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IETE Journal of Research
ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/tijr20
Performance Comparison of ANFIS, FOPID-
PSO and FOPID-Fuzzy Tuning Methodology for
Optimizing Response of High-Performance Drilling
Machine
Arti Saxena, Y.M. Dubey, Manish Kumar & Abneesh Saxena
To cite this article: Arti Saxena, Y.M. Dubey, Manish Kumar & Abneesh Saxena (2021):
Performance Comparison of ANFIS, FOPID-PSO and FOPID-Fuzzy Tuning Methodology for
Optimizing Response of High-Performance Drilling Machine, IETE Journal of Research, DOI:
10.1080/03772063.2021.1933625
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Published online: 14 Jun 2021.
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IETE JOURNAL OF RESEARCH
https://doi.org/10.1080/03772063.2021.1933625
Performance Comparison of ANFIS, FOPID-PSO and FOPID-Fuzzy Tuning
Methodology for Optimizing Response of High-Performance Drilling Machine
Arti Saxena 1,2,Y.M.Dubey
3, Manish Kumar 3and Abneesh Saxena 4
1Electronics Engineering, Dr. APJ Abdul Kalam Technical University, Lucknow, India; 2Department of Electronics & Communication Engineering,
PSIT College of Engineering (PSITcoe), Kanpur, India; 3Department of Electronics & Communication Engineering, Pranveer Singh Institute of
Technology (PSIT), Kanpur, India; 4Ordnance Factory Kanpur, MOD, Kanpur, India
ABSTRACT
A fractional-order proportional integral derivative (FOPID)controller has replaced the classical PID
controller used in industries for process control application. FOPID is less sensitive to the change of
control parameters than PID Controller, due to which better results are obtained. The FOPID provides
a robust and stable system for a higher-order system as of iso- damping property. This study aims to
find a stable and controlled structure by tuning the FOPID controller with the Particle Swarm Opti-
mization (PSO) algorithm, fuzzy-based logic approach, and Adaptive Neuro-fuzzy inference system
(ANFIS). The tuning of FOPID is done to overcome deficits of PID controller using the different types of
optimization method to overcome large overshoot and large settling time. This paper presented use-
ful techniques based on PSO, fuzzy logic, and ANFIS to optimize FOPID controlled high-performance
drilling machines. On the analysis and comparisons of simulation findings, it is observed that the
FOPID-PSO approach provides better performance over the Ziegler-Nichols (ZN)-FOPID and the
above-mentioned intelligent techniques in terms of less settling time (ts=0.823sec.) & optimized
peak overshoot (Mp=2.44%) for the mentioned target.
KEYWORDS
ANFIS; fuzzy logic;
high-Performance drilling
machine; FOPID; PSO; ZN
1. INTRODUCTION
Optimization algorithms in today’s industries are an
emerging trend on which researchers and the manu-
facturing industries are currently working. The opti-
mization algorithms are used to calculate the value of
maxima and minima of goal function with constraint.
A well-known recognized mathematical approach of
optimization, i.e. articial intelligence or computational
intelligence, is used here in this paper for estimation.
Computational intelligence provides relative opinion.
The traditional tactics, just like ZN approach, modied
ZN approach do have a specic, truthful considerable
percentage in tuning possibilities to attain the optimized
values. Saxena et al. [1] proposed optimized PID tun-
ing methods in dierent forms like PID-PD, PI-PD,
two-degree freedom controller (PID-D, PID-PD), and
lead compensator using ZN and modied ZN method.
They found out that PID controlled drilling machine
optimized the overshoot, rise time, and settling time
at Mp=5.55%, tr=0.174sec, ts=1.28 sec., using the
modiedZNmethod[1]. However, for above-stated
paper’sdicultyisofovershootsandupwardrisetime
in higher-order systems, requiring extra deliberation on
this work to locate dierent optimizing methods for the
tuning methodology. Current optimization method, such
as PSO, fuzzy logic, and ANFIS, consists of capabili-
ties to develop an additional stable system and extra
profound results simultaneously considering the tuning.
This research paper worked on optimization algorithms
to enhance the high-performance drilling machine’s per-
formance and compare the PID controller results with
FOPID controller. This paper is dedicated to design-
ing a ZN tuned FOPID controller, fuzzy tuned FOPID
controller, ANFIS controller, and PSO tuned FOPID con-
troller for a high-performance drilling machine. The
paper is fragmented to show the best highlights: Section 1
presents the general introduction; Section 2discussion
on crucial aspects of the drilling machine, literature sur-
vey, motivation, and contribution of the present work;
Section 3discuss the modelling of drilling machine and
FOPID, explain the algorithm of PSO, fuzzy logic, and
ANFIS; Section 4simulation outcome and compare the
transient response of the system using a various opti-
mization algorithm, and Section 5conclude the paper
and discuss the future scope of this study.
2. LITERATURE REVIEW
Today’sindustriesdrillingprocessisthemostcommon
processthatiswidelyimplementedinvariousforms
© 2021 IETE
2 A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY
like underground tunnel diggers, oil diggers, Jig bor-
ing, or various types of CNC drilling operations. CNC
drilling is also done in various forms like drilling, ream-
ing, or honing operations. The drilling machine is also
describedbasedonsingle-shotorpolyshot.Thesingle-
shot machine forms one hole, while the poly shot is for
multiple drilling holes. Typical drilling machines are spe-
cially used in automobile industries with a rotating spin-
dle head and turn-table on which the job is mounted.
