Corresponding Author: Rizky
Ramadhan
E-mail: [email protected]
INTRODUCTION
DC motors are devices that generate
mechanical energy by means of the current that results from a wire coil inside
the motor (Osman et al.,
2022). They can deliver strong beginning torque
and the ability to control speed over a broad range. DC motors are now again
increasing in popularity as highly practical equipment. They are commonly used
in various applications, such as industrial, automobile, and home appliances (Kumar et al.,
2014).
Implementing DC motors for water pumping has emerged
as a possible solution to the growing need for resource sustainability and
efficient water pumping. DC motors are reliable, efficient, and controllable in
terms of controlling speed. Due to its superior electrical properties, such as
high starting and accelerating torque, quick response performance, and simple
linear control, high-performance DC motor drives are employed increasingly
frequently in factories (Akpama et al., 2021). DC motors require a controller to increase their
efficiency because without using a controller, a DC motor has a long response
to reach a set point, which will later affect the level of efficiency (Guo & Mohamed, 2020)
There
are many different methods for controlling the DC motor, including PI, PID, and
fuzzy logic controllers. This is because all control systems have issues with
undesirable overshoot, prolonged settling times, vibrations, and stability when
changing states. Real-world systems are not linear, which makes correct
modelling challenging and expensive (Akpama
et al., 2021). With its three-term
functionality that can handle transient and steady-state responses,
proportional-integral-derivative (PID) control offers an easy-to-understand and
highly effective solution to many real-world issues. PID controllers are,
therefore, often used in traditional speed control loops. Traditional PID
controllers suffer from unwanted overshoots, slow response, sensitivity to
controller gains, and rapid changes in load torque. Two major issues with motor
control are the unstable behaviour of the motor parameters under operating
conditions and noise in the system. Therefore, employing standard methods to
regulate motion in complex, nonlinear, and time-varying systems becomes
difficult. To achieve an ideal state under field conditions, tuning the PID
controller's parameters is obviously necessary (Sharma
& Palwalia, 2018).
It
makes an adaptive Fuzzy Logic Controller based on PID superior to conventional
PID controllers. These advantages such as cheaper to develop, covering a wider
range of operating conditions (Al-Odienat
& Al-Lawama, 2008), not needing an accurate
mathematical model, and being more robust than a PID controller (Eltamaly,
2018).
Akpama
et al presents. The dynamic behaviour of the motor was assessed in terms of
transient response, such as settling time and peak overshoot for both the Fuzzy
Logic Controller (FLC) and PID controller. It was found that the Fuzzy Logic
Controller (FLC) offers faster dynamic response and better motor performance
than traditional PID Controllers. When a disturbance, such as a change in the
applied load condition, the Fuzzy Logic Controller (FLC) offers better
resilience and a quicker transient reaction. This demonstrates how effectively
a DC motor pump can replace an AC motor pump (Akpama
et al., 2021).
Li
et al. present. Results show that the Fuzzy PID has a reasonably good
anti-disturbance capacity and outperforms the regular PID in terms of
adjustment time, rising time, peak overshoot, and peak time (Li
& Gong, 2022). Somwanshi et al. The
superiority of the Fuzzy-PID Controller was evident, particularly in terms of
robustness to parameter variations (Somwanshi
et al., 2019).
The study presents the
design of an Advanced Fuzzy Logic Controller to regulate the motor's speed. The
main problem in the PID Controller is parameter tuning, which can be solved by
utilizing optimization techniques or algorithms. To resolve this issue, fuzzy
logic can automatically adjust the PID parameters in real-time. Forty-nine
rules are formulated with various membership functions to generate equations
for speed control and parameter tuning of PID. The motor speed is controlled by
continuously adjusting the motor armature voltage. MATLAB/Simulink software is
utilized for simulation in this study. Two controllers, a PID controller and an
Advanced Fuzzy Logic Controller, are developed for comparison.
