T.M. Lynnyk,
Unmanned Aerial Vehicle motion modeling in Matlab/Simulink
The project is to use MathWorks package (Matlab and Simulink) to model the six degrees of
freedom of the dynamics of a particular UAV; and use the model to accurately simulate any UAV
by simply changing the variables. This will be achieved by using the equations of motion.
M-22 “Aerotester” motion model was created, according to the M-22 parameters, including
external disturbances. In this way it can be analyzed the dynamic stability parameters of the M-22
“Aerotester”, that would help to produce technical manuals for the UAVs with the same dimensions
and characteristics, and allow to estimate the maximum load that UAV can sustain. Further it would
allow producing UAV in shorter time and at less cost, because of unnecessary numerous test flights.
UNMANNED AERIAL VEHICLE, SIMMULATION, STATIC AND DYNAMIC
STABILITY, DISTURBANCE, MODEL, RESPONSE, LONGITUDINAL AND LATERAL
DERIVATIVES
Unmanned Aerial Vehicles, or UAVs, as they have sometimes been refered to, have only been
in service for the last 60 years. UAVs are now an important addition to many countries air defences.
Modern UAVs have come a long way since the unmannned drones used by the USAF in the 1940s.
These drones were built for spying and reconnaissance, but were not very efficient due to major
flaws in their operating systems. Over the years UAVs have been developed into the highly
sophisticated machines in use today. Modern UAVs are used for many important applications
including coast watch, news broadcasting, and the most common application, defense.
The same approach has been adopted by companies such as BAE (British Aerospace) systems
when developing the Eagle 150. BAE SYSTEMS Controls Develops Autopilot for Unmanned
Aerial Vehicle Using MathWorks Tools. BAE Systems chose MATLAB®, Simulink®, and
Stateflow® to model the UAV system. They decided to save time and costs by reusing existing
software designs. These designs included an autopilot model, developed using MATLAB,
Simulink, Stateflow, and an integrated navigation algorithm.
For their new system, the engineers needed to include a six-degrees-of-freedom nonlinear
dynamic model of the Eagle 150 aircraft with all variables computed as outputs. The first monitored
flight of the UAV was a great success. The basic autopilot functions were checked and found to be
satisfactory. System requirements were validated during additional flight tests.
As highlighted above, the use of UAVs is becoming more popular in both defence and
environmental research industries. However, there is still high developmental cost. The UAV
testing phase has the highest budget in the development cycle. [1]
There is also high risk that the UAV might be unstable or fail when subjected to different
parameters. One cannot be absolutely sure whether the UAV meets the specifications without test
flights. This project is a solution to the problems outlined. Modelling the UAV dynamics will
enable a thorough analysis in the behaviour and stability of the UAV at different conditions. Real
time simulations will save time cost and eliminate risk.
During the simulations numerous graphs that shows UAV M-22 “Aerotester” reaction on the
external and control surface changes were obtained. As tested UAV already has the flight trials, it
can be asserted that the created model work in proper way. Simulation shows positive dynamic and
static stability of M-22, and according to the obtained graph it can be seen that aircraft returns to its
equilibrium state, that involves the ability of the aircraft to flight.
The UAV’s state of equilibrium is where the sum of forces and moments at its centre of
gravity are zero.[2]
Stability is the tendency for an aircraft to return to its equilibrium position after a disturbance.
The disturbance can be due to various inputs such as turbulence, gusts winds and pilot inputs. The
UAV must be stable even after being exposed to these external disturbances and also manoeuvrable
at different speeds to ensure success of the intended mission. The ability for the UAV to easily
achieve this with minimal workload is considered as its handling qualities.
Static stability is the initial tendency for the UAV to return to its equilibrium position after a
displacement due to external disturbances. If the UAV return to its equilibrium position after a
displacement, then it has positive static stability and if it moves away from its equilibrium position,
then it has negative static stability. If the UAV stays at its new position after a displacement, it is
considered to have neutral static stability.
Dynamic stability is the motion of the UAV with respect to time after a disturbance from its
equilibrium position. If the maximum displacement of the UAV from its equilibrium position
decreases with time, then the UAV has positive dynamic stability (Figure 1) subsidence motion).
However, if it increases with time then it has negative dynamic stability (Figure 1) divergence
motion). If the motion remain constant with time the UAV has neutral dynamic stability.[3]
Figure 1 – Dynamic Stability
The UAV must be statically stable to be dynamically stable but static stability does not
guarantee dynamic stability.
