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1234567890 ‘’“”
5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
Implementation of Dryden Continuous Turbulence Model into
Simulink for LSA-02 Flight Test Simulation
Teuku Mohd Ichwanul Hakim
1
, Ony Arifianto
2
Abstract. Turbulence is a movement of air on small scale in the atmosphere that caused by
instabilities of pressure and temperature distribution. Turbulence model is integrated into flight
mechanical model as an atmospheric disturbance. Common turbulence model used in flight
mechanical model are Dryden and Von Karman model. In this minor research, only Dryden
continuous turbulence model were made.
Dryden continuous turbulence model has been implemented, it refers to the military specification
MIL-HDBK-1797. The model was implemented into Matlab Simulink. The model will be
integrated with flight mechanical model to observe response of the aircraft when it is flight
through turbulence field. The turbulence model is characterized by multiplying the filter which
are generated from power spectral density with band-limited Gaussian white noise input.
In order to ensure that the model provide a good result, model verification has been done by
comparing the implemented model with the similar model that is provided in aerospace blockset.
The result shows that there are some difference for 2 linear velocities (vg and wg), and 3 angular
rate (pg, qg and rg). The difference is instantly caused by different determination of turbulence
scale length which is used in aerospace blockset. With the adjustment of turbulence length in the
implemented model, both model result the similar output.
Introduction
Along with national needs in the area of airborne remote sensing and surveillance [1], Aeronautics
Technology Center of LAPAN in cooperation with TU Berlin, Germany, develop a project to investigate
the implementation of an Electronic Flight Control System (EFCS) into a light utility aircraft. The
project itself started from 2014 and planned to be finish in 2019 [1]. Goal of the EFCS development in
the future is to provide the control system that can help and even replace the pilot in missions that are
extremely difficult, long or dangerous. In order to fulfill that goal, the EFCS have to have full authority
and highly reliable. Furthermore, the EFCS shall be able to fly the aircraft to follow predefined
trajectories with high precision, to stabilize the aircraft and measurement system during flight in calm
and turbulence atmosphere. In the project a demonstrator aircraft which called as an LSA-02 is
developed in order to investigate the flight control function and flight control laws [2]. The LSA-02 will
1
LAPAN, Bandung Institute of Technology, TU Berlin
2
Bandung Institute of Technology
2
1234567890 ‘’“”
5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
use to perform research in the area of UAV technology, especially for new flight control functions.
During the testing, safety pilot will be on board for safety reason and conduct the experiment.
In the aircraft, the EFCS is installed to supplement the basic mechanical flight control system. When
engaged, the EFCS uses the mechanical linkage of the mechanical FCS to command control surfaces
via electro-mechanical actuators. The commands are computed by Flight Control Laws (FCL). Basic
FCL are implemented in the flight control computer (FCC) of the Basic Electronic Flight Control System
(BEFCS). The BEFCS provides all standard autopilot modes [3].
Flight control laws (FCL) testing is an important part in the development of Electronic Flight Control
System (EFCS) of an LSA-02. The testing is used to verify and validate the developed FCL against the
requirements in order to ensure the functionality and safety. Verification and validation of the FCL can
be performed through several type of test e.g. software in the loop simulation (SILS), hardware in the
loop simulation (HILS) and flight testing (FT).
On ground test facility such as SILS and HILS, the dynamic behavior of the aircraft is simulated in flight
mechanical model. The environmental disturbances e.g. wind, gust and turbulence are also simulated to
provide real condition that may be faced by the aircraft during flight testing. It is not sufficient to
simulate and to evaluate the aircraft only in calm condition.
Objective of the research is to provide atmospheric turbulence model in the form of Simulink model
which has been verified to support the simulation. Later, the model will be integrated to the flight
mechanical model to observe response of the aircraft when it is flight through turbulence field and how
the FCL response to stabilize the aircraft. Figure 1 shows environment for FCL test, where the
atmospheric disturbance integrated to flight mechanical model block.
