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Improved PID controller design for a two-stage technological workflow
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IFAC PapersOnLine 51-30 (2018) 226–230 Improved PID controller design for a two-stage technological workflow Improved PID controller design for aa two-stage technological workflow Improved PID controller design for two-stage technological workflow Improved PID controller design for a two-stage technological Yury R. Vladov. Alla Yu. Vladova Improved PID controller design for a two-stage technological workflow workflow
Yury R. Vladov. Alla Yu. Vladova Yury R. Alla Yu. Vladova Yury R. Vladov. Vladov. Alla Yu. Vladova *Orenburg Scientific Centre of the Ural BranchAlla Russian Academy of Sciences, Orenburg, of the Yury R. Vladov. Yu. Vladova Russia (Tel: +7 (353) 277-54-17; e-mail: [email protected]). *Orenburg Scientific Centre of the Ural Branch of the Russian Academy of Sciences, Orenburg, *Orenburg Centre of the Ural Branch Russian Academy *Orenburg Scientific Scientific Centre of+7 the(353) Ural 277-54-17; Branch of of the the Russian Academy of of Sciences, Sciences, Orenburg, Orenburg, Russia (Tel: e-mail: [email protected]). *Orenburg Scientific Centre of+7 the(353) Ural 277-54-17; Branch of the Russian Academy of Sciences, Orenburg, Russia (Tel: e-mail: [email protected]). Russia (Tel: +7 (353) 277-54-17; e-mail: [email protected]). Russia (Tel: +7 (353) 277-54-17; e-mail: [email protected]). Abstract: Background. Despite the wide use of controllers with proportional-integral-differential control law (PID controllers), issue of thecontrollers limited functionality of not taking into account the trend Abstract: Background.the Despite theexpanding wide use of with proportional-integral-differential control Abstract: Background. Despite the wide use controllers with proportional-integral-differential control of changing technological parameters is open. Methods. The control action istaking formed taking intothe account Abstract: Background. Despite theexpanding wide use of of controllers with proportional-integral-differential control law (PID controllers), the issue of the limited functionality of not into account trend Abstract: Background. Despite theexpanding wide use of controllers with proportional-integral-differential control law (PID issue of the limited functionality of not into account the trend the predicted value of the the technological parameter. Verification. Theaction proposed method wasinto verified for law (PID controllers), controllers), the issue of expanding the limited functionality of notistaking taking into account the trend of changing technological parameters is open. Methods. The control formed taking account law (PID controllers), the issue of expanding the limited functionality of not taking into account the trend of changing changing technological parameters is open. open. Methods. The control control action is isUsing formed taking into account account the reactor that processes the waste gases in sulfur production. Conclusions. a PID controller with of technological parameters is Methods. The action formed taking into the predicted value of the parameters technological parameter. Verification. The proposed method was verified for changing technological is open. Methods. The control action is the formed taking into account the predicted value of technological parameter. Verification. The proposed method was verified for aof predictive component significantly improves the quality of control, maximum deviations of the predicted value of the the technological parameter. Verification. Thereduces proposed method was verifiedwith for the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller predicted value of the technological parameter. Verification. The proposed method was verified for the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller with process parameters from specified values, contributing to additional energy saving and a significant the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller with aathe predictive component significantly improves the quality of control, reduces Using the maximum deviations of reactorinthat theofwaste gases inprocess sulfur production. a PIDand controller with component significantly improves the of maximum deviations of increase theprocesses efficiency automated units to in control, theConclusions. oil reduces and gasthe industry mechanical a predictive predictive component significantly improves the quality quality of control, reduces the maximum deviations of process parameters from specified values, contributing additional energy saving and a significant aengineering. predictive component significantly improves the quality to of control, reduces thesaving maximum deviations of process parameters from specified values, contributing additional energy and a significant process parameters from specified values, contributing to additional energy saving and a significant increase in the efficiency of automated units in the oil and gas industry and process parameters from specified values,process contributing to additional energy saving and a mechanical significant increase in the efficiency of automated process units in the oil and gas industry and mechanical increase inControl the efficiency of automated process units Intelligent in the oilSystems and gasand industry and mechanical engineering. Keywords: and Automation to Improve Stability; Applications increase in the efficiency of automated process units in Hosting the oilbyand gas industry and reserved. mechanical © 2018, IFAC (International Federation of Automatic Control) Elsevier Ltd. All rights engineering. engineering. engineering.Control and Automation to Improve Stability; Keywords: Intelligent Systems and Applications Intelligent Keywords: Keywords: Control Control and and Automation Automation to to Improve Improve Stability; Stability; Intelligent Systems Systems and and Applications Applications specification and its and rateApplications of specification, without any Keywords: Control and Automation to Improve Stability; Intelligent Systems 1. INTRODUCTION predictive component. specification and its rate of specification, without any specification and 1. specification and its its rate rate of of specification, specification, without without any any The controller with a proportional-integral-differential 1. INTRODUCTION INTRODUCTION predictive component. 1. INTRODUCTION specification and its rate of specification, without any predictive component. predictive component. control (PID controller) is one of the most common types of 1. INTRODUCTION The controller with aa proportional-integral-differential predictive component. The controller with proportional-integral-differential regulators: of them use the most appropriate algorithm. The with proportional-integral-differential controlcontroller (PID90-95% controller) isaa one of the common types of The controller with proportional-integral-differential control (PID controller) is of most common types The popularity of PID can be attributed partly to control (PID90-95% controller) is one oneuse of the the common types of of regulators: of controller them the most appropriate algorithm. control (PID controller) is one of the most common types of regulators: 90-95% of them use the appropriate algorithm. their popularity robust90-95% performance toattributed their algorithm. functional regulators: of controller themand use partly the appropriate The of PID can be partly to regulators: 90-95% them useAmong the appropriate algorithm. The of can attributed partly to simplicity (Shakya etofal,controller 2014). controllers, 64% The popularity popularity of PID PID controller can be bePID attributed partly to their robust performance and partly to their functional The of controllers PID controller can36% be toattributed partly to their popularity robust performance performance andandpartly partly theirmulti-circuit functional are single-loop are their robust and to their functional simplicity (Shakya et al, 2014). Among PID controllers, 64% their robust performance and partlycontrol to controllers, their functional simplicity (Shakya et 2014). Among PID 64% controllers. Instruments feedback occupy 85% of simplicity (Shakya et al, al,with 2014). Among PIDare controllers, 64% are single-loop controllers and 36% multi-circuit simplicity (Shakya et al, 2014). Among PID controllers, 64% are single-loop controllers and 36% are multi-circuit the total number of controllers, with direct control 6%, and are single-loop controllers and 36% are multi-circuit controllers. Instruments with feedback control occupy 85% of are single-loop and 2006). 