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Computer Animation Education Online: A Tool to Teach Control Systems

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Article in Education Sciences · April 2022

DOI: 10.3390/educsci12040253

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 education
sciences
Article
Computer Animation Education Online: A Tool to
Teach Control Systems Engineering throughout the
COVID-19 Pandemic
Anna Patete 1, * and Ronald Marquez 2,3, *

1 Departamento de Sistemas de Control, Facultad de Ingeniería, Universidad de Los Andes,

Mérida 5101, Venezuela
2 Escuela de Ingeniería Química, Facultad de Ingeniería, Universidad de Los Andes, Mérida 5101, Venezuela
3 École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI), PSL Research University,
10 rue Vauquelin, F-75231 Paris, France
* Correspondence: annapatete.ula.ve@gmail.com (A.P.); marquezronald.ula.ve@gmail.com (R.M.)

Abstract: The world is changing, and university education must be able to adapt to it. New tech-
nologies such as artificial intelligence and robotics are requiring tools such as simulation and process
control to develop products and services. Thus, control systems engineering schools are adapt-
ing to new educational frameworks tailored to deploy promising and feasible new technologies.
Herein, we have relied on computer animation-based education and its implementation as an online
project-based strategy to attain the objectives and goals of the control systems engineering courses
at University of Los Andes, Venezuela. The ControlAnimation library developed in Mathematica



program in 2002 has been used as a tool to teach control systems engineering courses since 2008 and


with greater prominence since 2020, when the stay-at-home orders due to the COVID-19 pandemic
Citation: Patete, A.; Marquez, R.
Computer Animation Education
were enacted. Consequently, computer animation-based education has proven its feasibility as an
Online: A Tool to Teach Control online tool combined with project-based learning techniques, thus allowing students to interact with
Systems Engineering throughout the an animated control system by changing the mathematical model and the design parameters of
COVID-19 Pandemic. Educ. Sci. 2022, control laws in a comfortable and somewhat playful way. This enabled new capabilities to study
12, 253. https://doi.org/10.3390/ the dynamic behaviors of primordial control systems online. In addition, it allowed students to
educsci12040253 co-identify and relate in a more intuitive way to the mathematical models and control equations with
Academic Editors: Konstantinos
the physical behavior of the real control systems.
Katzis, Maria Meletiou-Mavrotheris,
Angelos Sofianidis, Nayia Keywords: computer animation; project-based learning; COVID-19; control systems; online education;
Stylianidou and Panagiota engineering education
Konstantinou-Katzi

Received: 11 March 2022

Accepted: 30 March 2022
1. Introduction
Published: 1 April 2022
The history of humankind indicates that continuous technological advances have
Publisher’s Note: MDPI stays neutral
occurred, particularly in the 20th century, and with an accelerated pace nowadays [1–3].
with regard to jurisdictional claims in
The development of computers and computational capabilities have led to the deployment
published maps and institutional affil-
of promising technologies that are helping humans to perform crucial activities in scenarios
iations.
such as product manufacturing facilities [4], robotic prosthetic implants [5,6] and even
educational tools [7].
Since the beginning of 2020, the COVID-19 pandemic [8] has struck the life of more
Copyright: © 2022 by the authors.
than 1.5 billion students worldwide, according to UNESCO [9–12], including control sys-
Licensee MDPI, Basel, Switzerland. tems engineering undergraduates [13]. Stay-at-home orders were enacted, and university
This article is an open access article education transitioned from presential to online education [10,14]. Thus, new teaching
distributed under the terms and strategies were deployed to make online education feasible, including computer animation-
conditions of the Creative Commons based education [7,15–17].
Attribution (CC BY) license (https:// The 2017 UNESCO report [18] calls for a transformation in engineering education,
creativecommons.org/licenses/by/ thus identifying an engineer’s profile as three-faceted: as a designer, researcher, and man-
4.0/). ager [19,20]. Moreover, the UNESCO 2030 Agenda acknowledges Science, Technology and

Educ. Sci. 2022, 12, 253. https://doi.org/10.3390/educsci12040253 https://www.mdpi.com/journal/education

Educ. Sci. 2022, 12, 253 2 of 20

Innovation (STI) as “key drivers for sustainable development,” supporting the “sustainable
economic development, entrepreneurship and youth employability” [18]. Thus, engineer-
ing education must simultaneously work on two complementary tasks: on the one hand,
the definition of the skills and competencies for graduating engineers, and on the other
hand, the development of effective teaching methods that help to reduce the gap between
knowledge and action [19–21].
In the present work, computer animation-based education and its implementation as
an online teaching and learning strategy through project-based learning is reviewed. The
strategy has been used to attain the objectives and goals of the control systems engineering
courses since 2020, after the lockdown and stay-at-home orders were implemented in
Latin American countries. Thus, we used innovative teaching and learning strategies, such
as project-based learning to attain the educational goals and overcome the challenges of
reaching out to students through online education [22,23]. The research products (computer
animations) that were attained through 20 years of studies in the Department of Control
Systems at the University of Los Andes are reviewed, and their implementation is discussed.
We end with a perspective on incorporating such approaches to control systems engineering
education even after the pandemic finishes.
The present work is divided into seven sections. Sections 1 and 2 present a brief
introduction with a rationale of the paper, computer animation definition, and main
applications. Then in Section 3, the use of computer animation in teaching control systems
at the university level is described. Section 4 introduces project-based learning as a strategy
that can be deployed with online education and computer simulation. Section 5 displays
how the ControlAnimation library has been implemented and used as an educational tool in
the teaching and learning of control systems engineering. In Sections 6 and 7, the challenges
and opportunities of implementing computer animation as an educational tool in control
systems engineering undergraduate programs and conclusions are discussed, respectively.

2. Computer Animation
Technological advances in computer science have led computer animation to thrive
over the past few decades [17,24,25]. The main reason being the need to interact with what
we will call animated digital objects [16,26]. This need arises mainly due to the limitations,
costs, or non-existence of such objects in reality [27–29].
Computer animation, also called computational graphics, digital animation, or compu-
tational mimics, consists of a series of images, frames, or graphics designed on a computer,
which describes states or positions of a certain digital object at different time frames [30].
Mathematically speaking, time is defined discreetly: t = kT0 , where time belongs to the
natural numbers: t ∈ N, the sampling period T0 belongs to the real numbers: T0 ∈ R and k
are the instants of time: 1, 2, 3, 4, 5, ..., n [26]. In the computational world, we can define
Tc = T0 , where Tc represents the sampling period with which each computer graph is pre-
sented. Hence, it is intuitive to think that, at a lower value of Tc, the reproduction of the set
of computational graphics will resemble a representation or graphic animation. Thus, the
human eye’s perception of the representation will seem continuous. However, the value of
Tc must be chosen in such a way to balance the proper visualization of the computationally
animated digital object and the Random Access Memory (RAM) consumption used in the
number of images generated and that afterward must be reproduced sequentially.
Therefore, the computational sampling period defined in this work as Tc is chosen
according to the animated digital object’s visualization requirements. The latter is per-
formed by accounting for both the computer’s hardware and software limitations. This
is in contrast with the scope of the sampling period T0 in linear control systems, defined
by Isermann [31]. According to Kerlow [32], computer graphics technology as a digital
animation application was developed in the 1950s, and its technical development took
place in the 1980s, with the deployment of 3D animation [15,33]. One of the first and most
crucial computer animation applications dates back to the 1980s, when flight simulators
were used to train pilots [34]. This allowed the avoidance of the risk of exposing pilots
 Isermann [31]. According to Kerlow [32], computer graphics technology as a digital ani-
mation application was developed in the 1950s, and its technical development took place
Educ. Sci. 2022, 12, 253 in the 1980s, with the deployment of 3D animation [15,33]. One of the first and most crucial3 of 20
computer animation applications dates back to the 1980s, when flight simulators were
used to train pilots [34]. This allowed the avoidance of the risk of exposing pilots to flying
a real
to plane
flying without
a real plane proper
withouttraining, thus preventing
proper training, accidentsaccidents
thus preventing [35]. Since[35].
then,Since
computer
then,
animation has been developed for entertainment, training simulators, creating
computer animation has been developed for entertainment, training simulators, creating objects
non-existent
objects in reality,
non-existent cartography,
in reality, industrial
cartography, and architectural
industrial design, design,
and architectural teachingteaching
and ed-
ucational
and purposes
educational [36–44].
purposes [36–44].

