500


     Methods of using mobile Internet devices in the
   formation of the general professional component of
 bachelor in electromechanics competency in modeling of
                     technical objects

   Yevhenii O. Modlo1[0000-0003-2037-1557], Serhiy O. Semerikov2,3,4[0000-0003-0789-0272],
    Ruslan P. Shajda1[0000-0002-7942-9592], Stanislav T. Tolmachev3[0000-0002-5513-9099],
 Oksana M. Markova3[0000-0002-5236-6640], Pavlo P. Nechypurenko2[0000-0001-5397-6523] and
                      Tetiana V. Selivanova2[0000-0003-2635-1055]
                        1 State University of Economics and Technology,

                       5 Stephana Tilhy Str., Kryvyi Rih, 50006, Ukraine
                      eugenemodlo@gmail.com, rps21@mail.ru
  2 Kryvyi Rih State Pedagogical University, 54 Gagarin Ave., Kryvyi Rih, 50086, Ukraine

 semerikov@gmail.com, acinonyxleo@gmail.com, vitro090@gmail.com
  3 Kryvyi Rih National University, 11 Vitalii Matusevych Str., Kryvyi Rih, 50027, Ukraine

         stan.tolm@gmail.com, markova@mathinfo.ccjournals.eu
      4 Institute of Information Technologies and Learning Tools of NAES of Ukraine,

                          9 M. Berlynskoho Str., Kyiv, 04060, Ukraine



       Abstract. The article describes the components of methods of using mobile
       Internet devices in the formation of the general professional component of
       bachelor in electromechanics competency in modeling of technical objects: using
       various methods of representing models; solving professional problems using
       ICT; competence in electric machines and critical thinking. On the content of
       learning academic disciplines “Higher mathematics”, “Automatic control
       theory”, “Modeling of electromechanical systems”, “Electrical machines”
       features of use are disclosed for Scilab, SageCell, Google Sheets, Xcos on Cloud
       in the formation of the general professional component of bachelor in
       electromechanics competency in modeling of technical objects. It is concluded
       that it is advisable to use the following software for mobile Internet devices: a
       cloud-based spreadsheets as modeling tools (including neural networks), a visual
       modeling systems as a means of structural modeling of technical objects; a
       mobile computer mathematical system used at all stages of modeling; a mobile
       communication tools for organizing joint modeling activities.


       Keywords: mobile Internet devices, bachelor of electromechanics competency
       in modeling of technical objects, general professional component of bachelor in
       electromechanics competency in modeling of technical objects, a technique of
       using mobile Internet devices in learning bachelors of electromechanics.




___________________
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
                                                                                       501


1      Introduction

Modernization of professional training of specialists in mechatronics at Ukrainian
technological universities [21] based on a balance between the fundamental [19] and
technological component of the training process necessitates the search for ICT training
tools [20], which not only provide the opportunity for active experimentation anytime,
anywhere, but also support the development of professionally important qualities of the
future electrical engineer, among which the main place is taken by competence in the
modeling of technical objects. Today, such universal teaching tools are mobile Internet
devices (MID) [12; 26; 35].
   This work is a further development of the research begun in articles [20] and [19],
the purpose of which is to develop methods of using MID in the formation of bachelor
in electromechanics competency in modeling of technical objects. The purpose of the
article is the selection and justification of the MID-based software tools, the use of
which contributes to the formation of the general professional component of this
competency.


2      Results

2.1    Use of mobile Internet devices in the formation of competence in
       using various methods of representing models
The formation of such a general professional component of the competence of a
bachelor of electromechanics in the modeling of technical objects, as a competence in
the application of various methods of representing models, involves the acquisition of
knowledge and skills in the construction of computer mathematical and simulation
models, their algorithmic and structural description, and the selection of adequate ways
of representing computer modeling tools. Based on the content of the competence, its
formation and development takes place throughout the entire training of the bachelor
of electromechanics, therefore, it is inexpedient to single out the leading disciplines for
this process.
   So, in the teaching the “Computing Engineering and Programming”, it is possible to
solve the problem of numerical integration considered in module 9 “Definite and
improper integrals” of the discipline “Higher Mathematics” in a different formulation
[19]: instead of using the table representation of the function, use analytic, and instead
of interpolating formulas, use stochastic Monte Carlo method. In this case, the mean
value theorem for integrals is used, according to which for a curved trapezoid whose
area under the graph of a continuous function on a closed, bounded interval is equal to
the area of a rectangle whose base is the length of the interval and height is the mean
value of the integrand in the interval.
   Ilia M. Sobol in [34] proposes an algorithm for the approximate calculation of a
definite integral by the Monte Carlo method, noting that “in practice [one-time]
integrals ... are not calculated by the Monte Carlo method: for this there are more exact
methods – quadrature formulas. However, the transition to multiple integrals changes
502


the situation: quadrature formulas become very complex, and the Monte Carlo method
remains almost unchanged” [34, p. 52].
   So, to determine the volume under the surface of a function, the following stochastic
algorithm can be applied:
1. Limit the surface of a rectangular box, the volume of which Vpar calculated as the
   product of length (determined by the integration limits [a; b] by Ox axis) by width
   (determined by the integration limits [c; d] by Oy axes) by height (determined by the
   maximum value of the integrand f(x, y) on integration D).
2. Place in a certain parallelepiped a certain number of points N, the coordinates of
   which we will randomly choose.
3. Determine the number of points K that will be located below the surface of the
   function.
4. The volume V, limited by the function and coordinate axes, is given by the
   expression V = VparK/N.
In order to implement interdisciplinary integration, it is advisable to jointly use this
algorithm and the mean value theorem for integrals of a multiple integral:
1. We limit the integration plane to the corresponding limits [a; b] by Ox axes and [c; d]
   by Oy axes.
2. Place on a certain plane a certain number of points N, the coordinates of N we will
   choose at random.
3. At each point we measure the value of the integrand f(x, y) and find the arithmetic
   mean M for all N points.
4. The value of the double integral is given by the expression I = M(b–a)(d–c).
The first implementation is performed in the same SageCell modeling environment [17;
25], with which the value of the integral was calculated by deterministic methods
(fig. 1):
x,y=var('x,y') # symbol integration variables