36% are multi-circuit controllers. with control occupy 85% of cascaded -Instruments 9%ofcontrollers (Denisenko, Analogue-digital controllers. Instruments with feedback feedback control occupy 85%and of the total number controllers, with direct control 6%, controllers. Instruments with feedback control occupy 85% of the total number of controllers, with direct control 6%, and converters on a microprocessor basis allowed to use the total number of controllers, with direct control 6%, and cascaded -- 9% (Denisenko, 2006). Analogue-digital the total number of controllers, with direct control 6%, and cascaded 9% (Denisenko, 2006). Analogue-digital automatic parameter adjustment, adaptive cascaded -on 9% (Denisenko, 2006). Analogue-digital converters a microprocessor basis algorithms, allowed toneural use cascaded -on 9% (Denisenko, 2006). Analogue-digital converters microprocessor basis allowed use networks, genetic and adaptive fuzzy logic methodsto (Ahn, converters on aa algorithms microprocessor basis allowed toneural use automatic parameter adjustment, algorithms, converters on a microprocessor basis allowed to use Fig. 1. Dynamic of PID-controllers patenting. automatic parameter adjustment, adaptive algorithms, neural Bahgaat, China, Zhu et al). However, despite the long automatic genetic parameter adjustment, adaptive algorithms, neural networks, algorithms and fuzzy logic methods (Ahn, automatic parameter adjustment, adaptive algorithms, neural networks, genetic algorithms and fuzzy logic methods (Ahn, history of China, development and aand great number of publications Fig. networks, genetic algorithms fuzzy logic methods (Ahn, Bahgaat, Zhu et al). despite the long Fig. 1. 1. Dynamic Dynamic of of PID-controllers PID-controllers patenting. patenting. networks, genetic algorithms andHowever, fuzzy logic methods (Ahn, Bahgaat, China, Zhu et al). However, despite the long Fig. 1. Dynamic of PID-controllers patenting. and patents, the issues of expanding the limited functionality Bahgaat, China, Zhu et al). However, despite the long history of development and aa great number of publications Fig. 1. Dynamic of PID-controllers Authors of the patent (Tararykin patenting. et al, 2005) proposed an Bahgaat, China, Zhu et al). However, despite the long history of development and great number of publications of these devices remain unresolved. history of development and a great the number of functionality publications approach of controlling dynamic objects with external and patents, the issues of expanding limited history of development and a great number of publications Authors of the patent (Tararykin et al, 2005) proposed an and patents, the issues expanding and patents, the remain issues of of expanding the the limited limited functionality functionality Authors of patent (Tararykin et al, 2005) proposed an of these devices unresolved. perturbations by building a control signal on theexternal results Authors ofofthe the patent (Tararykin et objects al, based 2005)with proposed an and patents, the remain issues of expanding the limited functionality approach controlling dynamic of these devices unresolved. 1.1 Patent analysis Authors of the patent (Tararykin et al, 2005) proposed an of these devices remain unresolved. approach of controlling dynamic objects with external of comparing specifies signal and an amount of measured approach of controlling dynamic objects with external of these devices remain unresolved. perturbations by building aa control signal based on the results approach of controlling dynamic objects with external perturbations by building control signal based on the results 1.1 Patent analysis values characterized ansignal technical condition. The perturbations byspecifies building aobject’s control signal based on the results 1.1 analysis comparing and an amount of measured Positive dynamic 1.1 Patent Patent analysisof PID-controllers patenting is confirmed of perturbations byspecifies building a control signal based on the results of comparing signal and an amount of measured main drawback of this approach is measuring the object's of comparing specifies signal and an amount of measured 1.1 Patent analysis values characterized an object’s technical condition. The by the analysis of more than 30 thousand international patents of Positive dynamic of PID-controllers patenting is confirmed comparing specifies signal and technical an amount of measured values characterized an object’s condition. The condition variables behind the points of perturbation. values characterized an object’s technical condition. The Positive dynamic of PID-controllers patenting is confirmed main drawback of this approach is measuring the object's (granted in countries that develop thispatenting topic, such as patents China, values Positive dynamic of PID-controllers is confirmed characterized an approach object’s is technical condition. The by the analysis of more than 30 thousand international main drawback of this measuring the object's Positive dynamic of PID-controllers patenting is confirmed main drawback of this approach is measuring the object's by the analysis of more than 30 thousand international patents condition variables behind the points of perturbation. USA, Russia, Canada, Holland, UK and etc.) received by the analysis of morethat than 30 thousand international patents Method of identifying an object with test signals bases upon main drawback of this approach is measuring the object's (granted in countries develop this topic, such as China, condition by the analysis of more than 30 thousand international condition variables variables behind behind the the points points of of perturbation. perturbation. (granted in countries countries that develop this topic, such as patents China, between 2006 and 2015 and defined bytopic, using the method of control (granted in that develop this such as China, actions summarizing components. The first of condition variables behind the two points oftest perturbation. USA, Russia, Canada, Holland, UK and etc.) received Method of identifying an object with signals bases upon (granted in countries that develop this topic, such as China, USA, Russia, Canada, Holland, UK and etc.) received Method of identifying an object with test signals bases upon semantic search in the Exactus Patent system (Fig. 1). USA, Russia, Canada, Holland, UK and etc.) received them depends on the values of output variables of an object, Method of identifying an object with test signals bases upon between 2006 and 2015 and defined by using the method of control actions summarizing two components. The first of USA, Russia, Canada, Holland, UK and etc.) received control between 2006 and 2015 and by using the method Method of identifying anonobject with test signalsThe bases upon actions summarizing two components. first of between 2006 and 2015 and defined defined by using(Fig. the 1). method of of and the second depends errors of regulation. Test signals control actions summarizing two components. The first of semantic search in the Exactus Patent system them depends on the values of output variables of an object, between 2006 and 2015 and defined by using(Fig. the method of them semantic control actions summarizing two components. The first of depends on the values of output variables of an object, semantic search search in in the the Exactus Exactus Patent Patent system system (Fig. 1). 1). help to fix a trajectory of output variables and to evaluate them depends on the values of output variables of an object, and the second depends on errors of regulation. Test signals semantic search in the Exactus Patent system (Fig. 1). them depends on the values of output variables of an object, the second depends on errors of regulation. Test signals A different control method was proposed in (Kostogryz, and dynamic performance of the controlled object and (Verevkin et al, and the second depends on output errors of regulation. Test signals help to fix aa trajectory variables to evaluate and the second depends of onofoutput errors of regulation. Test signals help to fix trajectory of variables and to evaluate 1994): in that approach, a specification is formed, the 2006). The disadvantage this method is the necessity of help to fix a trajectory of output variables and to evaluate A different control method was proposed in (Kostogryz, dynamic performance of the controlled object (Verevkin et al, A different control method was proposed in (Kostogryz, help to fix a trajectory of limits output variables and to evaluate dynamic performance of the controlled object (Verevkin et al, controlled parameter is measured, and the deviation of the A different control method was proposed in formed, (Kostogryz, test signals. It severely the possibilities of this dynamic performance of the controlled object (Verevkin et al, 1994): in that approach, a specification is the 2006). disadvantage of this method is the necessity of A different control methodaa was (Kostogryz, 1994): in that approach, specification is the