While recent studies have highlighted the
superiority of fuzzy logic-based controllers over traditional PID controllers
in terms of dynamic response and resilience (Akpama et al., 2021; Li &
Gong, 2022; Somwanshi et al., 2019), the practical implementation of advanced
fuzzy logic controllers in real-world water pumping systems warrants further
examination. Potential challenges, including computational complexity and
sensitivity to environmental factors, need to be thoroughly addressed to ensure
the viability and scalability of such control systems (Khairudin et al., 2019;
Hakim et al., 2024; Flores et al., 2023).
In this
study, propose an Advanced Fuzzy Logic Controller for water pumping systems
that aims and focusing to improve energy efficiency and performance. While our
controller shows promising results in simulation studies, it is important to
acknowledge its limitations and consider potential challenges associated with
its real-world implementation. By addressing these challenges, we aim to
enhance the practical relevance and applicability of our proposed controller in
real-world water pumping systems.
METHOD
In this study,
we implemented an Advanced Fuzzy Logic Controller (AFLC) in a water pumping
system to enhance energy efficiency, with a focus on improving speed response.
The AFLC was compared to a conventional PID controller to evaluate its
performance in achieving these objectives. While the AFLC demonstrated superior
energy efficiency and control precision, an important aspect that we considered
was its ability to maintain speed response under varying system parameters and
environmental conditions.
To address
potential limitations regarding the robustness and scalability of the AFLC, our
method included conducting comprehensive tests to evaluate its speed response
and energy efficiency under different scenarios. We subjected the controller to
varying pump speeds and environmental conditions especially torque response in
variation load, to assess its performance over time.
The data
obtained from these tests supported the AFLC's effectiveness in enhancing
energy efficiency, especially in speed response systems. This suggests that the
AFLC has the potential to perform well in real-world applications, maintaining
stable speed response and improving energy efficiency over long periods of
time.
By
demonstrating the AFLC's robustness and scalability in achieving these
objectives, our study provides valuable insights for future research. This
includes further analysis of the AFLC's performance under different operating
conditions and its potential for long-term stability in real-world
applications, particularly in enhancing energy efficiency in speed response
systems.
DC Motor Modelling
It is well accepted that a linear relationship
exists between the torque produced by a DC motor, the armature current, and the
magnetic field intensity. The torque (T) of the motor and the armature current
(i) are directly related, assuming that the magnetic field stays constant (Somwanshi et
al., 2019). Eq. (2.1) illustrates how this relationship
is characterized by a constant variable (Kt), the torque constant. These motors
are frequently referred to as armature-driven motors.
|
|
(2.1)
|
Eq. (2.1)
shows that the back electromotive force (EMF) (e) is directly connected to the
shaft's rotational motion (θ) through a constant factor (Kb),
also called the electromotive force constant.
|
|
(2.2)
|
The
subsequent governing equations are obtained by using Newton's second law, as
expressed in Eq. (2.3), and Kirchhoff's mesh law, as stated in Eq. (2.4)(Ramadan et al., 2014).
|
 �= Kt x i
|
(2.3)
|
|
 �= V - K
|
(2.4)
|
(J)
is the rotor's moment of inertia; (b) is the motor's viscous friction constant;
(La) is the electrical inductance; (Ra) is the electrical
resistance; and (V) is the voltage source. Eq. (2.5) and (2.6) demonstrate how
the modelling equations can be represented in terms of Laplace variables by
utilizing the Laplace transform(Nassim & Abdelkader, 2021) (Goswami & Joshi, 2018).
|
|
(2.5)
|
|
|
(2.6)
|
After removing I(s) from Eq. (2.7), the
rotational speed was considered the input and the armature voltage output,
resulting in the derivation of the open-loop transfer function.