Figure 1 Environment for FCL test [4]
By definition, turbulence is a movement of air on small scale in the atmosphere that caused by
instabilities of pressure and temperature distribution in clouds, near ground and in the jet-stream region.
Based on [5] and [6], turbulence is defined as a stochastic process which are determined by velocity
spectra. The turbulence field is assumed to be visualized as frozen in time and space
There are 2 common continuous turbulence models that are usually used in flight mechanical model,
those are:
Dryden Continuous Turbulence Model; and
Von Karman Continuous Turbulence Model
Flight Control
Laws
Flight Simulation
(Aircraft Dynamics,
Sensors and
Actuators)
Data
Recording
Disturbance
Initial Conditions
Command
3
1234567890 ‘’“”
5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
In practical, Dryden turbulence model is used more frequently, it is caused by the Dryden model has
simpler form and the ease to produce [7]. The Dryden wind turbulence model, or it is also called as the
Dryden gusts, is a mathematical model of continuous gusts which is accepted by the United States
Department of Defense to be used in aircraft design and simulation applications.
Atmospheric Turbulence Model Theory
Dryden and Von Karman model are the common turbulence model that are used in flight mechanics. In
this case, Dryden model will be used because it is easier to implement in simulation even though both
of them tends to similar result. According to [8] there are four assumptions are taken in turbulence
modeling for statistical properties of the turbulence
stationary (independent of time)
homogeneous (independent of location in space)
isotropic (independent of direction)
larger than the airplane (all parts of the airplane are equally affected)
In Dryden turbulence model, the linear and angular velocity components of continuous gusts treated as
spatially varying stochastic processes and specifies each component's power spectral density. It is
applying shaped noise with known spectral properties as velocity and angle rate perturbations to the
body axes of the vehicle, the effect of turbulence is captured during discrete time simulations [9]. The
noise spectrum for each of the perturbations is described by a turbulence scale length (L), the airspeed
(V), and the turbulence intensity (σ). The turbulence scale length L is the length of turbulence field
which expressed in longitudinal, lateral and vertical axis (Lu, Lv and Lw). Turbulence intensity is the
magnitude of the turbulence which expressed in longitudinal, lateral and vertical (u, v and w). It has
dimension ft/s or m/s which is root-mean-square of its magnitude.
Figure 3 shows the aircraft with velocity of V fly into a turbulence field with sine-type vertical velocity
distribution with the length of L in longitudinal axis (Lu). To traverse the turbulence, the aircraft takes
time
𝑇=𝐿
𝑉 (1)
The aircraft experiences the turbulence wave with the temporal frequency of
𝜔=2𝜋
𝑇=2𝜋
(𝐿𝑉
⁄ ) (2)
The turbulence wave not just consist of one frequency, whole spectrum are exist from low to high
frequency. Turbulence spectral density that are modeled in Dryden function expressed in non-