dynamicThe performance of the controlled object (Verevkin et do al, 2006). The of this method is necessity of parameter the specification isproposed determined, alongofwith 1994): in from that approach, specification isin formed, formed, the approach fordisadvantage most varieties of objects that 2006).signals. The disadvantage oflimits thistechnological method is the the necessity of controlled parameter is measured, and the deviation the test It severely the possibilities of this 1994): in that approach, a specification is formed, the controlled parameter is measured, and the deviation of 2006). The disadvantage of this method is the necessity of test signals. It severely limits the possibilities of this the rate of deviation. The disadvantage of this approach is controlled parameter is measured,isand the deviation ofwith the test not permit additional influences. Another problem is the signals. It severely limits the possibilities of this parameter from the specification determined, along approach for most varieties of technological objects that do controlled parameter is measured, the control deviation ofwith the parameter from thecapabilities, specification isand determined, along test signals. It severely limits the possibilities of this approach for most varieties of technological objects that do limited functional since the signal is parameter from the specification is determined, along with dependence one of the components from control errors.that approach most varieties of technological objects do the rate of deviation. The disadvantage of this approach is not permitfor influences. Another problem is the parameter from the specification is determined, along with the rate of deviation. The disadvantage of this is foradditional most varieties of technological objects that do not permit additional influences. Another problem is the formed based on capabilities, the deviation from the the rate functional of deviation. Theparameter’s disadvantage of control this approach approach is approach not permit additional influences. Another problem is the limited since the signal is dependence one of the components from control errors. the rate functional of deviation. The disadvantage of control this approach limited capabilities, since the signal is not permit additional influences. Another problem is the one of the components from control errors. limited functional capabilities, since the control from signal is dependence formed based on the parameter’s deviation limited functional capabilities, since the control signalthe is dependence one of the components from control errors. formed formed based based on on the the parameter’s parameter’s deviation deviation from from the the dependence one of the components from control errors. formed based on the parameter’s deviation from the 226 Copyright © 2018 IFAC 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic Copyright 2018 responsibility IFAC 226Control. Copyright © 226 10.1016/j.ifacol.2018.11.291 Copyright © 2018 2018 IFAC IFAC 226 Copyright © 2018 IFAC 226
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Thus, there was revealed the limited functionality of PID controllers. The study of patents made it possible to formulate the goal of this research, sounds as extending the functionality of PID controllers by introducing a forecasting component.
Fig. 2. Functional diagram of an automatic control system for a technological parameter (a); determination of the trend in the parameter (b); and generation of the control signal by a PID controller (c). In the functional diagram of the system for determining trends in the controlled parameter (Fig. 2b), we note the following modules: (9) a module of the technological parameter’s accelerating characteristic processing. Its values, measured at first stage, are normalized according to expression:
2. TECHNICAL SOLUTION Fig. 2a shows a functional diagram of the automatic control system for objects whose workflow starts with acceleration up to the nominal values of the controlled parameter y(t). The system contains the following modules: (1) a specification module; (2) a comparison module; (3) a PID controller; (4) a control module; (5) a module for determining the predictive impact; (6) an algebraic adder; (7) a controlled object; (8) a sensor.
y0 ti
(1)
The weighting factor of control signal from PID controller could be found according to the expression: Ak = 1 – Apc.
(3)
The module (10) defines dynamic characteristics of the object. Knowledge of normalized values of a controlled parameter allows to determine the amount of transport lag according to expression:
(2)
Calculating the weights, we took into account the condition 2
A 1. i 1
y ti y t0 , yn y t0
where y0(ti) is the normalized value of the controlled parameter at time ti; y(ti) is the current value of the controlled parameter at time ti; y(t0) — the value of controlled parameter in the initial time t0; yn is the nominal value of the controlled parameter. Normalizing values of a controlled parameter values is required to incorporate its initial value, as well as to reduce converting errors.
The weighting factor of the predictive term is calculated on a polynomial dependency of the coefficient of variability v of the controlled parameter with coefficients of approximation b0, b1, b2, b3, specified for the object: Apc = b0 + b1v + b2v2 + b3v3.
227
i
t2 lg 1 y01 t1 lg 1 y02 , lg 1 y01 lg 1 y02
(4)
where t1 is time required to achieve the range (0.1 ... 0.2) • yn by the controlled parameter; t2 is time required to achieve the range (0.8 ... 0.9) • yn by the controlled parameter; y01 –the controlled parameter value at time t1; y02 – the controlled parameter value at time t2. Module (10) also calculates time constant T according to an expression:
T
t2 . 2,3lg 1 y02
(5)
Module (11) determines parameter measurements (d) increments to find basic share in the form of 0, as small enough magnitude 0.01T, at the same time providing a sampling of the measured values of the controlled parameter. Module (12) serves for measuring values of the controlled parameter x1(t), x2(t), …, xn(t) with defined discretization. Module (13) determining the mathematical expectation, which is calculated after each measurement of the technological parameter, on the basis of the formula: n
mx
x t i 1
i
n
,
(6)
where xi (t) is the measured value of the controlled parameter; n – a number of measurements.
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3. VERIFICATION
Module (12) is the verification module, which compares the difference between the mathematical expectation and the specified value of the controlled parameter with the threshold value ε. When the difference reaches the threshold value, the measurement time interval dТi. is determined.
The proposed method is verified for the reactor that processes the waste gases in sulphur production. The reactor operates in two stages. (1) Adsorption. Regeneration gases heated in a tube array pass to the reactor at 120–140°С, at a rate of at least 25000 m3/h.
(15) is the module for determining the trend, from the formula:
(2) Catalyst regeneration, which itself consists of(7) two stages.
(7) k* = mx/dТi. In the functional diagram of the system for generating the control signal (Fig. 1c), we note the following modules: (16) the module for determining the statistical parameters, in which the following formula is used to calculate the standard deviation, taking account of the measured values of the controlled parameter: n
sx
x t m i 1
i
x
n 1
(2.1) Heating of the catalyst to 260°С, with sulphur desorption from its surface at 200–250°С (Vladov et al, 2011). (2.2) Catalyst cooling. Functional diagram of the formation of the control action is shown in Figure 2. Within the workflow at the first stage of operation it is necessary to warm up the reactor to the nominal temperature. Figure 3 shows the transition from first to second stage.
2
,
(8)
where xi(t) is the normalized value of the controlled parameter; and mx is the normalized value of the mathematical expectation. Module (17) calculates the variability of the technological parameter from the formula
v = sx/mx.
(9)
Module (18) allows determining the prediction time tpr for the controlled parameter, based on the polynomial equation with approximation coefficients а0, а1, а2, а3, specified for the object. 2
3
tpr = a0 + a1v + a2v + a3v .
Fig. 3. Chart of temperature variation during the first and second stages of the workflow
(10)
At the first stage of regeneration gas is heated until its nominal value yn = 658 °C, at the second stage the reactor maintains a specified temperature gases regeneration xz = 650 °C. Values of controlled parameter, measured at the first stage are normalized in accordance with table 1.
Module (19) for calculating the predicted value tpr of the controlled parameter from the formula: xpr = k*tpr.