Drilling machines in today’s market are fully ooded
depends on the applications performed. The enhance-
ment in the drilling machine’s performance is done by
optimizing the constraints of the drilling process. The
productive drilling process includes a reduction in cycle
time, tool breakage, and cost. Optimized cutting param-
eters are generally provided in the data handbook but
cutting parameters are manually adjusted by the oper-
ator for the rst job, after which parameters are freeze
and then handover to automatic control. The drilling pro-
cess in industries has modelled diversely. The drilling
machine’s modelling relies upon several constraints like
cutting speed, feed rate, etc. Drilling of the job is also
best performed by using high-quality coolant like Blaser,
Grenova, Gulf that keep drill bit cooled through proper
heat transfer that benets for extra prolonged operation
performed on high speed without tool breakage which
in turn increase eciency. The selection of drill bits also
plays a vital role, which depends on the grade of material
on which operation is to be performed as it increases pro-
ductivitybyimprovedtoollife.Kimetal.[2]studiedthat
feed rate (f) and thrust force (F) are prime factors in the
drilling process [2]. Hsu P. and Fann W. [3]presentedthe
constant-force control for CNC machine centers using an
adaptive fuzzy logic controller with dierent cutting con-
ditions. They also proposed self-learning FLC for obtain-
ing better cutting performance. Results obtained from
the proposed adaptive SL-FLC have shown that it attains
a signicant enhancement of machining processes, and
it is useful in both sensitivity and stability under many
cutting settings. The adaptive SL-FLC’s eective use in
the CNC machining center indicated that the smart con-
trol approach incorporated in the adaptive SL-FLC is
feasible for many processing units.[3]. Liang et al. [4]
proposed a change in feed rate is the easiest option as
the feed knob is on the dashboard, which will override
feed [4]. S. M. Giriraj Kumar et al. [9]discussedthe
optimal regulation of PID controlled high-performance
drilling machine by PSO algorithm in governing the out-
put attained and hence reducing the integral of absolute
errors (IAE). The acquired value is equated with the con-
ventional tuning methods like the ZN method and has
shown improvement with less overshoot. The system is
less sluggish and decreases the IAE [9]. Lahoty et al. [20]
presented the modern optimization methods for tuning
the PID parameters for an unstable arrangement. The
main aim pertains to nd out the stable and fast sys-
tem by optimizing the PID controller by GA and PSO
algorithm and compared the attained outcomes with a
Ziegler Nichols conventional tuning method. The results
show that tuning of the PID controlled high-performance
drilling machines using evolutionary tuning approaches
provides a stable and fast system with lesser overshoot
[20].V. C h o p a r a e t a l . [ 5]proposedthetuningofthePID
controller through numerous intelligent techniques like
fuzzy logic, articial neural network (ANN), ANFIS, and
GA. They found that the AI-based technique provides
improved performance as compared to the conventional
approach [5]. Y. Z. Maulana et al. [6]revealedtheper-
formance comparison for tuning of PID controller using
ZN, Cohen Coon, cascade PID, FIS, and ANFIS sys-
tem for pasteurization process. They show that the PID
controller tuning using ANFIS provided a 0.27% over-
shoot, which is minutest as equated to other controllers.
Theneededpowerfortheheaterisalsothesmallest,
i.e. 0.48 KW using ANFIS. Finally, they concluded that
ANFIS tuned PID controller provided enhanced perfor-
mance compared to others [6]. Amar Kumar Barik et al.
[38] projected a community-based renewable μGmodel
with battery storage for load frequency studies. They
used a grasshopper optimization algorithm (GOA) for
a single objective function for tuning two PID regula-
tors utilized in the framework to oversee load demand
economically [38]. Atal Anil Kumar et al. [19]proposed
an optimized PID controlled high-performance drilling
machine by meta-heuristic algorithm Whale Optimiza-
tion Algorithm (WOA). It revealed a signicant enhance-
ment in the transient performance. It also revealed that
WOA-PID is better for several error measures [19]. Amar
Kumar Barik et al. [37]discussedtheoptimalload-
frequency regulation of 4-interconnected unequal hybrid
microgrids(μG) with the demand pattern. They tracked
down that the PSO-tuned PID regulators in individual
hybrid microgrids to encourage optimal load-frequency
regulation. [37].Md.AsifHasanetal.[7]presentedthe
DC motor’s speed control by ANFIS-PID technique and
compared this controller’s performance with a conven-
tional PID controller about ISE and ITAE. They con-
cluded that the ANFIS-PID controller’s performance is
on the upper hand compared to the conventional PID
controller [7]. Saxena et al. [8]comparedPIDtuned
third-order drilling machine system response for a dier-
ent optimizing algorithm such as PSO, Fuzzy, and mod-
ied ZN, which shows that PSO tuned PID controller
provided an optimized response in terms of less over-
shoot (MP=6.404%), minimum rise time and settling
time (tr=0.114 sec.& ts=0.836 sec.), respectively [8].
