CC BY
23
Луцька Наталiя МиколаСвна
Доцент, кандидат технгчних наук Нацюнальний унгверситет харчових технологш
Кротковський Дмитро Олегович
Доцент, кандидат технгчних наук Нацюнальний унгверситет харчових технологш
МОДЕЛЮВАННЯ ОПТИМАЛЬНИХ РЕГУЛЯТОР1В ДЛЯ ТЕПЛОВОГО РЕЖИМУ НАХИЛЕНО1 ДИФУЗ1ЙНО1 УСТАНОВКИ ЦУКРОВОГО ЗАВОДУ
Lutska Nataliia PhD
National university of food technologies Луцкая Наталья Николаевна Доцент, кандидат технических наук Национальный университет пищевых технологий Крониковский Дмитрий Олегович Доцент, кандидат технических наук Национальный университет пищевых технологий Kronikovskyi Dmytro PhD
National university of food technologies
SIMULATION OF OPTIMAL CONTROLS FOR THERMAL MODE OF SUGAR FACTORY INCLINED DIFFUSION APPARA TUS
МОДЕЛИРОВАНИЕ ОТИМАЛЬНЫХ РЕГУЛЯТОРОВ ДЛЯ ТЕПЛОВОГО РЕЖИМА НАКЛОНЕННОЙ ДИФУЗИОННОЙ УСТАНОВКИ САХАРНОГО ЗАВОДА Abstract
The work compares two regulators for optimal temperature regime inclined diffusion apparatus of sugar factory. First synthesized by standard algorithms ACOr and second with same algorithm, but with the introduction of an integrated component on error signal. Based on the heat balance of the mathematical model of control object, which consists of eight linear differential equations, the model coefficients are calculated and presented it to the space of state variables. Based on the simulation show that the control system, which is synthesized by ACOr insignificant static error that allowed for technological regulations diffusion process. The use of optimal control algorithm with integral component of the error signal by significantly delaying transients in the system although it eliminates static error, because the latter algorithm impractical to use. Key Words
Mathematical model of the control object, heat exchange, mass transfer, diffusion apparatus, algorithm of optimal control.
Анотацгя
В роботi проводиться поргвняння двох оптимальних регуляторгв для температурного режиму нахилено'1' дифузтноИ установки цукрового заводу. Перший синтезований за стандартним алгоритмом АКОР, а другий за вказаним алгоритмом, але з введенням iнтегральноi складовоi за сигналом розузгодження. На основi теплового балансу розроблено математичну модель об 'екта керування, що складаеться з восьми лiнiйних диференщальних рiвнянь, розраховат коефщенти моделi та приведено ii до простору змтних стану. На основi моделювання показано, що система з регулятором, який синтезований за АКОР мае несуттеву статичну похибку, що допустима за технологiчним регламентом процесу дифузш. А застосування алгоритму оптимального керування з ттегральною складовою за сигналом розузгодження значно затягуе перехiднi процеси в системi хоча i лiквiдуе статичну похибку, тому останнш алгоритм недоцшьний в застосувант. Ключовi слова
Математична модель об'екта управлтня, теплообмiн, масообмiн, дифузшний апарат, алгоритм оптимального управлiння. Аннотация
В работе проводится сравнение двух оптимальных регуляторов для температурного режима наклоненной диффузионной установки сахарного завода. Первый был синтезирован по стандартному алгоритму АКОР, а второй при помощи указанного алгоритма, но с введением интегральной составляющей по сигналу рассхождения. На основе теплового баланса разработана математическая модель объекта управления, состоящая из восьми линейных дифференциальных уровнений, рассчитаны коэффициенты модели. На основе моделирования показано, что система с регулятором, который синтезирований за АКОР имеет несущественную статическую погрешность, что допустимая по тех-нологических регламентам процесса диффузии. А применение алгоритма оп-минимального управления с интегральной составляющей по сигналу рассогласования значительно затягивает переходные процессы в системе хотя и ликвидирует статическую погрешность, поэтому последний алгоритм нецелесообразен в применении.