(11)
Module (20) for determining the discrepancy between the predicted and specified values of the controlled parameter: dxpr = xpr – xz.
Table 1. Heating characteristic of an object No 1 2 3 … 59 60 61
(12)
The control signal from the PID controller, is defined corresponding to the formula:
d x x t Ak k p x ki xdt kd . dt
(13)
The equation (13) shows that the control signal contains three components: a proportional one with the coefficient kp, an integral one with the coefficient ki, numerically equals to 1 ⁄ Ti and a differential one with coefficient numerically equal kd that equals Td. Here Ti is the constant of integral time and Td is the constant of differentiation time. Between the observed coefficients there are supported certain relationships, but their specific values exhibited at tuning process of the PID controller for a specific technological object when searching for the transition process with acceptable dynamic performance. ∆x is a misalignment signal between the signal xz and the signal of negative feedback xoc.
y(ti), оС 535 537 545 … 656 657 658
yо(ti) 0.00 0.02 0.08 … 0.98 0.99 1.00
For normalized values of temperature y01= 0.12 and y02 = 0.8 we identify appropriate moments: t1 = 24 m and t2 = 83 min.
Using (4), the value of transport lag was found = 19 min. Followed by (5) we determine the time constant T = 40 min Elementary resolution d equals 1 min. Regeneration gas temperature Q (ti) are represented in the table. 2. mx is calculating according to (6) during temperature changes of regeneration gas.
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The temperature in the reactor measured until (m x-xz)/xz drops below the threshold e = 1%. Next, we define the interval of measurement time dTi = 7 min (fig. 4). Then we calculate the range of forecasting time dTpr = 33 min. According to (9), we find standard deviation sx = 13.7%, and followed by (10) we calculate v = 0.21. Basing upon the polynomial dependence (11) we determine forecasting time tpr = 19.08-26.02 ν + ν2 3.504-0.157 ν3 = 14 min. This time is within the range of forecasting time dTpr = 33 min.
2:38 2:39
657 645
229
658.33 656.43
1.28 0.99
Also defines the corresponding deviations of the established value of the gas temperature in the furnace heating regeneration of specified size curves and 1 x 2 (see fig. 5 and table 3). 6. CONCLUSIONS
On the polynomial dependence (1) we define a weighting of forecasting component Apc = 0.727-0.529 ν + 0.059 ν2-0.002 ν3 = 0.61. Basing on (2) we find Apc = 0.39 and on (7) we calculate k* = 94 deg/min. According to (12) we defines a hpr = 1313° c, then by (13) we forecast the deviation dxpr = 663 °C. In an algebraic adder (module 6) we do form a control signal x(t) at the actuator of our object in accordance with the expression (15): x* (t) = 1086 °C; xpr(t) = 404 °C.
The general disadvantage of PID controllers is that their functional capabilities are limited because the trends in the controlled parameters cannot be taken into account. The functional capabilities are expanded by introducing a predictive component in the control signal, according to patents (Vladov et al, 2012.). This research is a part of the project on the smart control of high-tech systems (Vladov et all, 2018).
The developed model of control system of gas regeneration temperature in reactor with a random signal as input (with specified mx and sx) is implemented in the application named VisSim (Visual Simulation environment). To control the used controller with PID-regulation law, and to assess the quality of control the normalized quadratic integral criterion J2 was applied. We obtained two plots of gas temperature changes. Simulation results are displayed in Fig. 4.
Usage of the PID controller with a predictive component significantly improves the quality of control and reduces the discrepancy between the actual and specified reactor temperatures in the processing of smokestack gases by 47.7%. In addition, the gas consumption in heating is reduced by 12.6%, on average, while the energy conservation for the whole system amounts to 13.1%. REFERENCES Ahn, K.K. and Truong, D.Q. (2009). Online tuning fuzzy PID controller using robust extended Kalman filter. Journal of Process Control, Vol. 19. Iss. 6. p. 1011–1023. Bahgaat, N.K., El-Sayed, M.I., Moustafa Hassan, M.A. and Bendary, F.A. (2014). Load frequency control in power system via improving PID controller based on particle swarm optimization and ANFIS techniques. International Journal of System Dynamics Applications, Vol. 3. Iss. 3. p. 1–24. DOI: 10.4018/ijsda.2014070101 Chiha, I., Liouane, N. and Borne, P. (2012). Tuning PID controller using multiobjective ant colony optimization. Applied Computational Intelligence and Soft Computing. p. 1–7. DOI: 10.1155/2012/536326 Denisenko, V. (2006), PID controllers: construction principles and modification. Sovrem. Tekhno. Avtom., Vol. 4, pp. 66–74. Kostogryz, P.V. (1994), RU Patent 2017196. Mohanty B., Panda S. and Hota P.K. (2014), Controller parameters tuning of differential evolution algorithm and its application to load frequency control of multi-source power system. International Journal of Electrical Power & Energy Systems, Vol. 54. p. 77–85. Neath, M.J., Swain, A.K., Madawala, U.K. and D.J. Thrimawithana (2014). An optimal PID controller for a bidirectional inductive power transfer system using multiobjective genetic algorithm. IEEE Transactions on Power Electronics, Vol. 29. No. 3. p. 1523–1531. Shakya, R., Rajanwal, K., Patel, S., and Dinkar, S. (2014). Design and simulation of PD, PID and fuzzy logic controller for industrial application. International Journal of Information and Computation Technology, 4(4), p. 363-8.
Fig. 4. A fragment of the simulation results When you change the temperature of the gases in the process of regeneration operation of the AUTOPILOT with the elaboration of control action PID controller without forecasting component value normalized quadratic integral 2 quality criterion amounted J1 . In the case of the formulation of control action on two pillars, one of which is from the PID-controller with appropriate weighting of AK, and the second is predictive component with its weighting of Apc, the value of the normalized quadratic integral criterion amounted
J 22 (table 2).
Table 2. Temperature of gas regeneration in heaters Time 2:33 2:34 2:35 2:36 2:37
Q(ti), °С 658 660 657 661 657
mx(ti), °С 658.00 659.00 658.33 659.00 658.60
% 1.23 1.38 1.28 1.38 1.32 229
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Tararykin, S.V., Tyutikov, V.V., Kotov, D.G., and Varkov, E.A. (2005), RU Patent 2261466. Verevkin, V.I., Zel’tser, S.R., Galitskaya, L.V., and Lizogub, P.P. (2006). RU Patent 2277259. Vladov Yu.R., and Vladova, A.Yu (2018). Control Signals of a Predictive Industrial PID Controller // Russian Engineering Research. Vol. 38, No. 5. С. 399–402 DOI: 10.3103/S1068798X18050210 Vladov, Yu.R., Pavlova, Yu.S., Vladova, A.Yu., and Kalmykov, A.V. (2012). RU Patent 2459255. Vladov, Yu.R., Pavlova, Yu.S., Vladova, A.Yu., and Turkov, V.V. (2011). RU Patent 2450303. Zhu Q., Taher Azar A.T. (2015). Complex System Modelling and Control Through Intelligent Soft Computations. Berlin: Springer, 856 p.
