Bio inspired technique for controlling angle of attack of aircraft

IAES International Journal of Artificial Intelligence (IJ-AI)
Vol. 13, No. 4, December 2024, pp. 4206~4216
ISSN: 2252-8938, DOI: 10.11591/ijai.v13.i4.pp4206-4216  4206
Journal homepage: http://ijai.iaescore.com
Bio inspired technique for controlling angle of attack of aircraft
Subhakanta Bal1
, Srinibash Swain2
, Partha Sarathi Khuntia3
1
Department of Electrical Engineering, Bijupattnaik University of Technology, Rourkela, India
2
Department of Electrical Engineering, Nalanda Institute of Technology, Bhubaneswar, India
3
Department of Electronics and Telecommunication Engineering, Konark Institute of Science and Technology, Khurda, India
Article Info ABSTRACT
Article history:
Received Jan 23, 2024
Revised Jun 11, 2024
Accepted Jun 14, 2024
This paper deals with the design of a proportional–integral (PI) controller for
controlling the angle of attack of flight control system. For the ﬁrst time
teaching learning-based optimization (TLBO) algorithm is applied in this area
to obtain the parameters of the proposed PI controller. The design problem is
formulated as an optimization problem and TLBO is employed to optimize
the parameters of the PI controller. The superiority of proposed approach is
demonstrated by comparing the results with that of the conventional methods
like genetic algorithm (GA) and particle swarm optimization (PSO). It is
observed that TLBO optimized PI controller gives better dynamic
performance in terms of settling time, overshoot, and undershoot as compared
to GA and PSO based PI controllers. The various performance indices like
mean square error (MSE), integral absolute error (IAE), and integral time
absolute error (ITAE) are improved by using the TLBO soft computing
techniques. Further, robustness of the system is studied by varying all the
system parameters from −50% to +50% in step of 25%. Analysis also reveals
that TLBO optimized PI controller gains are quite robust and need not be reset
for wide variation in system parameters.
Keywords:
Genetic algorithm
Mean square error
Particle swarm optimization
Proportional–integral
Teaching learning-based
optimization
This is an open access article under the CC BY-SA license.
Corresponding Author:
Subhakanta Bal
Department of Electrical Engineering, Bijupattnaik University of Technology
Rourkela, Odisha, India
Email: bal.subhakanta@gmail.com
1. INTRODUCTION
For smooth flying of an aircraft, managing of three controlling surfaces viz rudder, elevator, and
aileron becomes inevitable. The movement of a flight is controlled by the help of above three surfaces about
the pitch, roll, and yaw axes. For the orientation of aircraft, elevator performs an essential position in changing
the angle of attack along with pitch. Different soft computing techniques like fuzzy model reference learning
(FMRL) and radial basis function neural controller (RBFNC) are applied previously for obtaining a better result
for a dynamic system. But a new soft computing technique named teaching learning-based optimization
(TLBO) is incorporated in this paper mainly for adjusting the angle of attack as well as upgrading the overall
achievement of the proposed system. Finally, a comparison is made between the results of TLBO and other
optimization methods like genetic algorithm (GA) and particle swarm optimization (PSO) in each and every
aspect.
Literature survey reveals most of the early works on flight control system. The selection of gain of a
proportional–integral (PI) controller for nonlinear second order plants was suggested by Kumar et al. [1] in an
organized manner. The regulating of a PI controller for a control system was verified by Xiang et al. [2] in a
number of ways. A better proposal was proposed by Saxena and Hote [3] for determining the gain of a PI
controller. An easy and quick method for tuning a proportional–integral–derivative (PID) controller was jointly

Int J Artif Intell ISSN: 2252-8938 
Bio inspired technique for controlling angle of attack of aircraft (Subhakanta Bal)
4207
analyzed by Ghany et al. [4] in a precise manner. The various types of methods needed for estimating the angle
of attack of a flight were clearly described by Sankaralingam and Ramprasadh [5]. Two-stage TLBO method
for flexible job-shop scheduling was suggested by Buddala and Mahapatra [6]. Suganthi et al. [7] proposed an
improved TLBO algorithm. Niu et al. [8] suggested a modified TLBO algorithm for numerical function
optimization. Shahrouzi et al. [9] suggested a hybrid bat algorithm and TLBO.
