International Journal of Research In Science & Engineering
Volume: 2 Issue: 3
e-ISSN: 2394-8299
p-ISSN: 2394-8280
TITLE: A REVIEW ON FOPID CONTROLLER AND ITS VARIOUS
APPLICATION
Shweta Bajpai1, Dr. Md. Sanawer Alam2
1
M. Tech student, Electronics Instrumentation and Control Engineering, Azad IET,
[email protected]
2
Assistant Professor, Electronics Instrumentation and Control Engineering, Azad IET,
[email protected]
ABSTRACT
The main aim of this paper is to describe FOPID a new generation of PID controllers, which is called the
fractional-order PID (FOPID) or PIλDμ controllers. This paper also briefs about the proposed application of
FOPID in various fields It should be noted that since FOPIDs have five parameters to tune (i.e., two more than
the conventional PID controllers), they can be applied to more complicated control problems. Moreover, the
performance of control is often much better when these controllers are applied. The fractional order controllers
are less sensitive to changes of parameters of a controlled system and controller. Fractional order PIDs are used
in automatic voltage regulation, load frequency control, cardiac pacemaker and etc. FOPIDs are more stable
than PIDs.
Keywords: FOPID, Active Magnetic Bearing System, Automatic Voltage regulation, Load frequency control,
Cardiac Pacemaker, Stability of FOPID.
----------------------------------------------------------------------------------------------------------------------------1. Introduction
Proportional integral derivative (PID) controllers have been used for several decades in industries for
process control applications. The reason for their wide-ranging popularity lies in the simplicity of design and good
performance including low percentage overshoot and small settling time for slow process plants. [5]. Nevertheless,
because of the limitations of this type of controller, there had always been a continuous attempt to improve the
performance and robustness of PID controllers. According to the advances in the field of fractional calculus, there
had been a great interest to develop a new generation of PID controllers, which is commonly known as the
fractional-order PID (FOPID) or PIλDμ controller. A fractional PID controller is an extension of the classical PID
controller. The fractional order controllers are less sensitive to changes of parameters of a controlled system and
controller [5].
In general, the FOPID controller is more flexible than the PID controller and provides us with an
opportunity for better adjustment of the dynamical properties of the feedback system under consideration, of course
at the cost of using a more complicated setup.
1.1 Fractional Order PID controller
A fractional PID controller is an extension of the classical PID controller. Fig.1 shows block diagram of
FOPID used with feedback system. The fractional order controllers are less sensitive to changes of parameters of a
controlled system and controller. A fractional order controller can attain the property of iso-damping very easily [1].
𝑼(𝒙)
𝑲
The generalized transfer function of this fractional PID controller is given by C(s)=
= 𝝀𝑰 + 𝑲𝑫 𝒔μ
𝑬(𝒙)
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𝒔
International Journal of Research In Science & Engineering
Volume: 2 Issue: 3
e-ISSN: 2394-8299
p-ISSN: 2394-8280
Where, where, C(s) is the controller output, U(s) is the control signal, E(s) is the error signal, KP is the proportional
constant gain, KI is the integration constant gain, KD is the derivative constant gain, λ is the order of integration, and
μ is the order of differentiator. [5]
Fig.1 Block diagram of fractional PID controller
Fig.2 Fractional PID controller converge
2. APPLICATIONS OF FOPID IN VARIOUS FIELDS
FOPID is being used in many fields like automatic voltage regulation, various industrial application, load
frequency control, DC motor control, intelligent cardiac pacemaker control and many more.