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IFAC PapersOnLine 51-30 (2018) 226–230 Improved PID controller design for a two-stage technological workflow Improved PID controller design for aa two-stage technological workflow Improved PID controller design for two-stage technological workflow Improved PID controller design for a two-stage technological Yury R. Vladov. Alla Yu. Vladova Improved PID controller design for a two-stage technological workflow workflow
Yury R. Vladov. Alla Yu. Vladova Yury R. Alla Yu. Vladova Yury R. Vladov. Vladov. Alla Yu. Vladova *Orenburg Scientific Centre of the Ural BranchAlla Russian Academy of Sciences, Orenburg, of the Yury R. Vladov. Yu. Vladova Russia (Tel: +7 (353) 277-54-17; e-mail: [email protected]). *Orenburg Scientific Centre of the Ural Branch of the Russian Academy of Sciences, Orenburg, *Orenburg Centre of the Ural Branch Russian Academy *Orenburg Scientific Scientific Centre of+7 the(353) Ural 277-54-17; Branch of of the the Russian Academy of of Sciences, Sciences, Orenburg, Orenburg, Russia (Tel: e-mail: [email protected]). *Orenburg Scientific Centre of+7 the(353) Ural 277-54-17; Branch of the Russian Academy of Sciences, Orenburg, Russia (Tel: e-mail: [email protected]). Russia (Tel: +7 (353) 277-54-17; e-mail: [email protected]). Russia (Tel: +7 (353) 277-54-17; e-mail: [email protected]). Abstract: Background. Despite the wide use of controllers with proportional-integral-differential control law (PID controllers), issue of thecontrollers limited functionality of not taking into account the trend Abstract: Background.the Despite theexpanding wide use of with proportional-integral-differential control Abstract: Background. Despite the wide use controllers with proportional-integral-differential control of changing technological parameters is open. Methods. The control action istaking formed taking intothe account Abstract: Background. Despite theexpanding wide use of of controllers with proportional-integral-differential control law (PID controllers), the issue of the limited functionality of not into account trend Abstract: Background. Despite theexpanding wide use of controllers with proportional-integral-differential control law (PID issue of the limited functionality of not into account the trend the predicted value of the the technological parameter. Verification. Theaction proposed method wasinto verified for law (PID controllers), controllers), the issue of expanding the limited functionality of notistaking taking into account the trend of changing technological parameters is open. Methods. The control formed taking account law (PID controllers), the issue of expanding the limited functionality of not taking into account the trend of changing changing technological parameters is open. open. Methods. The control control action is isUsing formed taking into account account the reactor that processes the waste gases in sulfur production. Conclusions. a PID controller with of technological parameters is Methods. The action formed taking into the predicted value of the parameters technological parameter. Verification. The proposed method was verified for changing technological is open. Methods. The control action is the formed taking into account the predicted value of technological parameter. Verification. The proposed method was verified for aof predictive component significantly improves the quality of control, maximum deviations of the predicted value of the the technological parameter. Verification. Thereduces proposed method was verifiedwith for the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller predicted value of the technological parameter. Verification. The proposed method was verified for the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller with process parameters from specified values, contributing to additional energy saving and a significant the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller with aathe predictive component significantly improves the quality of control, reduces Using the maximum deviations of reactorinthat theofwaste gases inprocess sulfur production. a PIDand controller with component significantly improves the of maximum deviations of increase theprocesses efficiency automated units to in control, theConclusions. oil reduces and gasthe industry mechanical a predictive predictive component significantly improves the quality quality of control, reduces the maximum deviations of process parameters from specified values, contributing additional energy saving and a significant aengineering. predictive component significantly improves the quality to of control, reduces thesaving maximum deviations of process parameters from specified values, contributing additional energy and a significant process parameters from specified values, contributing to additional energy saving and a significant increase in the efficiency of automated units in the oil and gas industry and process parameters from specified values,process contributing to additional energy saving and a mechanical significant increase in the efficiency of automated process units in the oil and gas industry and mechanical increase inControl the efficiency of automated process units Intelligent in the oilSystems and gasand industry and mechanical engineering. Keywords: and Automation to Improve Stability; Applications increase in the efficiency of automated process units in Hosting the oilbyand gas industry and reserved. mechanical © 2018, IFAC (International Federation of Automatic Control) Elsevier Ltd. All rights engineering. engineering. engineering.Control and Automation to Improve Stability; Keywords: Intelligent Systems and Applications Intelligent Keywords: Keywords: Control Control and and Automation Automation to to Improve Improve Stability; Stability; Intelligent Systems Systems and and Applications Applications specification and its and rateApplications of specification, without any Keywords: Control and Automation to Improve Stability; Intelligent Systems 1. INTRODUCTION predictive component. specification and its rate of specification, without any specification and 1. specification and its its rate rate of of specification, specification, without without any any The controller with a proportional-integral-differential 1. INTRODUCTION INTRODUCTION predictive component. 1. INTRODUCTION specification and its rate of specification, without any predictive component. predictive component. control (PID controller) is one of the most common types of 1. INTRODUCTION The controller with aa proportional-integral-differential predictive component. The controller with proportional-integral-differential regulators: of them use the most appropriate algorithm. The with proportional-integral-differential controlcontroller (PID90-95% controller) isaa one of the common types of The controller with proportional-integral-differential control (PID controller) is of most common types The popularity of PID can be attributed partly to control (PID90-95% controller) is one oneuse of the the common types of of regulators: of controller them the most appropriate algorithm. control (PID controller) is one of the most common types of regulators: 90-95% of them use the appropriate algorithm. their popularity robust90-95% performance toattributed their algorithm. functional regulators: of controller themand use partly the appropriate The of PID can be partly to regulators: 90-95% them useAmong the appropriate algorithm. The of can attributed partly to simplicity (Shakya etofal,controller 2014). controllers, 64% The popularity popularity of PID PID controller can be bePID attributed partly to their robust performance and partly to their functional The of controllers PID controller can36% be toattributed partly to their popularity robust performance performance andandpartly partly theirmulti-circuit functional are single-loop are their robust and to their functional simplicity (Shakya et al, 2014). Among PID controllers, 64% their robust performance and partlycontrol to controllers, their functional simplicity (Shakya et 2014). Among PID 64% controllers. Instruments feedback occupy 85% of simplicity (Shakya et al, al,with 2014). Among PIDare controllers, 64% are single-loop controllers and 36% multi-circuit simplicity (Shakya et al, 2014). Among PID controllers, 64% are single-loop controllers and 36% are multi-circuit the total number of controllers, with direct control 6%, and are single-loop controllers and 36% are multi-circuit controllers. Instruments with feedback control occupy 85% of are single-loop and 2006). 