CC BY
25M
Nguyen Tat Tuan1, Pham Thanh Chung1
Le Quy Don Technical University, Ha Noi, Viet Nam1 Nguyen Van Bang2, Vu Quang Luong2, Ngo Van Dung2
Air Defence - Air Force Academy, Ha Noi, Viet Nam2
SYNTHESIS OF GUIDANCE LAW FOR AIR-TO-AIR MISSILES TO DESTROY HIGHLY
MANEUVERING TARGETS
DOI: 10.31618/ESSA.2782-1994.2023.1.86.313 Abstract. This paper presents the results of synthesis of guidance law for air-to-air missiles to destroy highly and complexly maneuvering targets. The aim is to realize the guidance methods applied to modern self-guided missiles. The algorithm is simple, highly convergent, stable and has small errors. The efficiency of the algorithm is verified through simulation, the results are reliable.
Key words: Guidance law, air-to-air missile, target, maneuver.
1. Introduction
The maneuver of the target causes the appearance of higher older derivative components of the tracking coordinates at input of the tracking system. Therefore, the tracking error will increase. The proportional navigation guidance (PNG) law is only optimal for the linearized transfer function of missile, constant speed missiles, and non-maneuvering target models 0, 0. For maneuvering targets, the perfomance of the PNG law significantly decreases 0, 0, 0.
In order to solve the problem of destroying maneuvering targets, the augmented proportional navigation guidance (APNG) law has been researched and the results are acceptable 0, 0. However, with complexly maneuvering targets in terms of both intensity and frequency of maneuvers, the performance of the APNG law also decreases.
Therefore, the paper proposes a method to improve the perfomance of the PNG law by supplementing the guidance law with the components that compensate for the dynamic error caused by the target's maneuver to achieve good guidance performance when the maneuvering targets with high acceleration and complicated trajectory.
2. Synthetizing the proportional navigation guidance law based on adaptive control for air-to-air missiles to destroy highly maneuvering targets
The geometrical correlation describing the missile-target relative kinematics is shown in figure 1, with the assumptions 0, 0, 0, 0:
- Missiles and targets are considered as point model;
- Velocity of missile and target VM ; VT .
M
o
Fig.1. Geometrical relationship between missile and target
M - Missile; T - Target.
- Relative distance and distance changing rate between missile and target;
dp , 0mt - Orbital tilt angle of missile and target;
CJ. (7 - Angle of elevation between missile and target and the line of sight rotation speed;
WM , WT - Missile normal acceleration and target acceleration.
From the geometry of the target-missile, we can mathematically represent the differential equations as follows 0, 0:
D
Dà
Vcos(6 -a)-V cos(6 -a) t t mm
V cos(6
(1)
a)-Vcos(e-a) (2) m m
.J
0 = Wm
m
9 =
V
m
m vt
(3)
(4)
According to 0, 0, the target acceleration is considered to be uncertain and that value will be processed by a switch containing the sign function component of the sliding mode control (SMC). Furthermore, it is assumed that the target has a high maneuverability equivalent to the maximum acceleration of the missile. Therefore, air-to-air missiles need to ensure fast response to the complex maneuvers of the target.
To evaluate the target acceleration, the adaptive control method uses an improved optimal control law 0. This algorithm allows to use large adaptive gain for fast response without causing large fluctuations in frequency. Furthermore, an additional signal is introduced to compensate for the nonlinear term arising from the saturation of guidance command. Therefore, the desired response performance is still guaranteed even when the guidance command is saturated.
The essence of the traditional proportional approach is to make the line-of-sight rotation always go to zero, which keeps the missile in the kill zone 0:
(5)
S - The sliding surface.
When building the guidance law, considering the time derivative of the sliding surface (1), combined with the geometrical dynamic equations built from figure 1, we get the following results 0:
S — (7 (6) In which:
2D
a
1 1 — &- —— W cosq W cosq
D Dm p p D t
(7)
From (6) and (7) the sliding surface derivative is obtained as follows:
W =W (u) = m m
(9)
sign(u)Wmax
when |u| >W when |u|<W
max m
max m
rmax
In which, W is the maximum acceleration
m
of the missile.
