Neural Network Algorithm for Stabilizing Mechanized Systems

SHMAKOVA ELENA G., FILORETOVA OLGA A., NIKOLAEVA OLGA M.,

VASILKIN DENIS P.

Department of Information Systems in Chemical Technology

Lomonosov Institute of Fine Chemical Technological, MIREA-Russian Technological University

Vernad-sky Ave 86, Moscow, 119571

RUSSIA

Abstract: The article describes an experimental model of stabilization of a mechanized system. The following

are shown: a skate; an element of the program code; an algorithm for stabilizing a proportional-integral-

differential controller (PID). The experimental model uses the calculation and adjustment of the regulator

according to the Ziegler-Nichols method. For the case of applying the neural network approach to the search for

equilibrium, the Hopfield neural network is used. The technology of calculating the balancing of the values of

the coefficients: proportional, integral, differential components are described. The design of the rolling system

is described. The experimental model is designed to identify the balancing range of the rolling system of small-

diameter balls. The experimental module balances the ball at a distance of 4.5 to 7 cm (SW-range). The

shortcomings of the experimental model of stabilization of the mechanized system are revealed. The analysis of

experimental studies of spacecraft stabilization is carried out. It is determined that it is advisable to use the

mathematical tools of the sixth-order Butterworth polynomial in the training of a neural network. Complex

neural network calculations make it possible to calculate the stabilization coefficients of the spacecraft when

the coordinate system does not coincide with the axes of inertia. An overview of the authors ' research on the

use of intelligent quality control systems for the production of medicines is given. An overview of neural

network solutions for stabilizing the turning angle of high-speed cars is given. The expediency of selecting the

stabilization coefficients of a proportional-integral-differential regulator by a trained neural network for various

rolling ranges is proved.

Key-Words: neural network, stabilization of the rolling system, experimental model, Butterworth polynomial,

selection of stabilization coefficients of the proportional-integral-differential regulator.

Received: April 12, 2021. Revised: November 18, 2021. Accepted: December 20, 2021. Published: January 8, 2022.

1 Introduction

The stabilization of mechanized systems is realized

with the highest possible accuracy. The stabilization

of mechanized systems is required for unmanned

aerial vehicles, industrial robotics, chemical

industry, mechanical engineering, power

engineering (control of boiler rooms), mechanics

(regulation of servos), high-precision equipment of

the space industry. The stabilization of mechanized

systems includes the following processes: design of

an automated stabilization system, organizational

and technical design, neural network processing of

input and output parameter values. The improved

stabilization algorithm increases accuracy, safety,

and minimizes the probability of errors. The authors

develop a neural network software algorithm for

stabilization and propose a model of its prototype.

The process of developing a stabilization module

based on a PID controller is described, the technical

features of the module development are identified.

To accomplish this task, the authors needed to

analyze the available hardware and software

implementation tools, identify advantages and

disadvantages, develop a neural network algorithm,

develop a prototype of the system and test it. The

main goal of the experiment is to develop a rolling

system for small-diameter metal balls on a 3D

printer. To develop and apply an algorithm for

stabilizing the rolling system by combining

technical capabilities: a microcontroller, a

minicomputer and a neural network algorithm. The

computing device is a proportional-integral-

differential controller. The study shows: a skate; an

element of the program code; an algorithm for

stabilizing a proportional-integral-differential

regulator (PID). The experimental model uses the

calculation and adjustment of the regulator

according to the Ziegler-Nichols method. For the

case of applying a neural network approach to the

search for equilibrium, the Hopfield neural network

is used. The technology of calculating the balancing

of the values of the coefficients: proportional,

integral, differential components is described. The

WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS

DOI: 10.37394/232011.2022.17.3

Shmakova Elena G., Filoretova Olga A.,

Nikolaeva Olga M., Vasilkin Denis P.

E-ISSN: 2224-3429

Volume 17, 2022

design of the rolling system is described.

The experimental model was developed in

order to identify the balancing range of the rolling

system of small diameter balls. The

experimental module balances the ball at a

distance of 4.5 to 7 cm (SW-range). The

shortcomings of the experimental model of

mechanized system stabilization are revealed. The

advantage of the work is the design on a 3D

printer of an experimental model of the

rolling system (Fig.6, Fig. 7, Fig.8) and the

development of a program for the Arduino C

microcontroller and a proportional-integral-

differential controller.

