Performance analysis of optimized controllers with bio-inspired algorithms

Bulletin of Electrical Engineering and Informatics
Vol. 9, No. 6, December 2020, pp. 2507~2517
ISSN: 2302-9285, DOI: 10.11591/eei.v9i6.2619  2507
Journal homepage: http://beei.org
Performance analysis of optimized controllers with bio-inspired
algorithms
Ibarra Alexander, Caiza Daniel, Ayala Paúl, Arcos-Aviles Diego
Department of Electrical, Electronic and Telecommunication Engineering, Universidad de las Fuerzas Armadas-ESPE, Ecuador
Article Info ABSTRACT
Article history:
Received Jan 3, 2020
Revised Mar 22, 2020
Accepted Apr 24, 2020
This article proposes tuning of PID controllers through optimization
techniques known as collective intelligence algorithms: the colony of ants
and cuckoo search, applied to the temperature control of a PCT-2 plant.
The dynamic behavior analysis of the controllers tuned by the application of
collective intelligence algorithms were performed in comparison to a controller
tuned by the genetic algorithm method and a controller designed with the
PID tuner tool, obtaining favorable results in the tuning of the algorithms
cuckoo search and ants colony in comparison to the PID tuner method
and with a faster execution speed than the genetic algorithms method.
Keywords:
Bio-inspired algorithm
Chromosomes
Controllers
Genetic algorithm
Intelligence algorithm
PID controller
This is an open access article under the CC BY-SA license.
Corresponding Author:
Ibarra Alexander,
Department of Electrical, Electronic and Telecommunication Engineering,
Universidad de las Fuerzas Armadas-ESPE,
Av. Gral. Rumiñahui y Ambato, Sangolquí, Ecuador.
Email: oaibarra@espe.edu.ec
1. INTRODUCTION
Bio-inspired algorithms are a novel method that has been developed to solve multiple problems in
the scientific field since they are based on emulating the behavior of biological systems to solve problems [1].
The genetic algorithm method is currently the most widely used in the field of evolutionary computing.
This method has become one of the most popular and developed in recent years because it is inspired
by genetic variation and natural selection of species [2]. However, there are methods not yet fully explored
within the scope of bio-inspired algorithms, which have incredible potential and whose field of research
is still young. An example of these is the ant colony method, inspired by the ability of ants to find the shortest
route between the power source and its nest [3]. Another optimization method also used is the Cuckoo
Search, which is a technique inspired by the lifestyle of cuckoo birds, known to be a type of "parasitic" bird
that lays its eggs in other nests, and that, based on due to the environmental characteristics and migration
of their societies, they seek the best habitat for the breeding and reproduction of their species [4].
Currently, the most widely used controllers at an industrial level are the so-called: proportional (P),
proportional-integral (PI) and proportional-integral-derivative (PID), since these have a simple structure
and relatively easy to design. However, this same simplicity usually becomes its weakness, since it limits
the range of plants in which they can be used satisfactorily. This article will contribute to the analysis
and application of new optimization alternatives in the design of controllers and the use of bio-inspired
algorithms for the resolution of control problems based on optimization, focused on the temperature control
of a PCT-2 temperature module. Available at the Universidad de las Fuerzas Armadas ESPE (Ecuador).
This leads to the research development on novel robust and fast controller alternatives, which is beneficial
both for the industry and for the scientific and student community.

