-suited to urban air
environments [13], where electrification has
become a focal point in sustainability efforts.
Despite the emphasis on control in this paper,
the broader context of sustainability in aircraft
design remains pertinent. As the industry
moves towards developing more sustainable
aircraft, the challenges of control persist.
Therefore, design decisions made in this paper
are intended to ensure that its focus remains
relevant for future aircraft designs, even as
sustainability considerations become
increasingly prominent in the field.
3. MATHEMATICAL MODELLING
As in similar works [6, 4, 14], to ensure the
validity of the control system a robust
mathematical model was developed. The
resolution of the model affects the validity of
the control system and thus we must ensure
the model considers all parameters within the
scope of the chosen configuration.
3.1 Degrees of Freedom (DOF)
To limit the scope of the problem we will only
consider a 3 DOF problem, constrained within
the X-Z plane. The force component acting on
the aircraft in the X and Z directions and the
pitching moment acting about the aircraft
centre of gravity (CG) are defined as , and
respectively.
4
3.2 Wing & Tail
Assuming that a control method is capable of
stabilising altitude, allows us to approximate
the flightpath angle to be zero. Using this
assumption, the forces and moments from the
wing and tail , and  are formulated in
Eq. (1). The expression is based on the lift
generated by the wing and tail (,󰇜as well
as the geometry defined by the configuration
design where and are the distances from
the centre of pressure of the wing and tail to
the CG position


 
󰇛󰇜
(1)
Similarly, the aircraft Drag force and distance
from the CG to the centre of drag is included
to capture the aerodynamic forces acting on
the wing and tail.
3.3 Thrust
We can group the four wing mounted engines
and the two rear together and define them as
and respectively, where the max thrust
available for is two times greater than .
The force contribution from the engines are
captured in Eq. (2), with pitch and tilt angle
represented by and ,respectively.


󰇯󰇛󰇜󰇛󰇜
󰇛󰇜󰇛󰇜
󰇛󰇜󰇛󰇜 󰇰
(2)
The lever arm of each thrust group, are
described by linear functions 󰇛󰇜 and 󰇛󰇜
based on the constant, configuration
geometry, and the time-varying, tilt angle.
3.4 Rotor Inertia
As each engine rotates by an angle , the
rotational acceleration, 󰇘 ,induces an adverse
torque on the body of the aircraft.
The scale of the moment produced is
proportional to the rotational acceleration and
the inertia of the engine, , attained in section
2.4 and shown in Eq. (3).
3.5 Disturbance
The model has outlined the aircraft's
anticipated behaviour under normal
conditions. However, to accommodate for
known variables, such as wind gusts, we need
to enhance the model. Introducing a
disturbance term,
, into each aspect of the
model, allows us to accurately predict the
aircraft's response to these environmental
factors. This refinement ensures a more
thorough representation of the aircraft's
dynamics in real-world scenarios.
3.6 Summation of Body Forces
Combining the forces derived in sections 3.2-
3.5, we get Eq. (4), with
being the weight of
the aircraft acting downward.






(4)
These equations, govern the aircrafts motion
in altitude, pitch and longitudinal position for
all three flight modes.
4. CONVERSION CORRIDOR
Establishing a conversion corridor, defines the
bounds within which a stable transition can be
achieved [6]. The following procedure outlines
the formulation of each constraint, culminating
in the development of a conversion corridor
tailored to our prescribed aircraft design.
4.1 Normal Operative Modes
The positions of helicopter and fixed-wing
flight modes are highlighted in Figure 2,
wherein the transition mode is described as
any angle of tilt, bounded by these two flight
modes.
Figure 2 Aircraft Conversion Corridor
While the velocity in helicopter mode can be
negative, this has not been represented, as
conversion can only occur at positive
velocities.