A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY 3
Manufacturing industrial hubs are prominently using
PID controllers for several years due to design ease
and costing. On the contrary, PID controller useful-
ness downsizes for the higher-order system due to the
introduction of resonance, integrator etc. Working of
researchersonthelatesttrendproposedaFOPIDcon-
troller, which provides benets to overcome decits of
the classical PID controller. Due to the nature of the
FOPID controller having the iso-damping property, they
are less sensitive to the variables aecting the system
and their tuning parameters, which helps to obtain an
optimized response. Fractional order calculus has been
acknowledged in the previous few years. J Liouville pri-
marily proposed the most signicant study of fractional
calculus in the year 1832. Riemann evolved the idea of
fractional integration in 1892. Previously limited knowl-
edge of available approaches, a fractional-order system
is worked out as an integer order version. However, sev-
eral methods have algebraic approaches to estimate the
fractional-order derivatives and integrals at the current
time. Saptarshi Das et al. [25]proposedthatnotuning
system for a FOPID controller is unequivocally valu-
able as they compared the performance of two design
methodologies called the frequency and time domain
tuning of the FOPID controllers. The rst approach has
improved performance in terms of robustness, enhanced
high-frequency noise elimination capability, lesser con-
trol signal value, and compact cylinder size. The sec-
ond tuning method is quicker but has lower robust-
ness, higher capacity to eliminate load disturbances, and
not remove the high-frequency noises eciently [25]. E.
Sahin et al. [24] projected the PSO optimized FOPID
controller for the DC-boost converter used in a pho-
tovoltaic system. They compared the system’s transient
response using FOPID and classical PID for various
power conditions and nd that the PSO-FOPID system
shown better performance in terms of minimum over-
shoot (Mp=0.8%) [24]. Ruchi V. Jain et al. [28]compared
PSO-PID and PSO-FOPID for controlling the speed of
DC motor. They nd out that FOPID controlled dc motor
given optimum response in terms of minimum overshoot
(Mp=2%) compared to the PSO tuned PID controlled
DC motor [28]. R. Singhal et al. [29] proposed the com-
parative study ofFOPID controlled DC motor for distinct
values of λand μ with PID controlled DC motor. They
have shown that FOPID controlled DC motor give an
optimized performance at λ=1.7 and μ =1.15[29]. M.
Al-Dhaifallah et al. [30] compared industrial pneumatic
pressure systems’ performance using conventional PID,
FOPID, and FFOPID(fuzzy FOPID) controller. They
have shown that the proposed FFOPID has improved
performance than the other two-controller as it has min-
imum settling time and less overshoot, and a proposed
controller scheme is simple and eective[30]. Abdul Latif
et al. [36] proposed Yellow Saddle Goatsh Algorithm
(YSGA) optimized dual-stage PIFOD-(1 +PI) controller
fordemandresponsesupportedco-ordinatedsystem.
After execution correlation of the dierent upgraded
calculation like PSO, GA, SSA, and YSGA, and they
found that YSGA advanced PIFOD-(1 +PI) regula-
tor is better at these boundaries, for example, top
deviations ( +Opt, −Upt), settling time, JFOD and
JISE/JIWSE [36].
Motivation of the Present Work:
The survey of various literature discloses that very few
previousresearchershaveworkedonthePIDandFOPID
controller’s tuning for optimizing the performance of the
high-performance drilling machine. The earlier research
works simulation outcomes have some decits. The pre-
vious research done on PID tuned high-performance
drilling machine by S. M. Giriraj Kumar et al. [9], Atal
Anil Kumar et al. [19]&Lahotyetal.[20]hashighover-
shoot 18%,31%, and 36.2%, respectively, and A. G. Mar-
tin et al. [18] rise time is very high, nearly 2.34 sec. It has
motivated the author to work in this arena to develop a
system that provides less overshoot, fast response, and
better stable response for optimized performance. The
author has gone through various previous research work,
which is shown in Table 1.FromtheanalysisofTable1,
it is found out that when PID and FOPID are applied
onthesamesystem,thenFOPIDprovestobeabetter-
optimized system in terms of less overshoot and less
settling time. FOPID controller, tuned by modern opti-
mization techniques like PSO, which may overcome these
limitations of the high-performance drilling machine by
reducing ts,andM
P,whichmaydecreasetheobjective
function value in an overall manner to optimize the sys-
tem performance. Thus, an approach has been worked
outsothatthehigh-performancedrillingmachinesys-
tem’s transient response may be closer to the optimal
one. Thus, an eort has been made to deploy the PSO,
Fuzzy, and ANFIS algorithm as a tool for nding the
optimum values of the transient performance parameters
for high-performance drilling machines in the present
work.
Contribution of the Present Work:
The signicant compilation of work done is given below:
•Optimize the ZN tuned FOPID controller val-
ues (Kp=0.525, Ki=1.722, Kd=0.040, λ=1.1, μ =
1.15) for the high-performance drilling machine
system.