Zhai et al. [10] proposed a novel TLBO with error correction for path planning of unmanned air
vehicle. Zhang et al. [11] suggested an improved TLBO with logarithmic spiral and triangular mutation for
global optimization. Nayak et al. [12] proposed an Elitist teaching–learning-based optimization (ETLBO)
with higher-order Jordan Pi-sigma neural network. Yang et al. [13] proposed a multiobjective GA on an
accelerator lattice. In addition, Gaing [14] proposed a PSO method to solve the economic dispatch. Evtushenko
and Posypkin [15] suggested a new method in 2013 for global box-constrained optimization. Yassami and
Ashtari [16] proposed a novel hybrid optimization algorithm. Storn and Price [17] proposed a diferential
evolution for global optimization over continuous spaces. A fuzzy adaptive diferential evolution algorithm. on
soft computing was suggested by. Liu and Lampinen [18]. Several researchers proposed on ant colony
optimization [19], [20].
Placement of wind turbines using GA was suggested by Grady et al. [21]. Graphic processing unit
(GPU)-based parallel PSO was proposed by Zhou and Tan [22]. A survey on new generation metaheuristic
algorithms was jontly suggested in 2019 by Dokeroglu et al. [23]. Hussain et al. [24] did a comprehensive
survey on artificial intelligence review. Various works on PSO using different techniques ware proposed in
[25]‒[28]. PSO-based memetic algorithm for fow shop scheduling was suggested by Liu et al. [29].
Yang et al. [30] suggested an improved PSO-based charging strategy of electric vehicles in electrical
distribution grid. This paper shows a better result by applying TLBO method for managing the attacking angle
of an air craft system. After comparison the results between TLBO, GA and PSO methods, it was found that
TLBO performs better in all aspects than GA and PSO methods for tuning the PID controller.
2. BLOCK DIAGRAM FOR DETERMINING THE ANGLE OF ATTACK
Figure 1 shows the block diagram for controlling the angle of attack of an aircraft. The intended angle
of attack (α) is the output. The elevator's deflection (𝛿𝐸) serves as the input.
Figure 1. Schematic diagram of angle of attack for an aircraft system
where 𝛿𝐸(𝑠) is the deflection angle of elevator, 𝛼(𝑠) is angle of attack of the aircraft, G(s) is the forward path
gain, and C(s) is proposed PI controller.
3. RELATION BETWEEN THE ELEVATOR DEFLECTION (𝜹𝑬) AND ANGLE OF ATTACK (𝜶)
Generally, angle of attack is the angle between relative wind and the chord line of the aircraft. The
angle of attack is obtained due to the deflection in control surface (elevator) is exhibited in Figure 2. Aircraft