3.3. Computer
ComputerAnimation
Animationin
inTeaching
TeachingControl
ControlSystems
Systemsatatthe
theUniversity
UniversityLevel
Level
The
TheMatlab
Matlab(MathWorks)
(MathWorks) and Mathematica
and Mathematica (Wolfram)
(Wolfram)computer programs
computer have been
programs have
used
been since the end
used since the of
endthe
of 1990s as the
the 1990s main
as the maincomputational
computational tools for
tools forthe
theanalysis
analysisandand
design
design of
of both
both continuous
continuous and and discrete
discrete control
control systems
systems at at the
the University
University of of Los
Los Andes,
Andes,
Venezuela
Venezuela[45].
[45]. Version
Version 4.04.0 ofofMathematica
Mathematica presented
presented the the possibility
possibility of of designing
designing andand
graphing primitive digital objects or elements, such as lines, circles, rectangles,
graphing primitive digital objects or elements, such as lines, circles, rectangles, triangles, triangles,
among
among others,
others, in
in 2D
2Dand
and3D 3D[27,46].
[27,46]. These
These digital
digital objects
objects could
could be be graphed
graphed at at different
different
time
time instants and then reproduced in the same frame or workspace in such a way
instants and then reproduced in the same frame or workspace in such a waythat
that
they
theygave
gavethe
thefeeling
feelingofofvisualizing
visualizingan ananimated
animateddigital
digitalobject.
object. However,
However, at atthat
thattime,
time,no
no
computer
computerprogram
programoffered
offeredthethepossibility to interact
possibility withwith
to interact control systems-related
control animated
systems-related ani-
digital
mated objects.
digital objects.
In
In2002,
2002,an anapplication
application (library) forfor
(library) thethe
Mathematica
Mathematica software
software(Figure 1) was
(Figure 1) developed
was devel-
in the Department of Control Systems at the University of Los Andes,
oped in the Department of Control Systems at the University of Los Andes, the Control- the ControlAnima-
tion library [30,47,48].
Animation The ControlAnimation
library [30,47,48]. library was
The ControlAnimation created
library was on a personal
created on a desktop
personal
computer with the following technical characteristics: 2 Gb RAM,
desktop computer with the following technical characteristics: 2 Gb RAM, ProcessorProcessor Intel Core Duo
Intel
2.20 GHz, and a 300 Gb hard drive, under Windows operating
Core Duo 2.20 GHz, and a 300 Gb hard drive, under Windows operating system. system.

Figure 1. ControlAnimation library command in Mathematica software (version 8.0), Wolfram,

Figure 1. ControlAnimation library command in Mathematica software (version 8.0), Wolfram,
Oxfordshire, UK.
Oxfordshire, UK.

Mathematica Version
Mathematica Version 4.0
4.0installation
installation requirements
requirements were:
were: 15 15 Gb
Gb of
of hard
hard disk
disk space,
space,
1.8 GHz or greater processor, and 2.0 Gb minimum RAM. These
1.8 GHz or greater processor, and 2.0 Gb minimum RAM. These were specifications thatwere specifications that
by 2002 were commonly found in most personal computers and desktops
by 2002 were commonly found in most personal computers and desktops available in the available in the
digital laboratory of the Department of Control Systems at the University
digital laboratory of the Department of Control Systems at the University of Los Andes. of Los Andes.
Installingthe
Installing theControlAnimation
ControlAnimation library
library requires
requires no more
no more computational
computational requirements
requirements than
than installing Mathematica.
installing Mathematica.
TheControlAnimation
The ControlAnimationlibrary
libraryconsists
consistsofofaaseries
seriesof
oflibraries
librariesin infunction
functionformat
format(work
(work
files with extension .m) grouped in a folder called ControlAnimation
files with extension .m) grouped in a folder called ControlAnimation and which must be and which must be
installed in any version of Mathematica software within the following
installed in any version of Mathematica software within the following address: Wolfram address: Wolfram
Research\Mathematics\4.0\AddOns\Applications.
Research \Mathematics\4.0\AddOns\Applications. After After installing
installing thethe ControlAnima-
ControlAnimation
tion library,
library, the student
the student doesneed
does not not access
need access
to theto the internet
internet or anyorother
any other program.
program.
The up-to-date
The up-to-date version
version ofof Mathematica
Mathematica software
software isis 13.0.
13.0. Its
Its computational
computational require-
require-
mentsare
ments areas
asfollows:
follows:Disk
DiskSpace
Space19 19GB;
GB;RAM
RAM44 GB;GB; Internet
Internet Access
Access(required
(requiredto touse
useonline
online
data sources from the Wolfram Knowledgebase).
data sources from the Wolfram Knowledgebase).
The ControlAnimation library is an integrated symbolic-graphic-numerical computa-
tional tool, which allows visualizing by computer animation both the dynamics in open
loop and the controlled dynamics of some linear and non-linear physical systems [47,48].
The main reason Mathematica software was chosen for the deployment of computa-
tional animations of some control systems in 2001 was its integration of symbolic-graphic-
Educ. Sci. 2022, 12, 253 4 of 20