󰇘
(3)
5
4.2 Wing Stall Constraint
In figure 2, an unstable region is shown,
characterised by a wing stall constraint, where
the conditions described in Eq. (5), are not
satisfied.
Here, the maximum component of thrust
acting upward, 󰇛󰇜, combined with the lift
produced by the wing and tail,
, are less
than the aircraft's weight, thus the aircraft is
not in equilibrium. Hence, the stability region
must lie above this constraint line.
4.3 Maximum Power
The power requirements on the engine exhibit
a proportionality to the forward flight speed. As
velocity increases, the oncoming blades
experience higher velocity, leading to a
quadratic increase in drag. While the
propeller's thrust can be sustained, as this also
scales quadratically, the power necessary to
overcome drag escalates, eventually reaching
a threshold where it cannot be maintained.
Figure 2 depicts this phenomenon, through the
representation of the maximum power line on
the conversion corridor. This signifies the
region by which the engine cannot sustain a
sufficient level of thrust to satisfy Eq. (5).
4.4 Velocity Constraint
The velocity constraint describes the maximum
velocity that the aircraft is designed to achieve.
Due to the large blades, ‘whirl flutter’ can occur
at high speeds [13], a phenomenon where the
rotors induce resonant aeroelastic instabilities
that can reduce efficiency and cause
catastrophic failure of the aircraft. However,
the exact nature of this phenomenon adds an
additional layer of complexity to our aircraft,
and thus is outside the scope of this paper,
hence the velocity constraint was formulated
from historic data.
4.5 Safety Margin
Incorporating a safety margin into our
conversion corridor serves to alleviate the
impact of potential errors in our formulation.
While various mathematical methods have
been employed to derive the data presented in
figure 2, significant uncertainties persist, due
to the utilisation of simplified models for thrust
and lift. Introducing a safety factor into the
formulation reduces the safe operating area,
but ensures that through most of the
transition, stability is feasible. However, as the
final stability point should lie within this safety
margin, uncertainty closer to the end of
transition will persist. This is due to our
requirement to control height, leading to a
single trim position at the border of the wing
stall constraint, hence the end stability point is
located within the margin of safety.
4.6 Observations & Control
Given the derived safe operating area, we can
select several points, within the region, as
design points for our control simulation [14].
At each point, we will tune the PID gains to
achieve the best result and then use gain
scheduling to tie the design points together, as
the aircraft transitions.
5. CONTROL IMPLEMENTATION
The following section describes the derivation
of a control methodology aimed at regulating
four key parameters: rotor angle, pitch angle,
altitude, and velocity. By exerting control over
these variables, our objective is to maintain
the aircraft in straight and level flight
throughout its transition, thereby fulfilling our
overarching project aim of developing a robust
control method for the transition mode.
The model is formulated under several key
assumptions:
1. Uniform Tilt Angle: The tilt angle of each
rotor is assumed to be identical.
2. Uniform Thrust Output: Thrust is
assumed not to be a function of tilt rate.
3. Non-Negative Thrust: The thrust
generated by the propulsion system is
constrained to be non-negative.
4. Symmetric Thrust Generation: The left
and right-side engines are assumed to
generate an equal amount of thrust.
5.1 Rotor Angle Control
From the Conversion Corridor established in
section 4, for varying forward flight speeds, we
have defined a range of stable tilt angles. As
such we will define a flight profile within this
defined region of the conversion corridor and
discretise it into several sections. We will then
use this as the basis to define a desired tilt
angle, where a simple closed loop proportional
controller will be used to moderate the tilting
angle toward its desired position.
5.2 Pitch Control
For the duration of transition, large variations
in pitch will cause large instabilities due to its
coupled effect on thrust vectoring, as shown in
Eq. (2). To negate this effect, the initial pitch
condition is set to 0 degrees, with an objective
to stabilise any disturbance and ensure
sufficient sensitivity throughout the transition.
This will be implemented with a gain scheduled
PID approach.
󰇛󰇜
(5)
6
5.3 Altitude & Velocity Control
In helicopter mode, altitude-based control will
be employed to stabilise the system, given its
influence on the vertical dynamics. However, in
fixed-wing mode, lift generated by the wing
becomes the primary determinant of height,
and this lift force is directly proportional to the
aircraft's velocity. Thus, during fixed-wing
mode, control based on forward velocity
becomes more relevant. Therefore, the
objective of this method is to transition from
altitude control to forward velocity control
during the transition mode, aiming to enhance
performance in the control simulation.
5.4 Error System
To control each parameter, we will define an
error term 󰇛󰇜 as the difference between the
desired state of the system and the actual
measured state of the system, where error is
a function of time. The error terms for altitude,
velocity, and pitch 󰇟󰇛󰇜󰇗󰇛󰇜󰇛󰇜󰇠 are shown
in Eq. (6), where the desired altitude and pitch
angle are defined as 0 and the desired
velocity, 󰇗󰇛󰇜 is a function of time.
󰇯󰇗󰇛󰇜
󰇛󰇜
󰇛󰇜󰇰󰇗󰇛󰇜
󰇯󰇗󰇛󰇜
󰇛󰇜
󰇛󰇜󰇰
(6)
The objective of this method is to make the
error terms tend to zero, within an amount of
time to maintain the aircraft stability.
5.5 Error Derivatives
The derivatives of Eq. (6) are taken to produce
Eq. (7), where the right-hand side (RHS) of the
equation defines the linear and rotational
acceleration of the aircraft.
5.6 System Dynamics
Modifying Eq. (7) by introducing the mass, M,
and inertia, J, results in a force term equal to
the forces and moments acting on the aircraft,
presented in section 3.1, this can then be
equated to the error derivatives, resulting in
Eq. (8).
󰇯󰇗󰇗󰇛󰇜
󰇘󰇛󰇜
󰇘󰇛󰇜 󰇰󰇯󰇘󰇛󰇜
󰇘󰇛󰇜
󰇘󰇛󰇜󰇰
(8)
Then finally, substituting the left-hand side of
this equation into the aircraft mathematical
model,(section 3.6) results in Eq. (9).
󰇯󰇗󰇗󰇛󰇜
󰇘󰇛󰇜
󰇘󰇛󰇜 󰇰