By adding and subtracting an amount equal to the right hand side of formula (8), the result is:
s = — \_-2Dà-ucosqm +A Wmcosqm +Wf ] (10)
This is the nonlinear component resulting from the saturated guidance command. If the navigation
command is not saturated, i.e. W =u, the
' m '
component AW will be zero.
A m
From (10), the guidance law has the following
form:
1
u = -
cosqm
[kà-2Dà+Wt] (11)
In which, k> 0 and W is the target
acceleration;
When the guidance command in equation (11) is
not saturated, from formula (9) (Wm =u), the
guidance law can be rewritten as follows:
k-2D W =-<7
m cosqm
Wt
cosqm
(12)
The guidance law (12) can be considered as a form of the augmented proportional navigation guidance
law. If set k = -k'D, in which k' 0 . then (12) can be rewritten as:
W =-N'V tt +-l—
m cosqm c cosqm
(13)
s =
1
15
[-2DÔ
W cosq +W1 m m t
(8)
In which,
Wt = Wc°s^ is the component of
the tangential acceleration of the target.
In practical situations, the maneuverability of missile is limited, or the missile's navigation acceleration is limited. This limited acceleration is described as the following saturation function 0, 0:
Where, N' = k'+ 2 and V =-D - denotes the
c
closing velocity. The guidance law (13) has a guidance
N'
coefficient-.
cosqm
3. Simulation results and analysis
Compare the performance of the newly synthesized guidance law (13) with the guidance laws PN; APNs; with the assumption that the target and missile parameters are as follows:
- Missile parameters:
+ Missile velocity: VM = 1200 (m / s)
u
M
+ Distance: 0(km) + Height: 0(km)
+ Missile's orbit tilt angle: 10°
- Target parameters:
+ Target velocity V = 60° ( m / S )
Fig.2. When maneuvering target with acceleration Wt = 2g
- The miss distance between Missile and Target
Fig.4. When maneuvering target with acceleration Wt = 2g
- Comments:
When the target maneuvers with different accelerations, the missile trajectory will also change differently according to each guidance law. The traditional proportional guidance law has a large orbital curvature. The proposed guidance law and the augmented proportional navigation guidance law have a much better orbital curvature than the traditional navigation proportional guidance law.
The miss distance of the proposed guidance law (13) increases as the target more highly maneuvers. The PN guidance law gives a miss distance value that is
+ Distance: 15(km) + Height: 10 (km)
+ Target's orbit tilt angle: 100 3.1. One-sided maneuvering target - Missile - Target Trajectory
Fig.3. When maneuvering target with acceleration Wt = 4g
Time (s)
Fig.5. When maneuvering target with acceleration Wt = 4g
always larger than the ANP laws and proposed guidance law. The proposed guidance law gives a much more optimal slip result, so the guidance accuracy will be higher.
3.2. Maneuvering target as a style of "Snake" Snake maneuvering target with normal acceleration:
W = 10g.sin ( at), where a = 0,5 (rad / s)
- Trajectory Missile - Target
.J
Missile - Target trajectory
Horizontal distance (km)
Fig. 6. When Snake style maneuvering target - Miss distance
-500 -1-1-1
0 5 10 15
Time (s)
Fig. 7. The miss distance when Snake style maneuvering target
- Comments:
When the target is maneuvering as a style of Snake, the missile's trajectory will also have a more complex shape. Compared with the PN guidance law, the new proposed guidance law takes less time to enter the dynamic trajectory and has smaller orbital curvature. Therefore, the performance of destroying the target will be significantly higher.
The missile and target miss distance of the proposed guidance law are always lower than that of
the traditional guidance methods. Therefore, the guidance accuracy will be higher.
4. Conclusion
The article has proposed a guidance method for air-to-air missiles to intercept targets with high maneuverability, suitable for practical conditions and capable of quickly adapting to different complex maneuvers of the target.
The proposed algorithm has a simple structure, high convergence and stability. Easily realized in
reality. Destroy complexly maneuvering targets, improve combat performance for air-to-air missiles.