@interact # interactive model with controls
def _(f=input_box(default=x*y-x^2+y^2, label="$f(x,y)=$", width=20),
   a=input_box(default=0, label="$Lower\ integration\ limit\ by\ Ox\ "
                                "axis\ a=$", width=3),
   b=input_box(default=2, label="$Upper\ integration\ limit\ by\ Ox\ "
                                "axis\ b=$", width=3),
   c=input_box(default=1.2,label="$Lower\ integration\ limit\ by\ Oy\ "
                                "axis\ c=$", width=3),
   d=input_box(default=7, label="$Upper\ integration\ limit\ by\ Oy\ "
                                "axis\ d=$", width=3),
   N=slider(vmin=1, vmax=100000, step_size=1, default=1000,
            label="$Grid\ points\ quantity$"),
   eps=input_box(default=0.1, label="$Accuracy $", width=6)):
                                                                                  503


  # analytic integration of the double integral
  I0=integrate(integrate(f,x,a,b),y,c,d)
  v=html("The analytic value of the double integral %1.4lf"%I0)

  # Monte Carlo numerical integration
  # with a known number of experiments
  sum=0 # sum of function values f(x,y)
  for i in range(N): # grid points quantity cycle
    xi=random()*(b-a)+a # random value generation for x and y
    yi=random()*(d-c)+c #in range [a; b] and [c; d]
    sum=sum+f(xi,yi) # sums accumulation
  I=(sum/N)*(b-a)*(d-c) # integral calculations
  v=v+html("\nThe numerical value of the double integral "
           "calculated by the Monte Carlo method for %s grid"
           " points,\nis %1.4lf"%(N,I))

  # Monte Carlo numerical integration
  # with predetermined accuracy
  sum=0 # sum of function values f(x,y)
  N=1 # minimum quantity of experiments
  while true: # cycle without quantity of experiments limit
    xi=random()*(b-a)+a # random value generation for x and y
    yi=random()*(d-c)+c # in range [a; b] and [c; d]
    sumnext=sum+f(xi,yi) # calculating the next sum
    # break condition for the cycle - the module of the
    # difference between the next and previous
    # sum becomes less than the specified accuracy
    if(abs(sumnext-sum)<eps):
      break
    else:
      sum=sumnext
    N=N+1 # move on to the next experiment

  I1=(sum/N)*(b-a)*(d-c) # integral calculations
  v=v+html("\nThe numerical value of the double integral "
  "calculated by the Monte Carlo method with accuracy %1.4lf,\n"
  "equals %1.4lf and demanded %s grid lines"%(eps, I1, N))
  # function surface visualization
  show(plot3d(f, (x,a,b), (y,c,d)))
  show(v)

Another implementation will be directed by students to conduct as many experiments
as possible in order to clarify the fact that with the same number of experiments, the
simulation results can differ significantly.
504




  Fig. 1. The use of various models to calculate the value of a definite integral in a computer
                                     mathematics system

To do this, we use the mobile version of the spreadsheets, and enter the following values
corresponding to the previous code. At first, the limits of integration:
         A1       a
         B1       0
         A2       b
         B2       2
         C1       c
         D1       1.2
         C2       d
         D2       7
   The next step is to enter formulas for random values of x and y and calculate the
function of them:
         F1       x
         F2       =RAND()*($B$2-$B$1)+$B$1
         G1       y
         G2       =RAND()*($D$2-$D$1)+$D$1
         H1       f(x, y)
                                                                                            505


        H2        =F2*G2-F2^2+G2^2
  The last step is to calculate the average value of the function and the integral:
        I1        sum/N
        I2        =AVERAGE(H:H)
        J1        I
        J2 =I2*($B$2-$B$1)*($D$2-$D$1)
  In order to increase the number of points, you must copy the range F2:H2 in any
number of other lines. The simulation results are presented in fig. 2.




Fig. 2. Usage of the Monte Carlo method to calculate the value of a definite integral in mobile
                                       spreadsheets

A discussion of two implementations of the same model allows us to draw conclusions
both on the correct implementation and on the advisability of using the selected
modeling tool. So, when using spreadsheets, an increase in the number of experiments
is possible only by adding new lines, however, any changes on the worksheet lead to
the generation of new random numbers – instead of clarifying the results of the previous
experiment, the student conducts a new experiment. At the same time, when using the
model in a computer mathematics system, you can verify the erroneousness of the
condition for completing the cycle – instead of abs(sumnext-sum)<eps must use
condition abs(sumnext/N-sum/(N-1))<eps for all steps except the first:
applying the precondition can lead to both early completion of the cycle (if the function
value is close to zero in the first steps) and an overestimation of the number of iterations
(if the function value becomes close to zero after reaching the required accuracy), and
even to the “eternal” cycle (if the value of the function on the selected area will not be
less accurate).
    An important component of competence in the application of various methods of
representing models is the formation of the ability to select an adequate way of
506