Ключевые слова
Математическая модель объекта управления, теплообмен, массообмен, дифузионный аппарат, алгоритм оптимального управления.
Abbreviations
ACO- ant colony optimization
ACOr- ant colony optimization for continuous domains
Problem formulation
In the process of complex with continuous type function technological objects, which are characterized by many interconnected regulated coordinates. Often several controlled origin, whose number n > 4 have the same physical nature and contours of regulation are based on the same structure. This applies, for example, diffusion plants gentle slope-type sugar mills, which are governed by n > 4 temperatures in different zones.
Thus, food enterprises can be identified class of objects [1], which are characterized by the following properties:
- Have the same coordinate state n>4 a physical
nature;
- Have significant internal relationships between variables;
- Similar in structure to describe mathematical models;
- Governed by a similar scheme.
In traditional systems automation to adjust each of the coordinates of the object class uses a separate automatic regulator, leading to undesirable influences one path to the other and, consequently, deterioration in the quality of transients and increase energy.
Highlight unsolved parts of the general problem
The use of autonomous systems leads to complexity of the structure of the system by including joints and does not provide a significant improvement of quality of transients. Therefore, to build a system of such objects must use an approach in which the optimality conditions will be carried out on the quality of the transition process, reducing the cost of energy and the autonomy of individual control channels. Among a variety of algorithms for optimal control of industrial objects [2] are algorithms for multidimensional systems with control criterion corresponds to the aim of the study. This algorithm analytic construction of optimal regulators (LQR), for which at present there are many additions and extensions.
The purpose of the research problem
Compare discrete system of automatic regulation of the optimal control for the diffusion apparatus of the sugar factory, a synthesis algorithm ACOr with the introduction of an integrated component on error signal and without during task change.
Comparison of optimal controls carried out by simulation using application package Matlab, which are ready mentioned algorithms that significantly reduce the time writing and debugging programs.
Materials and Method
The mathematical model of control object. The object is inclined diffusion apparatus for sugar production, which has four zones with one steam chamber (Fig. 1) [1].
A mathematical model is developed under the following assumptions:
- Object (diffusion part of heat exchange apparatus) consider lumped parameters;
- Diffusion apparatus has an ideal thermal insulation for neglecting losses to the environment;
- The couple of steam chambers is in the state of saturation, and the enthalpy of the heating steam and the enthalpy of the steam chamber adopt the same as the consumption of steam and condensate;
- Takes in a constant specific heat capacity beet chips and juice, heat transfer coefficient and density of juice and beet chip mixture;
- Thermal diffusion facility design capacity is not considered.
Derive the equation for the second heat exchange zone beet chips and juice mixture, which make up the heat balance equation
GXl1^ + GHC1103 + kF(0„2 -e2) = G23C2302 + g^c2^,
(1)
where Gl, G'^c, Cc , Cic - consumption and heat capacity beet chips and juice from the i-th to the j-th zone under; d1,Onj - temperature juice and chips mixture of steam in a steam chamber in the i-th zone under;
k, F - heat transfer coefficient and area heating steam chamber.
Fig.l. Simplified flowsheet gentle slope diffusion apparatus
When imbalance will occur a change in heat capacity at a speed dependent on the imbalance
MH2Lpc2 6 = A(gJ2C1c261 + GfCf^ + kF(en2 -62) - gcCfd2 - GfC>2), (2)
dT
where M, Ht, L, p, ci - width, height and length In deviations of variables based on linearization
„ , , . , . 1 ,, 1 . ,. . . . equation becomes:
of the device, density and heat capacity chips juice mixture,
respectively.
d62 _
1
(GC12 + AG12 + Ав3 + C£63o АОдс
-12,
■Л2
-32 ^32
-32/
32
+
0
dr MH2Lpc2
+ kFAdп2 - kF AO 2) - G^C? AO 2 - Cc?3^20 AG? - GС C^ - C>20 A
For other areas beet chips and juice mixture equations are derived similarly.