|
|
(2.7)
|
Table 1. Parameters of the DC Motor
|
Parameter
|
Value
|
Unit
|
|
Armature
Resistance (Ra)
|
4.0
|
Ohms
(Ω ))
|
|
Armature
Inductance (La)
|
0.3
|
Henry (H)
|
|
Torque
Constant (Kt)
|
0.24
|
N-m/A
|
|
Input
Voltage (Va)
|
60
|
Volts (V)
|
|
Frictional
Coefficient (B)
|
0.0011
|
N-m/(rad/sec)
|
|
Moment
of Inertia (J)
|
0.0043
|
kg.m2
|
|
Rated
Speed (Nm)
|
5000
|
RPM
|
|
Back
Emf Constant (Kb)
|
0.24
|
V/(rad/sec)
|
Using the parameters of our engine,
which are in the table above in equation (2.7), we obtain the following
equation:
|
|
(2.8)
|
The equation
mentioned earlier can be subsequently translated using the Simulink figure
below.
Figure 1.
Representation of a DC motor in Simulink
Controller Design
PID Controller Design
The
function of the PID controller is mainly to adjust an appropriate proportional
gain (KP), integral gain (KI) and differential gain (KD) in order to achieve
optimal control performance. General Structure of PID
Controller:
Figure 2. General
Structure of PID Controller
The error at time t, or the difference
between the set point and the current process value, is represented by e(t),
whilst the control signal applied to the system is indicated by u(t). The gains
connected to the proportional, integral, and derivative components are denoted
by Kp, Ki, and Kd, respectively. It is
important that tuning is frequently necessary in order to determine the values
of Kp, Ki, and Kd. This system tuning
procedure can be carried out by systematic system experimentation or based on
experience and techniques like Ziegler-Nichols (Daraz et al., 2020) or by system experiments; in our case, we will use
the "self-tuning method"; the values obtained are Kp = 12, Ki = 10,
Kd = 0.2.
Figure
3. Design PID Controller system on Simulink/MATLAB
Advanced Fuzzy Logic Controller
Figure
4. Structure of Advanced Fuzzy Logic Controller
A PID controller's
performance can only be improved by optimizing its parameters. Ziegler Nichols
and the self-tuning method presented a popular method for fine-tuning the PID
controller to improve performance through parameter optimization (Huang et al., 2022). With the help of the fuzzy structure, approximate relationships
between the input and the desired output can be expressed in linguistic words.
A group of fuzzy components are used to depict the relationship. If-then rules
link a potential response to an approximation of the system's state.
The structure of an Advanced Fuzzy Logic Controller comprises two
segments: Conventional PID Controller and Fuzzy Logic Controller (FLC); Kp1,
Ki1, and Kd1 are the preliminary values parameters of
Conventional PID Controller Kp2, Ki2, and Kd2 are
the gain outputs of Fuzzy Logic Controller (FLC), The equation of tuned
parameters will be in Eq. 3.1:
|
Kp = Kp1 x Kp2
Ki = Ki1 x Ki2
Kd = Kd1 x Kd2
|
(3.1)
|
The output of the control action of the Conventional PID
Controller after tunning with the Fuzzy Logic Controller (FLC) will be in
equation (3.2).