representing models of computer modeling tools. One of the traditional ICT training
tools for modeling is computer mathematics systems. In [23] it was pointed out that it
should be used together with support systems for teaching bachelors in
electromechanics for modeling technical objects, such as the Moodle LMS,
supplemented by the developed SageCell filter [18]. The specified filter is able to
implement a numerical solution of systems of differential equations describing
mathematical models directly in the learning management system.
   However, the use of only computer mathematics systems (even such powerful ones
as SageMath [27]) for teaching modeling of technical objects of bachelors in
electromechanics is not enough, since the synthesis and calculation of models of control
systems, electric drive elements, etc. primarily use visual modeling tools that provide
the opportunity to build dynamic models (discrete, continuous and models of systems
with discontinuities elements). This determines the necessity and expediency of
combining traditional computer mathematics systems with specialized libraries for
modeling technical objects in environment for the visual construction of models. At the
same time, the choice of environment for modeling should take into account the
specifics of future professional activity, which for bachelors of electromechanics is the
synthesis of the corresponding technical objects – electromechanical systems.
   Mastering the modeling of technical objects provides theoretical and practical filling
of the fundamental, general and specialized professional training for a bachelor’s of
electromechanics. In this regard, it is desirable that the environment for their modeling
gives the user access not only to traditional libraries for modeling continuous and
discrete dynamic systems, but also to libraries for electric machines and power
converters. In addition, to achieve the goal of learning mobility, the modeling
environment must have a high level of cross-platform access (in particular, access via
a Web interface) and be freely distributed.
   In order to make a reasonable choice of the environment for technical objects
modeling for bachelors of electromechanics, an expert assessment of the most common
systems of visual modeling was carried out, the results of which are presented in the
table 1.
   Currently, the Scilab has the highest expert assessment, the advantages of which
were recognized in 2011 by the French Ministry of National Education, Higher
Education and Science, giving Scilab a recognition of its pedagogical significance for
teaching mathematics “Reconnu d'Intérêt Pédagogique” [29].
   According to [28], Scilab is a package of scientific programs for numerical
calculations that provides a powerful open environment for calculations, similar to the
Matlab language and a set of functions for mathematical, engineering and scientific
calculations. The package is suitable for professional use and use in the universities,
providing tools for various calculations from visualization, modeling and interpolation
to differential equations and mathematical statistics. Execution of scripts written for
Matlab is supported.
   Scilab was created in 1990 by INRIA scientists (Institut national de recherche en
informatique et en automatique – State Institute for Computer Science and Automation
Research) [9] and ENPC (École nationale des ponts et chaussées – National School of
Bridges and Roads). At first it was called Ψlab (Psilab). The Scilab Consortium was
                                                                                      507


created in May 2003. To promote the use of Scilab as open source software in the
academic and industrial fields. In July 2008, Scilab joined the Digital Foundation to
improve technology transfer [10].

            Table 1. Comparison of environments for technical objects modeling
             A freely
           distributed The num-                                      Lib-
                                         The   Librari- Libra-              Librari-
              version    ber of sup-                                raries
                                      Web in- es for     ries for             es for
           availability ported ope-                                for mo-
                                       terface modeling mode-                mode-
Modeling (“yes” – 3 rating sys-                                     deling
                                       availa- conti- ling disc-            ling po- To-
 environ-     points,     tems (for                                electric
                                        bility  nuous rete sys-             wer con- tal
   ment      “no” – 0 each system                                    ma-
                                      (“yes” – systems    tems               verters
           points, “yes – 0.5 points,                               chines
                                        3 po- (“yes” – (“yes” –             (“yes” -
            (with rest- for “∞” – 1                               (“yes” –
                                        ints) 5 points) 5 points)           2 points)
           rictions)” –     point)                                2 points)
             1 point)
             yes (with
Analytica                   1 (W*)       yes      no        no        no        no     4,5
           restrictions)
AnyLogic        yes       3 (WML)        no       no        no        no        no     4,5
 GoldSim        no          1 (W)        no       no        no        no        no     0,5
  Insight
                yes         ∞ (JS)       yes      no        no        no        no      7
  Maker
MapleSim        no        3 (WML)        no       no        no       yes       yes     5,5
  Minsky        yes       3 (WML)        no       no        no        no        no     4,5
Rand Mo-
del Desig-      no          1 (W)        no      yes       yes        no        no    10,5
    ner
  Scilab
                yes       3 (WML)        yes     yes       yes        no        no    17,5
   Xcos
Simantics
  System        yes         1 (W)        no       no        no        no        no     3,5
Dynamics
             yes (with
  Simile                  3 (WML)        yes      no        no        no        no     5,5
           restrictions)
Simulink        no        3 (WML)        no      yes       yes       yes       yes    15,5
Temporal
  Reaso-
ning Uni-
                no          1 (W)        no       no        no        no        no     0,5
   versal
Elaborati-
    on
  Vensim        yes        2 (WM)        no       no        no        no        no      4
  VisSim        no          1 (W)        no       no        no        no        no     0,5
 Wolfram
 System-        no        3 (WML)        no       no        no       yes       yes     5,5
 Modeler
  *
      W – Windows, M – macOS, L – Linux, JS – JavaScript

   In June 2010, the Scilab Consortium announced the creation of Scilab Enterprises
[4]. Scilab Enterprises develops and sales, directly or through an international network
508


of affiliate service providers, a comprehensive suite of services for Scilab users. Scilab
Enterprises also develops and maintains Scilab software. Scilab Enterprises’ ultimate
goal is to help make using Scilab more efficient and easier. Since February 2017, Scilab
has been developed and published by ESI Group, an industrial virtual reality
development company [5].
   Scilab contains hundreds of mathematical functions with the ability to add new ones
written in various languages (C, C++, Fortran, etc.). Various data structures are
supported (lists, polynomials, rational functions, linear systems), an interpreter and a
high-level language.
   Scilab was designed as open system in which users can add their data types and
operations on this data by overloading.
   Many tools are available in the system:
─ 2D and 3D graphics, animation;
─ linear algebra, incl. work with sparse matrices;
─ polynomial and rational functions;
─ interpolation, approximation;
─ differential equations;
─ Scicos: a hybrid tool for modeling dynamic systems;
─ optimization;
─ signal processing;
─ parallel computing;
─ statistics;
─ work with computer algebra;
─ Fortran, Tcl/Tk, C, C++, Java, LabVIEW interfaces;
Scilab has a programming language similar to MATLAB; the system includes a utility
that allows to convert Matlab documents to Scilab.
   Scilab allows to work with elementary and a large number of special functions
(Bessel, Neumann, integral functions), has powerful tools for working with matrices,
polynomials (including symbolic), performing numerical calculations (for example,
numerical integration) and solving linear algebra problems, optimization and
simulation, powerful statistical functions, as well as a tool for building and working
with charts. For numerical calculations, the libraries Lapack, LINPACK, ODEPACK,
Atlas and others are used.
   The package also includes Scicos, a tool for editing block diagrams and simulations
(the Xcos add-on is an analogue of the Simulink package in MATLAB). There is the
possibility of collaboration between Scilab and LabVIEW.
   Distinctive features of Scilab:
─ fee free;
─ small size (distribution takes less than 150 Mb);
─ the ability to run in the console without using a graphical interface. This allows
  automated calculations in batch mode.
                                                                                       509