speed (u), is changed due to the deflection in control surfaces and atmospheric turbulence. Mainly the
approximation relating to short period deals with varying flight speed (u) and it consists of very short duration.
The speed of the aircraft 𝑈0 almost remains constant throughout the process i.e., 𝑢 = 0. So that the motion
related equation involving ′𝑢′ is generally neglected. Hence the equations for longitudinal motion may be
dictated as:
𝒘
̇ = 𝒁𝒘𝒘 + 𝑼𝟎𝒒 + 𝒁𝜹𝒔
𝜹𝑬 (1)

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Int J Artif Intell, Vol. 13, No. 4, December 2024: 4206-4216
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𝒒 = 𝑴𝒘
̇ 𝒘 + 𝑴𝒘𝒘
̇ + 𝑴𝒒𝒒 + 𝑴𝜹𝒛
𝜹𝑬 (2)
= (𝑀𝑤
̇ + 𝑀𝑤𝑍𝑤)𝑤 + (𝑀𝑞 + 𝑈0𝑀𝑤)𝑞 + (𝑀𝛿𝑧
+ 𝑍𝛿𝑧
𝑀𝑤
̇ )𝛿𝐸
Figure 2. Description of angle of attack
Calculation of state vector for short period motion may be written as:
𝑥 = [
𝑤
𝑞
]
where 𝛿𝐸 and ‘𝑢’ are the angle of deflection and control vector respectively, then the state equation for the
above two equations can be written as:
𝑥̇ = 𝐴𝑥 + 𝐵𝑢 (3)
where as:
𝐴 = [
𝑍𝑤 𝑈0
(𝑀𝑤 + 𝑀𝑤
̇ 𝑍𝑤) (𝑀𝑞 + 𝑈0𝑀𝑤
̇ )
],𝐵 = [
𝑍𝛿𝐸
𝑀𝛿𝐸
+ 𝑍𝛿𝐸
𝑀𝑤
̇
]
∴ [𝑠𝐼 − 𝐴] = 𝑠 [
1 0
0 1
] − [
𝑍𝑤 𝑈0
̇ )
]
= [
𝑠 0
0 𝑠
] − [
𝑍𝑤 𝑈0
̇ )
]
= [
𝑠 − 𝑍𝑤 −𝑈0
−(𝑀𝑤 + 𝑀𝑤
̇ 𝑍𝑤) [𝑠 − (𝑀𝑞 + 𝑈0𝑀𝑤
̇ )]
]
𝛥𝑠𝑝(𝑠) = 𝑑𝑒𝑡[𝑠𝐼 − 𝐴]
= 𝑠2
+ [−(𝑍𝑤 + 𝑀𝑞 + 𝑈0𝑀𝑤
̇ )]𝑠 + [𝑍𝑤𝑀𝑞 − 𝑈0𝑀𝑤
̇ ]
= 𝑠2
+ 2𝜁𝑠𝑝𝜔𝑠𝑝𝑠 + 𝜔𝑠𝑝
2
(4)
In (4):
2𝜁𝑠𝑝𝜔𝑠𝑝 = −(𝑍𝑤 + 𝑀𝑞 + 𝑈0𝑀𝑤
̇ ),
𝜔𝑠𝑝 = [𝑍𝑤𝑀𝑞 − 𝑈0𝑀𝑤
̇ ]
1
2
(5)
𝑤(𝑠)
𝛿𝐸(𝑠)
=
(𝑈0𝑀𝛿𝐸
+𝑀𝑞𝑍𝛿𝐸
){1+
𝑍𝛿𝐸
𝑈0𝑀𝛿𝐸
−𝑀𝑞𝑍𝛿𝐸
𝑠}
𝛥𝑠𝑝(𝑠)
=
𝐾𝑤(1+𝑠𝑇1)
𝛥𝑠𝑝(𝑠)
where:
𝐾𝑤 = (𝑈0𝑀𝛿𝐸
+ 𝑀𝑞𝑍𝛿𝐸
) and 𝑇1 =
𝑍𝛿𝐸
𝐾𝑤

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Again, 𝑎̇ =
𝑤
̇
𝑈0
⇒ 𝛼(𝑠) =
𝑤(𝑠)
𝑈0
⇒ 𝑤(𝑠) = 𝑈0𝛼(𝑠)
⇒
𝛼(𝑠)
𝛿𝐸(𝑠)
=
𝐾𝑤(1+𝑠𝑇1)
𝑈0𝛥𝑠𝑝(𝑠)
(6)
3.1. Stability derivatives of aircraft
The standard values of stability derivatives for CHARLIE aircraft in three different conditions are
depicted in Table 1. These are intended for the aircraft's longitudinal dynamics. The transfer function for a
specific flight condition can be found using stability derivatives.
Table 1. Stability derivatives of aircraft for three distinct flight conditions [31]
Flight condition
FC-1 FC-2 FC-3
𝑈0(𝑚𝑠−1) 67 158 250
𝑋𝑢 -0.021 0.003 -0.00002
𝑋𝑤 0.122 0.078 0.026
𝑋𝛿𝐸
0.292 0.616 0.0
𝑍𝑊 -0.512 -0.433 -0.624
𝑍𝑞 -1.9 -1.95 -3.04
𝑍𝛿𝐸
-1.96 -5.15 -8.05
𝑀𝑊 -0.006 -0.006 -0.005
𝑀𝑞 -0.357 -0.421 -0.668
𝑀𝛿𝐸 -0.378 -1.09 -2.08
3.2. Transfer functions of different flight conditions
Table 2 show the transfer function for FC-1, FC-2, and FC-3 respectevely. FC stands for flight condition.
FC-1, FC-2, and FC-3 in Table 2 can be obtained by putting the parametric values from Table 1 in (6).