|
|
(3.2)
|
Design of Fuzzy Rule
Base
A
rule base refers to a collection of decision-making logics that aim to
replicate the cognitive process of human judgment-making (Varshney,
2023). The rule base is constructed by
utilizing the inputs and their related outputs, specifically determining the
desired outputs for a given set of inputs (Tripathy
et al., 2022). Seven membership functions are
considered for inputs and seven membership functions for output; thus, it will
give a total of 49 rules:
Table
2. Fuzzy Rules for Kp
|
e/de
|
NB
|
NM
|
NS
|
Z
|
PS
|
PM
|
PB
|
|
NB
|
PB
|
PM
|
PS
|
NB
|
NB
|
NB
|
NB
|
|
NM
|
PM
|
PS
|
Z
|
PS
|
NB
|
NS
|
Z
|
|
NS
|
PB
|
PM
|
PS
|
PM
|
PS
|
PM
|
PB
|
|
Z
|
PB
|
PM
|
PS
|
Z
|
PS
|
PM
|
PB
|
|
PS
|
PB
|
PM
|
PS
|
NS
|
PS
|
PM
|
PB
|
|
PM
|
Z
|
NS
|
NM
|
NS
|
Z
|
PS
|
PM
|
|
PB
|
NB
|
NB
|
NB
|
NS
|
PS
|
PM
|
PB
|
Table
3. Fuzzy Rules for Ki
|
e/de
|
NB
|
NM
|
NS
|
Z
|
PS
|
PM
|
PB
|
|
NB
|
PB
|
PB
|
PB
|
PB
|
PM
|
PS
|
Z
|
|
NM
|
PB
|
PB
|
PB
|
PM
|
PS
|
Z
|
Z
|
|
NS
|
PB
|
PM
|
PS
|
PS
|
Z
|
NS
|
NM
|
|
Z
|
NM
|
NS
|
Z
|
Z
|
Z
|
NS
|
NM
|
|
PS
|
NM
|
NS
|
Z
|
PS
|
PS
|
PM
|
PB
|
|
PM
|
Z
|
Z
|
PS
|
PM
|
PM
|
PB
|
PB
|
|
PB
|
Z
|
PS
|
PB
|
PB
|
PB
|
PB
|
PB
|
Table
4. Fuzzy Rules for Kd
|
e/de
|
NB
|
NM
|
NS
|
Z
|
PS
|
PM
|
PB
|
|
NB
|
PB
|
PB
|
PB
|
PB
|
PM
|
PS
|
Z
|
|
NM
|
PM
|
PM
|
PS
|
PS
|
PS
|
Z
|
Z
|
|
NS
|
PM
|
PS
|
Z
|
Z
|
Z
|
NS
|
NM
|
|
Z
|
PS
|
PS
|
Z
|
Z
|
Z
|
NM
|
NB
|
|
PS
|
NM
|
NS
|
Z
|
Z
|
Z
|
PS
|
PM
|
|
PM
|
Z
|
Z
|
PS
|
PM
|
PB
|
PB
|
PB
|
|
PB
|
Z
|
PS
|
PB
|
PB
|
PB
|
PB
|
PB
|
Simulink
diagram of the DC motor in series with Advanced Fuzzy Logic Controller
Figure 5. Design of Advanced Fuzzy Logic
Controller on Simulink/MATLAB
RESULTS AND DISCUSSION
Figure 6.
Step Response plotted for the DC Motor with Advanced Fuzzy
Logic
Controller Method and PID Controller Method
Table 5. Characteristics Response from
Advanced Fuzzy Logic
Controller
Method and PID Controller method
|
Characteristics
|
Advanced
Fuzzy Logic Controller (AFLC)
|
PID
Controller (Self-Tuning)
|
|
Rise
Time (tr)
|
0.048
Seconds
|
0.048
Seconds
|
|
Maximum
Overshoot (Mp)
|
0,7
%
|
10%
|
|
Time
Peak (Tp)
|
0.05
Seconds
|
0.078
Seconds
|
|
Settling
Time (ts)
|
0.052
Seconds
|
0.23
Seconds
|
|
Steady
State Error (SSE)
|
0
|
0
|
The advanced fuzzy logic controller
responds better to the motor when it is run at 3000 RPM regularly. This
includes improvements in all parameters related to rise time, settling time,
and overshoot. Figure 4.1 illustrates how the system is tested for tracking
reference speed values, and Table 4.1 displays the parameter's outcome.
The next test involves varying the speed
of the DC motor every two seconds at four different speeds (RPM 1000, 2000,
3000, and 4000) to see the response generated by the advanced fuzzy logic
controller and PID Controller that has been designed. The advanced fuzzy Logic
controller generates a response as needed, namely having a low overshoot value,
the same rise time, and a fast settling time, as seen in Table 4.1.
additionally, this advanced fuzzy Logic controller responds consistently to any
changes that have occurred
Figure 7.