4 A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY
Table 1: Previous work related to FOPID and PID controller for different systems
Controller/ Rise Time Peak Time Settling Peak Over-
References System Algorithms (tr) (tp) Time (ts) Shoot (Mp%)
Hekimoglu, Baran [31] DC Motor ASO-PID 0.0483 - 0.0982 0
ASO-FOPID 0.0531 - 0.0650 0.3577
ChASO-FOPID 0.0183 0.0282 0.5256
S. Chaudhary et al. [32] Twin Rotor MIMO 1-DoF PID 0.9976 - 2.371 1.018
System (Horizontal 2-DoF PID 0.9976 - 1.999 1.012
Plane) FOPID 1 - 1.652 0
M. Al-Dhaifallah et al. [30] Pneumatic Pressure PID - - 14 6.5
System FOPID - - 12 2
Fuzzy-FOPID - - 7 0
Mohamed A. K. Level process PID 22 - 155 15
El-Shafei et al. [33] control FOPID 16.4 - 43 5.6
Basu et al. [34] Heating Furnace PID - - 295.5 36
FOPID - - 258.6 8.5
RuchiV.Jainetal[28] DC Motor PSO-PID 2.82e−5- - 6.89
PSO-FOPID 7.0e−5-- 2
A. Singh and CSTR PSO-PID 0.107 0.271 1.164 25.14
V. Sharma[13] PSO-FOPID 0.136 0.276 0.321 3.80
Vishal et al. [14] DC Motor PID 0.175 0.53 9
FOPID 0.2065 0.3 4
Rinku et al. [29] DC Motor PID - 1.9937 5.5025 29.5939
FOPID - 2.1774 5.0176 15.2073
K.Sundaravadivu et al [15] Spherical Tank PID - - 60 20.1
(liquid level control) FOPID - - 38.1 0
M.Zamani et al [16] Autumatic Voltage PID - - - 88
Regulator PSO-FOPID - - - 20
∗ChASO- Chaotic Atom Search Optimization, DoF-Degree of Freedom, CSTR- Continuous Stirred Tank Reactor
•Optimize the PSO tuned FOPID controller values
(Kp=0.473,Ki=0.874, Kd=0.114, λ=1.05, μ =1.05)
for the high-performance drilling machine system.
•Optimize the fuzzy tuned FOPID controller val-
ues (Kp=0.252, Ki=0.55, Kd=0.0554, λ=0.988,
μ=1.05) for the high-performance drilling machine
system.
•The model projected on ANFIS is veried as the dier-
ence in training RMSE(root mean square error), and
checking RMSE is 0.016, which is acceptable.
•Compare the step responses of high-performance
drilling machine tuned by ZN-FOPID, PSO-FOPID,
Fuzzy-FOPID, and ANFIS with other optimization
methods stated in the recent literature references.
•The analysis and examination of simulation results
are bring out in Table 7.Ithasbeenfoundthatthe
proposed PSO approach has shown improved perfor-
mance regarding less rise time (tr=0.175 sec.) and
optimized peak overshoot (Mp=2.44%) for the sys-
tem. That means the PSO-tuned FOPID controlled
system shows faster and better responses with con-
trolled overshoot.
3. SYSTEM MODELLING AND OPTIMIZATION
METHODS
3.1 Modelling of a High-Performance Drilling
Machine
The drilling machine modelling comprises the modelling
of the spindle system, feed drive system, and cutting
force. The transfer function of the proposed system
(high-performance drilling machine) is the ratio of cut-
ting force and command feed [21]. It has been mod-
elled as a third-order open-loop system, which makes it
possible to estimate drilling procedure while operating
in close proximity to formal parameters as indicated in
Equation (1).
G(S)=F(s)
f(s)=1958
s3+17.89s2+103.3s+190.8 (1)
Where s - Laplace operator, F - cutting force, and f -
command feed.
The third-order closed-loop transfer function of a high-
performance drilling machine is described by Equation
(2), and its step response is revealed in Figure 1.
T(s)=1958
s3+17.89s2+103.3s+2148.8 (2)
Figure 1shows an unstable response of a drilling machine
that is stabilized through the PID controller’s tunning
usingtheZNandmodiedZNmethod[1]. However,
using a traditional ZN tuned PID controlled drilling
machine, overshoot is very high (Mp=46.6%), and the
system takes more time to reach the steady-state value[1].
The same limitations of the ZN-PID method for the pro-
posed system are also discussed by S. M. Giriraj Kumar[9]
&PranayLahoty[20]. To overcome the limitations of
tuning of PID controlled using the traditional method,
previous researchers [8,9,18,19,20] tuned the PID con-
troller for the drilling machine using AI-based meth-
ods like PSO, fuzzy, and ANFIS. They found that the
A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY 5
Figure 1: Transient response for step input high-performance
drilling machine
AI-based method, as mentioned earlier shown better per-
formance as compared to the traditional. However, some
scope is still there for the betterment of system’s response
in terms of overshoot. The author is applying the FOPID
using various tuning methods for drilling machines to
bring down the peak overshoot.
3.2 Modelling of a FOPID controller
Podlubny released the paper on fraction PID controller
in 1994 [26–27]. He considered a fractional-order sys-
tem, and it has been detected that the FOPID controller
hasanadequatemeansofcontrollingafractional-order
system. FOPID is the latest development over conven-
tional PID.FOPID, in simple terms, can be dened as
aparameterrelatedtotheoptimizedchangingcoe-
cient. FOPID has overcome decits of classical PID in
terms of robustness and stability. For the higher-order
system, FOPID produces better results than PID with
low overshoot and short settling time. FOPID attains the
property of iso damping, which helps a lot for improved
performance. The P, I, D, λ(lambda), μ(mu) coecients
are taken into account to control the system’s dynamic
properties. The number of pending control parameters
is reduced from which estimation model is derived to
get optimized FOPID controller parameters that are then
calculated numerically.
The mathematical pattern of the FOPID controller
dynamics is given below in Equation (3).
C(s)=U(s)
E(s)=Kp+KI
sλ+KDsμ(3)
Where C(s)-controller transfer function, U(s)-control
signal, E(S)-error signal, KP-proportionalgain,K
I-
Figure 2: a) Classical controller b) FOPID controller
integral gain, KD- derivative gain, λ- integration order,
and μ- derivative order.