Derive the equation of heat transfer for steam capacity. Putting the heat balance equation:
G^ = kF(6nX -6!), (4) where Gni, ri - steam flow in the steam chamber
and heat of vaporization in the i-th zone diffusion apparatus. When imbalance will occur a change in heat capacity at a speed dependent on the imbalance:
Vc„
dO
= A(Gn1r1 - kF6nl + kF6j), (5)
dT
where cni - volume of the steam chamber and heat of steam in the i-th zone, respectively. Turn to deviations:
dO
1
dr Vc
-(TiAGnl - kFAOi + kF AO 1). (6)
n1
The heat capacity of steam depends on the internal energy of steam un and vapor density p" :
(3)
Cn1 = Una + p 'A,
p" =p' + авп;
un = un + bOn;
un, a, b
P
(7)
determined
where experimentally.
In [2, 3], the concentration of sugar in the juice and chips on the current length of the diffusion apparatus l is described exponential dependence. According consumption and heat capacity of chips and juice for long diffusion apparatus can be described : Gc = 31,25e_c''007591 , [kg/sec],
[kg/sec], (8) [kJ / kg 0C], ~0-006231 [kJ /kg 0C]. The result is a mathematical model of heat transfer diffusion apparatus:
Gdc = 37,5e
Cc = 3,40e'
Gdc = 3,61e0
0.006231 0.007591
dA0
dr MLH 1pc1
(G0C01A0c + (CcX -Cc2^ln)AGc + G20Cl]A02 +
+ (C0 - C0, )AGdc + kFA0nX - (kF + G12C12 + GjC,С )A0;
чЮ
12^12
-.10 c 10 N
cn
dA0
1
(G12C12A0 + (CX - C0)AGe + G£ C32A03 +
12
23
32 32
dr MLH 2pc2 + (CX - C0 )AGdc + kFA0n2 - (kF + G?C? + G20 C£)A02;
dA0
1
(G"Cf A0 2 + (C0 - C0)AGe + G? C43 A04 +
23
34
43 43
dr MLH 3pc3 + (CX - CX )AGgc + kFA0n3 - (kF + G34Cc34 + g£ C£)A03;
dA0
1
dr MLH Apc 4
(Gc3n4Cc34A03 + (C3403n - Cc4e04n)AGc + G,n СeA06 +
+ G С A0 - C430 AG, + С0 AG + CB^ AG + kFA0. -
' dc^ 4,
' dc
6"6n
n4
- (kF + G4eC + Gg43n Cd43)A04;
dA0ni 1
dr Vc n1
dA0n 2 1
dr Vc n2
dA0n3 1
dr Vc n3
dA0n 4 1
dr Vc n4
(riAGni -kFA0ni + kFA0i); (r2AGn2 -kFA0n2 + kFA02); (r3AGn3 -kFA0n3 + kFA03); (r4AGn4 -kFA0n4 + kFA04);
(9)
where A6c, A66, A0x - deviation chips A 6. - to change A 6 n, which in turn will also affect A
temperature at the entrance of the diffusion apparatus, Q... Change of AG , AG6, 6 , 66 leads to changes A
barometric and pulp water respectively; x x
AG6, AGX, AC6, AC^ - deviation expenses and heat 64 , acting on a return Path to change A 6i Ta A 6n .