The UAV can be statically stable but dynamically unstable. The UAV must be statically
stable to be dynamically stable but static stability does not guarantee dynamic stability.
If the UAV has positive static stability but negative dynamic stability, it will have divergent
oscillation. If the UAV has positive static stability but neutral dynamic stability, it will have
undamped oscillation or simple harmonic motion (Figure 2).
Figure 2 – Oscillatory motions
The design aim is for the UAV to have both positive and dynamic stability, thus a damped
oscillation. If this condition is mate the UAV will always return to its equilibrium position after a
disturbance.
A generic Simulink model was created to simulate the UAV dynamics. The derivatives were
computed to determine the forces and moments. The inputs to the model were the control surfaces
and the atmospheric disturbances. The outputs of the model were the angles and rates.
Figure 3 – Elevator response test.
The figure 3 graphically shows the elevator response test. The oscillations start after the
elevator step input disturbance and continued until the UAV back into the state of equilibrium.
There can be observed damped oscillations, it means that M-22 “Aerotester” has positive static and
dynamic stability.
Figure 4 – Long term response to elevator step input.
The figure 4 shows that the UAV returns to equilibrium position in approximately 80 seconds
after an elevator step input disturbance. This shows that the UAV longitudinal dynamics are stable.
The pitch rate (q) returns to zero steady state from a maximum pitch rate of 9°/s. The angle of
attack (α) has decreased by 2° due to the influence of elevator response.
The characteristic equations show clearly the influence of derivatives to the longitudinal
motion.
The longitudinal motions to be analysed is the short pitching period oscillation (SPPO) and
the phugoid motion. SPPO is a highly damped motion characterised by change in incidence angle
and pitch angle in phase at constant forward speed. Phugoid – is the lightly damped oscillation with
a long period. It is characterised by change in pitch attitude angle with very small changes in
incidence. The change in forward speed is out of phase with pitch attitude angle by 90°.
If the damping ratio and the frequency of the SPPO motion is high; the UAV will have a
faster response to elevator input without overshoot. However if the UAV has lightly damped motion
with low frequency, the UAV will be difficult to control.[4]
Estimating UAV SPPO frequency calculates according to the formula (1) and damping ratio –
formula (2):
(1)
(2)
- is the derivative for pitching moment due to pitch rate
,
- are the derivative for pitching moment due to change in incidence
- is the derivative for change in normal force due to incidence
- is change in forward speed
Estimating UAV phugoid frequency perform according formula (3) and damping ratio –
formula (4):
(3)
(4)
Where
and
- are derivatives due to forward speed
- is the forward speed
g - is the acceleration due to gravity
Influence of stability derivatives of longitudinal motions:
and Mά these are SPPO damping derivatives. Increasing
and Mά increases the
damping of the SSPO motion.
– is the SPPO frequency derivative. Increasing
increases the frequency of the SPPO
motion.
– is the damping derivative for phugoid motion. Increasing
increases the damping
ratio of the phugoid motion.
– is the derivative for the frequency of the phugoid motion. Increasing
increases
frequency of the phugoid motion. [5]
The UAV should be easy to control therefore it should be designed to have heavily damped
motions with high frequency. Therefore the
,
and
derivatives should be large.
The research can be used to develop an advanced UAV capable of different missions. The
stability and augmentation study can be used to design a very stable UAV that can also be easily
controlled. The simulations can be used for UAV design optimisation, flight testing, and mission
simulations.
References
1. BAE SYSTEMS Controls Develops Autopilot for Unmanned Aerial Vehicle Using
MathWorks Tools. Feng Liang © 2003 [Viewed 20 October 2013] available from:
http://www.mathworks.com/company/user_stories/BAE-Systems-Controls-Develops-Autopilot-forUnmanned-Aerial-Vehicle.html
2. Brief History of UAVs (c) January 2003 LIST lab, University of Florida [Viewed 22
December 2013] available from: http://www.list.ufl.edu/uav/UAVHstry.htm
3.
Airborne Autonomous system [Viewed 4December 2013], available from:
http://www.unmannedaircraft.org/page/page/1357249.htm
4. Defence industry daily. An Enhanced Predator for the Army. Gray Eagle © 05 October
2010 [Viewed 22 October 2013] available from: http://www.defenseindustrydaily.com/warriorermp-an-enhanced-predator-for-the-army-03056/
5. Dictionary of Military and Associated Terms. US Department of Defence 2005 [viewed
January 2014], available from: http://www.thefreedictionary.com/Unmanned+Aerial+Vehicle
Supervisor – S. V. Pavlova, PhD, prof