Traditional PID controllers are one specic case of frac-
tional controllers, in which λ=μ=1(Figure2a). In
the PID plane, rather than bouncing between four xed
focuses in the plane, it is feasible then to travel through-
out the plane constantly. The order of fractions taken into
consideration lies between 0 and 2 here (Figure 2b). It
may be anticipated that the FOPID can oer higher over-
all performance with controller parameters’ right prefer-
ence. However, the related optimization trouble might be
extra tough to deal with for tuning of extra parameters.
It is inspired to extend a precise method for the FOPID
optimization to obtain overall enhanced performance.
3.3 Particle Swarm Optimization (PSO)
PSO (optimization algorithms) optimize the PID con-
troller’s benet for advanced system performance. Dr.
Eberhart and Dr. Kennedy in the year 1965 dened rules
for computational optimization based totally on collabo-
rationandanimalactivitiessuchasbirdsthatcongregate
referred to as PSO. PSO could be very appropriate for
locating the solution to a non-linear problem [10–12,35].
The use of PSOs has been signicantly increased in this
contemporary area. PSO has decided on a top-notch
improvement measure because of its eortlessness, little
computational expense, and good execution. The algo-
rithmic procedure is as follows for getting the iteration
done and nding the optimum tuning:
Start
1. Initialize particles with the random place and velocity,
i.e. (xi,y
j)and vpfor all sample iterative values.
2. Check for the threshold value for each particle.
xi≥rd(all random sample should be higher than
threshold rd)
yjerd(all random sample iteration should be spaced
equally within the sample size of the threshold)
6 A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY
vp↔xierd(all iterative sample values should have
dierent velocities within the sample size)
3. Mark the current value of the threshold to get stored
rd=stored threshold
Rrd =new reference
4. Compare the current threshold value with the next
iterative particle sample.
rd≤Rrd
if condition follows the update
Rrd =Stored threshold
If else
Rrd +1=new threshold
Compare and make a new threshold
Rrd +1≤Rrd +2
Repeat above till the number of iterations
5. Update after comparison
6. Repeat if criteria not met (Step 3)
7. Stop if criteria met
3.4 Fuzzy Logic
Lot A. Zadeh, in the year 1965, evolved a conceptual
approach based on reasoning, termed as a fuzzy logic
concept. Fuzzy common sense idea decreases the sys-
tem’s complexity by introducing fuzziness. Fuzzy works
on an anticipated value in preference to a denite value.
Function approximation is profound within the fuzzy
system wherein an appropriate set of rules is primarily
based on membership functions the usage of linguistic
labels is evolved. Figure 3shows the fuzzy control sys-
tem using the functional pattern [6]. Fuzzy inference
systems are of two types Mamdani and Sugeno. The pro-
cessing of those two structures is very much identical;
the numerical calculation of the output is dierent.Fuzzy
Figure 3: Outline schematic of the fuzzy system [6]
logic implementation has overcome traditional PID con-
trollers’ decits for the non-linear system, which have
substantial overshoot.
3.4.1 Fuzzy-FOPID Controller
Figure 4shows a fuzzy FOPID controller structure with
having two inputs (e & de/ dt) and ve outputs (Kp,K
i,
Kd,λ,μ). The input (e & de/ dt) is shown in Table 2.
Membership function is assigned in seven linguistic lev-
els. The limits for input variables are [−3to3].Therange
of these outputs (Kp,K
i,K
d, λ, μ) is from 0.2–0.3, 0.4–0.7,
0.04–0.08, 0–2, and 0–2, respectively.
Fuzzy 3-D control surface for one of the control output
variables (Kp), (Ki), (Kd), (λ), and(μ) is shown in Figure
5,Figure6,Figure7,Figure8,andFigure9,respectively.
Optimized value of Kp=0.252, Ki=0.55, Kd=0.0554,
λ=0.988 and μ =1.05 is calculated from Figures [5–9]
respectively.
3.5 Adaptive Neuro-Fuzzy Inference System
(ANFIS)
The theory of ANFIS was presented by Jang in 1993
[17], and its outcomes are incredible in the modelling of
complex non-linear problems. According to Jang, ANFIS
is a distinct form of neural network which syndicates the
Figure 4: Mamdani structure (fuzzy FOPID controller)
Table 2: Membership function parameters (params) for e &
de/ dt
Linguistic Member Function Membership function
Input Level Type parameters (params)
e & de/ dt NB Trapezoidal [−3−2.8 −2.5 −1]
NM Triangular [−3−20]
NS Triangular [−3−11]
Z Triangular [−202]
PS Triangular [−113]
PM Triangular [0 2 3]
PB Trapezoidal [1 2.5 2.8 3]
A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY 7
Figure 5: Control surface viewer for proportional gain (Kp)
Figure 6: Control surface viewer for Integral gain (Ki)
Figure 7: Control surface viewer for derivative gain (Kd)
characteristics of equally neural networks and fuzzy logic.
That means ANFIS has knowledge rules of ANNs and the
linguistic transparency of the fuzzy logic concept within
adaptive networks’ structure.
