Abstract: -
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 GA and 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) etc. 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.
K
ey-Words: Proportional–Integral (PI), ParticleSwarmOptimization (PSO), TeachingLearningbased
Optimization (TLBO), Genetic Algorithm (GA), Mean Square Error (MSE), Integral Absolute Error (IAE).
Received: February 25, 2023. Revised: November 17, 2023. Accepted: December 18, 2023. Published: January 30, 2024.
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. [5] Different
soft computing techniques like Fuzzy Model
Reference Learning (FMRLC) 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 TLBO is incorporated in this
paper mainly for adjusting the angle of attack as
well as upgrading the overall achievement of the
proposed system. [6-12]. Finally a comparison
is made between the results of TLBO and
conventional 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 PI controller for nonlinear
second order plants was suggested by Rahul
kumara, IdamakantiKasireddy, Abhishek Kumar, A
K Singh. in an organized manner. [1] The regulating
of a PI controller for a control system was verified
by Zhenglong Xiang, Xiangjun Shao et all in a
number of ways. [2] A better proposal was proposed
by SahajSaxena, Yogesh V Hote, for determining
the gain of a Proportional Integral controller. [3]
Later an easy and quick method for tuning a PID
controller was jointly analyzed by M. A. Abdel
Ghany, M. E. Bahgat, W. M. Refaey, SolimanSharaf
in a precise manner [4]. The various types of
methods needed for estimating the angle of attack of
a flight were clearly described by L.Sankaralingam,
C.Ramprasadh in 2019. [5] Two-stage teaching-
learning-based optimization method for flexible job-
Determination of Attacking Angle of Aircraft in Bio Inspired
Optimized Technique
SUBHAKANTA BAL1, SRINIBASH SWAIN2, PARTHA SARATHI KHUNTIA3,
BINOD KUMAR SAHU4
1Dept. of Electrical Engineering, Bijupattnaik University of Technology, SIT, Odisha, INDIA
2Dept. of Electrical Engineering, Nalanda Institute of Technology, Bhubaneswar, Odisha, INDIA
3Dept. of Electronics & Telecommunication Engineering, KIST, Khurda, Odisha, INDIA
4Dept.of Electrical Engineering, ITER, SOA University, BBSR, Odisha, INDIA
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.7
Subhakanta Bal, Srinibash Swain,
Partha Sarathi Khuntia, Binod Kumar Sahu
E-ISSN: 2769-2507
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Volume 6, 2024
shop scheduling was suggested by R. Buddala and
S. S. Mahapatrain 2019. [6] S. T. Suganthiet all
proposed an improved teaching learning based
optimization algorithm. [7]. A modified teaching–
learning-based optimization algorithm for numerical
function optimization was suggested by P. Niuet all.
[8]M. Shahrouzi, F. Rafiee-Alavijeh and M.
Aghabaglou suggested an hybrid bat algorithm and
teaching–learning based optimization.[9] A novel
TLBO with error correction for path planning of
unmanned air vehicle was proposed by Z. Zhai, G.
Jia and W. Kai. [10] Z. Zhang, H. Huang, C. Huang
and B. Han suggested an improved TLBO with
logarithmic spiral and triangular mutation for
global optimization. [11] Nayak et al proposed
an Elitist teaching–learning-based optimization
(ETLBO) with higher-order Jordan Pi-sigma
neural network. [12]. Yang et al. proposed a
multiobjective genetic algorithm on an accelerator
lattice [13]. In addition, Gaing proposed a particle
swarm optimization method to solve the economic
dispatch [14]. Evtushenko and Posypkin suggested a
new method in 2013 for global box -constrained
optimization [15]. Yassami M & Ashtari PA in 2013
proposed a novel hybrid optimization algorithm
[16]. Storn R, Price K on 1997 proposed on.
Diferential evolution for global optimization over
continuous spaces [17]. In 2005, a fuzzy adaptive
diferential evolution algorithm on soft computing
was suggested by. Liu J, Lampinen J. A [18].
Dorigo M et al proposed on ant colony optimization
in 2006 & 2008 respectevely [19 20]. Placement of
wind turbines using genetic algorithms was
suggested by Grady SA, Hussaini MY, Abdullah
MMin 2005[21]. On 2009, GPU-based parallel
particle swarm optimization was proposed by Zhou
Y & Tan Y. [22]. A survey on new generation
metaheuristic algorithms was jontly suggested in
2019 by Dokeroglu T, Sevinc E, Kucukyilmaz T &
Cosar A [23]. Hussain K, Salleh MNM, Cheng S,
Shi Y. done a comprehensive survey on Artificial
Intell Rev.in 2019[24]. Various works on Particle
Swarm Optimization using different techniques
ware proposed by Fang H, Zhou J et al [25 28].