Starting with version 6, the program is distributed under the GPL compatible license
CeCILL license [1].
   Despite the lack of usability of the text interface, it is easier to adapt to MID. Among
the well-known Scilab implementations for the Android OS, we distinguish two –
Scilab on Aakash and Scilab Console Free.
   Scilab on Aakash [30] is an Indian development that is supported in both the Android
and GNU/Linux Aakash versions. In Android, Scilab is part of the APL library (Aakash
Programming Lab [7], developed by Indian Institute of Technology Bombay), which
provides Scilab 5.4. All Scilab functions cannot be runnging on Android, so the
developers provide the user interface with only 2 windows (fig. 3): enter commands
and view the results of their execution.




                         Fig. 3. Scilab on Aakash window interface

When executing graphic commands with the Plot option selected, the results of
execution will be displayed in a separate window (fig. 4). This version of Scilab may
be admitted as mobile, but not fully functional.
   Scilab Console Free (fig. 5) – is a mobile version of Scilab for Android and iOS.
Like Scilab on Aakash, this is not a fully functional version of Scilab 5.4.1: the graphic
functions of Scilab and Xcos are not activated. The developers of this product went the
easy way – to achieve mobility on the device you first have to install one of the Linux
options (for example, using GNURoot Debian [2]).
   The mobility of this version of Scilab is achieved by transferring the Linux mobile
operating system and its software environment to Android and iOS. Therefore, Scilab
Console Free is quite demanding on the internal memory of the mobile device and the
version of the operating system.
510




                         Fig. 4. Graphic plotting in Scilab on Aakash

The standard Web interface to Scilab, which is proposed by Cloud Scilab [36], does not
provide an interface similar to the full-featured version – it is only possible to host user-
created models with a Web interface (application deployment – “deploying” programs
to the cloud server [15]) by creation and publication of interactive documents, the
                                                                                 511


software part of which is performed on the server side, saves the resources of a MIDs
(fig. 6).




                       Fig. 5. Scilab Console Free launch window




              Fig. 6. An example of an interactive document in Scilab Cloud

This provides several advantages:
─ centralization of data used and created by the user program;
─ no need to install software on the client side;
─ concealment of code from end users (as a component of intellectual property
  protection);
─ centralization of Scilab code to ensure the effective operation of programs.
512


Programs deployed on the Scilab Cloud are described by the Scilab language (both
algorithms and the user interface). This allows you to create programs with a visual
interface both for deployment in the cloud (work in Scilab Cloud with display via a web
browser) and traditional execution (launch in Scilab on the user’s computer).
   Despite the high level of mobility, the use of Cloud Scilab is accompanied by a
number of problems:
─ deployment of programs is only available with administrative privileges (requires an
  additional fee to the cloud service provider);
─ the interface is provided only for user models, and not to the entire Scilab interface.
In terms of functionality, this service is similar to the Wolfram Demonstrations Project,
however, unlike the latter, all users can publish demonstrations, and not only service
administrators comply with the document distribution model in CoCalc [14]. However,
Scilab Cloud does not provide access to the Xcos module. In addition, in fact, the only
source about Scilab Cloud is the materials of webinars conducted by Scilab Enterprises
[3], which does not contribute to the widespread use of this Web-interface.
   W3 Scilab is significantly more open [13]. W3 Scilab is the Indian Web-based
interface to Scilab, which is the basis of Scilab on Aakash. The interface allows users
to send short fragments of Scilab code to a remote server, receive Scilab code on this
server, return and display execution results in a browser.
   Xcos is an addition to Scilab, which allows the synthesis of mathematical models in
the fields of mechanics, hydraulics, electronics and electromechanics. This visual
modeling environment is designed to solve the problems of dynamic modeling of
systems, processes, devices, as well as testing and analysis of these systems. In this
case, the object is modeled (system, device, process), supplied graphically in the form
of a block diagram that includes blocks of system elements and the connections
between them (fig. 7).




                            Fig. 7. Scilab Xcos model example

The most significant criteria that led to the choice of Scilab as a tool of teaching
modeling of technical objects of bachelors in electromechanics are the availability of
modeling continuous systems libraries (5 points), modeling discrete systems libraries
                                                                                      513


(5 points) and the presence of a Web interface (3 points). The latter makes it possible
to use it on MID.
   The Xcos on Cloud service provides the ability to build simulation models of
technical objects (in particular, electromechanical systems) in a mobile Web browser.
The current goal of the Xcos on Cloud project (formerly Xcos on Web [22]) is to
recreate a fully functional version of Scilab Xcos with access via a mobile Web browser
[6].
   The main components of the Xcos on Cloud main window are presented in fig. 8.




                     Fig. 8. Xcos on Cloud main window components

The main part of the Xcos on Cloud main window is occupied by the model building
area. On the left side is the so-called palette of blocks – a library of elements from
which the model is built. To use any block, just drag it from the palette to the model
building area. Blocks are interconnected by communication lines.
   In fig. 9 shows a DC motor model built in Xcos on Cloud. Blocks of the model have
various parameters, user-configurable by double-clicking on the selected block.
Unfortunately, the project is still at the preliminary development stage, so some settings
are not available: for example, the first-order aperiodic unit (CLR) and amplifier
(GAIN) blocks in the constructed model are unstable, as evidenced by the format
specifier ‘%s’. This makes it impossible to conduct experiments on the model by the
click of a button. Simulate. A temporary workaround for this problem is the ability of
514


Xcos on Cloud to exchange data with the traditional version of Scilab Xcos through
data export tools.




