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Two-stage workflow control with a predictive component
17th IFAC Workshop on Control Applications of Optimization 17th IFAC IFAC Workshop Workshop on on Control Control Applications Applications of of Optimization 17th Yekaterinburg, Russia, 2018 of Optimization 17th IFAC Workshop onOctober Control 15-19, Applications Optimization Yekaterinburg, Russia, October 15-19, 2018 17th IFAC Workshop on Control Applications of Optimization Available at www.sciencedirect.com Yekaterinburg, Russia, October 15-19, 2018 17th IFAC Workshop on Control Applications ofonline Optimization Yekaterinburg, Russia, October 15-19, 2018 17th IFAC Workshop on Control 15-19, Applications of Optimization Yekaterinburg, Yekaterinburg, Russia, Russia, October October 15-19, 2018 2018 Yekaterinburg, Russia, October 15-19, 2018
ScienceDirect
IFAC PapersOnLine 51-32 (2018) 712–716
Two-stage workflow control with aa predictive component Two-stage workflow control with component Two-stage workflow control with aa predictive predictive component Two-stage workflow control with predictive component Two-stage workflow control with a predictive component Two-stage workflow control with a predictive Yury control R. Vladov*.with Alla Yu. Vladova** component Two-stage workflow a predictive component
Yury R. Vladov*. Alla Yu. Vladova** Yury Yu. Yury R. R. Vladov*. Vladov*. Alla Alla Yu. Vladova** Vladova** Yury R. Vladov*. Alla Yu. Vladova** Yury R. Vladov*. Alla Yu. Vladova** Yury R.Ural Vladov*. Alla Yu. Vladova** *Orenburg Scientific Centre of the Branch of the Russian *Orenburg Scientific Scientific Centre Centre of of the the Ural Ural Branch Branch of of the the Russian Russian Academy Academy of of Sciences, Sciences, Orenburg, Orenburg, *Orenburg Academy *Orenburg Scientific Centre of+7 the(353) Ural 277-54-17; Branch of the Russian Academy of of Sciences, Sciences, Orenburg, Orenburg, Russia (Tel: e-mail: [email protected]). Russia (Tel:of +7 (353) 277-54-17; e-mail: [email protected]). *Orenburg Scientific Centre the Ural Branch of the Russian Academy of Sciences, Orenburg, 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, Russia (Tel:of+7 (353) 277-54-17; e-mail: [email protected]). **Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia (e-mail: *Orenburg Scientific Centre the Ural Branch of the Russian Academy of Sciences, **Institute of of Control Control Sciences of(353) the Russian Russian Academy of [email protected]). Sciences, Moscow, Moscow, Russia RussiaOrenburg, (e-mail: Russia (Tel: +7 277-54-17; e-mail: **Institute Sciences of the Academy of Sciences, Russia (Tel: +7 (353) 277-54-17; e-mail: [email protected]). **Institute of Control Sciences of(353) [email protected])} Russian Academy of [email protected]). Sciences, Moscow, Russia (e-mail: (e-mail: Russia (Tel: +7 277-54-17; e-mail: [email protected])} **Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia (e-mail: **Institute Russian Academy of Sciences, Moscow, Russia (e-mail: [email protected])} **Institute of of Control Control Sciences Sciences of of the [email protected])} Russian Academy of Sciences, Moscow, Russia (e-mail: [email protected])} [email protected])} [email protected])} Abstract: Abstract: Background. Background. Despite Despite the the wide wide use use of of controllers controllers with with proportional-integral-differential proportional-integral-differential control control Abstract: Background. Despite the wide controllers with control Abstract: Background.the Despite theexpanding wide use use of of controllers with proportional-integral-differential proportional-integral-differential control law (PID controllers), issue of the limited functionality of not taking into account the trend law (PID controllers), the issue of expanding the limited functionality of not taking into account the trend Abstract: Background. Despite the wide use of controllers with proportional-integral-differential control law (PID the issue of expanding the limited functionality of into account the trend Abstract: Background. Despite the wide use of controllers with proportional-integral-differential control law (PID controllers), controllers), the issue of expanding the limited The functionality of not notistaking taking into account the trend of changing technological parameters is open. Methods. control action formed taking into account Abstract: Background. Despite the wide use of controllers with proportional-integral-differential control of changing technological parameters is open. Methods. The control action is formed taking into account law (PID controllers), the issue of expanding the limited functionality of not taking into account the trend of changing technological parameters is open. Methods. The control action is formed taking into account law (PID controllers), the issue of expanding limited functionality of not into account trend of changing technological parameters is parameter. open.the Methods. The control action istaking formed taking intothe account the predicted value of technological Verification. The proposed method is verified for the law (PID controllers), the issue of expanding the limited functionality of not taking into account the trend the predicted value of the technological parameter. Verification. The proposed method is verified for the of changing technological parameters is open. Methods. The control action is formed taking into account the predicted value of the technological parameter. Verification. The proposed method is verified for the of changing technological parameters is open. Methods. The control action is formed taking into account the predicted value of the technological parameter. Verification. The proposed method is verified for the reactor that processes waste gases in sulfur production. Conclusions. Using a PID controller with aa of changing technological parameters is open. Methods. The control action is formed taking into account reactor that processes waste gases in sulfur production. Conclusions. Using a PID controller with the predicted value of the technological parameter. Verification. The proposed method is verified for the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller with a the predicted value of technological parameter. Verification. The proposed method is verified for the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller with a predictive