(9)
5.7 Controller Formulation
Whilst Eq. (9) describes a theoretical system
where the error in: altitude, velocity and pitch,
tend to zero, it has no method of imparting
force onto the system nor any method of
reducing error. Solving Eq. (9) for the
controllable forces, defined in section 3.3 (
and ), we can solve for the required thrust at
any time. Then substituting an autonomously
stable system, into the error derivatives,
produces a complete control method. However,
looking at Eq. (2), it is evident that and
cannot be combined into a single variable that
satisfies all three control equations. For this
reason, we must define temporary control
parameters for each control equation, then
formulate a method to convert these
temporary control parameters, into real values
of thrust output, that satisfy all three
equations.
5.8 Autonomously Stable System
We have formulated a controller by which the
control forces and , stabilise the system,
though the error variables are still unknown.
Thus, we have selected the autonomously
stable differential equation, defined in Eq.
(10). The benefit of using this system is that it
is a differential equation whose solution is a
decay function determined by the appropriate
selection of the three gains: ,
and .
Hence selecting this system autonomously
causes the error to decay over time, thus,
system stability can be achieved by the
appropriate selection of each of these
constants for each control variable.
󰇘󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜
(10)
The velocity error is in a different form than
that described in Eq. (10). So, an alternative
form of this equation is used in the control of
the velocity.
5.9 Temporary Controller
A solution for the force outputs of Eq. (9) are
presented in Eq. (11) & (12) and expressed as
a linear combination of temporary control
parameters. These temporary control
parameters are simply the grouping of terms
from Eq. (9) and represent the control
requirement from the altitude and position
󰇯󰇗󰇗󰇛󰇜
󰇘󰇛󰇜
󰇘󰇛󰇜󰇰󰇯󰇘󰇛󰇜
󰇘󰇛󰇜
󰇘󰇛󰇜󰇰
(7)
7
dynamics, 󰇗 as well as the control
requirement from the pitch dynamics, .
󰇗
󰇛󰇜
󰇛󰇜󰇛󰇜
(11)
󰇗
󰇛󰇜
󰇛󰇜󰇛󰇜
(12)
Here, the systems equilibrium positions are
satisfied, as when the control requirement of
pitch is zero, the thrust outputs relationships
are determined based on each engine’s
respective lever arm.
5.10 Parameter Selection
When selecting: and , for each
controller, we must obey the Routh-Hurwitz
stability criterion [15], for which a routh table
was generated. Notable observations of the
stability criterion led to the conclusion, that the
variations in the pitch and rotor angle exert an
influence on the bounds of stability. This
phenomenon, implies that the responsiveness
of the controller is subject to variation,
depending on the prevailing system conditions.
Table 2 Control Gains for Helicopter
and Fixed-Wing Modes
Helicopter
Mode
Fixed-Wing
Mode