36% are multi-circuit controllers. with control occupy 85% of cascaded -Instruments 9%ofcontrollers (Denisenko, Analogue-digital controllers. Instruments with feedback feedback control occupy 85%and of the total number controllers, with direct control 6%, controllers. Instruments with feedback control occupy 85% of the total number of controllers, with direct control 6%, and converters on a microprocessor basis allowed to use the total number of controllers, with direct control 6%, and cascaded -- 9% (Denisenko, 2006). Analogue-digital the total number of controllers, with direct control 6%, and cascaded 9% (Denisenko, 2006). Analogue-digital automatic parameter adjustment, adaptive cascaded -on 9% (Denisenko, 2006). Analogue-digital converters a microprocessor basis algorithms, allowed toneural use cascaded -on 9% (Denisenko, 2006). Analogue-digital converters microprocessor basis allowed use networks, genetic and adaptive fuzzy logic methodsto (Ahn, converters on aa algorithms microprocessor basis allowed toneural use automatic parameter adjustment, algorithms, converters on a microprocessor basis allowed to use Fig. 1. Dynamic of PID-controllers patenting. automatic parameter adjustment, adaptive algorithms, neural Bahgaat, China, Zhu et al). However, despite the long automatic genetic parameter adjustment, adaptive algorithms, neural networks, algorithms and fuzzy logic methods (Ahn, automatic parameter adjustment, adaptive algorithms, neural networks, genetic algorithms and fuzzy logic methods (Ahn, history of China, development and aand great number of publications Fig. networks, genetic algorithms fuzzy logic methods (Ahn, Bahgaat, Zhu et al). despite the long Fig. 1. 1. Dynamic Dynamic of of PID-controllers PID-controllers patenting. patenting. networks, genetic algorithms andHowever, fuzzy logic methods (Ahn, Bahgaat, China, Zhu et al). However, despite the long Fig. 1. Dynamic of PID-controllers patenting. and patents, the issues of expanding the limited functionality Bahgaat, China, Zhu et al). However, despite the long history of development and aa great number of publications Fig. 1. Dynamic of PID-controllers Authors of the patent (Tararykin patenting. et al, 2005) proposed an Bahgaat, China, Zhu et al). However, despite the long history of development and great number of publications of these devices remain unresolved. history of development and a great the number of functionality publications approach of controlling dynamic objects with external and patents, the issues of expanding limited history of development and a great number of publications Authors of the patent (Tararykin et al, 2005) proposed an and patents, the issues expanding and patents, the remain issues of of expanding the the limited limited functionality functionality Authors of patent (Tararykin et al, 2005) proposed an of these devices unresolved. perturbations by building a control signal on theexternal results Authors ofofthe the patent (Tararykin et objects al, based 2005)with proposed an and patents, the remain issues of expanding the limited functionality approach controlling dynamic of these devices unresolved. 1.1 Patent analysis Authors of the patent (Tararykin et al, 2005) proposed an of these devices remain unresolved. approach of controlling dynamic objects with external of comparing specifies signal and an amount of measured approach of controlling dynamic objects with external of these devices remain unresolved. perturbations by building aa control signal based on the results approach of controlling dynamic objects with external perturbations by building control signal based on the results 1.1 Patent analysis values characterized ansignal technical condition. The perturbations byspecifies building aobject’s control signal based on the results 1.1 analysis comparing and an amount of measured Positive dynamic 1.1 Patent Patent analysisof PID-controllers patenting is confirmed of perturbations byspecifies building a control signal based on the results of comparing signal and an amount of measured main drawback of this approach is measuring the object's of comparing specifies signal and an amount of measured 1.1 Patent analysis values characterized an object’s technical condition. The by the analysis of more than 30 thousand international patents of Positive dynamic of PID-controllers patenting is confirmed comparing specifies signal and technical an amount of measured values characterized an object’s condition. The condition variables behind the points of perturbation. values characterized an object’s technical condition. The Positive dynamic of PID-controllers patenting is confirmed main drawback of this approach is measuring the object's (granted in countries that develop thispatenting topic, such as patents China, values Positive dynamic of PID-controllers is confirmed characterized an approach object’s is technical condition. The by the analysis of more than 30 thousand international main drawback of this measuring the object's Positive dynamic of PID-controllers patenting is confirmed main drawback of this approach is measuring the object's by the analysis of more than 30 thousand international patents condition variables behind the points of perturbation. USA, Russia, Canada, Holland, UK and etc.) received by the analysis of morethat than 30 thousand international patents Method of identifying an object with test signals bases upon main drawback of this approach is measuring the object's (granted in countries develop this topic, such as China, condition by the analysis of more than 30 thousand international condition variables variables behind behind the the points points of of perturbation. perturbation. (granted in countries countries that develop this topic, such as patents China, between 2006 and 2015 and defined bytopic, using the method of control (granted in that develop this such as China, actions summarizing components. The first of condition variables behind the two points oftest perturbation. USA, Russia, Canada, Holland, UK and etc.) received Method of identifying an object with signals bases upon (granted in countries that develop this topic, such as China, USA, Russia, Canada, Holland, UK and etc.) received Method of identifying an object with test signals bases upon semantic search in the Exactus Patent system (Fig. 1). USA, Russia, Canada, Holland, UK and etc.) received them depends on the values of output variables of an object, Method of identifying an object with test signals bases upon between 2006 and 2015 and defined by using the method of control actions summarizing two components. The first of USA, Russia, Canada, Holland, UK and etc.) received control between 2006 and 2015 and by using the method Method of identifying anonobject with test signalsThe bases upon actions summarizing two components. first of between 2006 and 2015 and defined defined by using(Fig. the 1). method of of and the second depends errors of regulation. Test signals control actions summarizing two components. The first of semantic search in the Exactus Patent system them depends on the values of output variables of an object, between 2006 and 2015 and defined by using(Fig. the method of them semantic control actions summarizing two components. The first of depends on the values of output variables of an object, semantic search search in in the the Exactus Exactus Patent Patent system system (Fig. 1). 1). help to fix a trajectory of output variables and to evaluate them depends on the values of output variables of an object, and the second depends on errors of regulation. Test signals semantic search in the Exactus Patent system (Fig. 1). them depends on the values of output variables of an object, the second depends on errors of regulation. Test signals A different control method was proposed in (Kostogryz, and dynamic performance of the controlled object and (Verevkin et al, and the second depends on output errors of regulation. Test signals help to fix aa trajectory variables to evaluate and the second depends of onofoutput errors of regulation. Test signals help to fix trajectory of variables and to evaluate 1994): in that approach, a specification is formed, the 2006). The disadvantage this method is the necessity of help to fix a trajectory of output variables and to evaluate A different control method was proposed in (Kostogryz, dynamic performance of the controlled object (Verevkin et al, A different control method was proposed in (Kostogryz, help to fix a trajectory of limits output variables and to evaluate dynamic performance of the controlled object (Verevkin et al, controlled parameter is measured, and the deviation of the A different control method was proposed in formed, (Kostogryz, test signals. It severely the possibilities of this dynamic performance of the controlled object (Verevkin et al, 1994): in that approach, a specification is the 2006). disadvantage of this method is the necessity of A different control methodaa was (Kostogryz, 1994): in that approach, specification is the dynamicThe performance of the controlled