Table 2. Transfer functions for three different flight conditions
Flight conditions G(S)
FC-1 𝐺1(𝑆) =
0.04936𝑆 + 0.65835
1.695𝑆2 + 2.1546𝑆 + 1
FC-2 𝐺1(𝑆) =
0.0128𝑆 + 0.978
0.8849𝑆2 + 1.59469𝑆 + 1
FC-3 𝐺3(𝑆) =
0.0193𝑆 + 1.26
0.599𝑆2 + 1.525𝑆 + 1
4. PROPOSED OPTIMIZATION SOFT COMPUTING TECHNIQUES
There are so many methods for determining the gain of PI controller. Among them GA and PSO
methods are applied here for tuning the controller. Numerous optimization techniques have been used to
address the different kinds of real-world issues in various sectors. The TLBO approach is thought to be superior
to the rest among them.
4.1. Teaching learning-based optimization
Following its introduction by Rao et al. [32], TLBO has gained a lot of popularity in the engineering
domain. Its stability analysis, time consumption, and solution quality are superior than those of other methods.
In general, TLBO operates in two stages: In the first stage, known as the teacher phase, students learned from
their individual teachers; in the second stage, known as the learner phase, students learn from one another
through interaction. The following steps are part of the TLBO algorithm.
4.1.1. Initialization
The population size is taken as [NP D]. In this case NP indicates size of population i.e. number of
learners and D indicates the dimension of the problem i.e. number of subjects offered. The ith column of the
initial population represents the marks secured by different learners in ith subject.

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Initial population=
𝑥1,1 𝑥1,2 … 𝑥1,𝐷
𝑥2,1 𝑥2,2 … 𝑥2,𝐷
. . . .
. . . .
𝑥𝑁𝑃,1𝑥𝑁𝑃,2.. . . . .. . 𝑥𝑁𝑃,𝐷
4.1.2. Teacher phase
During this phase, the designated instructor puts up their best effort to raise the class mean. Since
teachers are the ones who train the students, the best learner's solution always goes to that specific teacher. The
average grades obtained by various pupils in various assignments are computed (7).
𝑀𝑑 = [𝑚1,𝑚2, …, 𝑚𝐷] (7)
whereas 𝑚1 is the aggregate marks secured by the students in 𝑖𝑡ℎ paper. The dissimilarity in mean results of
a particular teacher is represented as 𝑀𝑑𝑖𝑓𝑓 = 𝑟𝑎𝑛𝑑(0,1)[𝑋𝑏𝑒𝑠𝑡 − 𝑇𝐹𝑀𝑑]. In which rand (0,1) is chosen
arbitrarily as 0 or 1 and 𝑇𝐹 as teaching factor. 𝑇𝐹 is taken arbitrarily either 1 or 2.
𝑇𝐹 = 𝑟𝑜𝑢𝑛𝑑[1 + 𝑟𝑎𝑛𝑑(0,1)] (8)
In (9) the exiting population is renewed as (9):
𝑋𝑛𝑒𝑤 = 𝑋 + 𝑀𝑑𝑖𝑓𝑓 (9)
𝑋𝑛𝑒𝑤 is accepted if (𝑋𝑛𝑒𝑤) < 𝑓(𝑋), where 𝑓(𝑋) is taken as the objective function.
4.1.3. Learner phase
In this case, the teacher chooses a student at random through contact in order to advance their
knowledge. If other pupils are more knowledgeable than him, then he can effectively learn more from them
through interaction. The steps involved in learning stage are as follows. Randomly select two learners Xi and
Xj such that i =/ j.
𝑋𝑛𝑒𝑤 = 𝑋𝑖 + 𝑟𝑎𝑛𝑑(0,1)(𝑋𝑖 − 𝑋𝑗). If(𝑋𝑗) < 𝑓(𝑋𝑗) (10)
𝑋𝑛𝑒𝑤 = 𝑋𝑖 + 𝑟𝑎𝑛𝑑(0,1)(𝑋𝑗 − 𝑋𝑖). Take 𝑋𝑛𝑒𝑤 as granted if better performance is found.
