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日期：2024-12-12 09:26

2024-2025 AVDC UAS Modelling and Simulation Assignment

Centre for Autonomous and Cyber-Physical Systems, SATM

Introduction

This is an individual assignment comprising a report and accompanying computer (software)

codes on dynamics and control, design and performance analysis of UAS. This assignment

handout consists of 11 pages. Submission is on Canvas, and for the deadline refer to the

module's Canvas site as normal.

The things you will (hopefully) gain are as follows:

1. Evaluate and implement an example UAV model in terms of their aerodynamic, control,

mass and inertia characteristics. Appraise and critically compare the resultant motion.

2. Distinguish the requirements for model testing, verification and validation, and

demonstrate their application to an UAV model.

3. Communicate and present results of individual work.

In this assignment you are asked to develop and analyse a high-fidelity nonlinear model of a

flying wing UAV; example of the UAV is given in Fig. 1 for the illustration purposes. The

small fixed-wing UAV has two control surfaces, elevons, and they operate both as ailerons and

elevators, and it has a brushless pushing DC electric motor to produce thrust.

The simulation model should contain the equations of motions, the aerodynamics model, the

propulsion model, the actuator model, environment model and control. All parameters required

to build this model are provided in the Appendix.

Fig. 1. Example of flying wing UAV1

1 https://flightory.com/2022/12/03/stingray-new-fpv-flying-wing-design/

2

The assignment comprises three sections, namely, modelling, trimming/linearization/stability

analysis and control. Details for the assignment are given in the following paragraphs.

The work must be presented as follows:

• A pdf document (assignment report), which provides the answers with supporting

plots/figures to each of the questions of the following paragraphs.

• A folder containing all MATLAB/Simulink codes used to answer the questions.

The evaluation criteria for the final assignment are the following

• Quality of the results (25%)

• Quantity of the results (25%)

• MATLAB/Simulink code quality and clarity (25%)

• Assignment report quality (25%)

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Part 1 - Modelling (40%)

The first task of the assignment is to build the simulation model of the UAV system using

MATLAB/Simulink. The system considered in this assignment will include:

• The equations of motion (6-DOF equation, navigation equation, kinematic equation).

• The model of aerodynamic loads.

• The propulsion model, incl. motor model.

• The environment model (wind model and atmosphere model).

• The actuator models.

Question 1: Model Conceptualization (2%)

Develop a schematic diagram of the system (conceptual model) and explain the interactions

between the sub-systems.

Hints:

1) No MATLAB/ Simulink code needed.

2) The schematic diagram means a high-level block diagram representing relationship between

the substantial subsystems described above.

Question 2: Flight Dynamics (3%)

Most aerospace systems use the same equations of motions including 6-DOF equation, the

kinematic equation, and the navigation equation. It means that you can utilize the same model

structure discussed during the module. Before development the simulation model, please,

explain the equation of motion in details.

Hint:

No MATLAB code needed.

Question 3: Modelling (10%)

Mathematical models of sub-systems, such as the aerodynamics model, the actuator model, the

propulsion model and control for the UAV are provided in the Appendix. Using the equations

of motion and provided mathematical models, please, develop the simulation model of the

UAV using MATLAB/Simulink and explain it.

Hints:

1) You may include all parameters needed to build this model in a separated MATLAB file

named “UAV_data.m” similar to the MBD Exercises.

2) While building the model, you can utilize “Aerospace Blockset” from the Simulink Library.

3) When you compute arctangent function, please use the function named “atan2” instead of

“atan”.

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4) Solver setting: Go to “simulation” tab -> “model configuration parameter” -> “Solver”

Please set the solver as follows:

- Type: Fixed-step

- Solver: ode4(Runge-Kutta),

- Fixed-step size: Step_Size (this value is already defined in “Sim_Parameters.m”)

5) Initialization setting: Go to “File” tab -> “Model Properties” -> “Callbacks” -> “InitFcn*”

Please set the following initializations:

clc ;

clear all ;

close all ;

UAV_Data ;

Sim_Parameters ;

Question 4: Model Verification (25%)

After building the model, please verify the simulation model using the model verification

techniques, which were introduced within the module.