numerical computational software, allowing at that time the symbolic calculation and
the development of graphic elements. Symbolic calculation is of utmost importance in
analyzing and designing control systems. It allows all the mathematical calculations to
be performed symbolically (without using numerical values) on the analysis and subse-
quent design of control laws. Therefore, it was crucial that suitable software that includes
symbolic calculations should be used, which is the case of Mathematica. Furthermore, it
is worth noting that symbolic calculation involves complex operations for the analysis
and design of control systems that require non-trivial variable isolation and the symbolic
calculation of integrals and derivatives. Thus, libraries (work files in Mathematica) were
developed, taking into account the latter properties of symbolic computation that contain
all the symbolic calculations for control laws analysis and design of the physical systems
under study. Also, a simple interface was created that allows the operator of the library
(the professor or students) to enter the corresponding or desired numerical values and
obtain the variables. Therefore, the results are the interest variable traditional simulations
vs. time and the computer animation of the physical system under study, showing its
behavior similar to the physical reality of the system. This is a property that at the time
other software, such as Matlab or Maple, did not offer, since the latter did not allow the
development of graphic elements. Moreover, Matlab or a programming software such as
Easy Java/Javascript Simulations (EJS) [49–51] did not enable symbolic calculation.
One of the disadvantages of using Mathematica software is that it is not open-source
software. This means that Mathematica software, like Matlab, involves licensing costs.
However, these types of software are the most used in control theory analysis and design.
The Department of Control Systems at the University of Los Andes includes a simulation
laboratory equipped with several desktops with Matlab and Mathematica software installed.
However, the availability of this laboratory is limited by the course schedule and the
computer requirements of all the students.
The latter are commonly used as tools in teaching analysis and design of control
systems in universities worldwide. Thus, throughout the application of the Comput-
erAnimation library framework, control systems were developed, and among them can
be mentioned:
1. Mass-spring-damper system;
2. Simple pendulum;
3. Inverted pendulum;
4. Inverted pendulum mounted on a cart;
5. Double inverted pendulum mounted on a cart;
6. Two inverted pendulums mounted on a cart;
7. Watt Governor (Figure 2);
8. Centrifugal pendulum;
9. Airplane.
In 2005, new functions were added to the ControlAnimation library in order to analyze
the discretization (sampling) of non-linear systems [46,52]. This allowed the library to
serve as teaching support in post-graduate courses in the field of control systems, such
as at the master’s level. As an example, in Velasco’s master’s degree work in 2010 [53],
new discretization techniques were applied for non-linear systems, and non-linear control
design adapted to the inverted pendulum control system. First, on the computer animation
of the inverted pendulum [53] and later, once its proper functioning was confirmed, these
techniques were applied to the actual physical systems deployed in the laboratory [54].
The ControlAnimation library was and is still used to teach the dynamic behaviors
of primordial control systems, such as a greater approach and understanding of the op-
eration of these systems and visualizing their responses to different inputs or control
laws. For example, it complements the instructional framework through variable vs. time
graphs [55,56]. This highlighted the advantages of the teaching technique, allowing stu-
dents to co-identify and relate in a more intuitive way to the mathematical models and
control equations with the physical behavior of the real system.
Educ.
Educ.Sci. 2022,12,
Sci.2022, 12,253
x FOR PEER REVIEW 55 of
of2020

Figure2.2.Watt
Figure WattGovernor
Governorcomputer
computeranimation:
animation:(a)
(a)Initial
Initialposition
positionininzero
zerodegree;
degree;(b)
(b)Desired
Desiredposition
position
at 45 degrees. Adapted from [26].
at 45 degrees. Adapted from [26]. Supplementary Materials Video S1 and Document S2 show a video
of the computer animation of the Watt Governor and the Mathematica software code, respectively.
In 2005, new functions were added to the ControlAnimation library in order to ana-
lyzeFor
theinstance,
discretization (sampling)
a physical controlofsystem
non-linear
can be systems [46,52].
on a solid planeThis allowed
surface, andthe library
students
to serve
would as teaching
perform supportand
the analysis in post-graduate
design on such courses in theusually
a system, field of forgetting
control systems,
certainsuch
re-
strictions
as at the or physical
master’s limitations
level. of the realinsystem’s
As an example, Velasco’s behavior.
master’sThese
degree restrictions
work in 2010 include
[53],
designing control laws
new discretization that work
techniques werewell mathematically
applied for non-linear speaking,
systems,meeting the system’s
and non-linear control
objective to the desired
design adapted to the final conditions.
inverted pendulumHowever,
control it system.
is physically
First,impossible to implement
on the computer anima-
them in the mentioned real system, since the dynamics of the real
tion of the inverted pendulum [53] and later, once its proper functioning was confirmed,system in terms of its
position, in some instants of time, present negative values (below
these techniques were applied to the actual physical systems deployed in the laboratory the physical surface
supporting
[54]. the system). These are mistakes students usually make due to their inexperi-
ence andThe the lack of visualization
ControlAnimation libraryand
wasunderstanding
and is still used of the system’s
to teach behavior behaviors
the dynamic through
traditional
of primordialtwo-dimensional
control systems, graphs
such(variable vs. approach
as a greater time). and understanding of the oper-
ationByofthe yearsystems
these 2010, the usevisualizing
and of computer animations
their responses in control systems
to different wasorbooming.
inputs Ma-
control laws.
jor computer programs such as Matlab and Mathematica already
For example, it complements the instructional framework through variable vs. time included some commands
and libraries
graphs thatThis
[55,56]. allowed interaction
highlighted thewith certain animated
advantages digitaltechnique,
of the teaching objects, mainly the sim-
allowing stu-
ple and the inverted pendulum. However, these versions were not
dents to co-identify and relate in a more intuitive way to the mathematical models andfree or easily accessible
tocontrol
most students
equations inwith
the Department
the physicalofbehavior
Control of Systems
the realatsystem.
University of Los Andes.
For instance, a physical control system can be on a solid plane surface, and students
4. Project-Based Learning and Online Education through Computer Animation
would perform the analysis and design on such a system, usually forgetting certain re-
Project-based
strictions learning
or physical (PBL)of
limitations has
thebeen
real established throughout
system’s behavior. Thesethe 20th century
restrictions as
include
adesigning
tool to improve classical (or traditional) education practices [23]. It is
control laws that work well mathematically speaking, meeting the system’s ob-a methodology
developed
jective to thefrom the Aalborg
desired UniversityHowever,
final conditions;. Model in itthe
is early 1970simpossible
physically [57–59], which is based
to implement
on three principles: cognitive learning, the contents, and social approaches
them in the mentioned real system, since the dynamics of the real system in terms of [58,60,61]. Theits
latter is linked
position, to the
in some UNESCO
instants education
of time, presentgoals, including
negative learning
values (belowtothe know, learning
physical to
surface
do, learning to live together and learning to be, which require new teaching and learning
supporting the system). These are mistakes students usually make due to their inexperi-
strategies to be applied as an alternative to old educational ways [62,63]. Recent works
ence and the lack of visualization and understanding of the system’s behavior through
have discussed PBL characteristics, highlighting commonalities and specific contrasts
traditional two-dimensional graphs (variable vs. time).
with other strategies, such as problem-based learning, with a distinctive difference in the
By the year 2010, the use of computer animations in control systems was booming.
effectiveness of the methods [23,59,61–66]. Moreover, the UNESCO report in 2010 [67,68],
Major computer programs such as Matlab and Mathematica already included some com-
indicates the importance of an innovative mindset in engineering graduates. Thus, using
mands and libraries that allowed interaction with certain animated digital objects, mainly
project- and product-based educational strategies would allow engineering students to
the simple and the inverted pendulum. However, these versions were not free or easily
attain the know-how crucial for their professional practice and reach their goals of self-
accessible to most students in the Department of Control Systems at University of Los
being and social development, representing the broader objectives of education [22,69],
Andes.
highlighting the need for engineers’ education to develop interactions, diversity and
information searching skills [8]. Additionally, project- and product-based learning have
4. Project-Based Learning and Online Education through Computer Animation
been involved in the current discussion on how to fulfill industry needs and satisfy the
Project-based
requirements learningof(PBL)
of knowledge has beenfundamentals
engineering established throughout
[22,39,57,63].the 20th century as a
toolAnother
to improve classical (or traditional) education practices
component of the project-based learning framework is the [23]. It is a methodology
connection be- de-
veloped from the Aalborg University Model in the early 1970s [57–59],
tween the industry requirements and the global management of economic development. which is based on
three principles: cognitive learning, the contents, and social approaches [58,60,61]. The
Educ. Sci. 2022, 12, 253 6 of 20