5. SIMULATION RESULT
In this part, TLBO technique is used for designing the best variables of a PI system employing the
transfer function of first flight condition. A comparison is made between TLBO with PI and conventional
methods for comparing the advantages of proposed controllers. Step responses of the flight control system
employing TLBO–PI, GA and PSO methods are obtained by varying three different parameters from-50% to
+50% are shown from Figures 3 to 14. Similar figures can also be drawn by varying the remaining parameters.
It is evident from these figures that settling time of the suggested TLBO approach is lower in comparison to
PSO and GA procedures.
Figure 3. Deviation of 𝑍𝑊 by -50%
0 5 10 15 20 25 30 35 40 45
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Step Response of GA, PSO & TLBO
(Deviation of Zw by -50%)
Time (seconds)
Amplitude
GA
PSO
TLBO

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Figure 4. Deviation of 𝑍𝑊 by -25%
Figure 5. Deviation of 𝑍𝑊 by +25% Figure 6. Deviation of 𝑍𝑊 by +50%
Figure 7. Deviation of Mq by-50% Figure 8. Deviation of Mq by-25%
Figure 9. Deviation of Mq by+25% Figure 10. Deviations of Mq by+50%
0 5 10 15 20 25 30 35 40 45
0
0.2
0.4
0.6
0.8
1
1.2
1.4
(Deviation of Zw by -25%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25
0
0.5
1
1.5
Step Response ofGA, PSO & TLBO
(Deviation of Zw by +25%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25
0
0.5
1
1.5
(Deviation of Zw by +50%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25 30 35 40 45
0
0.2
0.4
0.6
0.8
1
1.2
1.4
(Deviation of Mq by-50%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25 30 35 40 45
0
0.2
0.4
0.6
0.8
1
1.2
1.4
(Deviation of Mq by-25%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25
0
0.2
0.4
0.6
0.8
1
1.2
1.4
(Deviation of Mq by+25%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25 30
0
0.5
1
1.5
(Deviation of Mq by +50%)
Time (seconds)
Amplitude
GA
PSO
TLBO

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Figure 11. Deviation of Mw by -50% Figure 12. Deviation of Mw by -25%
Figure 13. Deviation of Mw by +25% Figure 14. Deviation of Mw by +50%
6. ROBUSTNESS ANALYSIS
For testing the toughness of the CHARLIE Aircraft, the parameters are changed from-50% to +50%.
Then robustness is measured by using the optimum values obtained from TLBO optimized PI controller. A
comparison results among GA, PSO and TLBO are also depicted in Table 3 and 4 respectively. Different
analysis results related to integral absolute error (IAE), integral time absolute error (ITAE), and mean square
error (MSE), settling time, peak under-shoots and peak overshoots are given in these tables. Now it is obvious
that the proposed technique is quite powerful when subjected to a large range of parametric variation. But also
retuning of controller parameters does not necessary over the wide range. Similarly, the performance indices
obtained from TLBO is less than that obtained from conventional methods like GA and PSO.
Table 3. Variation of settling time, under shoot, and over shoot, IAE, ITAE, and MSE for GA and TLBO
Deviation of parameters (%) GA TLBO
Ts Ush Osh IAE ITAE MSE Ts Ush Osh IAE ITAE MSE
-50 8.27 30.86 12.4 1.1 2.56 0.5 3.9 75.47 35.4 0.7 0.7 0.3
-25 13.9 40.14 19.9 1.1 5 0.6 3.51 57.55 27.7 0.8 1 0.4
+25 21.6 74.62 36.8 1.5 6.5 0.7 6.8 79.93 40.5 1.3 2.5 0.5
+50 22.3 84 46.6 1.7 6.9 0.8 8.4 38.9 48.5 1.4 4 0.6
Table 4. Variation of settling time, under shoot, and over shoot, IAE, ITAE, and MSE for PSO and TLBO
Deviation of
parameters (%)
PSO TLBO
Ts Ush Osh IAE ITAE MSE Ts Ush Osh IAE ITAE MSE
-50 5.56 61.8 29 1 1.3 0.4 3.9 75.47 35.4 0.7 0.7 0.3
-25 3.8 52.8 26.4 0.9 1.2 0.5 3.51 57.55 27.7 0.8 1 0.4
+25 8.4 76.61 37.6 1.4 2.7 0.6 6.8 79.93 40.5 1.3 2.5 0.5
+50 9.42 86 47.3 1.6 4.3 0.7 8.4 38.9 48.5 1.4 4 0.6
The above comparison values are also displayed in form of bar charts from Figures 15 to 18. Thus,
the analysis shows better result for TLBO optimized PI controller than PSO and GA methods. In Table 5 to 7,
variation of performance indices like ITAE, MSE, and IAE are demonstrated.