PSO-based memetic algorithm for flow shop
scheduling was suggested by. Liu B, Wang L, Jin
YH. in 2007[29]. Yang J, He L & Fu in 2014
suggested an improved PSO-based charging strategy
of electric vehicles in electrical distribution grid
[30].
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 and conventional methods, it was found that
TLBO performs better in all aspects than GA and
PSO methods for tuning the PI controller.
2. Block Diagram for determining the
Angle of Attack
Fig.1: (Schematic diagram of angle of attack for an
aircraft system.)
Where
s
E
= the deflection angle of elevator.
= angle of attack of the aircraft
G(s) = the forward path gain
C(s) = proposed PI controller
3. Relation between the Elevator
Deflection
E
and Angle of Attack
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
below.
Fig.2: (Description of angle of attack)
Aircraft speed (u), is changed due to the deflection
in control surfaces and atmospheric turbulence etc.
Mainly the approximation relating to short period
deals with varying flight speed (u) and it consists of
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.7
Subhakanta Bal, Srinibash Swain,
Partha Sarathi Khuntia, Binod Kumar Sahu
E-ISSN: 2769-2507
65
Volume 6, 2024
very short duration. The speed of the aircraft
0
U
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:
Ew s
ZqUwZw
0
(1)
Eqww z
MqMwMwMq
(2)
Ew
wqwww
MM
qMUMwZMM
z
0
Ewwqwww MZMqMUMwZMM zz
)()() 0
Calculation of state vector for short period motion
may be written as
q
w
x
Where
E
and ‘
u
’ are the angle of
deflection and control vector respectively, then
the state equation for the above two equations
can be written as
(3)
Where as
wqwww
w
MUMZMM
UZ
A
0
0
,
w
MZM
Z
B
EE
E
AsI
wqwww
w
MUMZMM
UZ
s
0
0
10
01
wqwww
w
MUMZMM
UZ
s
s
0
0
0
0
wqwww
w
MUMsZMM
UZs
0
0
AsIs
sp det
wqwwqw MUMZsMUMZs 00
2
22 2spspsp ss
(4)
In equation (4)
,2 0wqwspsp MUMZ
2
1
0wqwsp MUMZ
(5)
s
s
ZMMU
Z
ZMMU
s
sw
sp
q
q
E
EE
E
EE
0
01
s
sTK
sp
w
1
1
Where
EE ZMMUK qw
0
And
w
K
Z
TE
1
Again,
0
U
w
Again,
0
U
w
0
U
sw
s
sUsw
0
sU
sTK
s
s
sp
w
E
0
1
1
(6)
3.1 Stability Derivatives of Aircraft
(CHARLIE)
The standard values of stability derivatives for
CHARLIE aircraft in three different situations are
depicted below.
Table 1
BuAxx
Source: Donald Mc Lean (1990)
Flight Condition(FC)
FC-1
FC-2
FC-3
1
0
msU
67
158
250
u
X
-0.021
0.003
-0.00002
w
X
0.122
0.078
0.026
E
X
0.292
0.616
0.0
w
Z
-0.512
-0.433
-0.624
q
Z
-1.9
-1.95
-3.04
E
Z
-1.96
-5.15
-8.05
w
M
-0.006
-0.006
-0.005
q
M
-0.357
-0.421
-0.668
E
M
-0.378
-1.09
-2.08
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3.2 Transfer Functions of different Flight
Conditions
Transfer functions corresponding to three different
flight conditions can be obtained after putting the
above parametric values in equation (6) respectively
are shown below in table-2.
Table 2
4. Conventional Methods
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.
5. Proposed Optimization Soft
Computing Techniques
To tackle the various types of practical problems in
different fields, a number of optimization methods
have been applied. Among them TLBO method is
considered as better than others.
5.1 TLBO (Teaching Learning Based
Optimization)
After the application of TLBO in
engineering fields it has become very popular after
its initiation by Rao et al. Its quality of solution,
time consumption and stability analysis is better
than others. Generally, TLBO performs in two
different phases: In the preliminary phase, learner
acquired knowledge through their respective
teachers known as teacher phase but in second stage
learner learns among themselves by way of
interactivity is generally called as learner phase.
TLBO algorithm includes the following steps.
5.2 Initialization
Initially the size of population [NP D] is
taken arbitrarily during this step, where NP shows
the population strength and D shows the number of
subjects offered. The different marks scored by
students in the
th
i
subjects are shown in
corresponding
th
i
column respectively.