Both are related to engineering education, stressing the importance of an entrepreneurial

mindset in engineering graduates [19]. According to recent research work [60,70] more
engineering programs are including learning environments that enable experimenting with
entrepreneurial behavior. PBL experiences have multiplied in recent years, even more after
the COVID-19 pandemic started [13]. Accordingly, multiple examples of the deployment of
PBL strategies can be found in the literature, including courses in design and engineering
curricula [13,23,57,60,61,64].
Furthermore, new generational groups, such as Generation Z [68], are more inclined
to use computers and technological devices as tools to learn [63]. Thus, several univer-
sities have started implementing computer animation-based and project-based learning
strategies to attain the course goals [69,70]. The interest and application of such strate-
gies have been heightened during COVID-19, before and after the confinements were
enacted. Consequently, a more enriched field of online strategies related to project- and
product-based education have been developed and are available [9,10,13]. Among the
innovations is the extended use of online meeting tools such as Google Classroom, Zoom,
Teams, among others, that have been adapted to the virtual learning environment. In order
to do that, professors have developed creative initiatives to enhance the virtual teaching
experience [71]. In the following section, a thorough review of the research works and
the implementation of computer animation as a promising way to adapt control systems
engineering education to present times is performed.

5. Computer Animation as an Educational Tool in Teaching and Learning of Control

Systems Engineering
Since 2008, the ControlAnimation library has supported the process of undergraduate
students’ teaching and learning at the Department of Control Systems at University of Los
Andes, using a project-based learning framework as an educational tool. Each student or
pair of students was assigned one of the control systems from the ControlAnimation library.
All the concepts, theories, and techniques of the discrete control program were applied to
the control system. First, students had to develop all the calculations and mathematical
analyses according to their control system. Then they had to observe the dynamics given by
traditional graphs vs. time and finally visualize the dynamics on the computer animation
(computational mimics), thus connecting mathematics with the real system physics.
This project-based learning technique allows each student to interact with an animated
control system (virtually). The student has the possibility and freedom to change both
the parameters of the system’s mathematical model and the design parameters in control
laws in a comfortable and somewhat playful way. Thus, the student does not have the
pressure to interact with a real physical system, which can somehow be damaged due
to their inexperience (as sometimes happens). Hence, the student interacting with the
computer animation system can afford to make mistakes, learn from their mistakes, and
perform virtual tests before implementing the control laws designed in real control systems
(in case of having real physical systems available in the laboratory).
These educational tools were also implemented in undergraduate thesis projects at
the Department of Control Systems, such as the research work developed by Sánchez [54],
where computer animation of the inverted pendulum system was used (Figure 3). First,
different simulated experiments with designed control laws were performed, and their
behaviors were visualized on the inverted pendulum computer animation, before and
after perturbations in the pendulum bar length parameter value; then, control laws were
implemented over the real system built in the lab.
In 2015, Marquez [16] developed the Reflex Arc model in his degree thesis (Figure 4)
as a computer animated digital object using the Mathematica program. Thus, he was able
to analyze better the dynamics of its mathematical model and the behaviors of this system
and its subsystems before the designed control laws. In this case, it was impossible to
apply these control laws to the real system (human beings) without being invasive in the
 computer animation system can afford to make mistakes, learn from their mistakes, and
perform virtual tests before implementing the control laws designed in real control sys-
tems (in case of having real physical systems available in the laboratory).
These educational tools were also implemented in undergraduate thesis projects at
the Department of Control Systems, such as the research work developed by Sánchez [54],
Educ. Sci. 2022, 12, 253
where computer animation of the inverted pendulum system was used (Figure 3). 7First, of 20

different simulated experiments with designed control laws were performed, and their
behaviors were visualized on the inverted pendulum computer animation, before and af-
system, so computational
ter perturbations mimics were
in the pendulum barof great parameter
length help to understand the behaviors
value; then, beyond
control laws were
the traditional over
implemented graphs
theof response
real systemvariable vs. time.
built in the lab.

Educ. Sci. 2022, 12, x FOR PEER REVIEW 8 of 20

Figure3.3.Capture
Figure Captureofofa sequence
a sequenceof the Inverted
of the Pendulum
Inverted computer
Pendulum animation.
computer (a–f) Position
animation. change
(a)–(f) Position
of the mimic as a function of time (in some seconds). Reproduced from [51].
change of the mimic as a function of time (in some seconds). Reproduced from [51].

In 2015, Marquez [16] developed the Reflex Arc model in his degree thesis (Figure 4)
as a computer animated digital object using the Mathematica program. Thus, he was able
to analyze better the dynamics of its mathematical model and the behaviors of this system
and its subsystems before the designed control laws. In this case, it was impossible to
apply these control laws to the real system (human beings) without being invasive in the
system, so computational mimics were of great help to understand the behaviors beyond
the traditional graphs of response variable vs. time.

Figure 4.
Figure Physical pendulum
4. Physical pendulum diagram,
diagram, analogous
analogous to
to the
the patellar
patellar SLR.
SLR. Reproduced
Reproduced from
from [16].
[16].
At the beginning of 2020, due to the COVID-19 related confinement in Latin America,
At the beginning of 2020, due to the COVID-19 related confinement in Latin America,
most universities in Venezuela, including the University of Los Andes (ULA), went from
most universities in Venezuela, including the University of Los Andes (ULA), went from
face-to-face teaching to the distance education mode. Therefore, information and communi-
face-to-face teaching to the distance education mode. Therefore, information and commu-
cation technology (ICT) became essential to support distance education, implying a change
nication technology (ICT) became essential to support distance education, implying a
in the teaching characteristics of specific educational content in the Department of Control
change in the teaching characteristics of specific educational content in the Department of
Systems at the ULA. Accordingly, the use of computer animation educational tools and
Control Systems
project-based at thebecame
learning ULA. Accordingly, the use of
of utmost importance tocomputer animation
make feasible educational
these new ways of
tools and project-based
teaching [9,13]. learning became of utmost importance to make feasible these new
waysIn ofTable
teaching
1 is[9,13].
described the conceptual framework of some of the Control Systems
In Table 1 is described the
Engineering undergraduate conceptual
program, whichframework
includes 10ofacademic
some of the Control
periods of 6 Systems
months
Engineering
each, at the University of Los Andes, in which the ControlAnimation library 6has
undergraduate program, which includes 10 academic periods of months
been
each, at the University of Los Andes, in which the ControlAnimation library has been
used as support in the educational process since 2008. Table 2 presents traditional learning used
as supportand
strategies in the educational
Table process
3 project-based since 2008.
learning Tableapplied
strategies 2 presents traditional
to the Control learning
Systems
strategies
Engineering and Table described
courses 3 project-based learning
in Table 1. strategies applied to the Control Systems
Engineering courses described in Table 1.

Table 1. Conceptual framework of Control Systems Engineering courses.

Course Level Objectives

 Provide the student with the basic concepts and tools for mathemat-
Physics Systems Modelling
Educ. Sci. 2022, 12, 253 8 of 20

Table 1. Conceptual framework of Control Systems Engineering courses.