0 10 20 30 40 50 60
0
0.5
1
1.5
(Deviation of Mw by-50%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25 30 35 40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
(Deviation of Mw by -25%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25 30
0
0.5
1
1.5
(Deviation of Mw by+25%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25 30 35 40 45 50
0
0.5
1
1.5
(Deviation of Mw by+50%)
Time (seconds)
Amplitude
GA
PSO
TLBO

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Figure 15. IAE among TLBO, PSO, and GA Figure 16. MSE among TLBO, PSO, and GA
Figure 17. Ts among TLBO, PSO, and GA Figure 18. ITAE among TLBO, PSO, and GA
Table 5. Variation of IAE, ITAE, and MSE
Parameters %Deviation
GA PSO TLBO
IAE ITAE MSE IAE ITAE MSE IAE ITAE MSE
𝑍𝑤 -50 1.23 7.04 0.29 0.88 2.16 0.34 0.83 1.04 0.27
-25 1.22 6.6 0.31 0.89 1.85 0.36 0.88 1.18 0.30
+25 1.23 5.56 0.36 1.05 1.82 0.44 1.04 1.68 0.33
+50 1.24 4.98 0.39 1.24 2.45 0.51 1.11 2.40 0.37
𝑀𝑞 -50 1.25 7.11 0.31 0.89 2.07 0.35 0.86 1.14 0.30
-25 1.24 6.63 0.32 0.91 1.86 0.37 0.90 1.25 0.31
+25 1.21 5.62 0.35 1.02 1.74 0.43 1.01 1.62 0.34
+50 1.20 5.05 0.37 1.12 1.96 0.47 1.08 1.83 0.35
𝑈0 -50 1.01 1.86 0.44 2.12 7.18 0.83 0.82 1.04 0.34
-25 1.11 4.08 0.37 1.13 1.92 0.49 0.99 1.53 0.36
+25 1.27 7.29 0.41 0.97 2.82 0.35 0.44 1.37 0.32
+50 1.26 7.82 0.28 1.40 4.18 0.32 1.05 3.04 0.37
𝑀𝑤 -50 1.36 8.30 0.41 1.03 2.51 0.35 0.94 1.61 0.31
-25 1.29 7.25 0.42 0.96 2.03 0.37 0.93 1.37 0.33
+25 1.16 5.01 0.40 1.03 1.70 0.43 1.02 1.63 0.35
+50 1.12 3.93 0.38 1.17 2.08 0.49 1.05 1.98 0.37
MδE
-50 1.09 5.00 0.41 0.94 1.83 0.37 0.93 1.79 0.31
-25 1.15 5.49 0.42 0.95 1.78 0.38 0.94 1.15 0.32
+25 1.34 7.04 0.41 0.97 1.68 0.42 0.96 1.40 0.36
+50 1.45 8.27 0.42 0.99 1.58 0.47 0.97 1.45 0.35
𝑍𝛿𝛦 -50 1.15 4.73 0.37 1.03 1.55 0.46 0.82 1.08 0.36
-25 1.20 5.48 0.38 0.96 1.46 0.43 0.88 1.22 0.35
+25 1.21 6.36 0.36 1.17 2.51 0.37 0.99 2.07 0.32
+50 1.13 5.77 0.37 1.08 3.72 0.34 1.06 2.47 0.33
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
-50% -25% 25% 50%
Integral
absolute
error
Deviation of parameters in percentage
GA
PSO
TLBO
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-50% -25% 25% 50%
Mean
square
error
GA
PSO
TLBO
0
5
10
15
20
25
-50% -25% 25% 50%
Settling
time(Ts)
in
sec.