References
Paul Zarchan (2012), Tactical and Strategic Missile Guidance, six edition, Vol.2, Progress in Astronautics and Aeronautics, American Institute of Aeronautics and Astronautics, Inc., Washington, D.C.
Neil F. Palumbo, Ross A. Blauwkamp, and Justin M. Lloyd (2010), Modern Homing Missile Guidance Theory and Techniques, Johns Hopkins APL Technical Digest, Volume 29, Number 1.
H. Jin Kim and Min-Jea Tahk (2015), Fast Adaptive Guidance Against Highly Maneuvering Targets, Korea Advanced Institute of Science and Technology (KAIST) Daejeon, Korea.
K. Ravindra Babu, I.G.Sarma and K. N.Swamy (2006), Switched Bias ProportionalNavigation for
Homing Guidance Against Highly Maneuvering Targets, Journal of guidance, control, and dynamics, Vol. 17, No. 6, Indian Institute of Science, Bangalore 560 012, India.
Ming-Hsiung Hsueh, Chin-I Huang, Li-Chen Fu (2017), A Differential Game Based Guidance Law for the Interceptor Missiles, Industrial Electronics Society, IECON, 33rd Annual Conference of the IEEE, pp.665670.
Kadriye Tiryaki Kutluay (2019), Adaptive control of guided missiles, A Thesis Submitted to The Graduate School of Natural and Applied Sciences of Middle East Technical University.
Koren A, Idan M, Golan OM (2018), Integrated sliding mode guidance and control for a missile with on-off actuators, J Guid Control. Dyn;31(1):204-14.
Grigoryan David
senior mobile software engineer, Ozon Holdings PLC
APPLICATION OF AGILE APPROACHES IN TECHNICAL DEVELOPMENT AND SUPPORT OF MOBILE APPLICATIONS ON ANDROID AND IOS OPERATING SYSTEMS OF A CORPORATE
INFORMATION SYSTEM
DOI: 10.31618/ESSA.2782-1994.2023.1.86.314
Abstract. The article is devoted to solving an important topical scientific and applied problem, namely, the formation of the theoretical basis of agile-transformation of technical development and support of mobile applications on Android and IOS operating systems of a corporate information system.
The purpose of the study is to increase the effectiveness of technical development and support of mobile applications on Android and IOS operating systems of a corporate information system through the development and practical use of models and methods of project management for their development in the framework of agile-transformation.
The object of research is the processes of project management of technical development and support of mobile applications on Android and IOS operating systems of a corporate information system in the framework of agile-transformation.
The subject of the study is the technical development and support of mobile applications on Android and IOS operating systems of a corporate information system in the framework of agile-transformation.
As a result of research the actual scientific and applied problem is solved, namely, the theoretical basis of agile-transformation of management of projects of methodology of Agile approaches in the technical development and support of mobile applications on Android and IOS operating systems of a corporate information system is formed.
Key words: agile-transformation, mobile applications, Android, IOS, operating systems, scrum, flutter, development, technical support of corporate information systems, waterfall.
1 Introduction
Agile methods allow for the orderly process of project management, such as the transfer of part of the revision and adaptation, to the command robot, self-organization and soundness [1]. There are a number of advanced methods of development and support of mobile applications on Android and IOS operating systems, which are intended for a quick release of high-quality software security, and business-related processes, which link the development of the product to the customers' needs and the goals of the company [2]. Agile development can be used within iterative processes that can be used with the Agile Manifesto concepts. The Manifest of a group of seventeen software security experts and a presentation of the idea
that we will use in the field of software security technical support.
Poorly chosen process methodology leads to the risk of increasing costs or process time, which ultimately leads to significant losses at an early stage of development.
The purpose of the study is to research application of the methodology of Agile approaches in the technical development and support of mobile applications on Android and IOS operating systems of a corporate information system.
As a result of research the actual scientific and applied problem is solved, namely, the theoretical basis of agile-transformation of management of projects of development and support of mobile applications on Android and IOS operating systems is formed.