object (Verevkin et do al, 2006). The of this method is necessity of parameter the specification isproposed determined, alongofwith 1994): in from that approach, specification isin formed, formed, the approach fordisadvantage most varieties of objects that 2006).signals. The disadvantage oflimits thistechnological method is the the necessity of controlled parameter is measured, and the deviation the test It severely the possibilities of this 1994): in that approach, a specification is formed, the controlled parameter is measured, and the deviation of 2006). The disadvantage of this method is the necessity of test signals. It severely limits the possibilities of this the rate of deviation. The disadvantage of this approach is controlled parameter is measured,isand the deviation ofwith the test not permit additional influences. Another problem is the signals. It severely limits the possibilities of this parameter from the specification determined, along approach for most varieties of technological objects that do controlled parameter is measured, the control deviation ofwith the parameter from thecapabilities, specification isand determined, along test signals. It severely limits the possibilities of this approach for most varieties of technological objects that do limited functional since the signal is parameter from the specification is determined, along with dependence one of the components from control errors.that approach most varieties of technological objects do the rate of deviation. The disadvantage of this approach is not permitfor influences. Another problem is the parameter from the specification is determined, along with the rate of deviation. The disadvantage of this is foradditional most varieties of technological objects that do not permit additional influences. Another problem is the formed based on capabilities, the deviation from the the rate functional of deviation. Theparameter’s disadvantage of control this approach approach is approach not permit additional influences. Another problem is the limited since the signal is dependence one of the components from control errors. the rate functional of deviation. The disadvantage of control this approach limited capabilities, since the signal is not permit additional influences. Another problem is the one of the components from control errors. limited functional capabilities, since the control from signal is dependence formed based on the parameter’s deviation limited functional capabilities, since the control signalthe is dependence one of the components from control errors. formed formed based based on on the the parameter’s parameter’s deviation deviation from from the the dependence one of the components from control errors. formed based on the parameter’s deviation from the 226 Copyright © 2018 IFAC 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic Copyright 2018 responsibility IFAC 226Control. Copyright © 226 10.1016/j.ifacol.2018.11.291 Copyright © 2018 2018 IFAC IFAC 226 Copyright © 2018 IFAC 226
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Thus, there was revealed the limited functionality of PID controllers. The study of patents made it possible to formulate the goal of this research, sounds as extending the functionality of PID controllers by introducing a forecasting component.
Fig. 2. Functional diagram of an automatic control system for a technological parameter (a); determination of the trend in the parameter (b); and generation of the control signal by a PID controller (c). In the functional diagram of the system for determining trends in the controlled parameter (Fig. 2b), we note the following modules: (9) a module of the technological parameter’s accelerating characteristic processing. Its values, measured at first stage, are normalized according to expression:
2. TECHNICAL SOLUTION Fig. 2a shows a functional diagram of the automatic control system for objects whose workflow starts with acceleration up to the nominal values of the controlled parameter y(t). The system contains the following modules: (1) a specification module; (2) a comparison module; (3) a PID controller; (4) a control module; (5) a module for determining the predictive impact; (6) an algebraic adder; (7) a controlled object; (8) a sensor.
y0 ti
(1)
The weighting factor of control signal from PID controller could be found according to the expression: Ak = 1 – Apc.
(3)
The module (10) defines dynamic characteristics of the object. Knowledge of normalized values of a controlled parameter allows to determine the amount of transport lag according to expression:
(2)
Calculating the weights, we took into account the condition 2
A 1. i 1
y ti y t0 , yn y t0
where y0(ti) is the normalized value of the controlled parameter at time ti; y(ti) is the current value of the controlled parameter at time ti; y(t0) — the value of controlled parameter in the initial time t0; yn is the nominal value of the controlled parameter. Normalizing values of a controlled parameter values is required to incorporate its initial value, as well as to reduce converting errors.
The weighting factor of the predictive term is calculated on a polynomial dependency of the coefficient of variability v of the controlled parameter with coefficients of approximation b0, b1, b2, b3, specified for the object: Apc = b0 + b1v + b2v2 + b3v3.
227
i
t2 lg 1 y01 t1 lg 1 y02 , lg 1 y01 lg 1 y02
(4)
where t1 is time required to achieve the range (0.1 ... 0.2) • yn by the controlled parameter; t2 is time required to achieve the range (0.8 ... 0.9) • yn by the controlled parameter; y01 –the controlled parameter value at time t1; y02 – the controlled parameter value at time t2. Module (10) also calculates time constant T according to an expression:
T
t2 . 2,3lg 1 y02
(5)
Module (11) determines parameter measurements (d) increments to find basic share in the form of 0, as small enough magnitude 0.01T, at the same time providing a sampling of the measured values of the controlled parameter. Module (12) serves for measuring values of the controlled parameter x1(t), x2(t), …, xn(t) with defined discretization. Module (13) determining the mathematical expectation, which is calculated after each measurement of the technological parameter, on the basis of the formula: n
mx
x t i 1
i
n
,
(6)
where xi (t) is the measured value of the controlled parameter; n – a number of measurements.
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3. VERIFICATION
Module (12) is the verification module, which compares the difference between the mathematical expectation and the specified value of the controlled parameter with the threshold value ε. When the difference reaches the threshold value, the measurement time interval dТi. is determined.
The proposed method is verified for the reactor that processes the waste gases in sulphur production. The reactor operates in two stages. (1) Adsorption. Regeneration gases heated in a tube array pass to the reactor at 120–140°С, at a rate of at least 25000 m3/h.
(15) is the module for determining the trend, from the formula:
(2) Catalyst regeneration, which itself consists of(7) two stages.
(7) k* = mx/dТi. In the functional diagram of the system for generating the control signal (Fig. 1c), we note the following modules: (16) the module for determining the statistical parameters, in which the following formula is used to calculate the standard deviation, taking account of the measured values of the controlled parameter: n
sx
x t m i 1
i
x
n 1
(2.1) Heating of the catalyst to 260°С, with sulphur desorption from its surface at 200–250°С (Vladov et al, 2011). (2.2) Catalyst cooling. Functional diagram of the formation of the control action is shown in Figure 2. Within the workflow at the first stage of operation it is necessary to warm up the reactor to the nominal temperature. Figure 3 shows the transition from first to second stage.
2
,
(8)
where xi(t) is the normalized value of the controlled parameter; and mx is the normalized value of the mathematical expectation. Module (17) calculates the variability of the technological parameter from the formula
v = sx/mx.
(9)
Module (18) allows determining the prediction time tpr for the controlled parameter, based on the polynomial equation with approximation coefficients а0, а1, а2, а3, specified for the object. 2
3
tpr = a0 + a1v + a2v + a3v .
Fig. 3. Chart of temperature variation during the first and second stages of the workflow
(10)
At the first stage of regeneration gas is heated until its nominal value yn = 658 °C, at the second stage the reactor maintains a specified temperature gases regeneration xz = 650 °C. Values of controlled parameter, measured at the first stage are normalized in accordance with table 1.
Module (19) for calculating the predicted value tpr of the controlled parameter from the formula: xpr = k*tpr.