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Bulletin of Electr Eng & Inf, Vol. 9, No. 6, December 2020 : 2507 – 2517
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2. BIO-INSPIRED ALGORITHMS
Bio-inspired algorithms simulate the behavior of natural systems, applied to the design of
non-deterministic heuristic methods, focused on search, learning, behavior, among other qualities. For this
reason, bio-inspired algorithms are often used to solve optimization problems in nonlinear systems, where
conventional models have difficulty operating [5]. The interest in this novel solution is based on the fact that
these algorithms recreate several intelligent behaviors in changing and complex environments, which are
capable of learning, adapting, generalizing, abstracting, discovering, associating, among other qualities that
we can find within nature [2]. In general, we can cover these bio-algorithms in four large groups:
Evolutionary algorithms, the method of genetic algorithms being its main exponent; collective intelligence,
within which are the methods of ant colony and cuckoo search; neural networks, with optimization
techniques such as multilayer perception (MLP) and algorithms based on immune systems, such as clonal
expansion algorithms. It should be noted that this classification is not exclusive and that some algorithms
may cover more than one area of interest, depending on their objective [4].
2.1. Genetic algorithms (GA)
The optimization methods known as genetic algorithms fit into the category of evolutionary algorithms
and were developed by J. Hollan in the 70s, to emulate and understand the natural adaptive process of
the species and then apply it in processes of optimization in the 80s. This method is characterized by being
adaptive and robust, so they can be used to solve search and optimization problems coming from different areas.
2.2. Ants colony (AC)
Ants are one of the main examples of collective intelligence that can be found in nature.
These insects base their behavior on mutual collaboration to carry out multiple tasks that would be
impossible to perform from an individual ant. A very important skill that many species of ants have lies in
the expertise of finding the shortest route between their anthill and the nearest food source [3-7].
2.3. Cuckoo search (CS)
The cuckoo birds are a family of medium-sized birds characterized by several of these species
practice laying parasitism, since they lay their eggs in nests of other species and leave that they raise these,
thus eliminating the need to feed and care for their offspring [8-13]. To do this, the female cuckoo lays its
egg in the occupied nest, and pecks or throws the host's eggs in the nest, so it does not usually notice
the infiltrate in its nest. Shortly after birth, the baby of cuckoo usually throws the rest of the offspring
and eggs by pushing them with their backs, to receive all the food and care of their adoptive parents, until it
reaches sufficient size to leave the nest [13-15]. Based on this peculiar behavior, Xin-she Yang,
a professor at the University of Cambridge, and Suash Deb developed the Cuckoo Search optimization
algorithm in 2009, inspired by the laying parasitism used by cuckoo birds for reproduction [10].
Within this algorithm, each host egg in a nest represents a solution, while each cuckoo egg represents a new
and better solution. Figure 1 presents the general diagram of the cuckoo search algorithm.
Figure 1. General diagram of the cuckoo search algorithm

Bulletin of Electr Eng & Inf ISSN: 2302-9285 
Performance analysis of optimized controllers with bio-inspired algorithms (Ibarra Alexander)
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Therefore, the objective is based on using new and generally better solutions (cuckoo), to replace
to the not so good solutions of the nests. The algorithm can be described under three fundamental ideas [11]:
a. Each cuckoo deposits an egg in a randomly selected nest.
b. The best nests and eggs will survive and give way to the next generation.
c. There is a defined number of nests available, and each egg has a probability of being discovered. In this
case, the mother will leave the nest and create a new one.
3. SYSTEM DESCRIPTION
In order to apply the optimized controller with a cuckoo search algorithm to a real case, the PCT-2
module of the DEGEM SYSTEMS´s will be used. Figure 2 represents the physical model of the system to be
controlled, which consists of a solid-state temperature sensor (IC LM35) as a measuring element, a stainless
steel conduit through which air controlled by a fan flows and to increase the temperature in the system
is available a nickeline at the air duct inlet fed with a voltage input as the system actuator. In conclusion,
the control process is based on modifying the input voltage V(t) in the plant, in order to modify the output
temperature .
Figure 2. Module thermal process PCT-2 [16]
The PCT-2 module comprises:
a. Primary and measuring element: temperature sensor-transmitter IC (linear variation). It takes
the temperature at the heater outlet (20-70 [°C]) and sends an analog voltage signal (0-5 [V])
to the controller.
b. Actuator: Nickeline governed by a voltage signal in the range of 0 to 10 [V].
c. Metal Plate: Which has four holes, which determine the amount of air that will enter the process, will be
used for disturbance analysis.
In order to apply the design of optimized controllers to a real case, the implementation of these
controllers in the airflow Degem Systems module PCT-2 has been proposed. The mathematical model of
the plant was obtained by parametric identification techniques and is represented by:
On the other hand, the characteristics described in Table 1 have been determined as a control
objective to be optimized through the selected bioinspired algorithms.
Table 1. Control system specifications
Parameter Specification
Output 30°C
Overshoot <15%
Settling time <20 seconds
Steady state error <=2%
For the development of the aforementioned algorithms, a general structure has been determined
to facilitate the comparison between the different optimization methods, as presented below:

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3.1. Genetic algorithms
Figure 3 presents a simplified representation of the general scheme of genetic algorithms to facilitate
the programming of the algorithm.
Figure 3. Simulation scheme of the GA method
3.2. Ant colony
Figure 4 presents a simplified representation of the general scheme of ant colony to facilitate
algorithm programming [5].
Figure 4. Simulation scheme of the ant colony method
3.3. Cuckoo search
A simplified representation of the general cuckoo search scheme is presented in Figure 5 to facilitate
algorithm programming [12-20].
Figure 5. Simulation scheme of the cuckoo search algorithm
a. Generation of nests with eggs
The first phase of the algorithm corresponds to the generation of initial solutions, that is, the first
set of nests containing cuckoo eggs. For this, a solution matrix has been proposed under the following
configuration:
[ ] [ ]
where n represents the number of nests to be used for the optimization. Each solution can be represented by
the concatenation of the gains obtained for the PID controller:

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[ ] [ ]
b. Search for the best nests
This step takes place at the moment when the cuckoo eggs laid in the first generation of nests have
grown and are ready to give rise to a new generation of eggs. For this, the optimization algorithm cuckoo
Search requires the application of scanning techniques for the best nests within the search space. This process
has been carried out using the Lévy Flights search technique [11]. This procedure generates a set of random
values (with a normal distribution) interacting with each other, which are related to the measured distance
between each element of the solution and the elements of the best nest identified, and are added to the current
values of each nest. As a result, a set of newly available nests is obtained whose location within the search
space has been found based on random values and influenced to some extent by the best nest of the previous
generation [21-30].
where d corresponds to the number of elements within the solution, that is, the gains Kp, Ki, and Kd treated
individually, and Rand (norm) corresponds to a random value generated with a normal distribution. Also,
can be calculated from:
Being the elements of the nest with the best performance identified in the first place, and can be
obtained from the following equation:
[ ]
Being calculated as:
where sigma controls the size of the steps traveled during the search process.
c. Intruder detection
In [6], an intruder discovery technique based in Pa probability is proposed, with which an alteration
process of the selected nests is carried out and its performance is verified to know if the cuckoo is discovered
or not. The mentioned process is executed within the algorithm based on the following formulas:
where ss is calculated from:
Being rand (0 to 1) a random value generated between 0 and 1, mpa is an array with binary elements
determined by:
[ ]
{
If the new nests show better results, the cuckoo egg originally deposited in the nest is eliminated and the nest
is maintained with the new solution [21-30].

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4. RESULTS AND DISCUSSION
Based on the MATLAB PID tunner tool, preliminary tuning of the standard PID controller has been
carried out as shown in Table 2, which has determined a series of base parameters on which a search range
has been established for the proposed algorithms.
Table 2. Initial parameters for algorithm development
Parameters Values
Kp gain 0-12
Ki gain 0-5
Kd gain 0-2
Maximum overshoot percentage 15%
Maximum settling time 20 s
Steady state error 2%
Population size 20
Number of iterations 50
Reference voltage 1V
4.1. Results obtained
In the first place, an analysis of results in the transitory regime has been carried out, obtaining
the following results in the execution of each applied algorithm. Figure 6 presents the step response of the
controllers tuned by the described methods. In section a) we find the response of the controller tuned by the
method of genetic algorithms. In section b) we find the response of the controller tuned by the ant colony
method. In section c) we find the response of the controller tuned by the cuckoo search method. Table 3
presents the controllers tuned by the described methods. On the other hand, Table 4 presents the iteration
number in which each of the algorithms found the best individual of each execution performed.
(a)
(b)
Figure 6. Response of the best controllers to step function, (a) Genetic algorithms, (b) Colony ants