                        Fig. 9. DC Engine model in Xcos on Cloud

A fragment of an XML representation of a constructed model of a DC motor:
<?xml version="1.0" encoding="UTF-8"?>
<XcosDiagram background="-1" title="MavXcos">
    <mxGraphModel as="model">
        <root>
            <mxCell id="0"/>
            <mxCell id="1" parent="0"/>
            <BasicBlock blockType="c" id="2"
interfaceFunctionName="STEP_FUNCTION" parent="1"
simulationFunctionName="csuper"
simulationFunctionType="DEFAULT" style="STEP_FUNCTION">
...
        </root>
    </mxGraphModel>
  <mxCell id="1" parent="0" as="defaultParent"/>
</XcosDiagram>

The implementation of the full functionality of Scilab Xcos in Xcos on Cloud creates
the conditions for a using MID in the training of bachelors in electromechanics,
modeling of technical objects. Similar features are provided by the full virtualization of
Scilab on rollApp [31].
                                                                                      515


2.2    Use of mobile Internet devices in the formation of competence in
       solving professional problems using ICT
The formation of a general professional component of the competence of a bachelor of
electromechanics in the modeling of technical objects, such as competence in solving
professional problems using ICT, provides for the acquisition of knowledge in the field
of computer engineering and programming, the ability to create application software,
and the skills to work with ICT tools to solve problems in field of electromechanics.
The formation of this competence begins in the academic discipline “Computing
Engineering and Programming” and occurs along with the formation of the general
scientific component of the competence of the bachelor of electromechanics in the
modeling of technical objects, in particular competencies in information and
communication technologies and in applied mathematics. Its further development takes
place in the process of developing models; they are considered in the academic
disciplines “Theory of Automatic Control” and “Modeling of Electromechanical
Systems”.
   The purpose of studying the discipline “Theory of Automatic Control” is to master
the methods of setting tasks, the principles of building automatic control systems,
methods of analysis and synthesis of linear, nonlinear, impulse, digital, adaptive and
optimal systems using modern software systems for modeling dynamic systems.
   As a result of studying the discipline, students, in particular, should receive skills:
─ compose differential equations for elements of automatic control systems and the
  system as a whole;
─ draw up and transform structural diagrams of automatic control systems;
─ determine the time functions and time characteristics of the automatic control system
  and its elements under the conditions of various types of signals;
─ determine the frequency functions and characteristics of automatic control systems;
─ analyze the stability of linear, impulse and nonlinear automatic control systems;
─ calculate control devices (controllers) that provide the necessary quality indicators,
  including using the state space method;
─ synthesize automatic control systems in the presence of random signals;
─ apply adaptive methods to control non-stationary objects.

At the lectures of the second module “Properties and characteristics of closed control
systems. Synthesis of linear continuous control systems”, the issues of influence on the
system and requirements for the control process, stability of control systems, stationary
(stable) modes of linear control systems, quality assessment of control systems with
step and arbitrary actions, frequency methods for assessing the quality of control
systems, approximate methods for choosing the control method and parameters are
considered regulators, synthesis of control systems according to the logarithmic
frequency characteristics. To consolidate this material, we propose laboratory works
“Analysis of stability and quality of control systems” and “Synthesis and research of
control systems for objects with a delay”. Consider the use of ICT tools to solve the
second of them.
   Objective of the work: to study the influence of the delay link on the stability and
516


quality of the automatic control system.
  The content of the work
1. The study of the influence of the delay link on the characteristics of the automatic
   control system.
2. Experimental obtaining the transient and frequency characteristics of the system
   with delay.
Theoretical information
   The automatic control systems may include time delay, the equations of which are
of the form:
                                   y(t) = x(t – τ),                                  (1)

where  – delay time.
   The transfer function of a time delay in accordance with the delay theorem
(properties of the Laplace transform):
                                   Wdel(s) = e–sτ.                                   (2)
Automatic control systems, which include a time delay, are called time delay systems.
   It can be connected in the direct circuit of the system or to the feedback circuit.
Moreover, regardless of the location of the delay link, the characteristic equation of a
closed system with delay has the form:

                            Dτ(s) = Q(s) + R(s)e–sτ = 0,                             (3)
where Q(s) and R(s) – polynomials in the denominator and numerator of the transfer
function of the open system without delay.
   This characteristic equation is not a polynomial and has an infinite number of roots.
Therefore, to study the stability of delayed systems, it is necessary to use frequency
stability criteria, such as the Nyquist stability criterion. The conclusion about the
stability of the system can be made on the basis of the analysis of the amplitude-phase
frequency response of an open system with delay.
   It can be shown that the presence of a delay link does not change the module of A(ω)
but introduces only an additional negative phase shift of –ωτ. By varying the delay time
τ over a wide range, one can find its value at which the closed-loop system will be at
the stability boundary. In this case, amplitude-phase frequency characteristic of the
open-loop phase response of the delayed system will pass through the point
(-1; 0) = -1+j0.
   The latency cr and the corresponding value of the frequency ωcr, at which the AFC
passes through the point (-1; 0), are called critical. For a critical case, the following
conditions are true:

                              A(ωcr) = 1; ϕτ(ωcr) = –π.                              (4)

The automatic control system will be stable if the delay time  is less than critical:
 < cr.
                                                                                          517


  Work order
  The subject of the study is an automatic control system, with a delay link.
1. The transfer function of the open-loop automatic control system without delay has
   the form:

                                  ( )=                                                    (5)
                                           (     )(      )

The value of the transmission coefficient K and the time constants T1 and T2 are shown
in the table
 Num of var.          1              2                 3             4              5
   K, s–1             5              3                 1             10             8
   T1, s             0,5            0,1               0,05          0,05           0,04
   T2, s             0,01           0,05              0,01          0,2            0,1

Using the Scilab package, construct the transition characteristic h(t) of the closed-loop
system with unit negative feedback (fig. 10, 11). Make a conclusion about the stability
of the system.




               Fig. 10. Block diagram of a closed-loop system without delay




 Fig. 11. Transient response of a closed-loop system with a single negative feedback without
                                            delay
518


2. Insert a time delay function with the delay time  = 0,01 s (fig. 12), into the direct
   chain of the system, construct the transition characteristic of the system (fig. 13) and
   make a conclusion how the time delay affects the quality of the transition process.