(11)
Module (20) for determining the discrepancy between the predicted and specified values of the controlled parameter: dxpr = xpr – xz.
Table 1. Heating characteristic of an object No 1 2 3 … 59 60 61
(12)
The control signal from the PID controller, is defined corresponding to the formula:
d x x t Ak k p x ki xdt kd . dt
(13)
The equation (13) shows that the control signal contains three components: a proportional one with the coefficient kp, an integral one with the coefficient ki, numerically equals to 1 ⁄ Ti and a differential one with coefficient numerically equal kd that equals Td. Here Ti is the constant of integral time and Td is the constant of differentiation time. Between the observed coefficients there are supported certain relationships, but their specific values exhibited at tuning process of the PID controller for a specific technological object when searching for the transition process with acceptable dynamic performance. ∆x is a misalignment signal between the signal xz and the signal of negative feedback xoc.
y(ti), оС 535 537 545 … 656 657 658
yо(ti) 0.00 0.02 0.08 … 0.98 0.99 1.00
For normalized values of temperature y01= 0.12 and y02 = 0.8 we identify appropriate moments: t1 = 24 m and t2 = 83 min.
Using (4), the value of transport lag was found = 19 min. Followed by (5) we determine the time constant T = 40 min Elementary resolution d equals 1 min. Regeneration gas temperature Q (ti) are represented in the table. 2. mx is calculating according to (6) during temperature changes of regeneration gas.
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The temperature in the reactor measured until (m x-xz)/xz drops below the threshold e = 1%. Next, we define the interval of measurement time dTi = 7 min (fig. 4). Then we calculate the range of forecasting time dTpr = 33 min. According to (9), we find standard deviation sx = 13.7%, and followed by (10) we calculate v = 0.21. Basing upon the polynomial dependence (11) we determine forecasting time tpr = 19.08-26.02 ν + ν2 3.504-0.157 ν3 = 14 min. This time is within the range of forecasting time dTpr = 33 min.
2:38 2:39
657 645
229
658.33 656.43
1.28 0.99
Also defines the corresponding deviations of the established value of the gas temperature in the furnace heating regeneration of specified size curves and 1 x 2 (see fig. 5 and table 3). 6. CONCLUSIONS
On the polynomial dependence (1) we define a weighting of forecasting component Apc = 0.727-0.529 ν + 0.059 ν2-0.002 ν3 = 0.61. Basing on (2) we find Apc = 0.39 and on (7) we calculate k* = 94 deg/min. According to (12) we defines a hpr = 1313° c, then by (13) we forecast the deviation dxpr = 663 °C. In an algebraic adder (module 6) we do form a control signal x(t) at the actuator of our object in accordance with the expression (15): x* (t) = 1086 °C; xpr(t) = 404 °C.
The general disadvantage of PID controllers is that their functional capabilities are limited because the trends in the controlled parameters cannot be taken into account. The functional capabilities are expanded by introducing a predictive component in the control signal, according to patents (Vladov et al, 2012.). This research is a part of the project on the smart control of high-tech systems (Vladov et all, 2018).
The developed model of control system of gas regeneration temperature in reactor with a random signal as input (with specified mx and sx) is implemented in the application named VisSim (Visual Simulation environment). To control the used controller with PID-regulation law, and to assess the quality of control the normalized quadratic integral criterion J2 was applied. We obtained two plots of gas temperature changes. Simulation results are displayed in Fig. 4.
Usage of the PID controller with a predictive component significantly improves the quality of control and reduces the discrepancy between the actual and specified reactor temperatures in the processing of smokestack gases by 47.7%. In addition, the gas consumption in heating is reduced by 12.6%, on average, while the energy conservation for the whole system amounts to 13.1%. REFERENCES Ahn, K.K. and Truong, D.Q. (2009). Online tuning fuzzy PID controller using robust extended Kalman filter. Journal of Process Control, Vol. 19. Iss. 6. p. 1011–1023. Bahgaat, N.K., El-Sayed, M.I., Moustafa Hassan, M.A. and Bendary, F.A. (2014). Load frequency control in power system via improving PID controller based on particle swarm optimization and ANFIS techniques. International Journal of System Dynamics Applications, Vol. 3. Iss. 3. p. 1–24. DOI: 10.4018/ijsda.2014070101 Chiha, I., Liouane, N. and Borne, P. (2012). Tuning PID controller using multiobjective ant colony optimization. Applied Computational Intelligence and Soft Computing. p. 1–7. DOI: 10.1155/2012/536326 Denisenko, V. (2006), PID controllers: construction principles and modification. Sovrem. Tekhno. Avtom., Vol. 4, pp. 66–74. Kostogryz, P.V. (1994), RU Patent 2017196. Mohanty B., Panda S. and Hota P.K. (2014), Controller parameters tuning of differential evolution algorithm and its application to load frequency control of multi-source power system. International Journal of Electrical Power & Energy Systems, Vol. 54. p. 77–85. Neath, M.J., Swain, A.K., Madawala, U.K. and D.J. Thrimawithana (2014). An optimal PID controller for a bidirectional inductive power transfer system using multiobjective genetic algorithm. IEEE Transactions on Power Electronics, Vol. 29. No. 3. p. 1523–1531. Shakya, R., Rajanwal, K., Patel, S., and Dinkar, S. (2014). Design and simulation of PD, PID and fuzzy logic controller for industrial application. International Journal of Information and Computation Technology, 4(4), p. 363-8.
Fig. 4. A fragment of the simulation results When you change the temperature of the gases in the process of regeneration operation of the AUTOPILOT with the elaboration of control action PID controller without forecasting component value normalized quadratic integral 2 quality criterion amounted J1 . In the case of the formulation of control action on two pillars, one of which is from the PID-controller with appropriate weighting of AK, and the second is predictive component with its weighting of Apc, the value of the normalized quadratic integral criterion amounted
J 22 (table 2).
Table 2. Temperature of gas regeneration in heaters Time 2:33 2:34 2:35 2:36 2:37
Q(ti), °С 658 660 657 661 657
mx(ti), °С 658.00 659.00 658.33 659.00 658.60
% 1.23 1.38 1.28 1.38 1.32 229
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Tararykin, S.V., Tyutikov, V.V., Kotov, D.G., and Varkov, E.A. (2005), RU Patent 2261466. Verevkin, V.I., Zel’tser, S.R., Galitskaya, L.V., and Lizogub, P.P. (2006). RU Patent 2277259. Vladov Yu.R., and Vladova, A.Yu (2018). Control Signals of a Predictive Industrial PID Controller // Russian Engineering Research. Vol. 38, No. 5. С. 399–402 DOI: 10.3103/S1068798X18050210 Vladov, Yu.R., Pavlova, Yu.S., Vladova, A.Yu., and Kalmykov, A.V. (2012). RU Patent 2459255. Vladov, Yu.R., Pavlova, Yu.S., Vladova, A.Yu., and Turkov, V.V. (2011). RU Patent 2450303. Zhu Q., Taher Azar A.T. (2015). Complex System Modelling and Control Through Intelligent Soft Computations. Berlin: Springer, 856 p.
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