Course Level Objectives

• Provide the student with the basic concepts and tools
Physics Systems Modelling Classroom hours: 4 h for mathematical modeling, understanding,
Simulation laboratory hours: 1 h 5th period interpretation, and simulation of physical processes.
Academic units: 4 • Show the control system’s behavior through their
mathematical model.
• Provide the student with a historical vision of the
Automatic Control History (Elective Course) evolution of control from the Greeks to the present day,
Classroom hours: 3 h based on the associated systems and models,
6th period
Simulation laboratory hours: 2 h emphasizing the interrelation between advances in
Academic units: 4 technology, mathematics, and systems theory.
• Provide the methods and techniques for constructing
System Identification dynamic process models from processing experimental
Classroom hours: 4 h input and output data.
8th period
Simulation laboratory hours: 2 h • Provide the student with tools for validating
Academic units: 5 mathematical models of processes.
• Prepare the student to analyze, design, and implement
computer-based control systems.
Digital Control • Provide students with techniques and fundamentals to
Classroom hours: 4 h sample (discretize) control systems.
Simulation laboratory hours: 2 h 9th period • Present controller design techniques for sampled
Physics control process laboratory hours: 2 h systems.
Academic units: 6 • Provide students with implementation methods of
sampled (or discretized) control systems.
• Provide students with tools to study uncertain models
Robust Control (Elective Course) and process disturbances, observing their effects on
Classroom hours: 3 h 8th or 9th the performance of control systems.
Simulation laboratory hours: 2 h period • Provide students with tools for designing control
Academic units: 4 systems that consider uncertain models and process
disturbances.
Educ. Sci. 2022, 12, 253 9 of 20

Table 2. Traditional learning strategies in Control Systems Engineering courses.

Expected Competencies Students at the End

Course Name Teaching Goals Traditional Learning Strategies Evaluation
of the Course

• Expository Class:
The context is centralized in the
professor. • To know different techniques for the
(1) The professor is responsible for • Written evaluation: written tests of construction of mathematical models.
Teaching basic physical laws, including
preparing the content and material of all the knowledge attained on • To know which technique is the most
some techniques for constructing formal
classes. Classes are shown and explained mathematical calculation and appropriate for constructing
mathematical models of physical
to students. subsequent written analysis. mathematical models according to the
Physics Systems Modelling systems. Providing the basic knowledge
(2) The professor explains to students the • Traditional simulation of some physical system under study.
to represent and understand, through
step-by-step solution of mathematical exercises and subsequent written • Understand the dynamic behavior of the
mathematical models, the behavior of
exercises based on the contents of the analysis. physical systems studied according to
physical systems.
course. their characteristics and properties.
(3) The professor shows the different
behaviors of the control systems studied
through the traditional simulation
(variable of interest vs. time).
• Expository Class:
The context is centralized in the
professor.
Teaching the evolution of control • Written evaluation: written tests of
(1) The professor is responsible for • To know the main contributions of
systems from the Greeks to the present the knowledge attained.
Automatic Control History preparing the content and material of all automatic control to humanity
day, where each advance is based on the • Written bibliographic research
(Elective Course) classes. Classes are shown and explained throughout history.
mathematics of control systems theory projects.
to students.
and technology at the time.
(2) The professor shows the most
relevant control systems throughout
history and their main contributions to
control theory supported by images. • To know different techniques to identify
• Expository Class: physical systems.
• To know what technique is most
The context is centralized in the • Written evaluation: written tests of
Teaching how to use the different convenient to apply to a physical system
professor. the knowledge attained on
techniques and calculation tools to for its identification, according to its
(1) The professor is responsible for mathematical calculation and
obtain a physical control system characteristics and properties.
System Identification preparing the content and material of all subsequent written analysis.
mathematical model experimentally, • Obtain a mathematical model
classes. Classes are shown and explained • Traditional simulation of some
e.g., using the input-output data of the representing the dynamics of the real
to students. exercises and subsequent written
control system. physical system under study.
(2) Use of traditional calculation tools, analysis.
• Perform traditional simulations and
which are shown and explained by the analyze the dynamics (behaviors) of the
professor. physical systems studied.
Educ. Sci. 2022, 12, 253 10 of 20

Table 2. Cont.

Expected Competencies Students at the End

Course Name Teaching Goals Traditional Learning Strategies Evaluation
of the Course

• Expository Class:
• Written evaluation: written tests of
The context is centralized in the the knowledge attained on the • To know the different techniques to
professor. mathematical calculation and discretize (sample) control systems.
(1) The professor is responsible for subsequent written analysis. • Design control laws for discrete systems.
preparing the content and material of all • Applied project: The student • Perform traditional simulations. Both
The professor must show and teach to classes. Classes are shown and explained carries out a computational continuous time and discrete time.
use the different techniques and tools of to students. implementation (a graphical • Analyze the discrete dynamics
Digital Control
calculation for the analysis and design of (2) The professor explains to the students simulation of the dynamics of (behaviors) of the physical systems
linear control systems in discrete time. the step-by-step solution of interest of the system under study) studied when comparing them with
mathematical problems, based on the and digital implementation of the continuous dynamics.
contents of the course. control law in a real physical • Implement the control laws designed in
(3) The professor explains the system in the control process real physical systems.
step-by-step implementation of laboratory.
discretization techniques in a real
physical system.
• Expository Class:
The context is centralized in theprofessor.
(1) The professor is responsible for
preparing the content and material of all
classes. Classes are shown and explained • To know different techniques to control
Teaching the different techniques and
to students. • Written evaluation: written tests of systems with uncertainties.
calculation tools for analyzing and
(2) The professor explains the knowledge attained on • To know what type of robust control
designing control systems in their
step-by-step solution of mathematical mathematical calculation and technique is the most convenient to apply
practical performance, operating in
problems to the students, based on the subsequent written analysis. to a physical system according to the
Robust Control (Elective Course) restrictive, uncertain and limiting
course contents. • Traditional simulation of some characteristics and properties.
conditions. This is performed in such a
(3) The professor shows the changes in a exercises and subsequent written • Perform traditional simulations and
way that the control system can satisfy
control system with uncertainties analysis. analyze the dynamics (behaviors) of the
the operating criteria despite the
through traditional input-output graphs. physical systems studied.
disturbances present in the system.
(4) The professor shows how the design
of a robust controller can act in the
presence of a disturbance and continue
to control the system to the desired
conditions, through traditional
input-output graphs.
Educ. Sci. 2022, 12, 253 11 of 20

Table 3. Project-based learning strategies applied in Control Systems Engineering courses.