ANFIS builds up a Takagi Sugeno FIS with the input-
output data set. The Sugeno-type systems are more com-
putationally ecient than the Mamdani type. In the FIS,
Figure 8: Control surface viewer for lambda(λ)
Figure 9: Control surface viewer for mu(μ)
the membership functions usually have to be manually in
tune with trial and error. The FIS structure implements
like a white box signies that the structure designers can
determine how the model accomplished its goal. On the
otherhand,ANNsperformlikeablackboxconcerning
how the aim is succeeded. The general arrangement of
ANFIS is of ve layers with having two inputs and one
output, as shown in Figure 10. The rst layer of ANFIS
only has adaptive nodes, and each node produces the
membership positions of a linguistic label. The second
layer nodes are xed nodes (wi), where each node com-
putes the ring strength of every rule using the fuzzy
AND (e.g.min) or other operators. The third layer also
has xed nodes (−→
wi) where the nodes determine the pro-
portions of the rule’s ring strength to the sum of all
the rules ring strength. The fourth layer’s nodes are
adaptive, all using a node function (−→
wifi), and the fth
layer has a single xed node (i
−→
wifi)thatcalculatesthe
resulting output as the summation of all signals.
The design steps of ANFlS are as follows:
(1) Some complete input data sets are chosen.
(2) Specied the total data set into two measures a)
training data set b) checking data set.
8 A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY
Figure 10: General layout of ANFIS in Five layers [17]
(3) Sugeno FIS is used for the proposed ANFIS. (For this
work number of membership functions is seven, and
the rules are 49).
(4) Some epochs are selected to begin the training.
(5) The proposed model of ANFIS is veried & (root
mean square error) RMSE is calculated.
In this study, the error backpropagation algorithm
method is used for training the membership functions
ofANFIS.Theerror(e)andtherateofchangeoferror
(de/dt)aretheinputsfortheproposedadaptiveneuro-
fuzzy controller, while the outputs are u (control output).
Error(e) and the rate of change of error (de/dt) have seven
linguistic member functions and are dened for range
[−2to2],andu(controloutput)isalsodenedforrange
[−2 to 2]. The projected method has been realized using
ANFIS editor in MATLAB, as shown in Figure 11.
The training and checking data set (input-output) has
been taken from a PID controller tuned with the tradi-
tional technique. For modelling, data obtained from the
PID controller, which is tuned using the ZN method,
equaling 186 observations separated into two sets: a) 138
Figure 11: Sugeno fuzzy system for proposed ANFIS
Figure 12: Training data for the proposed ANFIS
Figure 13: Training error for proposed ANFIS
Figure 14: (a): Training data output for proposed ANFIS. (b):
Checking data output for proposed ANFIS
training data sets b) 48 checking data sets. The training
data used for the training of ANFIS, which is shown in
Figure 12. After the training of the process, the model is
validated using checking data.
The backpropagation method is used for an optimum
training of FIS in the ANFIS editor using 135 epochs
(no. of iterations), which is shown in Figure 13. Minimal
A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY 9
Figure 15: Block diagram of ZN-FOPID tuned proposed system
Figure 16: Step response of ZN-FOPID tuned high-performance
drilling machine
training and checking RMSE is calculated by 0.219796
and 0.203278, respectively. The dierence in training
RMSE and checking RMSE is 0.016, which is acceptable,
and it concluded that the proposed model is valid. FIS
output of training and checking data for the proposed
ANFIS system is shown in Figure 14(a) and Figure 14(b),
respectively. The average testing error for training data
and checking data is calculated at 0.14097 and 0.12874,
respectively.
4. RESULTS AND DISCUSSION
4.1 ZN Optimized FOPID Controlled
High-Performance Drilling Machine
Controller gain values (Kp=0.525, Ki=1.722,and
Kd=0.040)for tuning of FOPID controller are taken
from ZN-PID controlled proposed system [1]. The Block
diagram of ZN-FOPID controlled high-performance
drilling machine is shown in Figure 15.Stepresponsefor
the proposed system using distinct values of λand μ is
shown in Figure 16.
Table 3: Transient Parameters ZN-FOPID controlled
proposed system
Controller Gain λμt
rtptsMp(%)
Kp=0.525 1.05 1.05 0.147 0.37 1.26 35.6
Ki=1.722 1.05 1.1 0.149 0.37 0.993 30
Kd=0.040 1.05 1.15 0.152 0.379 1.08 24.7
1.11.15 0.155 0.381 0.746 22.4
1.15 1.15 0.184 0.388 0.876 20.3
Saxena et al.[1] - - 0.136 0.363 1.56 46.6
Figure 16 and Table 3show that using the FOPID con-
troller, settling time and peak overshoot are compara-
tivelyreducedtoagreaterextentrelatedtoclassicalPID
controller for a proposed system [1]. From Table 3,we
calculated the optimized value of MP=22.4%, tr=0.155
sec, and ts=0.746 Sec. at λ=1.1 and μ =1.15.
4.2 PS0-FOPID Controlled High-Performance
Drilling Machine
Number of sizable counts of iterations had been exe-
cutedtodiscoverappropriateoptimumstandardsitua-
tions under distinctive function coecients. We discover
the better results for all furnished factors. The initial val-
ues of the parameters for the PSO set of rules are kept in
Table 4.
For optimize tuning of a FOPID controller using the PSO
algorithm, the value of Kp,K
i,K
dis calculated at 475
populations for minimum values of the tness function,
which is shown in Equation 4 [23] as follows:
Kp=0.473, Ki=0.874, Kd=0.114
F=(1−e−0.5)∗(MP+Ess )+e−0.5 ∗(ts−tr)(4)
F=3.154
Where, F represents tness function [23], Ess represents
steady-state error
PSO-FOPID tuned proposed system is shown in Figure
17, and corresponding parameters for tuning of FOPID
controller are shown in Table 5.