dimensional frequency form as:
𝜔𝑇=𝜔𝐿
𝑉 (3)
4
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5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
Figure 2 Axes definition of turbulence linear velocity and angular rate follows body axis of the aircraft
V
Lu
-Wg
+Wg
Figure 3 Illustration of the aircraft flies into sine-type turbulence field
Power Spectral Densities
Dryden turbulence model is characterized by following power spectral densities () as the function of
temporal frequency. Power spectral densities for three linear velocity component (ug, vg, wg) are:
Φ𝑢(𝜔)=2𝜎𝑢
2𝐿𝑢
𝜋𝑉 ∙1
1+(𝐿𝑢𝜔
𝑉)2 (4)
Φ𝑣(𝜔)=2𝜎𝑣
2𝐿𝑣
𝜋𝑉 ∙1+12(𝐿𝑣𝜔
𝑉)2
[1+4(𝐿𝑣𝜔
𝑉)2]2 (5)
Φ𝑤(𝜔)=2𝜎𝑤
2𝐿𝑤
𝜋𝑉 ∙1+12(𝐿𝑤𝜔
𝑉)2
[1+4(𝐿𝑤𝜔
𝑉)2]2 (6)
Power spectral densities for three angular rate components (pg, qg, rg) are:
xy z
pg
qg
rgug
wg
vg
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5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
Φ𝑝(𝜔)=𝜎𝑤
2
𝑉𝐿𝑤∙0.8(2𝜋𝐿𝑤
4𝑏 )13
⁄
1+(4𝑏𝜔
𝜋𝑉 )2 (7)
Φ𝑞(𝜔)=±(𝜔
𝑉)2
1+(4𝑏𝜔
𝜋𝑉 )2∙Φ𝑤(𝜔) (8)
Φ𝑞(𝜔)=±(𝜔
𝑉)2
1+(3𝑏𝜔
𝜋𝑉 )2∙Φ𝑣(𝜔) (9)
where:
𝜎𝑢, 𝜎𝑣, 𝜎𝑤 indicate turbulence intensities
𝐿𝑢, 𝐿𝑣, 𝐿𝑤 indicate scale length
𝑏 indicates wing span
Continuous Dryden Filter
Continuous Dryden filters are derived from the square roots of the Dryden power spectrum equations as
it is expressed in equation 4 - 9. In order to generate turbulence signal that has similar frequency
spectrum as Dryden power spectral density in the simulation, the continuous filter is used. To excite
waves with full spectrum, white noise (band-limited Gaussian white noise) signal is used. It is passed
through the appropriate filters. White noise is a random signal that having equal intensity at different
frequencies, giving it a constant power spectral density.
Based on [10] Dryden continuous filter for velocity spectra are expressed as following transfer function:
𝐻𝑢(𝑠)=𝜎𝑢√2𝐿𝑢
𝜋𝑉 1
1+𝐿𝑢
𝑉𝑠 (10)
𝐻𝑣(𝑠)=𝜎𝑣√2𝐿𝑣
𝜋𝑉 1+2√3𝐿𝑣
𝑉𝑠
(1+2𝐿𝑣
𝑉𝑠)2 (11)
𝐻𝑤(𝑠)=𝜎𝑤√2𝐿𝑣
𝜋𝑉 1+2√3𝐿𝑤
𝑉𝑠
(1+2𝐿𝑤
𝑉𝑠)2 (12)
Dryden continuous filter [10] for angular rate spectra expressed as following transfer function:
𝐻𝑝(𝑠)=𝜎𝑤√0.8
𝑉(𝜋
4𝑏)1 6
⁄
(2𝐿𝑤)1 3
⁄(1+4𝑏
𝜋𝑉𝑠) (13)
𝐻𝑟(𝑠)=∓𝑠
𝑉
(1+3𝑏
𝜋𝑉𝑠)∙𝐻𝑣(𝑠) (14)
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5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
𝐻𝑞(𝑠)=∓𝑠
𝑉
(1+4𝑏
𝜋𝑉𝑠)∙𝐻𝑤(𝑠) (15)
Continuous Dryden filter is a kind of low-pass filter, where the frequency that higher than certain cut-
off frequency is eliminated. Cut-off frequency of the filter is determined by the ratio of turbulence scale
length to the airspeed.
Application of turbulence model is clearly defined in [5] [6]. In the references there are distinction of
the altitude, which are low-altitude and medium/high altitude.
Low-altitude region is defined as the altitude equal to and less than 1000 feet. In this region, following
values are defined:
Turbulence scale length is the function of altitude. According to [6], turbulence scale length for low
altitude is defined as follows: 2𝐿𝑤=ℎ (16)
𝐿𝑢=2𝐿𝑣=ℎ
(0.177+0.000823ℎ)1.2 (17)
Turbulence intensities 𝜎𝑤=0.1𝑊20 (18)
𝜎𝑢=𝜎𝑣=𝜎𝑤1
(0.177+0.000823ℎ)0.4 (19)
𝑊20 is typical values for wind speed at height of 20 feet, it is defined in [5] and [6]. Typical values
for 𝑊20 defined in the Table 1.