Expected Competencies Students at the

Course Name Teaching Goals Traditional Learning Strategies Evaluation
End of the Course
(1) Active-Learning: Students become protagonists and
individually or collaboratively manipulate the
ControlAnimation library. This is performed by
changing the parameters of the system’s mathematical
model to observe the dynamics through traditional
(1) Have all the knowledge simulation (variable of interest vs. time) and by Project-based evaluation: (1) They must acquire all the skills
Physics Systems Modelling
competencies and teaching skills following the control system’s computer animation According to the course and its described in Table 2 (expected
explained in Table 2 (teaching goals behavior. content, the evaluation is performed competencies students at the end of the
part) on the contents, according to (2) Visualizing Systems Thinking: students visualize through a specific rubric for each course part), according to the
the corresponding course. the dynamics (behavior) of the control theory project. corresponding course.
(2) Know how to play the tutor’s techniques in the proposed exercises, using the (2) Apply the ability to analyze and
role, making individual advice when ControlAnimation library. synthesize information critically.
(1) Problem-Solving: students individually or • The designed rubric allows a
the students require it. comprehensive evaluation, (3) Acquire and apply research skills.
(3) Motivate students to relate collaboratively choose a control system that has been (4) To associate the theoretical knowledge
representative in the history of automatic control (for both qualitative and
control theory and its application to quantitative. acquired, according to the course, with the
the control systems studied and example, the Watt Governor). Then, students build a real structure and behavior of physical
computer animation of the chosen control system using • The designed rubric allows
connect mathematics with physics. auto-evaluation and systems.
(4) Emphasize open-ended questions the new technologies currently available. Thus, they (5) Develop autonomous work and be
must understand their physical functioning, limitations, co-evaluation: the student
to promote discussion rather than participates as a self-evaluator active students in the learning processes.
Automatic Control History focusing on one type of answer the mathematical model, parameters, and dynamics. (6) Develop more creative skills.
(Elective Course) (2) Active-Learning: students become protagonists and of his work and their fellow
question about knowledge. students’ work.· The
(5) Guide or direct the discussions in individually or collaboratively manipulate the
ControlAnimation library or other open-source evaluation process is
such a way that knowledge about all continuous.
the contents of the course is covered. computer animation programs to develop a computer
animation of the chosen control system. • Part of the evaluation involves
(3) Visualizing Systems Thinking: the built computer reflective evaluation.
animation must be able to reproduce the control system
dynamics according to the given model parameters.
(1) Active-Learning: students individually or
collaboratively apply identification techniques to the
input-output data obtained from computer animation,
using the ControlAnimation library, and build the
System Identification mathematical model representing the physical system.
(2) Visualizing Systems Thinking: students validate
their models’ behavior with the dynamic behavior of
the computer animation under study, using the
ControlAnimation library.
Educ. Sci. 2022, 12, 253 12 of 20

Table 3. Cont.

Expected Competencies Students at the

Course Name Teaching Goals Traditional Learning Strategies Evaluation
End of the Course
(1) Active-Learning: students, individually or
collaboratively, apply the sampling techniques to the
control systems of the ControlAnimation library.
(2) Visualizing Systems Thinking: students analyze the
effects of the sampling period, T0 , on the dynamics of
the sampled system by observing the traditional
discrete graphs (variable of interest vs. time) and the
dynamic behavior of the computer animation using the
ControlAnimation library.
Digital Control
(3) Problem-Solving: students design the digital control
laws and observe the dynamics of the controlled system
in the same way. Supported by the ControlAnimation
library, students can analyze and design control laws
for control systems commonly studied in control theory.
(4) Experiential Activities and Case-Study: students
implement a real system that is carried out according to
the availability of real physical control systems in the
laboratory.
(1) Active-Learning: students, individually or
collaboratively, manipulate the existing parameter
values of models in the ControlAnimation library, to
Robust Control (Elective recreate perturbations of the parametric type.
Course) (2) Visualizing Systems Thinking: students observe the
computer animation’s dynamic behavior in the
presence of these perturbations using the
ControlAnimation library.
Educ. Sci. 2022, 12, 253 13 of 20

The ControlAnimation library has been used as an educational tool since 2008 in the
courses already mentioned above. In addition, the ControlAnimation library has been used
progressively in control theory courses, to the extent that the pre-established educational
contents, education and evaluation strategies of these courses have been adapted to the
inclusion of the ControlAnimation library. Therefore, the ControlAnimation library deploy-
ment can be valued quantitatively according to the course number of contents, activities,
and evaluations which are supported by the use of the tool. The latter is performed with
a 0 to 100% scale, 100% corresponding to all the content, activities, and evaluations the
course requires.
Project-based learning strategies increase the use of the ControlAnimation library in
the different courses (in % in Table 4), since these strategies allow the traditional course
contents to be adapted to innovative educational practices. It should be noted that the
traditional contents were designed under the concept of conventional education based on
masterclasses, where the professor is the active actor and the students are passive actors.
Project-based learning strategies however focus on learning, where students are the active
actors, and the professor becomes a guide or tutor. The most used project-based learning
strategies are active-learning, visualizing systems thinking (adapted to control systems),
problem-solving techniques, experiential activities and case-studies method. For example,
using the visualizing systems thinking strategy gives opportunities throughout the process
by means of computer animation tools to visualize the dynamics of the implementation of
control theory techniques in the proposed exercises.

Table 4. Average students’ grades before and during the pandemic in some Control Systems Engi-
neering courses.

Students Use of the

ControlAnimation Average Grades Students Approved
Year Course Name
Library in Their (Range 1–20 pts) Course (%)
Activities (%)
2011 Digital Control 30 12.3 ± 1.7 85
2011 Robust Control 30 13.7 ± 1.9 95
2012 Digital Control 40 13.1 ± 1.7 90
2012 System Identification 20 14.6 ± 2.1 98
2013 Digital Control 50 14.7 ± 2.0 100
2013 System Identification 30 15.8 ± 1.9 95
Physics Systems
2014 20 12.4 ± 1.5 89
Modelling
2014 System Identification 40 15.7 ± 2.0 100
Physics Systems
2015 30 13.8 ± 1.9 95
Modelling
2015 System Identification 40 16.2 ± 1.8 100
Physics Systems
2017 40 14.1 ± 1.8 98
Modelling
2017 System Identification 50 16.4 ± 2.0 100
Physics Systems
2018 40 13.9 ± 1.9 97
Modelling
2018 System Identification 50 16.3 ± 1.5 00
Physics Systems
2019 40 14.2 ± 1.6 98
Modelling
Physics Systems
2020 60 16.6 ± 1.8 97
Modelling
2021 System Identification 80 18.7 ± 1.9 100
Automatic Control
2021 80 17.8 ± 2.1 97
History

On the other hand, one of the significant limitations of the teaching of identification
techniques occurs when there is no provision of real control systems in the laboratory (they
Educ. Sci. 2022, 12, 253 14 of 20