Hint:

Verification techniques are the following: tracing, comparing outputs of simulation models

and outputs of mathematical models, checking the simulation model using prior knowledge.

In particular, a simulation model using prior knowledge should be checked as follows:

1. Check whether control inputs produce the desired motion

2. Check the longitudinal and lateral modes.

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Part 2 - Trimming/Linearization/Stability Analysis (50%)

The second task of the assignment is to find trim solutions at given operating conditions and

then get linearized models at the trim conditions found. Additionally, it is required to assess

the stability of the system.

Question 1: Process of Trimming and Linearization (5%)

Explain the process of trimming and linearization, incl. trimming constraints; discuss why we

need these additional constraints:

1. What is linearization from the mathematical point of view?

2. Why do we need Trimming and Linearization?

3. What is the trim point from the point of view of the governing equation?

4. Why do we need to apply constraints?

Hint:

No MATLAB/Simulink code needed.

Question 2: Finding Trim Solutions and Trim Analysis (20%)

Build the simulation model for trimming and the simulation model for checking the obtained

trim solutions.

a) Find a trim solution at the operating condition airspeed 𝑉 = 15 𝑚/𝑠 and h = 0 𝑘𝑚

(Altitude). Verify the trim solution found using the simulation model for checking trim

solutions.

b) Find trim solutions at the fixed altitude h = 0 𝑚 and various speeds 𝑉 = [15,

30, 45,60] 𝑚/𝑠. In this case, determine the trim angle-of-attack (i.e.,

e e e

= atan 2 , (w u )

), the

trim pitch control elevator deflection (i.e., 𝛿𝑒

), and the trim throttle (𝛿𝑡ℎ

). Discuss patterns of

these parameters as speed increases. Also, please, discuss the reason behind this behaviour.

c) Find trim solutions at the fixed airspeed 𝑉 = 15 𝑚/𝑠 and various altitudes as h =

[0,1, 2, 3, 4] 𝑘𝑚. In this case, determine the trim angle-of-attack (i.e.,

e e e

= atan 2 , (w u )

), the

trim pitch control elevator deflection (i.e., 𝛿𝑒

), and the trim throttle (𝛿𝑡ℎ

). Discuss patterns of

these parameters as Altitude increases. Also, please, discuss the reason behind such a behaviour.

Hints:

1) When you find trim solutions, the thrust needs to be included as the control input in order to

maintain a constant speed. Therefore, the control inputs are 𝛿𝑡ℎ

and 𝛿𝑒

.

2) Variation of trim solutions according to changes in airspeed and altitudes are closely related

to variations of the dynamic pressures. Note that the dynamic pressure is defined with

2 Q V = (1/ 2)

, where

V

is the speed and



is the air density.

3) Initialization setting: Go to “File” tab -> “Model Properties” -> “Callbacks” -> “InitFcn*”

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You can set the following initializations similar to the MBD Exercises:

UAV_Data;

Question 3: Numerical Linearization (10%)

Build the simulation model for linearization. Perform numerical linearization at the operating

condition 𝑉 = 15 𝑚/𝑠 and h= 0 𝑚. Determine the linear time invariant (LTI) model of the

longitudinal motion and the LTI model of the lateral motion.

Hints:

1) For UAV systems, the state vector and the input vector of the longitudinal motion are

 , , , 

T

lon x = u w q 

and 𝑢𝑙𝑜𝑛 = [𝛿𝑒

].

2) For UAV systems, the state vector and input vector of the lateral motion are

 , , , 

T

lat x = v p r 

and 𝒖𝑙𝑎𝑡 = [δ𝑎

].

3) Initialization setting: Go to “File” tab -> “Model Properties” -> “Callbacks” -> “InitFcn*”

Please set the following initializations:

UAV_Data;

Question 4: Stability Analysis (15%)

Determine the dynamics modes of the longitudinal and lateral motion. Discuss the dynamic

characteristics of these modes in the terms of the stability, the natural frequency, and the

damping ratio (plot zero-poles map). Identify these modes in the state responses.

Hint:

You can use MATLAB commands named “eig” and “damp”.