2 Devices for Controlling the Parameters of the

Stabilization Process

Most prototypes are developed using

microelectronic elements, microcontrollers, single-

board computers. Unicameral computers use

operating system programs. Combining the

technical capabilities of a microcontroller, a

minicomputer and a neural network algorithm, in

total, give a synergistic effect. Arduino boards read

data from sensors, output motor signals, LED

signals, network signal data. The software for

writing code (sketch) is free, multiplatform. The

development of a neural network algorithm uses the

theory of microelectronics, programming, design,

modeling of computer technology, analog-digital

data processing. A minicomputer based on a

Raspberry Pi microprocessor (memory, storage,

graphics driver, connection connectors) and an

Arduino microcontroller (central memory, RAM

and permanent storage devices) provide input and

output signals. All signals are processed by the

algorithm. The Arduino clock frequency is 16 MHz.

The clock frequency of the Raspberry Pi is 1.2 GHz.

Raspberry Pi is convenient for developing software

applications using the Python programming

language. Arduino is convenient for controlling:

LEDs; sensors; the position of the motors; the

coordinates of the motor movement; switching

buttons. Intelligent (neural network) digital control

of input and output parameters of mechanized

systems is the main task of stabilization. To create a

prototype, special functions are required, engine

drivers, an Ethernet connection, an SD card reader,

Wi-Fi, touch screens, cameras, GPS, RGB panels,

etc. The power requirements of the Raspberry Pi

and Arduino are different. Despite the fact that both

are powered by USB (micro-USB or USB Type C

for Raspberry Pi and USB Type B for Arduino),

Raspberry Pi requires more current than Arduino.

To work with the Raspberry Pi, a power adapter is

required, to work with the Arduino, it is enough to

simply connect to a computer via a USB port.

Interrupting the power supply of the Raspberry Pi

causes damage to the hardware, software or

applications. In the case of Arduino, when the

power is turned off, the microcontroller restarts.

Raspberry Pi must be properly connected and

properly turned off. It is used by the Arduino IDE

for code development. Raspberry Pi use the

languages Python IDLE, Eclipse IDE, supported by

Linux. Raspberry Pi programming is carried out

using a terminal, a text editor is used for this. The

Arduino open source hardware and software files

are used. Raspberry Pi is not open source software.

Important advantages of Arduino are: cross-

platform, practical IDE architecture, open source

code, additional ability to use AVR-C code.

2.1 Sketch, a sketch of the program code

All sketches and sketches of the program are saved

in a special extension - .ino. The message area

displays: feedback on saving and exporting; current

errors. The console displays the text output of the

Arduino software (IDE). Includes full error

messages and other information. The configured

card and serial port are displayed in the lower right

corner of the window. The toolbar buttons allow

you to check and load programs, create, open and

save thumbnails, and open a serial monitor (Fig.1).

Fig.1: Arduino IDE Interface

The Arduino software (IDE) uses the concept of a

notepad: a standard place to store programs (or

sketches). Thumbnails in the album can be opened

from the "File" menu, "Drawing Album" or using

the "Open" button on the toolbar. When you first

start the Arduino software, a drawing album catalog

is automatically created. Sketch Features:

1. connecting the code from an external file;

2. loading the sketch through the programmer

directly into the microcontroller;

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DOI: 10.37394/232011.2022.17.3

Shmakova Elena G., Filoretova Olga A.,

Nikolaeva Olga M., Vasilkin Denis P.

E-ISSN: 2224-3429

Volume 17, 2022

3. export the binary file and store the compiled file.

The output panel displays the following

information: about the successful compilation of the

code, in addition, an error message.

2.1.1 Proportional-integral-Differential

Controller (PID)

The PID controller is a device for controlling the

process parameters: pressure, fuel consumption,

temperature, speed. The PID controller is used for

small aircraft, regulates the control of the servo

drive. The PID controller is involved in stabilizing

the position of the flying object in space. In the

controller, the feedback device of the control loop is

used to regulate variable processes. In a closed-loop

controller, a control loop feedback device is used to

maintain the required output signal value. The

closed system of the PID controller includes a

feedback control system. The system evaluates the

variable feedback value. A fixed point of error

signal generation is used. The output values change.

The error is approaching zero, reaching zero.

When the value falls below a fixed point, the

controller turns off. The controller is turned off if

the value is higher than the fixed value. The output

signal of the PID controller is unstable, fluctuates

within a fixed point. The operation of the controller

is represented by a block diagram (Fig. 2).