do not exist or are outdated). Thus, experiential activities may be possible by using the
ControlAnimation library, providing input-output data from common computer-animated
control systems (including noise signals or disturbances in the system). This allows students
to work with control systems through computer animations as a black box, where the
system model and computer animation are not visible to students. Furthermore, different
objective-based strategies are designed to achieve the proposed student learning depending
on the content.
As for the percentage of the ControlAnimation library use under project-based learning
strategies in the control systems courses, its value is quantified as follows.
A value of 1% to 30% when the ControlAnimation library is used only as a support
tool for demonstrations. In this case, the professor operates the library and shows his
students the results obtained, analyzing the professor’s results.
From 31% to 50% when the professor operates the library in some content or activities
and shows students the results obtained. In contrast, in other content or activities, the
students themselves manipulate the ControlAnimation library to get the results and analysis
required by the professor, always under the supervision and guidance of the professor at
each step. The results are analyzed between the professor and students.
From 51% to 80% when students, according to indications given virtually by the
professor, manipulate the ControlAnimation library by themselves to complement the
theoretical studies taught by the professor in a virtual way (digital material, videos),
obtaining the results and analyses required by the professor. Performing the practical
exercises required by the professor; and sometimes the students themselves build computer
animations, either using Mathematica or other open-source computer animation programs
to represent new physical systems of control systems, reaching a new level of understanding
and understanding of the system under study.
Finally, a value of 81% to 100% is attained when all the activities are performed through
project-based learning, which is unfeasible according to the teaching required in control
systems engineering, which sometimes requires the professor’s intervention.
Thus, since 2020, when stay-at-home orders due to the COVID-19 pandemic were
enacted, the ControlAnimation library has been used with greater prominence by using
project-based learning strategies and the new open-source computer animation programs
available on the internet. In Table 4, the quantitative evaluative results throughout a 10-year
period (2011–2021) are shown. The data includes the average grades and percentage of
students that approved the course before the pandemic and during the pandemic in Control
Systems Engineering courses at the University of Los Andes.
Before the pandemic, students’ attendance at the Department of Control Systems at
the University of Los Andes was regulated. Thus, it was not crucial to have the necessary
technological resources to use the ControlAnimation library (for example, on their personal
computer). These resources were provided by the university as far as possible. However,
the stay-at-home orders and transition to online education enacted in 2020, impelled
professors and students to use technological resources, including having the software for
distance education to be feasible. Therefore, since 2020, the students enrolled in the courses
indicated in Table 4 must have their own technological resources, such as internet access,
personal computer, and Mathematica Software. This facilitated the inclusion of greater
use of the ControlAnimation library. However, due to the implementation of distance
education learning, the traditional way of classroom education had to be adapted to this
new modality. Therefore, project-based learning strategies were applied (these depend on
the content of the course, the activities and the type of evaluation that are desired) to meet
the teaching-learning objectives required by the course and the university program.
The results shown in Table 4 illustrate how the average grades have been progressively
increasing in the same courses. In addition, the percentage of ControlAnimation library
that the students use in their course activities has also increased to support the learning
process. Figures 5 and 6 summarize the main results from Table 4.
Educ. Sci. 2022, 12, x FOR PEER REVIEW 15 of 20
Educ. Sci.
Educ. Sci. 2022,
2022, 12,
12, 253
x FOR PEER REVIEW 15
15 of 20
of 20

Figure 5. System
System Identification course:
course: Percentage of
of students’ use
use of the
the ControlAnimation library
library
Figure
Figure 5.5. System Identification
Identification course: Percentage
Percentage of students’
students’ use of
of the ControlAnimation
ControlAnimation library
in their activities and average grades over the past few years.
in
in their
their activities
activities and
and average
average grades
grades over
overthe
thepast
pastfew
fewyears.
years.

Figure
Figure 6.6. Physics
Physics Systems
Systems Modelling
Modelling course:
course: Percentage
Percentage of
of students’
students’ use
use of
of the
theControlAnimation
ControlAnimation
Figure 6. Physics Systems Modelling course: Percentage of students’ use of the ControlAnimation
library in
library in their
their activities
activities and
and average
averagegrades
gradesover
overthe
thepast
pastfew
fewyears.
years.
library in their activities and average grades over the past few years.
Figures
Figures55andand66indicate
indicatethat,
that,inin
thethe
courses
coursesSystem
System Identification
Identificationandand
Physics Systems
Physics Sys-
Figures
Modelling, 5 and 6
the average indicate
grades that, in the
increased courses
during System Identification
the pandemic years and
by by Physics
implementing Sys-
tems Modelling, the average grades increased during the pandemic years implement-
tems Modelling,
project-based the average
learning grades
strategies usingincreased during the pandemic
the ControlAnimation inyears
librarylibrary by implement-
a higher percentage.
ing project-based learning strategies using the ControlAnimation in a higher per-
ing
Good project-based
results were learning
also strategies
observed in theusing the
Automatic ControlAnimation
Control History library
course in a higher
(Table per-
4), using
centage. Good results were also observed in the Automatic Control History course
centage.
the Good results were
ControlAnimation also
library andobserved in the Automatic
project-based learning Control History
strategies in 2021. course
The average
(Table 4), using the ControlAnimation library and project-based learning strategies in
(Table obtained
grades 4), using indicate
the ControlAnimation
a trend of library
increasing and project-based
grades, representing alearning
promising strategies
evolutionin
2021. The average grades obtained indicate a trend of increasing grades, representing a
2021.
of The average
students’ grades in
performance obtained indicate
the course. a trendthe
However, of latter
increasing
shouldgrades, representing
be further analyzed a
promising evolution of students’ performance in the course. However, the latter should
promising
in evolution(courses,
several instances of students’ performance
university programs) in theto course.
understand However,
if theretheis alatter should
connection
be further analyzed in several instances (courses, university programs) to understand if
be furtherstudents’
between analyzedperformance
in several instances
and learning(courses, university programs)
of functioning and analysis to of
understand
control dy- if
there is a connection between students’ performance and learning of functioning and anal-
there is compared
namics a connection between students’
to traditional education performance
strategies. and
Thus, learning
furtherofresearch
functioning
and aand anal-
broader
ysis of control dynamics compared to traditional education strategies. Thus, further re-
ysis of control dynamics
implementation compared
(in other courses or to traditional
other education strategies.
control engineering Thus, programs)
undergraduate further re-
search and a broader implementation (in other courses or other control engineering un-
should be performed.
search and a broader implementation (in other courses or other control engineering un-
dergraduate programs) should be performed.
dergraduate programs) should be performed.
6. Challenges and Opportunities of Implementing Computer Animation as an
Educational Tool in Control Systems Engineering Undergraduate Programs
Technological advances, both at the software and hardware level, and the approach
and expertise of control engineering students in using computational tools have shown
 Educ. Sci. 2022, 12, x FOR PEER REVIEW 16 of 20

6. Challenges and Opportunities of Implementing Computer Animation as an Educa-

Educ. Sci. 2022, 12, 253 tional Tool in Control Systems Engineering Undergraduate Programs 16 of 20
Technological advances, both at the software and hardware level, and the approach
and expertise of control engineering students in using computational tools have shown
theusefulness
the usefulnessand andfeasibility
feasibilityof ofimplementing
implementingcomputer computeranimations
animationsin indistance
distance courses.
courses.
Thetransition
The transitionhas has been
been smooth,
smooth, pleasant,
pleasant, and and even
evenfunfunfor
forstudents
studentsatatthetheDepartment
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ofControl
Control Systems.
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Nowadays, the the
feasibility of the
feasibility ofstrategy has allowed
the strategy students
has allowed to have
students toa
wideaset
have wideof applications, both in Matlab-Simulink
set of applications, both in Matlab-Simulinkand Mathematica, as well as as
and Mathematica, access-free
well as
access-free online software (V-Realm 3D, Clara.io, among others). This has allowedand
online software (V-Realm 3D, Clara.io, among others). This has allowed an easy intu-
an easy
itive way to build computer animations based on the physical
and intuitive way to build computer animations based on the physical characteristics of characteristics of control
systems
control commonly
systems used inused
commonly the teaching of control
in the teaching theory.theory.
of control
Todaythe
Today thesame
samelevellevelstudents
studentsare areable
abletotobuild
buildthethecomputer
computeranimations
animationsofofsome some
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control systemsand andconnect
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representsthe thephysical
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system.Additionally,
Additionally,allowing
allowing
visualization of the system’s dynamics through computational
visualization of the system’s dynamics through computational mimics (computer anima- mimics (computer anima-
tion),all
tion), allthis
thisininless
lessthan
thanaaweek.
week.ThisThisopens
opensup up aa toolbox
toolbox ofof great
great possibilities
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Figure
Figure77showsshowsan animage
imageof ofthethecomputer
computeranimation
animationof ofthe
theWatt
WattGovernor
Governorcontrol
control
system, developed by a student in the 6th period of the Automatic
system, developed by a student in the 6th period of the Automatic Control History course. Control History course.
ItItisisimportant
importanttotonote notethat
thatthis
thisstudent
student hashasonly
only taken courses
taken on on
courses modeling
modeling andandanalysis of
analysis
control
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Moreover, he hashenohastheoretical knowledge
no theoretical aboutabout
knowledge the design of control
the design laws
of control
nor
laws discretization
nor discretizationof control systems
of control yet. However,
systems he is able
yet. However, he istoable
construct computational
to construct computa-
mimics from the
tional mimics from understanding
the understanding of theof physics of theofreal
the physics the system and and
real system its mathematical
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ical model. he hashebeen
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beentoable
connect the Matlab
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the Matlab with other
program withapplications
other appli-
for the animated digital object design in such a way as to be
cations for the animated digital object design in such a way as to be able to visualize able to visualize both both
the
traditional
the traditional response dynamics of the signal (or variable) vs. time and the dynamicsthe
response dynamics of the signal (or variable) vs. time and the dynamics on on
computer
the computer animation. Thus, Thus,
animation. evaluating a system
evaluating with a behavior
a system similar tosimilar
with a behavior reality tothrough
reality
computer animation.animation.
through computer