Part 3 - Implementation of Control Laws (10%)

Control is an important element within the remit of aerial vehicle design. In this section, you

are required to implement the provided control laws to the simulation model.

Question 1: Implementing Control Law (10%)

In the UAV, the autopilot system consists of the longitudinal controller and the lateral

controller, and the roll controller. The controller has three parts: longitudinal controller, lateral

controller and speed controller. The longitudinal controller includes pitch rate control, pitch

angle control and height control and the lateral controller includes roll rate control, roll angle

control and course angle control, while the speed controller only controls the airspeed of the

aircraft. The proportional (PID)-control type controller is widely used for these types of the

controllers.

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The detailed information on the autopilot is provided in the Appendix. Implement the control

laws to the nonlinear simulation model. Evaluate the responses of the UAV under different

commands, namely, airspeed, course angle and altitude. In this case, the initial conditions are

set to be the trim solution at the operating condition 𝑉 = 15 𝑚/𝑠 and h= 0 𝑘𝑚. Is the tuning

of the coefficients sufficient? Does the flight control system require additional modifications?

If yes, perform coefficient tuning to improve system performance.

Hint:

The trim control inputs need to be added to the control inputs from the control system.

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Appendix

A. Geometric, mass and inertia characteristics of the UAV

The geometric and mass characteristics are provided in Table 1.

Table 1

Parameter Value

Aspect Ratio (AR) 3.68

Chord (c) 0.25 m

Reference area (S) 0.22 m2

Mass (m) 1 kg

Wing span (b) 1 m

Moment of inertia is provided in Table 1.

Table 2

Parameter Value [kg ∙ m2

]

𝐼𝑥𝑥 0.023

𝐼𝑦𝑦 0.02

𝐼𝑧𝑧 0.033

𝐼𝑥𝑧 ,𝐼𝑧𝑥 0.006

𝐼𝑦𝑧,𝐼𝑧𝑦,𝐼𝑥𝑦 ,𝐼𝑦𝑥 0

B. Aerodynamics Model

The force and moment coefficients are represented with the following model

𝐶D = 𝐶D0

+ 𝐶Dα

α + 𝐶Dα

2

α

2 + 𝐶Dβ

β + 𝐶D

β

2

β

2 + 𝐶Dδ𝑒

δ𝑒

, (1)

𝐶L = 𝐶L0

+ 𝐶Lα

α + 𝐶Lq

c

2𝑉

𝑞 + 𝐶Lδ𝑒

δ𝑒

, (2)

𝐶Y = 𝐶Y0

+ 𝐶Yβ

β + 𝐶Yp

b

2𝑉

𝑝 + 𝐶Yr

b

2𝑉

𝑟 + 𝐶Yδ𝑎

δ𝑎

, (3)

𝐶m = 𝐶m0

+ 𝐶mα

α + 𝐶mq

c

2𝑉

𝑞 + 𝐶mδ𝑒

δ𝑒

, (4)

𝐶l = 𝐶l

0

+ 𝐶lβ

β + 𝐶lp

b

2𝑉

𝑝 + 𝐶lr

b

2𝑉

𝑟 + 𝐶lδ𝑎

δ𝑎

, (5)

𝐶n = 𝐶n0

+ 𝐶nβ

β + 𝐶np

b

2𝑉

𝑝 + 𝐶nr

b

2𝑉

𝑟 + 𝐶nδ𝑎

δ𝑎

(6)

where the parameters

V

is the UAV speed. 

and



represent the angle-of-attack and the

side-slip angle, which are defined as

9

1 1 tan , sin w v

u V

 

− −    

= =        

. (7)

The parameters 𝐶(∗)

are the aerodynamic coefficients, which are given in the Table 3. δ𝑒

, δ𝑎

denote the elevator and aileron deflection of the UAV, respectively. Due to the particular

structure of the flying wing UAV, there is no rudder. Yaw control is implemented via aileron.

δ𝑒

, and δ𝑎

can be decoupled into expressions of left and right elevon deflections δ𝑒𝑙𝑣𝑙

and

δ𝑒𝑙𝑣𝑟

by the following equation.