capacity of barometric and pulp water respectively. For stationaiy mode operation of the sugar pla*
As can be seen from the model object is multiply capacity of 3000 tons 1 day, calculated values of the
connected, change the temperature of a beet chips and juice coefficients of the mathematical model of the object for the
n typical modes of operation based on the design features of
mixture Qi leads to changes in temperature and vapor beet the facility. Mathematical model of heat exchange
chips and juice mixture both direct and reverse. If the trace diffusion system brought to the form (machine time
variables AGdc, AGc, then rejection leads to changes v=100t, wherer, sec):
A 6. in direct (direct impact) and return path, and through
1
dAO
1.157-1 + Ав1 = 0.43Авс + 0.54Ав2 + 0.03Авп1 - 0.27AGc + 0.15AGdc;
dt
dAO2
1.169-1 + Ав2 = 0.43Ав1 + 0.54Ав3 + 0.03AOn2 - 0.14AGc + 0.04 AGdc;
dt
1.181
dAO3 dt dAO
+ AO3 = 0.43Ав2 + 0.54Ав4 + 0.03Авп3 -0.04AGc + 0.03AGdc;
1.193^-^- + AO4 = 0.43Ав3 + 0.33Авб + 0.03Авп4 + 0.21Авж + 0.92AG6 +
0.0887
0.0393
0.0489
0.0715
dt
.dO dt dAO dt dAO dt dAOn4
dt
+ 0.92AG^ - 0.87 AGdc + 0.09AGc; + AOn1 =Ав + 279.91AG
+ AOn 2 =Ав2 + 288.9AGn 2;
+ AOn3 =AO3 + 286.5AGn3;
+ AOn 4 =AO4 + 282.3AGn 4,
(10)
Transformed model to the space of state variables: x(t) = [A61, A62, A63, A64, A6m, A6n2, A6n3, A6n4 ]T
vector of perturbation, where
AGc, AGdc, AGg, AG^ - expenditure of chips, juice,
(11) barometric and pulp water, A6c, A6g, A6_ - chips Vector of state parameters consisting of c "
temperature beet chips and juice mixture and steam in temperature at the entrance of to diffusion apparatus, steam chambers in their respective areas of apparatus; barometric and pulp water respectively;
y(t) = [A6, A62, A63, A64 ]T - (14) vector of observations (measurements), consisting of a beet chips and juice mixture of temperatures in their respective areas of apparatus.
Then the matrix model (10) have the form:
u(t) = [AGm, AGn2, AGn3, AGn4 ]T - (12) vector control, consisting of steam consumption in their respective areas of apparatus;
z(t) = [A6c, AGc, AGdC, A6g, A6^, AGg, AG^ ]T
(13)
"-0.8643 0.4667 0 0
0.3678 - 0.8554 0.4619 0
A=
0
0.3641 - 0.8467 0.4572
0.0259 0 0
0
0.0257 0
0 0
0.0254
0 0 0.3604 -0.8382 0 0 0 0.0251
11.27 0 0 0 -11.27 0 0 0
0 25.45 0 0 0 -25.45 0 0
0 0 20.45 0 0 0 -20.45 0
0 0 0 13.99 0 0 0 -13.99
' 0 0 0 0 "
0 0 0 0
0 0 0 0
B= 0 0 0 0 (16)
3155.69 0 0 0
0 7351.15 0 0
0 0 5858.90 0
0 0 0 3948.25
(15)
G =
0.3717 0 0 0 0 0 0 0
- 0.2334
- 0.1198 -0.0339
0.0754 0 0 0 0
0.1299 0.0342 0.0254 -0.7293 0 0 0 0
00 00 00 0.2766 0.1760 00 00 00 00
0 0 0
0.7712 0.7712 00 00 00 00
(17)
1 0 0 0 0 0 0 0 C_ 01000000 C 00100000 0 0 0 1 0 0 0 0
Algorithm of optimal control. Several algorithms based on or inspired by the ACO metaheuristic have been proposed to tackle continuous optimization problems. One of the most popular ACO-based algorithm for continuous domains is ACOr. Today there are many additions to the classic problem ACOr particular solution to known external disturbances, or given values of vectors x(t) and u(t) in integral quadratic criteria. There are also discrete analogs of these problems.
An interesting variant of the problem ACOr with the introduction of an integrated component on error signal (e = r- y, where r - vector problem, y - vector stabilizing output).