Figure7.7.Watt
Figure WattGovernor
Governorcomputer
computeranimation
animationbuilt
builtby
byaastudent
studentof
ofthe
the6th
6thperiod
periodofofthe
theControl
Control
Systems courses at the University of Los Andes. Supplementary Materials Video S1 and Document
Systems courses at the University of Los Andes.
S2 show a video of the computer animation of the Watt Governor and the Mathematica software
code,Itrespectively.
should be noted that an animated digital object is not 100% comparable with a
real physical system, because the real physical system will always have subsystems or
It should be
supersystems, noted
some that an animated
components, digitalsignals,
disturbance object isfrictions
not 100%between
comparable with
parts, a real
among
physical system, because the real physical system will always have subsystems
others, not considered in their representation in a computer animation. However, to avoid or super-
systems, somecomplexities,
mathematical components,manydisturbance
of thesesignals, frictions
features are alsobetween
not fullyparts, among others,
incorporated into
the mathematical models that represent the physical system. Just as there is avoid
not considered in their representation in a computer animation. However, to math-
parsimony
ematical
in complexities,
the mathematical many of
modeling of these features
physical aresystems,
control also notthis
fully incorporated
concept into the
also applies to
constructing computer animations of physical control systems.
Furthermore, it is essential to note that only performing analysis and design of control
systems by students through traditional simulations and/or computer animations limits
the student from the experience that he can (and should) acquire when interacting with
Educ. Sci. 2022, 12, 253 17 of 20

real control systems. As mentioned above, unexpected or unconsidered situations arise

that do not occur in the digital simulations’ world, which is one of the main disadvantages
of distance education. This is the case of the Digital Control course, which requires within
its contents the implementation of discretization techniques (sampling) in a real physical
control system.
Finally, discussions were held with the students to understand better the advantages
and challenges of deploying the computer education and project-learning strategies online.
It could be observed that during the years prior to 2015, the students had some reluctance
to carry out their activities using the ControlAnimation library, mainly at the beginning of
the course. However, after applying this educational framework in the years 2020 and 2021,
we noticed that students are much more open and motivated to use the ControlAnimation
library to perform the different activities related to the course. In addition, they have been
participative and motivated to create their own computer animations. We believe these
are promising results due to technological advances that can be found nowadays in new
animation software. This could help to make more accessible and intuitive to include
computer animation strategies in online education, even for students of lower academic
level, such as those of the 5th period of the control systems engineering program.

7. Conclusions
Education goes far beyond an infrastructure that delimits academic spaces, thus it
is necessary to include as educational goals learning to know, learning to do, learning to
live together and learning to be, as described by UNESCO. In recent years the educational
system has started to use innovative learning tools, where the student is the center of
the teaching and learning process, to overcome new education challenges of the 21st
century, thus evolving from previous education strategies such as masterclasses where the
professor was the center of the educational process to innovative ones, where the student
is the center of the teaching and learning process. Furthermore, the COVID-19 pandemic
generated an increased urgency to change educational ways. As a result, the teaching and
learning process has ceased to be associated only with a physical space where learning
happens in person and synchronously, but rather in various ways, including virtual spaces.
Nowadays, Information and Communication Technologies (ICT) offer a wide range of new
communication channels and easy-to-use technological tools to support this process.
Computer animation is a handy teaching tool that has shown feasibility in different
fields and stages over the years. Particularly in the control systems engineering course at the
University of Los Andes, where students have been able to connect the physics behavior of
the control system with the mathematical model that represents it. The ControlAnimation
library has been a supporting tool for implementing project-based learning strategies in
the control systems courses at the University of Los Andes recently, especially since the
beginning of the COVID-19 pandemic. Therefore, computer animation could be extended
to other courses as an educational strategy, not only in the area of control systems or
engineering in general but in other fields and levels of education.
Technological advances have allowed students from less advanced courses in control
systems engineering to perform or develop computer animations that were possible only
by very advanced students just a couple of decades ago. This has also allowed for a fur-
ther understanding of theoretical principles, computational calculations, and connections
between software.
The use of the ControlAnimation library deployed under project-based learning strate-
gies in the control systems courses at the University of Los Andes will continue to be a
promising subject of research. The target is to incorporate the use of ControlAnimation
library in almost 100% in all the courses mentioned in this research work and continue
evaluating students’ performance by using quantitative data collection techniques such as
questionnaires. To this end, the education and evaluation strategies of the different course
contents will continue to be adapted to innovative teaching and learning strategies, tailored
to apply computer animation education online.
Educ. Sci. 2022, 12, 253 18 of 20

Currently, the term metaverse is already used to refer to a 3D virtual space that will
simulate reality (or reality unattainable in the tangible physical world). It is said that it
will be the future version of the internet, where encounters between people can take place
through their avatars. Thus, today it might be feasible for us to ask the following questions:
Can the educational future be in the metaverse?
Will it be possible to teach virtually on the metaverse?
In that way, universities and students would find broader possibilities to adapt to a
constantly changing world.

Supplementary Materials: The following supporting information can be downloaded at: https://
www.mdpi.com/article/10.3390/educsci12040253/s1, Video S1 Watt Governor computer animation
from the ControlAnimation library used to teach Control Systems courses at University of Los
Andes and Document S2 showing the Mathematica software code to generate the Watt Governor
computer animation.
Author Contributions: Conceptualization, A.P. software, A.P.; writing—original draft preparation,
A.P.; writing—review and editing, A.P. and R.M. All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no external funding.
Acknowledgments: The authors acknowledge fruitful discussions with professors and students
in the control system engineering courses at University of Los Andes. Jesús Rodríguez-Millán is
acknowledged, who had the idea and proposed the ControlAnimation library framework in the
year 2001.
Conflicts of Interest: The authors declare no conflict of interest.

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