Initial Population=
DNPNPNP
D
D
xxx
xxx
xxx
,2,1,
,22,21,2
,11,1
........
....
....
...
...
2,1
5.3 Teacher Phase
In this phase maximum effort is given by the
assigned teacher for improving the mean result of
the class. Since the learners are trained through the
teachers, the solution
best
X
for best learned person
automatically goes to that particular teacher. The
mean marks scored by different students in different
papers are calculated below.
Dd mmmM ,......,, 21
(7)
Whereas
1
m
is the aggregate marks secured by the
students in
ith
paper. The dissimilarity in mean
results of a particular teacher is represented as
dFbestdiff MTXrandM 1,0
In which rand
1,0
is chosen arbitrarily as
0
or
1
and
F
T
as teaching factor.
F
T
is taken arbitrarily
either1 or 2.
1,01 randroundTF
(8)
In equation (9) below, the exiting population is
renewed as
Flight
Conditions(FC)
G(S)
(Transfer Functions)
FC-1
11546.2695.1
65835.004936.0
2
1
SS
S
SG
FC-2
159469.18849.0
978.00128.0
2
2
SS
S
SG
FC-3
1525.1599.0
26.10193.0
2
3
SS
S
SG
diffnew MXX
(9)
new
X
is accepted if
new
X(
) <
)(Xf
, where
)(Xf
is taken as the objective function.
International Journal of Electrical Engineering and Computer Science
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5.4 Learner phase
Here, for improving the knowledge of a student a
selection is made by the teacher randomly through
interaction. A student can able in enhancing his
knowledge successfully than other students through
interaction if the others are better than him. The
learning procedure is given below.
i
X
And
j
X
are the two randomly preferred learners
in which
i
≠
j
jiinew XXrandXX 1,0
. If
jj XfX
(10)
ijinew XXrandXX 1,0
.Take
new
X
as
granted if better performance is found.
6. 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
Figure 3-14 below. 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 Particle Swarm Optimization (PSO) and Genetic
Algorithm (GA) procedures.
Fig. 3: Deviation of
W
Z
by -50%
Fig.4: Deviation of
W
Z
by -25%
Fig.5: Deviation of
W
Z
by +25%
Fig.6: Deviation of
W
Z
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 -25%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25
0
0.5
1
1.5
Step Response of GA, PSO & TLBO
(Deviation of Zw by +50%)
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 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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Fig.7: Deviation of
q
M
by -50%
Fig.8: Deviation of
q
M
by -25%
Fig.9: Deviation of
q
M
by +25%
Fig.10: Deviation of
q
M
by +50%
Fig. 11: Deviation of
W
M
by-50%
Fig.12: Deviation of
W
M
by-25%
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 Mq by-25%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25 30
0
0.5
1
1.5
Step Response of GA, PSO & TLBO
(Deviation of Mq by +50%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25 30
0
0.5
1
1.5
Step Response of GA, PSO & TLBO
(Deviation of Mq by +50%)
Time (seconds)
Amplitude
GA
PSO
TLBO
010 20 30 40 50 60
0
0.5
1
1.5
Step Response of GA, PSO & TLBO
(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
Step Response of GA, PSO & TLBO
(Deviation of Mw by -25%)
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
Step Response of GA, PSO & TLBO
(Deviation of Mq by-50%)
Time (seconds)
Amplitude
GA
PSO
TLBO
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Fig.13: Deviation of
W
M
by+25%
Fig.14: Deviation of
W
M
by+50%
7. 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 IAE, ITAE, and
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
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
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 figs.15-18.
Thus, the analysis shows better result for
TLBO optimized PI controller than PSO and
GA methods.