Results and Discussion
Compare discrete system of automatic regulation of the optimal control for diffusion plants, a synthesis algorithm ACOr with the introduction of an integrated component on error signal and no change in the task.
The purpose of the research problem is synthesis of optimal controls, so we used the Control System Toolbox
(18)
lqi and lqry, realizing set algorithms. For example, take a mathematical model that describes the diffusion zones of temperature settings, and we assume that all measured temperatures, and it is only necessary to stabilize the temperature beet chips and juice mixture reject external disturbances missing.
Lqry function implements a multidimensional array controller type u = -Kx the coordinates of the system while minimizing the criterion:
I(u) _ J (yTQy+uTRu)dt ^ min , (19) t0 u
Block diagram of the system with the introduction of error signal is shown in Fig. 2 lqi function returns multidimensional optimal regulator type u=-K[x;xJ, where xi - output of the integrator (Fig. 3). Data connectivity features implemented series, feedback and connect.
Fig.2. Block diagram of the system with optimal control (algorithm ACOr) and task signal
Fig.3. Block diagram of the system with the optimal regulator (ACOr algorithm) and an integral part of the task signal
0 50 100 150 200 250
Fig.4. Transient processes with different control algorithms
0 10 20 30 40 50 60 70 30 90 100
Fig.5. Simulation of system with harmonic task signal
As can be seen from the results (Fig.4. and Fig.5.) of the program at the step change task to a second output using an integrated component of this channel is observed elimination of static errors, although the transition process increases by about 200 times. By cross-linking observed transients on other channels. Also note that the static error for all channels using the algorithm ACOr minimization criterion for outputs does not exceed 0.3 0C, invested in production schedules (maximum deviation from the set temperature should not exceed 0.5 0C).
In addition, following the automatic control system optimal regulator with integral component does not have time to work out a signal problem.
Thus, for a given object the feasibility of using multivariate regulator with integral component of outgoing channels is not confirmed. In addition, a closed system optimal control has eigenvalues on the verge of stability, ie to further investigate system for robust stability.
References
1. Lutskaya N.N., Ladanyuk A.P. 2007. Use of optimal controllers for multidimensional technological objects. Journal of automation and information sciences, N° 3. - 16-24.
2. Pupkov K. and Yegupov N. 2004. Methods of classical and modern control theory: In Pupkov K. (ed) - M .: Publisher MSTU, Moscow;
3. Nehoda F., Ladanyuk A., Lysyansky V. 1983. Control of diffusion apparatus. - M .: FoodEng. Ser. 3, Kiev.
4. Ladanyuk A., Nehoda F., Janchenko Y. 1985. Analysis of dynamic characteristics of the inclined screw extractor as a control object. - UkrNIINTI., Kiev.
References
1. Lutskaya N.N. Use of optimal controllers for multidimensional technological objects. Journal of
automation and information sciences/ Lutskaya N.N., Ladanyuk A.P.// - 2007- № 3. - 16-24.
2. Pupkov K. Methods of classical and modern control theory: In Pupkov K. (ed) / Pupkov K. ,Yegupov N.//.- M .: Publisher MSTU, Moscow- 2004;
3. Nehoda F., Control of diffusion apparatus/ Nehoda F .,Ladanyuk A., Lysyansky V.//- M .: FoodEng. Ser. 3, Kiev- 1983.
4. Ladanyuk A., Analysis of dynamic characteristics of the inclined screw extractor as a control object. / Ladanyuk A., Nehoda F., Janchenko Y// -UkrNIINTI., Kiev-1985..