               Fig. 12. Block diagram of closed-loop control system with delay time




      Fig. 13. Transient response of a closed-loop system with a negative feedback with delay
                                               = 0,01 s

3. Increasing the time of delay, to trace how the transition characteristic of the system
   changes (fig. 14) to make the system lose stability (the transition process diverges).
4. To determine experimentally the value of the critical delay time cr, when the system
   will be at the stability boundary (the transition process will be undamped).
5. Repeat steps 2-4 for the case when the time delay function included in the feedback
   circuit. Make some conclusions.
Further development of competence in solving professional problems by means of ICTs
occurs in the process of completing term paper in the discipline “Theory of automatic
control”. In order to develop skills for conducting professionally directed educational
research, students can be invited to familiarize themselves with new results in the
subject area of scientific publications in professional publications and start the
coursework on their reproduction. So, in the work “Optimization of the servo-
controlled automatic control system” [11] an example of servo-controlled control
system of a working body of a paver with hydraulic drive is considered.
                                                                                                519




      Fig. 14. Transient response of a closed-loop system with a negative feedback with delay
                                               = 0,1 s

When moving the stacker along the base, which is ready for laying pavement on it, its
running equipment (tracked or wheeled) makes uncontrolled random movements in the
vertical direction under the influence of roughnesses in the microrelief of the base of
the road. These movements are transmitted through the stacker frame and suspension
of the screed to the working equipment, causing in turn uncontrolled movements of the
screed, which entail a random change in the thickness and angle of the transverse slope
of the stacked layer, thereby deteriorating the quality of the coating.
   A simulation model of the hydraulic drive tracking system for the screed plate can
be implemented in MATLAB Online, as suggested by the authors of [11]. The structure
of the simulation model circuit (fig. 15) includes the following elements: a bi-
directional hydraulic cylinder; three-position valve; hydraulic pump; controlled
hydraulic lock; ideal hydraulic pressure sensor; the “smooths the paver plate” element;
cylinder rod movement and speed sensor (feedback sensor) the ideal force sensor; the
element “hydraulic fluid” (Oil-30W oil) is proportional to the servo valve of the
hydraulic actuator (electro-hydraulic distributor that converts the electrical signal to
movement) element “viscous friction”; ideal source of strength; disturbing influence of
“microrelief”; PS-converter; capacity for working fluid; disturbing effects due to the
influence of the work of other elements.

2.3      Use of mobile Internet devices in the formation of competencies in
         electric machines and critical thinking
In the discipline “Electrical Machines”, the formation of both the general scientific
component of the competence of the bachelor of electromechanics in the modeling of
technical objects (the leading means of competencies in basic sciences formation were
mobile augmented reality tools), and such a general professional component as
competencies in electrical machines, including knowledge of the structure and
functioning principles of electrical machines, in particular: energy conversion
520


processes (electromagnetic and electromechanical), characteristics of certain types of
electrical machines, structure of asynchronous machines, synchronous machines, DC
machines, transformers; the ability to calculate the parameters and characteristics of
electrical machines. To form the latter, the leading tools are mobile computer
mathematics systems.




      Fig. 15. Structural model of the hydraulic drive tracking system for the screed slab

The last general professional component of a bachelor of electromechanics competence
in modeling technical objects is competence in critical thinking – the knowledge and
skills of setting a problem with an insufficient amount of input data, analyzing the
availability of methods and means of solving a problem, assessing your own readiness
to solve a problem, independently searching for missing data and ways to solve the
problem; the ability to control their own activities – both mental and practical; the
ability to control the logic of deploying your own thoughts; the ability to determine the
sequence and hierarchy of the stages of activity and the like. As well as for competence
in the application of various ways of representing models, leading academic disciplines
cannot be distinguished to this competence – its formation takes place throughout the
entire training of a bachelor of electromechanics.
   Neural network modeling is an effective means of modeling technical objects with
a hidden or fuzzy structure [32; 33]. As the editors of the book “Neuro-Control and its
Applications” note, the relevance of its application is due to the need to develop control
methods for complex nonlinear systems: “The first examples of the development of
                                                                                      521


control methods for nonlinear systems ... are mainly associated with methods for
solving nonlinear differential equations that are adequate to a single-processor
background of Neumann computational to cars. ... The development of computers with
mass parallelism ... has led to the creation of fundamentally new algorithms and
methods for controlling non-linear dynamic systems. They are associated with neural
network algorithms for solving ordinary nonlinear differential equations and, as a
result, with the inclusion of a neurocomputer in the control loop of a nonlinear dynamic
system. ... The sufficiently wide development and spread of such algorithms has led ...
to the creation of a whole branch of science called “neurocontrol” [24, pp. 9–10].
   In an engineering context, intelligent management should have the following
properties: learning ability and adaptability; survivability; simple control algorithm and
user-friendly man-machine interface; the ability to incorporate new components that
provide the best solutions in the face of limitations imposed by technical tools [24,
p. 15].
   The deep machine learning is a class of intelligent control algorithms that use
multilayer neural networks with non-linear nodes. Let us consider the construction of a
neural network model for approximating data described in Chapter 23 of “Neural
Network Design” [8], and obtained using an intelligent sensor – one or more standard
sensors connected to a neural network to obtain a calibrated measurement of one of the
parameters.
   The intelligent position sensor uses the voltage value from two photocells to estimate
the location of the object. In fig. 16, an object located between a light source and two
photocells is shown around. The object, moving along the y axis, casts a shadow on the
photocells, which leads to a change in the voltages v1 and v2. When the position of the
object y increases, the voltage v1 first decreases, then the voltage v2 decreases, then v1
increases and finally v2 increases (fig. 17).