GA
PSO
TLBO
0
1
2
3
4
5
6
7
8
-50% -25% 25% 50%
Integral
time
absolute
error
GA
PSO
TLBO

 ISSN: 2252-8938
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Table 6. Variation of settling time, under shoot, and over shoot
Parameters
%Deviation GA PSO TLBO
Ts Ush Osh Ts Ush Osh Ts Ush Osh
𝑍𝑤 -50 23.9 16.67 24 6.16 16.88 24 4.32 20.10 23.9
-25 21.1 17.54 26 6 18.3 27 5.62 21.26 25.6
+25 16 18.98 30.5 6.36 21.11 34.8 5.77 22.74 34.2
+50 13.5 19.86 33.4 6.71 22.27 40.4 6.28 20.89 33.1
𝑀𝑞 -50 23.5 17.23 25.2 6.07 17.73 25.6 5.58 20.67 25.1
-25 20.9 17.61 26.6 6.04 18.19 27.8 5.69 21.48 26.2
+25 16.4 18.93 29.8 6.29 20.48 33.6 5.84 22.88 29.6
+50 14.1 19.18 31.7 6.52 21.72 37.2 5.82 23.17 31.5
𝑈0 -50 7.11 17.79 25.6 12.6 23.84 52 4.39 22.52 25.1
-25 11.3 17.34 25.7 6.98 22.02 35.7 5.69 23.76 25.5
+25 27 18.92 30.6 7.99 18.78 29.4 5.74 21.46 29.3
+50 36.3 19.95 32.8 11.8 18.63 29.9 8.69 23.23 29.4
𝑀𝑤 -50 27 15.97 23.5 8.03 16.1 23.3 5.66 23.47 23.2
-25 22.8 17.05 25.7 6.15 17.78 26.6 5.66 22.36 25.5
+25 14.4 19.43 31 6.28 21.38 35.2 5.82 23.29 30.9
+50 10.4 20.98 34.2 6.57 23.49 40.8 6.22 21.81 33.8
MδE
-50 15.4 21.6 37.2 5.18 21.99 37.9 5.1 21.76 37.1
-25 17.1 20.4 33.3 5.56 20.9 34.6 5.25 17.1 20.4
+25 19.9 14.93 21.4 6.75 17.47 25.4 6.33 20.02 21.3
+50 20.8 9.02 11.7 5.04 14.2 18,7 4.81 15.56 11.6
𝑍𝛿𝛦 -50 12.9 14.59 20.3 5.5 20.16 30.2 5.48 20.89 20.2
-25 15.3 16.23 23.7 6.43 19.85 29.7 5.65 21.74 23.5
+25 22.7 20.23 34.1 7.56 20.62 33.6 6.34 23.03 33.1
+50 25.9 23.16 44 9.84 21.74 40.1 7.52 23.53 39.8
Table 7. Controller parameters for GA, PSO, and TLBO
Parameters %Deviation
GA PSO TLBO
Kp Ki Kp Ki Kp Ki
𝑍𝑤 -50 23.5 1.2 16.31 3.12 14.5 5.5
-25 21.5 1.25 14.94 3.3 13.8 5.7
+25 17.5 1.37 12.2 3.62 14.8 4.7
+50 15.6 1.45 10.8 3.84 13.2 2.7
𝑀𝑞 -50 22.3 1.2 15.5 3.2 14.6 5.2
-25 20.9 1.25 14.5 3.3 13.5 4.5
+25 18.2 1.35 12.6 3.6 12.9 5.6
+50 16.8 1.42 11.7 3.74 14.8 4.7
𝑈0 -50 8.2 1.9 5.72 5.26 13.5 5.8
-25 13.5 1.56 9.4 4.1 14.8 7.4
+25 26.4 1.12 18.32 2.95 13.8 5.7
+50 33.9 0.98 23.6 2.6 12.2 10.6
𝑀𝑤 -50 22.6 1.21 15.7 3.2 15 10.8
-25 21.1 1.25 14.65 3.3 14.6 7.4
+25 18 1.35 12.5 3.6 13.9 5.8
+50 16.5 1.42 11.43 3.74 13.2 2.72
𝑀𝛿𝐸
-50 19.5 1.06 13.6 2.8 13.6 2.74
-25 19.5 1.16 13.6 3.06 0.82 0.01
+25 19.5 1.5 13.6 3.96 13.9 5.4
+50 19.5 1.8 13.6 4.9 14.5 5.6
𝑍𝛿𝛦 -50 13 1.6 9.05 4.2 13.6 4.9
-25 15.6 1.45 10.9 3.84 14.5 5.4
+25 26 1.12 18.1 2.97 13.2 5.9
+50 39.1 0.9 27.2 2.4 12.2 5.8
7. RESULT ANALYSIS
Using the Simulink platform in MATLAB 2014, the time domain simulated results of various
reactions are achieved. With respect to this, the suggested flight control system model is created in the Simulink
environment; however, the necessary programmes for the suggested GA, PSO, and TLBO approach are written
in.m files. A step input is given for studying the behavior of a PI run flight system. Result obtained is compared
with that of GA and PSO methods. It is obvious that the TLBO optimized PI managed device additionally
offers higher dynamic response when subjected to a parametric change.