Fig. 2: Block diagram of the PID controller.

2.1.2 Two-position Control of the Regulator with

Feedback

The two-position controller moves the controlled

variable from the OFF position to the ON position,

depending on the variable. The PID controller

supports the output signal in such a way that there is

a zero error between the process variable and the set

value (in the case of performing feedback

operations) (Fig. 3).

Fig. 3: Block diagram of the experimental model

PID controller.

3 The Algorithm of Stabilization

using the PID Controller

To develop a stabilization algorithm, we will

determine the components of the experimental setup

of the stabilization system:

1. Servo drive;

2. Infrared sensor (tracking the movement of the

ball);

3. Swing (swinging the ball);

4. Arduino microcontroller (swing control, sensor

data processing, controller start-up, servo control);

5. Potentiometer (a measuring device for comparing

two voltage values in real time).

The experiment uses metal balls that swing on a

swing (Fig. 4).

Fig. 4: Metal balls with a diameter of 12 mm.

The main task of stabilizing the system is to balance

the values of the coefficients: proportional integral,

differential components.

The stabilization algorithm is defined by the

following procedure:

1. power supply to the circuit blocks

2. data linearization (from Lat. linearis-linear) is one

of the methods of approximate representation of

closed nonlinear systems, in which the study of a

nonlinear system is replaced by the analysis of a

linear system;

3. calculations of the two-position control of the

regulator with feedback;

4. data output to the servo;

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DOI: 10.37394/232011.2022.17.3

Shmakova Elena G., Filoretova Olga A.,

Nikolaeva Olga M., Vasilkin Denis P.

E-ISSN: 2224-3429

Volume 17, 2022

5. at the beginning: reading data from the sensor,

then the cycle enters the data linearization (Fig.

5).

Fig. 5: Linearization.

Linearization with feedback is a way to bring the

system to a form where there is an external

parameter of the control action. In this case, the

nonlinear system becomes linear, and external

control is provided for stabilizing and controlling

the remaining linear part of the system (Fig. 5).

Fig. 6: The algorithm of stabilization of the

experimental model

The Ziegler-Nichols method is a method of

automatic calculation and adjustment of regulators.

This method is empirical and is based on the use of

data obtained experimentally on a real object. For

the case of applying the neural network approach to

the search for equilibrium, the Hopfield neural

network is used — a fully connected neural network

with a symmetric matrix of connections. In

the process of operation, the dynamics of such

networks converges (converges) to one of the

equilibrium positions. These equilibrium

positions are determined in advance in the

learning process, they are the local minimum of

a functional called the network energy (in the

simplest case, the local minima of a negatively

defined quadratic form on an n-dimensional cube)

[3]. Such a network can be used as an auto-

associative memory. The trained neural network

selects the final values of the coefficients:

proportional integral, differential

components(Fig. 6, Fig. 7).

Fig. 7: The final values of the coefficients

The applied element base of the experimental

model:

1. Arduino Uno Board

2. Hitec HS-422 Analog servo drive

3. GP2Y0A41SK0F distance sensor

4. Potentiometer

5. Rocking Chair (Rolling system) Actobotics

Single Servo Arm

6. Metal ball

The design of the experimental rolling system was

carried out in Autodesk 3ds Max. Design of rolling

module parts: base (Fig.8), gutter (Fig.9), bracket

(Fig. 10).

Fig. 8: Module base

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Shmakova Elena G., Filoretova Olga A.,

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Volume 17, 2022

Fig. 9: Module gutter

Fig. 10: Module bracket

The experimental model was developed in order to

identify the range of ball rolling balancing. The

implementation of the software part of the

experimental module was carried out in the Arduino

C programming language (the C++ programming

language connected to the Wiring framework) and

the Arduino IDE development environment. To

program the board on the Arduino microcontroller, a

special development environment of the Arduino

IDE was chosen. This software is open source and

cross-platform, available for use on several

operating systems (Arduino IDE is available for use

on Windows, Mac OS, and Linux). The

programming language is Wiring, the syntax is

similar to such programming languages as C and

C++, the operating system is Windows. Before

creating a sketch, you need to perform the following

actions:

1. Connect the board via the USB port;

2. Specify the port in the Arduino IDE;

3. Develop a sketch.

Next, the sketch is uploaded to the board.