2513
(c)
Figure 6. Response of the best controllers to step function, (c) Cuckoo search (continue)
Table 3. Controllers tuned by genetic algorithms, ant colony, and cuckoo search
System Genetic algorithms Ant colony Cuckoo search
Measure Controller Measure Controller Measure Controller
System with
the best overall
performance
6.26
seconds
5.88
seconds
4.96
seconds
System with better
performance by
overshoot
6.82
seconds
7.97
seconds
5.17
seconds
System with better
performance
by settling time
5.33
seconds
5.81
seconds
4.89
seconds
Table 4. Iterations needed to find the best solution
System Best global performance Better overshoot Best settling time
Genetic algorithms 24 21 23
Ant colony 23 4 8
Cuckoo Search 24 24 6
When considering the controllers that obtained the best overall performance in each applied method,
we obtained the described results in Table 5. Table 6 shows the result of measurements obtained in rejection
of disturbances and illustrated in Figure 7. For the analysis in the permanent regime, a disturbance of -0.2V
has been simulated, obtaining the following results in response of the controllers, as shown in Figure 8.
Table 5. Summary of parameters measured in controllers
Controller Overshoot Settling time
PID Standard 6% 12.3 s
Genetic algorithms - 6.26 s
Ant colony - 5.88 s
Cuckoo Search - 4.97 s
Table 6. Measurements obtained in rejection of disturbances
Controller Settling time
PID Standard 7.6 s
Genetic algorithms 3.8 s
Ant colony 3.8 s
Cuckoo Search 3.4 s

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Figure 7. Comparison of simulated results
Figure 8. A comparative graph of controllers performance in rejection of disturbances
As shown in Figure 8, the responses obtained by the controllers tuned by bio-inspired algorithms
maintain a similar behavior and reaction values in response to the applied disturbance and without overlining
the signal and highlighting the controller tuned by cuckoo search, which recovers 12% faster. In summary,
the results obtained by each of the controllers can be compared in Table 7.
Table 7. Summary of features of each controller
Tuning method Genetic algorithms Ant colony Cuckoo Search
Measured settling times [s] 6.26 5.88 4.96
Percentage of overshoot 0% 0% 0%
Population size 20 20 20
Generations to achieve the best result 24 23 24
Maximum number of iterations performed 50 50 50
Simulation time measured 157.88 59.93 104.92
4.2. Measured results
After the implementation of the best controllers obtained from the execution of the bio-inspired
algorithms designed, the response shown in Figure 9 was obtained. Figure 8 shows the behavior of
the controllers applied to the PCT-2 temperature plant. It should be noted that the measures presented have
been taken with a sampling period of 50 ms. The measurements obtained in the signals corresponding
to the controllers optimized by genetic algorithms, ant colony, and cuckoo search, do not exceed 2%