Table 1 Typical value for W20
Turbulence Level
W20
Light
15 knots
Moderate
30 knots
Severe
45 knots
Medium/high altitude is defined for altitude higher than or equal to 2000 feet. In this region turbulence
is assumed isotropic, therefore following values are defined
Turbulence scale length in medium/high altitude is assumed to be constant. Relation for turbulence
scale length in each axes is defined as follow:
𝐿𝑢=2𝐿𝑣=2𝐿𝑤=1750 𝑓𝑡 (20)
Turbulence intensities in [5] and [6] are defined in a diagram that contains root-mean-square (RMS)
turbulence intensities as the function of altitude and probability of exceedance as it is shown in
Figure 4.
Relation for turbulence intensities for each axes is defined as follow:
7
1234567890 ‘’“”
5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
𝜎𝑢=𝜎𝑣=𝜎𝑤 (21)
Figure 4 Medium/high altitude turbulence intensities plot compared with [10]
Output of the filter are 3 linear velocity component (ug, vg, wg) and 3 angular rate component (pg, qg,
rg). Those output will goes to the flight mechanical model as a disturbance signal.
Model Development
Model for Dryden continuous turbulence was made in Simulink. It consist of input subsystem, scale
length subsystem, turbulence intensity subsystem, velocity filter subsystem and angular rate subsystem.
Input values and plotting commands are defined in Matlab script. High level structure of the developed
turbulence model is shown in Figure 5. Detail information of the developed model can be found in [4].
Figure 5 High level structure of developed turbulence model
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5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
In order to ensure that the Simulink models provide a good results, it is need to verify the model with
other models that has been proven. Therefore the developed model is compared with Dryden continuous
turbulence model which are available in Matlab Aerospace Blockset. Block structure comparison
between developed models with Dryden model can be seen in Figure 6. Both model use the same input
in order to provide comparable output. Those model are calculated using [6].
Figure 6 High level structure of comparison model
Result and Discussion
Turbulence model is simulated with the time of 100 seconds. Result of the simulation is described as
follow.
Output from both model stored in the workspace and then compared in the same plot to show how close
the developed model to the reference. Figure 7 shows the comparison of linear velocity (ug, vg and wg)
between developed model and aerospace blockset model. The result shows that output of linear velocity
ug is fit to the output that results from aerospace blockset. But it is not the same for output of vg and wg,
the magnitude are did not fit to the output of the reference. The same condition also occur for angular
rate pg, qg and rg as it is shown in Figure 8. Magnitude of three angular rate of developed model are
different from magnitude of reference.
With the same input values given, both model should result the same output. From further analysis
finally it is found that the difference between the models are the value of turbulence scale length (Lv
and Lw) that are used in calculation. Even though both models are use the same standard [6], in fact
[10] use turbulence scale length as it is defined in [5]. Therefore only ug that fit together, because [5]
and [6] has the same definition for Lu.
Reference [10] state that the use of different Lu as it is defined in standard [5] and [6] is acceptable,
despite it would result the difference turbulence characteristic. Turbulence length scale has direct impact
to the power spectral density and magnitude of the turbulence.
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5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
Furthermore, to ensure that the developed model result the same output as aerospace blockset, then the
turbulence scale length in developed model were adjusted. After adjustment in turbulence scale length,
the result are shown in Figure 9 and Figure 10. In those figure all output are fit together. As well as for
the power spectral density (PSD) for linear velocity and angular rate are fit together. Figure 11 shows
the sample for single sided PSD with FFT for ug and qg.