0 5 10 15 20 25 30 35 40 45 50
0
0.5
1
1.5
Step Response of GA, PSO & TLBO
(Deviation of Mw by+50%)
Time (seconds)
Amplitude
GA
PSO
TLBO
0 5 10 15 20 25 30
0
0.5
1
1.5
Step Response of GA, PSO & TLBO
(Deviation of Mw by+25%)
Time (seconds)
Amplitude
GA
PSO
TLBO
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.7
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E-ISSN: 2769-2507
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Fig.15: IAE among TLBO, PSO & GA
Fig16: ITAE among TLBO, PSO & GA
Fig.17: MSE among TLBO, PSO & GA
Fig: 18: Ts among TLBO, PSO & GA
0
5
10
15
20
25
-50% -25% +25% +50%
TLBO
PSO
GA
0
0.5
1
1.5
2
-50% -25% +25% +50%
TLBO
PSO
GA
0
0.2
0.4
0.6
0.8
1
-50% -25% +25% +50%
TLBO
PSO
GA
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Table 5
Parameters
% Deviation
GA
PSO
TLBO
IAE
ITAE
MSE
IAE
ITAE
MSE
IAE
ITAE
MSE
w
Z
-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
q
M
-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
0
U
-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
w
M
-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
E
M
-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
Z
-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
Table 6
Parameters
%Deviation
GA
PSO
TLBO
Ts
Ush
Osh
Ts
Ush
Osh
Ts
Ush
Osh
w
Z
-50
23.9
16,67
24
6.16
16.88
24
4.32
20.10
29.9
-25
21.1
17.54
26
6
18.3
27
5.62
21.26
33.6
+25
16
18.98
30.5
6.36
21.11
34.8
5.77
22.74
40.8
+50
13.5
19.86
33.4
6.71
22.27
40.4
6.28
20.89
36.1
q
M
-50
23.5
17.23
25.2
6.07
17.73
25.6
5.58
20.67
31.7
-25
20.9
17.61
26.6
6.04
18.19
27.8
5.69
21.48
34.2
+25
16.4
18.93
29.8
6.29
20.48
33.6
5.84
22.88
39.8
+50
14.1
19.18
31.7
6.52
21.72
37.2
5.82
23.17
42.7
0
U
-50
7.11
17.79
25.6
12.6
23.84
52
4.39
22.52
35.1
-25
11.3
17.34
25.7
6.98
22.02
35.7
5.69
23.76
41.7
+25
27
18.92
30.6
7.99
18.78
29.4
5.74
21.46
35.3
+50
36.3
19.95
32.8
11.8
18.63
29.9
8.69
23.23
48.4
w
M
-50
27
15.97
23.5
8.03
16.1
23.3
5.66
23.47
41.5
-25
22.8
17.05
25.7
6.15
17.78
26.6
5.66
22.36
37.5
+25
14.4
19.43
31
6.28
21.38
35.2
5.82
23.29
40.9
+50
10.4
20.98
34.2
6.57
23.49
40.8
6.22
21.81
36.8
E
M
-50
15.4
21.6
37.2
5.18
21.99
37.9
5.1
21.76
37.5
-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
30.3
+50
20.8
9.02
11.7
5.04
14.2
18,7
4.81
15.56
20.8
Z
-50
12.9
14.59
20.3
5.5
20.16
30.2
5.48
20.89
32
-25
15.3
16.23
23.7
6.43
19.85
29.7
5.65
21.74
34.2
+25
22.7
20.23
34.1
7.56
20.62
33.6
6.34
23.03
41.1
+50
25.9
23.16
44
9.84
21.74
40.1
7.52
23.53
44
In Table -5, variation of performance indices like Integral Time Absolute Error (ITAE), mean square error
(MSE), Integral Absolute Error (IAE) etc. are demonstrated.
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.7
Subhakanta Bal, Srinibash Swain,
Partha Sarathi Khuntia, Binod Kumar Sahu
E-ISSN: 2769-2507
72
Volume 6, 2024
8. Result Analysis
A step input is given for studying the
behavior of a PI run flight system. Result
obtained is compared with that of Genetic
Algorithm
(GA) and Particle Swarm
Optimization (PSO) methods.
It is obvious that
the TLBO optimized PI managed device
additionally offers higher dynamic response
when subjected to a parametric change.
In Table-3 & 4, deviation of performance
indices like ITAE (Integral Time Absolute
Error), MSE (Mean Square Error), IAE
(Integral Absolute Error) etc. are depicted
along with settling time, undershoots and
overshoots. In each and every case it
s
hows
less error for IAE, ITAE and MSE and less
settling time also in TLBO optimized PI
controller than that of Genetic Algorithm
(GA) and Particle Swarm Optimization (PSO
). In
addition to this, Table-5 and Table-6 indicate
the various analytical results of IAE, ITAE,
MSE, settling time, undershoots and
overshoots 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 figs.15-18. Thus, the
above analysis 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 figure 3-14 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.
9. 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 behaviour 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 favour of TLBO and retuning of
parameters is not necessary over a wide range.
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International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.7
Subhakanta Bal, Srinibash Swain,
Partha Sarathi Khuntia, Binod Kumar Sahu
E-ISSN: 2769-2507
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Volume 6, 2024
Contribution of Individual Authors to the
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Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
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International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2024.6.7
Subhakanta Bal, Srinibash Swain,
Partha Sarathi Khuntia, Binod Kumar Sahu
E-ISSN: 2769-2507
75
Volume 6, 2024