2515
of the measured signal, despite the increase in oscillation obtained by the instability of the plant, unlike
the controller optimized by PID Tunner, and whose measurements are summarized in Table 8. According to
the taken measures, we can notice better performance concerning the time of settling in the controller tuned
by ant colony (as in simulated case) with 10.95 seconds, however, since on this occasion, the measured
signals do show overshoot, that the response obtained by the controller tuned by cuckoo search delivers
the least overshoot of all with 3.9%.
Figure 9. Measured response of controllers in transitory regime
Table 8. Summary of characteristics measured in controllers
Controller Maximum voltage [v] Overshoot percentage Establishement time [s]
PID 1.261 26.1% -
Genetic algorithms 1.064 6.4% 12.65
Ant colony 1.061 6.1% 10.95
Cuckoo Search 1.039 3.9% 11.3
5. CONCLUSIONS
After performing the respective analysis of results, some fundamental parameters have been
determined to make the comparison between the designed algorithms. The settling time measured in the
simulated cases determines that the controller optimized by the CS algorithm is stabilized by 14.7% faster
than the controller optimized by GA and 11.76% faster than the controller optimized by AC, whereas in the
case of the controller implemented on the temperature module a higher settling speed could be measured in
the controller optimized by AC, being this is 15.52% faster than that optimized by GA and 3.19% faster than
the controller optimized by CS. In the second parameter, it was possible to measure the best performance in
terms of the percentage of overshoot in the controller designed by CS, this being 56.41% smaller than the
controller optimized by AC and 64.1% smaller than the controller optimized by GA. Similarly, the recovery
time in rejection of disturbances in the three optimized controllers has been measured, concluding that the CS
algorithm recovers 12.5% faster than the other two implemented algorithms. And finally, an execution time
of the implemented algorithms has been measured, observing a faster execution speed and a lower
computational cost in the AC algorithm, which is executed 75.07% faster than the CS algorithm and 163.34%
than GA.
Regarding the implementation in the PCT-2 temperature plant, the rapid control action can be
evidenced before the temperature changes measured in the controllers designed based on bio-inspired
algorithms, unlike the slow behavior of the standard PID controller that resulted in a signal unable to stabilize
in a range less than 2%. The obtained results show a better performance in the controllers tuned by the
bioinspired algorithms in comparison to the PID Tuner tool. Likewise, the ant colony and cuckoo search
present similar performance to the controller tuned by the genetic algorithms method, but a better response in
terms of computational cost.

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ACKNOWLEDGMENT
This work is part of the project 2019-PIC-003-CTE from the Research Group of Propagation,
Electronic Control, and Networking (PROCONET) of Universidad de las Fuerzas Armadas ESPE. This work
has been partially supported by VLIR-UOS project number EC2020SIN322A101.
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BIOGRAPHIES OF AUTHORS
Ibarra Alexander Electronic Engineering, Automation and Control at the Army Polytechnic
School where he obtained the title of Electronics, Automation and Control Engineer in 2010.
Master’s degree in University of the Armed Forces ESPE, where he obtained the title of Master
in Renewable Energies in 2013. Researcher at the University of the Armed Forces ESPE
in the Department of Electrical, Electronic and Telecommunication in the Area of Automation
and Robotics. He works in control algorithms and optimization techniques, industrial robotic
manipulators in open and closed kinematic chains, social robotics, collaborative robotics, cloud
computing and cloud robotic, as well as studies on the use of renewable energy for applications
in various energy fields with a variety of technologies where the main interest lies in low
and medium temperature solar thermal energy.
Caiza Daniel was born in Quito-Ecuador on July 21, 1993. Electronic engineer in automation
and control graduated from the ESPE Armed Forces University in 2018. His research supports
bioinspired control algorithms.
Ayala Paúl was born in Quito-Ecuador on July 7, 1974. I studied Electronic Engineering at the
Polytechnic Army School–ESPE, where I obtained the title of engineer in electronics,
automation and control in 1997, then I completed my master's degree in business administration,
mechatronics and PhD at ESPE, Polytechnic University of Catalonia-UPC and Technological
University of Havana-CUJAE, respectively. I have been an investigative professor at the
University of the Armed Forces since 1998, where I have held the post of Head of the Marketing
Unit, Master Coordinator, member of the Career Council of Electronic Engineering, Automation
and Control, Member of the Mechatronics Career Council and member of the Department of
Electrical and Electronics Council. Actually I am Principal Professor of Electrical, Electronics
and Telecommunications Department.
Arcos-Aviles Diego He received the B.Sc. degree in Electronics, Automation and Control
Engineering from Universidad de las Fuerzas Armadas ESPE, Sangolquí, Ecuador, in 2002, the
M.Sc. and PhD. degrees in Electronics Engineering from Universitat Politècnica de Catalunya,
Barcelona, Spain, in 2012 and 2016, respectively. His research interests include microgrid
energy management, power electronics, microgrids, and renewable power generation.

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