In Tables 3 and 4, deviation of performance indices like ITAE, MSE, and IAE are depicted along with
settling time, undershoots, and overshoots. In each and every case it shows less error for IAE, ITAE, and MSE
and less settling time also in TLBO optimized PI controller than that of GA and PSO. In addition to this,
Tables 5 and 6 indicate the various analytical results of overshoots, settling time, undershoots, IAE, ITAE and

4215
MSE corresponding to deviation of all parameters in four stages ranging from -50% to +50% at a stretch of
25%. These comparison values are also displayed in form of bar charts from Figures 15 to 18. Similarly,
Table 7 shows the controller parameters for GA, PSO, and TLBO respectively.
Thus, the presented observations shows better result for TLBO optimized PI controller than the GA
and PSO methods. Pictorial representation of overshoot, undershoot and settling time are also given from
Figures 3 to 14 for verification. The above result indicates that the suggested TLBO algorithm gives better
steady state output as compared to above two mentioned PI managed device.
8. CONCLUSION
To study the overall achievement of a flight control system, a PI controller is applied here along with
TLBO algorithm for getting the best gain of PI controller. Then a comparison is made between GA, PSO and
TLBO based PI controller for dynamic performance. A better result is achieved in TLBO managed PI controller
than GA and PSO. For studying the behavior of the aircraft under various hazardous conditions, its controlling
parameters are changed from -50% to +50% of nominal value in steps of 25%. Final results come in favor of
TLBO and retuning of parameters is not necessary over a wide range.
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BIOGRAPHIES OF AUTHORS
Mr. Subhakanta Bal was born on 5th July 1968 in Odisha, India. He completed
his M.Tech. degree in Power Electronics & Drives in 2012 from SOA University, BBSR,
Odisha India. Now he is continuing his Ph. D degree in BPUT, Rourkela, Odish, India. His
major field of study is control system analysis and design. He is now working as Assistant
Professor in Synergy Institute of Technology, BBSR since last eight years. He has published
three papers in international journals. His current research interest is soft computing
application in the field of control system. He is a life member in ISTE. He is also a senior
member in Institution of Engineers, India. He can be contacted at email:
bal.subhakanta@gmail.com.
Mr. Srinibash Swain was born on 21st May 1970 in Odisha, India. He completed
his M.E. degree in Power System Engineering in 2001 from VSSUT, Burla, Odisha, India. He
has completed his Ph.D. degree in BPUT, Rourkela, and Odisha, India in 2019. His major field
of study is control system analysis and design. He is now working as Professor in Rajdhani
Engineering College, BBSR since last one year. He has published five papers in international
journals. His current research interest is soft computing application in the field of control
system. He is a life member in ISTE. He is also a senior member in Institution of Engineers,
India. He can be contacted at email: swainsrinibash@gmail.com.
Dr. Partha Sarathi Khuntia was born on 06th oct. 1969 in Odisha, India. He
completed his M.E. degree in Automatic Control System and Robotics from MS University,
Varodara in 1999. He has completed his Ph.D. degree from ISM Dhanbad in 2011. India. His
major field of study is intelligent control, digital signal processing, and soft computing. He is
now working as Professor in GMRIT, Rajam, Srikakulum, and Andhra Pradeesh. He has
published many papers in national and international journals. His current research interest is
advanced control theory and its application. He is a life member in ISTE. He is also a senior
member in Institution of Engineers, India. Recent advances in Electrical Engineering and
Computer Science ISBN. He can be contacted at email: parthsarathi_K@yahoo.com.

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