Development of an algorithm for the operation of

the software component:

1. connect the Servo.h library to control

the servo;

2. determine the initial position of the

servo, specify the values of the PID

controller;

3. assignment and initialization of

variables, determination of the numbers

used in the operation of pins.

4. in the setup function, a serial connection

is initiated, the data transfer rate in

bits/s is set, and the port number from

which the drive will be controlled is

specified.

5. in the cycle, Δt is written, data from the

distance sensor is read, we get rid of

the" noise " and linearize the received

data.

6. we count the PID, output the data to the

servo.

If the ball position does not meet the set values, the

cycle is repeated, this happens until the set values

are reached.

The experimental module balances the ball well at a

distance of 4.5 to 7 cm. This is the SW range, not

the real range, the sensor is not 100% calibrated. If

you hit the ball, the module compensates for this

and returns the ball to the starting point. It also

responds to a change in the initial preset position

(using a potentiometer). The code is gradually

struggling more and more with large ranges. Over

time, it compensates for the established errors due to

the unevenness of the gutter.

4 Conclusion

In conclusion, it should be noted that the

experimental model allowed us to determine the

stabilization of the system for balancing the ball in

the range of 4.5 to 7 cm. This suggests that the

Ziegler-Nichols method of calculating and adjusting

regulators can be used for rolling systems with a

ball diameter of 12 mm.

In the study of the authors Vorobyov V. Yu.,

Sablina G. V. "Calculation and optimization of the

parameters of a discrete PID controller by the

Ziegler-Nichols method", the calculation of the

parameters of the PID controller was carried out

using the Matlab software and the Situlink library.

In the study of the authors, it was proved that the

Ziegler-Nichols method does not take into account

the requirements for the stability margin – this is the

main drawback. After calculating the parameters of

the controller, manual adjustment is required to

improve the quality [4], [5], [6].

The conducted experiment confirms the need to use

a neural network approach. The trained neural

network selects stabilization coefficients for

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DOI: 10.37394/232011.2022.17.3

Shmakova Elena G., Filoretova Olga A.,

Nikolaeva Olga M., Vasilkin Denis P.

E-ISSN: 2224-3429

Volume 17, 2022

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DOI: 10.37394/232011.2022.17.3

Shmakova Elena G., Filoretova Olga A.,

Nikolaeva Olga M., Vasilkin Denis P.

E-ISSN: 2224-3429

Volume 17, 2022

different ball diameters, taking into account the

ranges [2].

In the study of the authors Zubov N. E. and others

"Stabilization of the orbital orientation of the

spacecraft", the mathematical tools of the

Butterworth polynomial of the sixth order are

given [1]. The calculation of the roots of

the polynomial is used in the matrix, which forms

the coefficients of the regulator. Complex

neural network calculations make it possible to

stabilize the spacecraft when the coordinate system

does not coincide with the axes of inertia.

The neural network method solves the

problems of pole placement. Analytical

expressions of the feedback matrix of the

controller solve the problems of stabilization of

the spacecraft's orbital station [7]. In the study of the

authors Saikin A.M., Buznikov S. E., Shabanov

N. S., Elkin D. S. and others "Mathematical

model of the dynamic stabilization system of an

unmanned vehicle", a study of dynamic

stability stabilization along the course is carried

out. Stabilization is necessary for high-speed cars, in

case the car exceeds the speed limit [10].

Application of neural network solutions in the study

of the authors Kornyushko V. F. and others, the

issues of quality management of the chemical and

technological process of continuous synthesis of

pharmaceutical substances of medicinal compounds

in flow microreactors are considered. The necessity

of using intelligent control systems for quality

control of the production of medicines is proved [8].

Calculations and technologies of the team of authors

of the Department of Information Systems in

Chemical Technology under the leadership of

Shmendel E.V. are used for chemical industries [1].

The study of the authors Khitskov E. A, Veretekhina

S. V., Medvedeva A.V., Mnatsakanyan O. L.,

Shmakova E. G., Kotenev A "Digital transformation

of society: Problems entering in the digital economy

"examines the issues of building a parallel digital

reality. The main tool for building digital reality is

trained neural networks [9].

Conflicts of Interest

The authors have no conflicts of interest to

declare .

Contribution of Individual Authors to the

Creation of a Scientific Article

(Ghostwriting Policy)

The authors equally contributed in the

present research, at all stages from the

formulation of the

problem to the final findings

and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

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