From the transient response of the PSO-FOPID con-
trolled high-performance drilling machine in Figure
Table 4: Initialization constraints for PSO algorithm
Global & Personal Learning Coefficient 2
Inertia Weight Damping Ratio(wdamp) 0.99
Inertia Weight(w) 1
Iterations 100
Population 50–500
10 A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY
Figure 17: Block diagram of PSO-FOPID tuned proposed
system
Table 5: Transient Parameters PSO-FOPID controlled pro-
posed system
Controller Gain λμt
rtptsMp(%)
Kp=0.473 1.05 1.1 0.103 1.5 1.56 2.02
Ki=0.874 1.05 1.15 0.0976 1.47 1.79 2.53
Kd=0.114 1 1.05 0.107 0.202 0.824 4.11
1.05 1.05 0.175 0.224 0.823 2.44
Figure 18: Step response of optimized PSO-FOPID controlled
high-performance drilling machine
18,wecalculatedtheoptimizedvalueofM
P=2.44%,
tr=0.175 sec, and ts=0.823 sec. at λ=1.05 and μ =1.05,
which is shown by Table 5.
4.3 Fuzzy-FOPID Controlled High-Performance
Drilling Machine
A Block diagram of the FLC-FOPID tuned proposed sys-
tem is shown in Figure 19, and corresponding parameters
for tuning of FOPID controller are shown in Table 6.
The transient response of a high-performance drilling
machine optimized by an FLC-FOPID controller for a
step input is represented in Figure 20.
Table 6: Transient Parameters Fuzzy-FOPID controlled pro-
posed system
KpKiKdλμt
rtptsMp(%)
0.252 0.55 0.0554 0.988 1.05 0.504 1.36 0.828 1.76
Figure 19: Block diagram of FLC-FOPID tuned proposed
system
Figure 20: Step response of optimized FLC-FOPID controlled
high-performance drilling machine
4.4 ANFIS Controlled High-Performance Drilling
Machine
Block diagram of ANFIS controlled high-performance
drilling machine is shown in Figure 21.
Step response of an ANFIS controlled high-performance
drilling machine is shown in Figure 22.
The high-performance drilling machine’s performance
optimization has been done in this paper using the
ZN-FOPID, PSO -FOPID, Fuzzy FOPID, ANFIS, and
corresponding step response is shown in Figure 16,
Figure 18,Figure20,andFigure22,respectively.All
these simulations were carried out using MATLAB, and
Figure 21: Block diagram of ANFIS controlled proposed system
A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY 11
Figure 22: Step response of ANFIS controlled proposed system
(high-performance drilling machine)
Table 7: Comparison of Transient Response Parameters for
Proposed Third-Order System using different Optimization
Approaches
Rise Peak Settling Peak
Time Time Time Overshoot
Method (tr)(t
p)(t
s)(M
p)(%)
PSO-PID[9] 0.170 0.200 1.400 18
PSO-PID[20] 0.113 0.282 2.560 36.200
PSO-PID[8] 0.114 0.223 0.836 6.404
FLC-PID[8] 0.213 1.420 1.690 2.290
Modified ZN-PID[1] 0.174 0.857 1.280 5.550
WOA-PID[19] 0.054 0.130 0.588 31
ANFIS-IMC[18] 2.340 2.480 — 0.0
PSO-FOPID (proposed) 0.175 0.224 0.823 2.440
ZN-FOPID (proposed) 0.155 0.381 0.746 22.400
ANFIS (proposed) 0.802 1.345 2.300 0.505
Fuzzy – FOPID (proposed) 0.504 1.360 0.828 1.760
an evaluation of all of the transient response parame-
ters made the use of distinctive optimization methods, as
shown in Table 7.
4.5 Discussion
The comparative study of all tuning techniques, for
example, FLC-FOPID, ANFIS, PSO-FOPID, ZN-FOPID,
and Whale optimization algorithm (WOA-PID), shows
FOPID tuning utilizing PSO gives better strength as
of the above-examined tuning strategies. The opti-
mization of FOPID using PSO is done in overall
aspects, such as peak time, rise time, settling time,
and overshoot. The aim of well-designed servo tun-
ing is to minimize response time, settling time, and
overshoot. The comparison of various transient perfor-
mance parameters for system response is also shown
with Chart-1 and Chart-2. The mathematical calcula-
tion that appeared in Table 7is acknowledged as of
accomplishment in getting optimum outcomes. Utiliz-
ing the PSO method, global and local arrangements
may simultaneously be settled for improved controller
imperatives’ tuning. The FOPID controller’s gain val-
ues, which are obtained by the ZN, PSO, and Fuzzy
logic,arebetterfromthePSO-PID[8], FLC-PID [8], and
modied ZN-PID [1] techniques in achieving stability
performances.
Table 7, Chart 1, and Chart 2 show the three signicant
facts, whose details are contemplated below:
•ANFIS controlled systems have nearly zero overshoot
(0.505%) with a large settling time, and the system is
very slow due to a signicant rise time value (0.802
sec).
•The proposed PSO-FOPID controlled structure oers
a speedy response (rise time =0.175 sec) with con-
trolled overshoot(2.44%) compared to all previous
research work [1,8,9,18,19,20], and all proposed men-
tioned methods in Table 7.
•Fuzzy FOPID tuned proposed system provides opti-
mal outcome looking towards rise time, settling time
(0.828 sec), and overshoot at the cost of high peak time
(1.36 sec).