Speed Response at variable load conditions on both controller
Both of the controllers might experience
rapid load disturbances. At the onset, a load torque of 0.24 N-m is applied,
followed by subsequent instances at t = 2 and t = 4 seconds, where the load
torque experiences rapid increments to 3 N-m and 5 N-m, respectively. Figure 8
and Figure 9 illustrate the reaction of a system that incorporates an advanced
Fuzzy Logic control and PID Controller mechanism,
Figure 8. Speed Response at Variable Load
Conditions on Both Controller
Figure
9. Torque response at variable load conditions on both controller
Figures 8 and 9 show that the
scaling factors of the advanced fuzzy logic controller and PID controller
automatically adjust all three parameters when the load disturbance occurs at t
= 2 seconds and t = 4 seconds. Figure 4.3 compares the motor speed
characteristics derived by Advanced Fuzzy Logic controllers with PID
controllers. After the system stabilizes, the scaling factors generated by the
fuzzy controller return to their initial levels.
For Figure 4.4, when the advanced fuzzy
logic controller is loaded, the system will immediately correct the situation
again according to the given setpoint compared to the conventional PID
controller. However, the advanced fuzzy logic controller compensates with a
slight ripple result because the advanced fuzzy logic controller system is
multiplied to several PID parameters, one of which is Kd, which will
create a ripple system when Kd is multiplied.
While
this study has demonstrated the advantages of the Advanced Fuzzy Logic
Controller (AFLC) over a conventional PID Controller in improving energy
efficiency in water pumping systems, there is a need for further analysis of
the long-term stability and robustness of AFLCs in practical applications.
Future
research should focus on conducting long-term field tests to assess the
performance of AFLCs in real-world scenarios. This could involve monitoring the
controller's performance over extended periods, evaluating its ability to
maintain stable operation in varying environmental conditions, and assessing
any potential degradation in performance over time.
By
addressing these concerns, future studies can provide a more comprehensive
understanding of the performance of AFLCs in practical applications and ensure
their long-term effectiveness in improving energy efficiency in water pumping
systems.
CONCLUSION
In a comparative study between the
Advanced Fuzzy Logic Controller (AFLC) and a conventional PID Controller to
improve energy efficiency in water pumping systems, the AFLC, which regulates
input from the PID, shows significant advantages in terms of overshoot,
settling time, rise time, and overall performance. Here are the study's
conclusions: 1) Overshoot: AFLC produces lower overshoot than conventional PID.
This demonstrates AFLC's ability to regulate input more precisely, reducing
unwanted spikes in the system. 2) Settling Time: AFLC has a faster settling
time than conventional PID. AFLC's ability to adjust inputs quickly and
accurately allows the system to reach a steady state more efficiently. 3) Rise
Time: AFLC also shows the same rise time as conventional PID. �4) Overall Performance: AFLC consistently
performs better than conventional PID in improving energy efficiency in water
pumping systems across all aspects assessed. This shows that intelligent
controllers such as AFLC can benefit energy-sensitive applications
significantly. Thus, in the context of improving energy efficiency in water
pumping systems, the use of AFLCs that regulate the input from PIDs can be
considered a better option than conventional PIDs based on the results of this
comparative study. Advanced Fuzzy Logic Controller control produces a
responsive water pump, which can reduce water loss caused by over-pumping or
under-pumping. By adjusting the speed appropriately, the pump can maintain
stable water pressure and reduce the risk of leaks or wastage of water. By
optimizing speed response using precise controls, water pumps can work more
efficiently, reducing water loss and minimizing energy consumption. However, the study lacks discussion on
potential challenges and drawbacks associated with AFLC implementation, such as
computational complexity and sensitivity to environmental factors. Future
research should focus on addressing these challenges to ensure the controller's
effectiveness in practical settings. Additionally, the study highlights the
need for a more thorough analysis of the AFLC's robustness and scalability.
Despite these limitations, the AFLC shows promise in enhancing energy
efficiency and performance in water pumping systems.
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