Нужна Свтлана Анатоливна
кандидат економ1чних наук, доцент кафедри тформатики та комп'ютерних технологт, Дтпродзержинський державний технгчний утверситет, Галаганов Василь Олександрович студент, Дтпродзержинський державний технгчний унгверситет
ТЕОРЕТИЧН1 АСПЕКТИ РОЗВИТКУ 1НФОРМАЦ1ЙНО1 БАЗИ КОМП'ЮТЕРНИХ ТЕХНОЛОГ1Й
Svetlana Nuzhna
PhD, Associate Professor
Dniprodzerzhynsk State Technical University
Galaganov Vasyl
student
Dniprodzerzhynsk State Technical University
THEORETICAL ASPECTS OF THE DEVELOPMENT OF INMORMATION BASE OF COMPUTER TECHNOLOGIES
Анотацiя. У cmammi розглянуто процес розвитку тформацшно'1 бази комп'ютерних технологт, визначено основнi структурно-функцюнальт трансформацИ операцтних систем. Встановлено фактори, що впливають на кшьюсть користувачiв операцтно'1 системи, eid-значено ключовi характеристики та вимоги до апаратного забезпечення операцтних систем амейства Windows.
Ключовi слова: тформацтна база, операцтна система, трансформацИ, програмне забезпечення, зручнкть використання, Windows.
Summary. The article shows the development process of information base of computer technologies. Defined the basic structural and functional transformations of operating systems. Analyzed main factors that influence for the number of users of the operating system. Noted key features and hardware requirements of Windows operating systems. Key words: information base, operation system, transformation, software, usability, Windows.
Постановка проблеми. В умовах ринково! економши значно зростае роль шформацп, як одного з найважливших ресурав сустльства. Одним з засобiв обробки та аналiзу шформацп е персональш електронно-обчислювальш машини, тобто комп'ютери. Основою для роботи будь-якого персонального комп'ютера е наявшсть операцшно! системи. Вона е базовим системним програмним забезпечення, що керуе роботою комп'ютера i е посередником Интерфейсом) мiж апаратурою, прикладним програмним забезпеченням i користувачем комп'ютера. Фактично операцшна система з точки зору користувача - це продовження апаратури, надбудова над нею, що забезпечуе бшьш зручне, надшне i безпечне використання комп'ютерiв, комп'ютерних технологт i комп'ютерних мереж [7].
Аналiз останшх дослщжень та публшацш. Дане питання викликае штерес як в наукових, так i в суспшьних колах. Серед шоземних дослвджень необхщно ввдзначити аналггичш розрахунки мiжнародного статистичного вiдомства StatCounter [6]. Серед вичизняних вчених внесок у розвиток даного питанням зробили М.В. Макарова, Г.В. Карнаухова та С.Д. Мамченко [2, 3]. Не менш важливою залишаеться офiцiйна статистична база, яку надае корпорацiя Майкрософт [5].
Видшення iieiuipiiiieiiiix panirne частин загальноТ проблеми. Попри позитивний вплив дослвджень в даному питаннi необхiдно шдкреслити, що вони не охоплюють yci аспекти структурно-фyнкцiонального складу операцтних систем на рiзних iсторичних етапах, а концентруються на окремих промiжках часу, що зменшуе об'eктивнiсть аналiзy трансформацiй, що вiдбyвались в зазначенш галyзi. Надана в статтi комплексна порiвняльна характеристика операцiйних систем амейства Windows дае можливють проаналiзyвати i надати прогнози стосовно розвитку операцтних систем у короткостроковш та довгостроковш перспективi.
Мета CTaTTi. Метою дано! статп е дослiдження i аналiз трансформацiйних процесiв, якi вiдбyвались у структурному та функцюнальному складi операщйних систем рiзних перiодiв; визначення проввдних напрямкiв у розвитку iнформацiйноi бази комп'ютерних технологш для визначених промiжкiв часу; надання порiвняльного аналiзy операцтних систем амейства Windows i видшення на його основi ключових тенденцш змiни фyнкцiональних можливостей зазначених систем.
Виклад основного мaтepiaлу. У раннiх mainframe-комп'ютерах (1940-1950 рр.), першим з яких був комп'ютер ENIAC (1947 р США), операцшш системи були вщсутш. Звернення до пам'яп в цих