Chart 1
Chart 2
12 A. SAXENA ET AL.: PERFORMANCE COMPARISON OF ANFIS, FOPID-PSO AND FOPID-FUZZY
The proposed PSO-FOPID system is having a controlled
overshoot, which is desirable in real-world working.
The minimum overshoot system reduces oscillations and
vibrationinthesystem,whichareinvariablyintroduced,
and thus better performance achieved. Vibrations crop
up in the load and the machine base from load inertia
mismatch, compliance in the mechanism, and mechani-
cal issues like improperly tensioned belts and loose cou-
plings. These vibrations are inducted into the feedback
loop and get ringing, overshoot, and large settling times.
Thesolutionistotuneeachaxistosuppressthevibra-
tion’s eects. In a perfect system, the axis would move
the load to the commanded position or speed with no
overshoot [22].
5. CONCLUSION
In this work, four optimizing techniques for tuning
of FOPID in an ecient way for better performance
of high-performance drilling machine has been pro-
posed. As a result, derived from Table 7,thePSO-
FOPID proposed controlled system with numerical out-
put (rise time =0.175 sec., settling time =0.823 sec.,
peak overshoot =2.44%) nds out the best path which
will help out to design the optimized system. In real-
worldmachineswithlessovershootandotheroptimized
parameters is required as this will reduce oscillations
and vibrations in the system and which in turn pro-
vide high-end machines. Results conrmed better tran-
sient response due to decreased settling time and lower
overshoot. This research paper helps designers to get
an improved advantage from using PSO. This method
provides a reduction in the count of ways to design a
controllerandprovidesabettersolutionfordesigning
the control system’s dynamic actions. This method trans-
forms the design from a complicated system to a simplex
manner. The PSO-tuned PID and FOPID controller’s
overall performance for any order system is compara-
tively better than tuning the PID controller using con-
ventional techniques like ZN method. Fuzzy-based and
ANFIS tuning has also helped produce some of the opti-
mum results in the current paper, eectively reducing the
overshoot values (Mp=1.76% and Mp=0.505% in fuzzy
FOPID & ANFIS, respectively). It shows an improved
identication of the FOPID controller readings using
PSO, fuzzy-based tuning, and ANFIS over the classical
ZN method. Finally, it is concluded that the PSO-FOPID
controller provides better results than the ZN-FOPID,
fuzzy FOPID, ANFIS in the design of a high-performance
drilling machine. This research paper will help the man-
ufacturing industry to get out the robust system with
less overshoot while optimizing the other controlling
parameters.
6. FUTURE SCOPE
The future scope will include the tuning of FOPID for
extra eective governing of high-performance drilling
machine and its comparison by PID controller tuned by a
various intelligent algorithm like Salp-Swarm Algorithm
(SSA) and GOA. Other opportunities for more eective
controlling of high-performance drilling machine will be
included in future work, such as model predictive PID
controller (MPC-PID) and its comparison with FOPID
controller tuned by various intelligent algorithm PSO,
GOA, and SSA.
ACKNOWLEDGMENTS
The authors appreciate the organizers of SPIN-2020, the
opportunity to the authors for submitting the extended ver-
sion of paper ID-608(https://ieeexplore.ieee.org/xpl/conhome/
9055889/ proceeding) in IETE Journal of Research.
ORCID
Arti Saxena http://orcid.org/0000-0002-2344-5489
Manish Kumar http://orcid.org/0000-0002-1686-8467
Abneesh Saxena http://orcid.org/0000-0001-9519-4386
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AUTHORS
Arti Saxena awarded B.E. and master’s
from JEC, Jabalpur, in 2001 and HBTI,
Kanpur in 2013, respectively. She is cur-
rently pursuing her Ph.D. from AKTU,
Lucknow. Her current research inter-
est includes drilling machine, optimiza-
tion algorithms, and control systems. She
worked as an HoD, ECE in PSITcoe from
2010 to 2019. Presently, she is working as a strength in ECE,
PSIT College of Engineering, Kanpur. Her contribution to Aca-
demics is more than 19 years’. She is the Life Time Member of
the Institute of Engineers, India (IEI).
Corresponding author. Email: saxenaarti@yahoo.com
Dr.Y. M. Dubey acknowledged Ph.D.
on the topic “Emergence of wet soil
electronics circuit technology and its
novel applications” from Rani Durgavati
Vishwavidyal aya, Jabalpur. His cur re nt
research interest includes control systems
and Smart sensors. Presently, He is work-
ing as a Professor in ECE, PSIT Kanpur
HisacademicexperienceasaPrincipal,HeadofDepartment
&inchargeofAcademicsismorethan20years’.
Email: yogesh.ec@psit.ac.in
Dr. Manish Kumar awarded master’s
degree from IISC, Bangalore, in 2003. He
is awarded Ph.D. in “Realization of Some
Novel Active Circuits” from the Depart-
ment of ECE, JIIT, Noida, in 2012. His cur-
rent research interest includes IoT, control
systems, and machine learning. Presently,
He is working as a strength in ECE, PSIT
Kanpur. His contribution to Academics is more than 15 years.
He has published more than 20 research papers and six Patents.
Email: manishkumar.jiit@gmail.com
Mr. Abneesh Saxena awarded B.E.(ECE)
from MPCT, Gwalior, in 2000. He is cur-
rently working in strength of OFC (Min-
istry of Defence) as a works manager. He
has got vast and valuable 18 years of expe-
rience in defence manufacturing industry.
Email: saxenaabneesh@yahoo.co.in