[

δ𝑒

δ𝑎

] = [

1 1

−1 1

] [

δ𝑒𝑙𝑣𝑙

δ𝑒𝑙𝑣𝑟

] (8)

The aerodynamics coefficients are given in the Table 3.

Table 3. Aerodynamic force coefficients

Parameter Value Parameter Value

𝐶D0

0.0208 𝐶m0

-0.0112

𝐶Dα

0.0084 𝐶mα

-0.2625

𝐶D

α

2

1.3225 𝐶mq

-1.8522

𝐶Dβ

-0.0001 𝐶mδ𝑒

-0.2845

𝐶D

β

2

0.0796 𝐶l

0

0

𝐶Dδ𝑒

0.2 𝐶lβ

-0.0345

𝐶L0

0.0389 𝐶lp

-0.3318

𝐶Lα

3.2684 𝐶lr

0.0304

𝐶Lq

6.1523 𝐶lδ𝑎

0.182

𝐶Lδ𝑒

0.7237 𝐶n0

0

𝐶Y0

0 𝐶nβ

0.0252

𝐶Yβ

-0.1285 𝐶np

0.002

𝐶Yp

-0.0292 𝐶nr

-0.0192

𝐶Yr

-0.0355 𝐶nδ𝑎

-0.0102

𝐶Yδ𝑎

0.0299

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C. Aerodynamic Forces and Moments

The aerodynamic forces (Drag, Lift, Side force) are given by the equations:

𝐹𝐷 = QS𝐶D, 𝐹𝐿 = QS𝐶L

, 𝐹𝑌 = QS𝐶𝑌

. (9)

The aerodynamic moments (pitch, roll, yaw) are given by the equations

𝑚 = QSc𝐶𝑚, 𝑙 = QSb𝐶𝑙

, 𝑛 = QSb𝐶𝑛

(10)

where Q is the dynamic pressure, which is given by Q = (1/2)𝜌𝑉

2

.

D. Propulsion Model

In general, the thrust generated by the propeller depends not only on the rotating speed of the

propeller but also on the aircraft airspeed. Since the airspeed of the UAV considered in the

assignment is relatively small, only the influence of the rotating speed on the thrust is

considered to simplify the analysis. The thrust and the counter torque produced by the propeller

is described with the following equation

𝑇 = 𝐾𝑇𝑁

2

, (7)

𝑀 = 𝐾𝑀𝑁

2

. (8)

Where 𝐾𝑇 = 2.015 × 10−6 Kg · m, 𝐾𝑀 = 2.444 × 10−10 Kg · m2

.

E. Motor Model

The motor model includes the relationship between throttle and rotating speed by a simplified

linear dependency:

𝑅𝑃𝑀 = 7000 + 20000 𝛿𝑡ℎ

, (9)

where 𝛿𝑡ℎ

is the throttle command. The throttle has a dead zone below 0.1.

The motor is a first-order system with the time constant 𝜏 = 0.19 .

F. Actuator Model

The actuator system of each channel (roll, pitch, and yaw) is modelled as the second order

system as

𝛿

𝛿𝑐

=

𝜔𝑎𝑐𝑡

2

𝑠

2 +2𝜁𝑎𝑐𝑡𝜔𝑎𝑐𝑡𝑠+𝜔𝑎𝑐𝑡

2

, (10)

where the parameters 𝜔𝑎𝑐𝑡 and 𝜁𝑎𝑐𝑡 are the natural frequency and the damping ratio of the

actuator system; 𝜔𝑎𝑐𝑡 = 9.774, 𝜁𝑎𝑐𝑡 = 0.801.

G. Autopilot Model

The block diagram of the flight control is given in Fig. 2.

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Fig. 2. Flight control system diagram.

Table 4. Flight control system coefficients

Parameter Kp Ki Kd

Longitudinal Pitch rate 0.3 7.50 0.0591

Pitch angle 8.2978 0.2536 0.1088

Altitude 0.6879 0.2373 0.1282

Lateral Roll rate 0.2631 5.5033 0.047

Roll angle 22.2973 0.0329 0.7683

Throttle Course angle 1.02 0.0011 0

Airspeed 1.4665 0 0.2171