                            Fig. 16. Intelligent position sensor
522




  Fig. 17. An ideal model of the dependence of the voltages v1, v2 on the y coordinate of the
                                          object

The simulation purpose is to determine the position of the object by measuring two
voltages. In order to collect data for approximation, two voltages of photocells are
measured in a number of reference positions of the object. The authors of [8] used a
table tennis ball for these experiments. In total there are 67 sets of measurements
presented in the files ball_p.txt and ball_t.txt in the archive at the link
http://hagan.okstate.edu/CaseStudyData.zip. Each point in graph 18 represents a
voltage measurement in a calibration position. Coordinates are measured in inches and
voltages are in volts. Flat areas of 0 volts for each curve occur where the shadow of the
ball completely covers the sensor. If the shadow was large enough to cover both sensors
at the same time, we will not be able to restore the coordinate from the voltage.




        Fig. 18. The dependence of the voltages v1, v2 on the y coordinate of the object

To implement the deep learning model, we apply cloud-oriented Google Sheets with
the Solver addition according to the technique developed in [16].
                                                                                           523


   In order to determine the coordinate of the object, we will build a four-layer neural
network with the architecture shown in fig. 19:
─ input layer is a two-dimensional arithmetic vector (x1, x2), with the components are
  the corresponding measured voltages v1, v2, normalized according to the network
  activation function;
─ the first hidden layer will have dimension 5 and is described by the vector (h1(1), h2(1),
  h3(1), h4(1), h5(1));
─ the second hidden layer will have dimension 3 and is described by the vector (h1(2),
  h2(2), h3(2));
─ output layer is ynorm value normalized according to the network activation function.




Fig. 19. Neural network architecture for solving the problem of determining the position of an
                                            object
524


Displacement (bias) neurons are added to the neurons of the input and hidden layers.
Bias neurons value is always equal to 1 (in fig. 19 they are marked in red). A feature of
bias neurons is that they do not have input synapses, and therefore cannot be located on
the output layer.
   First, enter the data of the measured voltages in the spreadsheets. Since the data is
presented in a text file, we use the function of importing data into spreadsheets (fig. 20).




                             Fig. 20. Import data to spreadsheet

   As a result of import, the following values are entered in the table cells:
         B1:BP1 v1 voltage output data
         B2:BP2 v2 voltage output data
         B3:BP3 y coordinate
                                                                                       525


   For convenience of processing, we transpose the obtained data and put them in cells
A10:A76 for v1, B10:B76 for v2, C10:C76 for y. To do this, we add the following values
to the table cells:
          A8        data
          A9        v1
          B9        v2
          C9        y
          A10       =TRANSPOSE(B1:BP3)
   Based on the fact that the constructed neural network will have a polar activation
function, all values at the network input should be normalized (reduced to the range
[0; 1]). At the output of the network, you must perform the reverse operation –
denormalization.
   Normalizing is performed for each column separately. To do this, we find the
minimum and maximum values for them by entering the following formulas in the
cells:
          E5        v1
          F5        v2
          G5        y
          D6        max
          D7        min
          E6        =max(A10:A76)
          E7        =min(A10:A76)
   Further, the range E6:E7 is copied to F6:G7.
   The essence of normalizing is easy to understand by the expression (5):
                                           input value-minimum value
                  normalized value =                                   .               (5)
                                         maximum value-minimum value

With this approach, the minimum value is normalized to 0, and the maximum up to 1.
The normalized voltage values must be feed to the input layer of the neural network:
          E8        input layer
          E9        x1
          F9        x2
          E10       =(A10-E$7)/(E$6-E$7)
    Cell E10 is distributed in the range E10:G76.
    In accordance with the selected architecture of the neural network, add to the 2
neurons of the input layer a bias neuron. To do this, insert its name (x3), in cell G9, and
its value (1) in the range G10: G76. At this stage, the input layer is formed in the form
of a signal vector (x1, x2, x3).
    The next step is to transmit the signal from the input layer of the neural network to
the first hidden one. To determine the signal power, it is necessary to have weights of
the neural network. Denote by:
─ wijxh(1) the weight coefficient of the synapse, which connects the neuron xi (i = 1, 2,
  3) of the input layer with the neuron hj(1) (j = 1, 2, ..., 5) of the first hidden layer;
526


─ wkph(1)h(2) the weight coefficient of the synapse, which connects the neuron hk(1)
  (k = 1, 2, ..., 6) of the first hidden layer to the neuron hp(2) (p = 1, 2, 3) of the second
  hidden layer;
─ wdqh(2)y the weight coefficient of the synapse, which connects the neuron hd(2) (d = 1,
  2, ..., 4) of the second hidden layer with the neuron ynormq (q = 1) of the output layer.
Then the power of the signal arriving at the neuron hj(1) of the first hidden layer is
defined as the scalar product of the signal values at the input layer and the
corresponding weighting coefficients. To determine the signal, we will go further to the
second hidden layer, we apply the logistic activation function f(S) = 1/(1+e-S), where S
is the corresponding scalar product. The formulas for determining the signals on the
first (6) and second (7) hidden and output (8) layers are:
                                     ( )                          ( )
                                ℎ          =       ∑                     ,                (6)
                               ( )                         ( )   ( ) ( )
                           ℎ         =         ∑       ℎ                     ,            (7)
                                                                   ( )
                               norm        =       ∑                         .            (8)

Accordingly, it is necessary to create three matrices:

─ The wxh(1) matrix of size 35 contains the weights connections of 3 neurons of the
  input layer (the first two contain normalized stress values, and the third is the bias
  neuron) with the neurons of the first hidden layer;
─ The wh(1)h(2) matrix of size 63 contains the weights connections of 6 neurons of the
  first hidden layer (of which five are calculated, and the sixth is the bias neuron) with
  the neurons of the second hidden layer;
─ The wh(2)y matrix of size 41 contains the weights connections of 4 neurons of the
  second hidden layer (of which three are calculated, and the fourth is the displacement
  neuron) with the neurons of the output layer.
For an “unlearned” neural network, the initial values of the weights can be set either
randomly, or left undefined, or equal to zero. To implement the last method, fill the
cells with these values:
         I8       wxh(1)
         I9       input layer
         J8       first hidden layer
         J9       1
         K9       =J9+1
         I10      1
         I11      =I10+1
         J10      0
         I14      wh(1)h(2)
         I15      first hidden layer
         J14      second hidden layer
         J15      1
                                                                                              527


         K15      =J15+1
         I16      1
         I17      =I16+1
         J16      0
         I23      wh(2)y
         I24      second hidden layer
         J23      output layer
         J10      1
         I25      1
         I26      =I25+1
         J25      0
  To create matrices, it is necessary to copy K9 cell to the range L9:N9, I11 – to I12,
J10 – to J10:N12, K15 – to L15, I17 – to I18:I21, J16 – to J16:L21, I26 – to I27:I28,
J25 – to J26:J28 (fig. 21).