0.07
0.31

0.003
0.052

0.7
0.72
󰇗
N/A
1.1
󰇗
N/A
0.5
󰇗
N/A
0.7

0.29
0.6

0.0018
0.08

0.5
0.6
6. SIMULATION
The control simulation was developed in
MATLAB, SIMULINK Version 2021B.
6.1 Helicopter & Fixed Wing
A simulation was performed for the fixed-wing
and helicopter operating modes. A step input
of 100 metres in height and 6 degrees in pitch
was used as a baseline to assess the
performance of these two modes.
6.2 Transition Mode
The main simulation will focus on the
demonstration of the derived transition mode
control system where Figure 3 shows how the
derivations within the previous sections have
been used to build the control simulation.
Figure 3 Control Simulation Design
7. RESULTS & DISCUSSION
Whilst the aim of the project lies in the stability
of the transition mode, it's crucial to recognize
that the chosen aircraft configuration must
perform adequately in all three of its designed
operating modes. Since the scope of this
project is assessing the transition mode for a
developed aircraft configuration, invalidating
the configuration with instability in any of its
operating modes would not be conducive to a
robust control design.
7.1 Altitude Control
The altitude response for the step input, see
section 6.1, are shown in Figure 4, where we
see both modes capable of reaching stability at
its desired position.
Figure 4 Altitude Response to Step
Input
The more violent, and oscillatory behaviours of
the fixed-wing mode, is partly due to the
coupled effects of altitude and velocity control.
The performance in helicopter mode is shown
to be better, with lower overshoot and reduced
oscillations, though the time to reach stability,
in both cases, is significantly large. Whilst this
behaviour was observed from the respective
control gains, shown in Table 2, greater
performance may be achievable, though
unnecessary for our application. Notable is that
8
the method to select appropriate control gains
was sufficient to attain a reasonable stability
point but was not capable of determining the
most optimal control.
7.2 Velocity Control
The velocity fluctuations,
, were normalised
by their respective trim velocities, , as per
Eq. (13). Results are shown in Figure 5, where
we see both control methods capable of
directing the aircraft to respective trim
velocities.