2.1 Tuning of Fractional PID Controllers Using Adaptive Genetic Algorithm for Active Magnetic
Bearing System
This paper has proposed an improved adaptive genetic algorithm for the multi-objective optimization
design of a fractional PID controller and applies it to the control of an Active Magnetic Bearing system. The
proposed algorithm in this paper has better performance of convergence speed and better stability in the global
optimum result. Another merit of the proposed method was the way to define the fitness function based on the
concept of multi-objective optimization. This method allowed the systematic design of all major parameters of a
fractional PID controller and then enhanced the flexibility and capability of the PID controller. The simulation
results of this Active Magnetic Bearing system show that a fractional PID controller designed via the proposed
Adaptive Genetic Algorithm has good performance. [2]
2.2 Comparative Study of PID and FOPID Controller Response for Automatic Voltage Regulation
It can be seen from the result deduced in paper that while using the FOPID controller tuned by Ziegler
Nichols method the overshoots obtained is less as compared to the case when the PID Controller was tuned via
conventional methods i.e. Ziegler Nichols and Cohen Coon method. The settling time is also lesser in case of the
FOPID controller, also the rise time is reduced. The FOPID controller tuned by Z-N tuning rule tends to faster
response of AVR. The PID controller tuned by Ziegler Nichols and Cohen Coon have larger overshoot than FOPID
controller attain a steady state with larger settling time. [3]
2.3 FOPID Design for Load-Frequency Control Using Genetic Algorithm
An FOPID for a Load frequency control is put forward in a three-area power system using genetic
algorithm. Simulation results shown suggest that the presented controller entails better characteristics compared to
PID and FOPID designed using Imperialist Competitive Algorithm (ICA). In most cases, FOPID designed using GA
has lower maximum overshoot and settling time; however, in few results, PID or FOPID designed using ICA has
lower maximum overshoot and settling time. As can be seen, the results are not ideal for the designed FOPID and
PID controllers and there is still scope for improvement. Furthermore, dynamic behavior of the low-frequency
controller has been improved and lower oscillation rate has been achieved. Also, this controller has smoother
IJRISE| www.ijrise.org|[email protected]
International Journal of Research In Science & Engineering
Volume: 2 Issue: 3
e-ISSN: 2394-8299
p-ISSN: 2394-8280
response time in comparison to the PID or FOPID designed by ICA and this improved response time causes
frequency oscillation of the abrupt change in the load to damp easily. [4]
2.4 Intelligent Fractional-Order PID (FOPID) Heart Rate Controller for Cardiac Pacemaker
Efficient and robust control of cardiac pacemaker is essential for providing life-saving control action to
regulate Heart Rate (HR) in a dynamic environment. Several controller designs involving proportional-integralderivative (PID) and fuzzy logic controllers (FLC) have been reported but each have their limitations to face the
dynamic challenge of regulating HR. In this work, a robust fractional-order PID (FOPID) controller is designed
based on Ziegler-Nichols tuning method. The stable FOPID controller outperformed PID controllers with different
tuning methods and also the FLC in terms of rise time, settling time and % overshoot. The FOPID controller
displaced the complexities and limitations with other designs and outperformed offering huge promise which is also
feasible for rate-adaptive pacing [6].
3. STABILITY CONDITION OF FOPID
It is well-known that an integer order LTI system is stable if all the roots of the characteristic polynomial
P(s) are negative or have negative real parts if they are complex conjugate. This means that they are located on the
left of the imaginary axis of the complex plane s. Fig.3 shows the stability region of fractional order PID. When
dealing with fractional order system, the characteristic polynomial is a multivalued function of s, the domain of
which can be viewed as a Riemann surface. The stability region of fractional order systems is bounded by a cone,
with vertex at the origin, and that extends into the right half of the complex plane s such that it encloses an angle of
απ/ 2, as shown in Fig. When α=1, we get the stability domain of the integer order system. Thus, when α=0.5, the
stability domain is the entire s-plane less the area enclosed by the cone making 450. Hence, if all the roots of
fractional order system are placed anywhere outside the cone in Fig. 2, it will be stable, Moreover, a controller that
stabilizes the integer order system stabilize the integer order model as well as its fractional versions. [1]
Fig.3 Stability region of fractional order system.
3. CONCLUSION
The paper gives a brief description of FOPID and its application in various fields. There is a need to explore
different variations of the fractional PID controllers stated in this paper. Performance of FOPID can be enhanced by
several tuning techniques like Zeigler Nichols, PSO etc.
ACKNOWLEDGEMENT
This work was supported by Dr. Md. Sanawer Alam, Head of Department Electronics Instrumentation and Control
Engineering. Special thanks to all faculty members of Electronics Instrumentation and Control Engineering
Department for their co-operation.
IJRISE| www.ijrise.org|[email protected]
International Journal of Research In Science & Engineering
Volume: 2 Issue: 3
e-ISSN: 2394-8299
p-ISSN: 2394-8280
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