   Fig. 21. Fragment of a spreadsheet after normalizing input data and creating matrices of
                                   weighting coefficients

To calculate the scalar product of a row vector of input layer values by a column vector
of the matrix of weight coefficients wxh(1), it is advisable to use the matrix multiplication
function:
         P8       first hidden layer
         P9       h1(1)
         Q9       h2(1)
528


          R9       h3(1)
          S9       h4(1)
          T9       h5(1)
          U9       h6(1)
          P10      =1/(1+exp(-mmult($E10:$G10,J$10:J$12)))
          U10      1
   Next, copy cell P10 to the range P10: T76, and U10 to U11: U76.
   Given that all elements of the matrix of weight coefficients wxh(1) are initially equal
to zero, after copying the formulas, all measured elements of the hidden layer are equal
to 0.5.
   Similarly, we perform calculations of the elements of the second hidden and output
layers:
          W8       second hidden layer
          W9       h1(2)
          X9       h2(2)
          Y9       h3(2)
          Z9       h4(2)
          W10      =1/(1+exp(-mmult($P10:$U10,J$16:J$21)))
          Z10      1
          AB8      output layer
          AB9      ynorm
          AB10 =1/(1+exp(-mmult($W10:$Z10,J$25:J$28)))
   Next, copy cell W10 to the range W10:Y76, Z10 – to Z11:Z76, AB10 – to
AB11:AB76 (fig. 22).




      Fig. 22. Fragment of the spreadsheet after calculating the initial values of the weighting
                            coefficients of the hidden and output layer

To obtain the result ycalc from the normalized value of the output layer, it is necessary
to calculate it by the formula inverse to the original:

output value = minimum value + normalized value * (maximum value – minimum value)
To do this, enter the following values in the table cells:
         AD8       result
         AD9       ycalc
         AD10 =$G$7+AB10*($G$6-$G$7)
   Next, copy cell AD10 to the range AD11: AD76.
   Neural network training takes place by varying weights so that with each training
step, the difference between the calculated values of ycalc and the desired (reference)
                                                                                   529


values of y is reduced. To determine the difference between the calculated and the
reference output vectors, we calculate the squares of the deviations and their sum:
         AF8      squared deviation
         AH8      sum
         AF9      (y–ycalc)2
         AH9      S
         AF10 =(C10-AD10)^2
         AH10 =sum(AF10:AF76)
   Next, copy cell AF10 to the range AF11: AF76. Cell AH10 contains the sum of the
squared deviations.
   Within this formulation of training, the neural network can be considered as an
optimization problem in which the objective function (the sum of the squared deviations
in the cell AH10) should be minimized by varying the weights of the matrices wxh(1)
(range J10:N12), wh(1)h(2) (range J16:L21) and wh(2)y (range J25:J28). To solve this
problem, standard Google Sheets tools are not enough, so you need to install the Solver
add-on by choosing Add-ons → Get add-ons ... (fig. 23).




                     Fig. 23. Install the Solver Google Sheets add-on

In fig. 24 shows the settings of the Solver add-on for solving the task: the objective
function (Set Objective) is minimized (To: Min) by changing the values (By Changing)
530


of the weighting matrices in the range (Subject To) from -20 to +20 using one of the
optimization methods (Solving Method).




                  Fig. 24. Optimization result for selected Solver parameters

To reduce the sum of squared deviations, Solver can be called up many times: it is
advisable to experiment with the combined use of various optimization methods,
changing the limits of variation of the weight coefficients. In this case, it is not
necessary to try to prove the value of the sum of the distances to zero – this may be
more than a (rather small) value.
   For clarity of the simulation results, it is advisable to construct a graph of the ratio
of experimentally obtained (measured) y values and calculated (approximated) ycalc
(fig. 25). The quality of approximation is determined by the degree of deviation of the
graph points from the beam, divides the first quadrant in half. From the figure and the
sum of the squares of deviations obtained after optimization, we can conclude that the
constructed neural network model is adequate.
   To test the model limitations, we propose the next task: using given in the table 2
values of voltages v1, v2, calculate the y coordinate of the object, and explain the choice
of voltages and obtained result.

                                   Table 2. Model testing
No    v1     v2    ycalc                           Explanation
                     Measurement only with the second sensor. The result is adequate
 1 0.000 4.000 0.467
                     because the pair v1, v2 has a match in the test data set
 2 0.000 1.000 1.366 Measurement only with the second sensor. The result is inadequate
                                                                                       531


No v1        v2   ycalc                              Explanation
 3 5.000   0.000 1.187 Measure only with the first sensor. The result is inadequate
 4 1.000   0.000 1.368 Measure only with the first sensor. The result is inadequate
 5 6.660   3.800 2.493 The data set is on the trend line. The result is adequate
 6 3.000   3.000 0.809 Intersection of lines 1, 2. The result is adequate
 7 0.000   0.000 1.374 Minimal values. The result is inadequate due to incorrect regularity
                        Numbers beyond the range of measured values. The result is the
 8 10.000 10.000 2.825
                        maximum value of the position




                 Fig. 25. Graph of measured y values and approximated ycalc


3      Conclusions

Thus, in the process of formation of the general professional component of the
competence of a bachelor of electromechanics in the modeling of technical objects, it
is advisable to use the following software for mobile Internet devices:
─ cloud-based spreadsheets as modeling tools (including neural network);
─ visual modeling systems as a tools of technical objects structural modeling;
─ mobile computer mathematical systems used at all stages of modeling;
─ mobile communication tools for organizing joint modeling activities.
532


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