Figure 7 Comparison results for longitudinal linear velocity ug, vg and wg
Figure 8 Comparison results for longitudinal angular rate pg, qg and rg
010 20 30 40 50 60 70 80 90 100
-2
-1
0
1
2Linear Velocity
time (s)
ug (m/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-2
-1
0
1
2Angular Rate
time (s)
vg (m/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-2
-1
0
1
2Angular Rate
time (s)
wg (m/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-0.1
-0.05
0
0.05
0.1 Angular Rate
time (s)
pg (rad/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-0.05
0
0.05 Angular Rate
time (s)
qg (rad/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-0.1
-0.05
0
0.05
0.1 Angular Rate
time (s)
rg (rad/s)
Developed
Blockset
10
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5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
Figure 9 Comparison of linear velocity for adjusted Lv and Lw
Figure 10 Comparison of angular rate for adjusted Lv and Lw
010 20 30 40 50 60 70 80 90 100
-2
-1
0
1
2Linear Velocity
time (s)
ug (m/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-2
-1
0
1
2Angular Rate
time (s)
vg (m/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-2
-1
0
1
2Angular Rate
time (s)
wg (m/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-0.05
0
0.05
0.1
0.15 Angular Rate
time (s)
pg (rad/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-0.04
-0.02
0
0.02
0.04 Angular Rate
time (s)
qg (rad/s)
Developed
Blockset
010 20 30 40 50 60 70 80 90 100
-0.04
-0.02
0
0.02
0.04 Angular Rate
time (s)
rg (rad/s)
Developed
Blockset
11
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5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
Figure 11 Single sided PSD plot for ug and qg using FFT method
Conclusion
Dryden continuous turbulence model based on [6] has been successfully developed for low altitude and
medium/high altitude.
Linear interpolation has been introduced to calculate turbulence scale length and turbulence intensities
for altitude between 1,000 ft and 2,000 ft to provide value of L and for turbulence calculation in those
altitude range.
Verification of the Simulink model result the same output in ug as the model from aerospace blockset.
Other 2 linear velocity and 3 angular rate results in different magnitude. The differences caused by
different turbulence scale length definition for Lv and Lw as it is determined in [6]. The [10] choose Lv
and Lw as it is determined in [5].
The developed turbulence model is quite reasonable to be integrated to the flight mechanical model for
FCL testing, because it has been result a good output compared to the reference.
References
[1]
Pustekbang LAPAN, "Program Pengembangan LAPAN Light Surveillance Aircraft (LSA),"
Pustekbang, 2017. [Online]. Available:
http://pustekbang.lapan.go.id/index.php/subblog/pages/2014/13/Light-Surveillance-Aircraft-
LSA. [Accessed 27 June 2017].
[2]
S. Bahri, "TR LSA 02: Specification and Concept of LSA-02 (Technology Demonstrator),"
LAPAN, Berlin, 29.06.2016.
[3]
T. M. I. Hakim, "TR LSA 02: BEFCS Definition, Requirements and Concept," LAPAN, Berlin,
2016.
0 5 10 15 20 25 30 35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7 PSD Single Sided Spectrum
Frequency (rad/s)
Magnitude (|uwg|)
0 5 10 15 20 25 30 35
0
0.5
1
1.5
2
2.5
3x 10-3 PSD Single Sided Spectrum
Frequency (rad/s)
Magnitude (|qwg|)
12
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5th International Seminar of Aerospace Science and Technology IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1005 (2018) 012017 doi :10.1088/1742-6596/1005/1/012017
[4]
T. M. I. Hakim, "Minor Research Report: Dryden Continuous Turbulence Model," Bandung
Institute of Technology, Bandung, 2017.
[5]
MIL-F-8785C, " US Military Specification: Flying Qualities of Piloted Airplanes," 5 November
1980.
[6]
MIL-HDBK-1797, "US Military Handbook: Flying Qualities of Piloted Aircraft," 19 December
1997.
[7]
T. R. Beal, "Digital Simulation of Atmospheric Turbulence for Dryden and Von Karman
Models," Journal of Guidance, Control, and Dynamics, Vols. 16, No. 1, January - February
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[8]
P. H. Zipfel, Modeling and Simulation of Aerospace Vehicle Dynamics, Blacksburg, Virginia :
American Institute of Aeronautics and Astronautics, Inc. , 2007.
[9]
E. T. King, "Distributed Coordination and Control Experiments on a Multi-UAV Testbed,"
Massachusetts Institute of Technology, August 20, 2004.
[10]
S. Gage, "Creating a Unified Graphical Wind Turbulence Model from Multiple Specifications,"
in AIAA Modeling and Simulation Technologies Conference and Exhibit, Austin, Texas, 11-14
August 2003.