(13)
For helicopter mode, velocity stabilisation
occurs, despite only altitude control methods,
though the trim velocity changes post step
input. Notable here, is unlike fixed-wing mode,
helicopter mode has a range of stable trim
velocities. As no velocity control is
implemented the control loop has no method
to return the aircraft to its original velocity,
however, this could be achieved by setting a
desired trim pitch angle instead.
Figure 5 Velocity Response to Step
Input
The introduction of a velocity controller for
fixed-wing mode, is shown to dampen
oscillations more significantly. Conversely, the
velocity for helicopter mode has large
fluctuations, though the fast damping of
velocity is less important due to its minimal
effect on system stability. With further
iterations, the performance could be improved,
however, the aim of a successful transition
mode control only requires stable control for
the other two modes. Thus, the stability shown
in the data concludes that the controllers are
adequate for our purposes.
7.3 Transition Mode Control
The output, of the transition mode control
simulation, is illustrated in Figures 6, where
various system states are shown. The
simulation commences from helicopter mode,
where the helicopter control parameters are
utilized to bring the system to a stable trim
position. Once the aircraft reaches this stable
trim position, it is commanded to undergo
transition, with rotor angle control activated.
As the aircraft achieves a tilt angle of 85
degrees, the control switches from static
helicopter control to gain-scheduled transition
mode control, with static fixed-wing control
being reinstated, only after the tilt angle drops
below 5 degrees.
7.4 Altitude & Pitch Response
The results in Figure 6 (a & b) show the
variations in altitude and pitch. Whilst the pitch
angle is not zero, the observed variations are
significantly low, (<0.1 degrees) that we would
consider the aircraft stable. A notable increase
occurs post transitioning, however the
magnitude is small, further decaying over
time, hence the variation does not pose a
significant impact on our models’ stability. The
altitude variations are also small (<10m), but
non-trivial, as it affects our assumption of zero
flight path angle. It is seen that the fixed-wing
control can stabilise the height, though further
work is needed to characterize the effect of
small flight path angle variations.
7.5 Longitudinal Velocity Response
Velocity increases rapidly over the transition
period, where we see an almost linear
increase. Like the altitude, the fixed-wing
control stabilises the velocity post
transitioning, however, there is a small
discontinuity, caused by switching of control
methods.
7.6 Tilt Angle Fluctuation
The tilt angle desired position, is governed by
the conversion corridor set out in section 5.
The maximum thrust is below its limits and the
altitude variation is small which shows that our
tilt angle control method, can keep the aircraft
within stable bounds. Transitioning was
achieved in under 14 seconds, notably similar
to the bell XV-15, (12.5) [1], and whilst this
value could be further decreased, this was not
feasible due to the maximum thrust limits
imposed by both the model, and the
conversion corridor.
9
Figure 6 Transition Mode, Control Simulation Performance Data
7.7 Thrust Output Implications
For a 14 second tilt, the peak thrust observed,
fell below the maximum thrust limits placed on
each engine group. The thrust increases
steadily, until a peak, at which point the lift
force generated by the wings starts to overtake
the thrust output. This is followed by a sharp
decline, as the tilt angle approaches zero,
directing more thrust forward, as well as the
reduced thrust required by fixed-wing mode.
However, a discontinuity occurs in this region,
being a combination of rapidly changing thrust
requirements coupled with switching control
modes. More refinement in the switching of
control methods here, would improve the
simulation, though despite this, the system
reaches a stable fixed-wing operating state.
This is relevant, as the ability of our aircraft to
achieve such violent thrust levels is an
unknown. Notable here, for previous iterations
with lower tilt rates, the maximum observed
thrust was reduced. This observation is
important, as by defining an upper thrust limit,
we could effectively identify the maximum tilt
rate. Though outside the scope of this paper,
formulations of tiltrotors with defined
transitioning requirements would benefit from
this information.
7.8 Overall Stability
The results presented are important for our
aims, as a holistic view of performance is
required to assess the robustness of control.
The controllable elements of thrust output and
rotor angle are shown to produce minimal
variation in the altitude and pitch, while also
rapidly increasing and stabilising velocity.
Thus, we can conclude our control
implementation has been successful in
completing a transition, however this is only
valid for the given assumptions.
7.9 Simulation Improvements
Though the model has demonstrated its ability
to perform transition, it has done this under
idealized conditions. To improve the
robustness of the control, further simulations
should be able to characterise the effect of
10
external disturbance to see what effect it has
on performance, and at what point stability can
no longer be achieved.
8. FURTHER WORK
8.1 Relaxation of Assumptions
In our mathematical model, we have made
some assumptions. Whilst it is true that we
have achieved stable control, this method and
simulation is only valid for the set of
assumptions outlined throughout this paper.
We have evaluated that flightpath angle is non-
zero, hence, the mathematical model would
need to be re-evaluated to determine the
effect of small variations.
8.2 Simulation Refinement
As suggested, the control switching
discontinuity observed, could benefit from
more localised control. The region could be
further discretized, with more scheduled gains,
however the increased complexity from this
would necessitate a more refined method of
gain scheduling.
8.3 Thrust Transition Rate
Whilst the performance of the aircraft has
been captured in this paper, it would be
beneficial to analyse the relationship between
transitioning speed and thrust output. This
would be a beneficial metric as to compare to
other similar control methods, and would
establish the limitations of our model.
9. CONCLUSION
In summary, this paper introduces a novel
tiltrotor aircraft characterized by its large-size
and configuration featuring six distributed
engines. For this aircraft, a mathematical
model has been produced, and the bounds of
stability have been determined via the
construction of a conversion corridor. A control
method was then implemented to stabilise the
aircraft during helicopter, fixed-wing, and
transition mode, and through simulation, has
demonstrated its ability to stabilise the
aircraft. Although the altitude and pitch show
minor variation, the overall aircraft stability is
withheld over time. thus, for our given
assumptions, we can conclude that we have
advanced toward our aim of producing a robust
control method. However, significant caveats
to the validity of our controller remain, though
with further refinements to the control, and
analysis of relaxed parameters, the validity
could be significantly improved.
10. REFERENCES
[1]
M. Maisel, D. Giulianetti and D. Dugan, The History
of the XV-15 Tilt Rotor Research Aircraft from
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L. Zhong, H. Yuqing, Y. Liying and H. Jianda, “Control
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H. Sheng, C. Zhang and Y. Xiang, “Mathematical
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