component significantly improves the quality of control, reduces the maximum deviations of the predicted value of the technological Verification. Thereduces proposed verified for predictive component significantly improves theproduction. quality of control, control, themethod maximum deviations ofaa reactor thatcomponent processes waste gases gases inparameter. sulfur production. Conclusions. Using a PID PID iscontroller controller withthe predictive significantly improves the quality of reduces the maximum deviations of reactor that processes the waste in sulfur Conclusions. Using a with predictive component significantly improves the quality of control, reduces the maximum deviations of process parameters from specified values, contributing to additional energy saving and a significant reactor processesfrom the waste gases in sulfur Conclusions. Using a PID and controller withofa process that parameters specified values, contributing to control, additional energy saving significant predictive component significantly improves theproduction. quality of of control, reduces thesaving maximum deviations process from specified values, contributing to additional energy and aaa mechanical significant predictive component significantly improves the quality reduces the maximum deviations of process parameters parameters from specified values,process contributing to additional energy saving and significant increase in the efficiency of automated units in the oil and gas industry and predictive component significantly improves the quality of control, reduces the maximum deviations of increase in the efficiency of automated process units in the oil and gas industry and mechanical process parameters parameters from specified specified values,process contributing to additional energy saving and and a mechanical significant increase in the efficiency of automated units in the oil and gas industry and process from values, contributing to additional energy saving a significant increase parameters in the efficiency of automated process units to in additional the oil and gas industry anda mechanical engineering. process from specified values, contributing energy saving and significant engineering. increase in the efficiency of automated process units in the oil and gas industry and mechanical engineering. increase in the of automated process units the and industry engineering. increase inOptimal the efficiency efficiency of automated process units in inRobust the oil oil and gas gas industry and and mechanical mechanical Keywords: Control; Real-Time Control Problems; Control and Stabilization engineering. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. engineering. Keywords: Optimal Control; Real-Time Control Problems; Robust Control and Stabilization Keywords: Optimal Control; Real-Time Control Problems; Robust Control and Stabilization engineering. Keywords: Optimal Control; Real-Time Control Problems; Robust Control and Stabilization Keywords: Optimal Control; Real-Time Control Problems; Robust Control and Stabilization Keywords: Robust Keywords: Optimal Optimal Control; Control; Real-Time Real-Time Control Control Problems; Problems; Robust Control Control and and Stabilization Stabilization aa specification is formed, specification is is formed, formed, the the controlled controlled parameter parameter is is 1. INTRODUCTION a specification the controlled parameter is a specification is formed, the controlled parameter is 1. INTRODUCTION measured, and the deviation of the parameter from 1. measured, and the the deviation the of the the parameter parameter from the the 1. INTRODUCTION INTRODUCTION ameasured, specification is formed, controlled parameter is and deviation of from the a specification is formed, the controlled parameter is measured, and the deviation of with the the parameter from the 1. INTRODUCTION is along rate of The controller controller with with proportional-integral-differential aspecification specification is formed, the controlled is 1. specification is determined, determined, along with the rate parameter of deviation. deviation. The aaa proportional-integral-differential measured, and the deviation of the parameter from the 1. INTRODUCTION INTRODUCTION specification is along with the rate The controller with measured, and the deviation of the parameter from the specification is determined, determined, along with the rate of of deviation. deviation. The controller with a isproportional-integral-differential proportional-integral-differential Its disadvantage is its limited functional capabilities, since the control law (PID controller) one of the most common types measured, and the deviation of the parameter from Its disadvantage disadvantage is its its limited limitedalong functional capabilities, since the the control law (PID controller) one of the most common types specification is determined, with the rate of deviation. The controller with a is proportional-integral-differential is functional capabilities, since control law controller) is one most types specification is determined, along with the rate of deviation. The controller with Its disadvantage is formed its limited functional capabilities, since the control law (PID (PID controller) isproportional-integral-differential one of the most common common types Its control signal on the basis of the of regulators: 90-95% of aathem them use of thethe appropriate algorithm. specification is is determined, along with the rate ofparameter’s deviation. The controller withof proportional-integral-differential control signal is formed on the basis of the parameter’s use the appropriate algorithm. of regulators: 90-95% Its disadvantage is its limited functional capabilities, since the control law (PID controller) is one of the most common types control signal is on the of parameter’s of 90-95% of use the appropriate algorithm. disadvantage its limited capabilities, since control law controller) is the most common types control signal isis formed onfunctional theandbasis basis of the the parameter’s of regulators: 90-95% of them them use the appropriate algorithm. deviation from specification its rate of Theregulators: reasons for this popularity areof simplicity of construction Its disadvantage is formed its limited functional since the the control law (PID (PID controller) is one one of the most of common types Its deviation from the the specification andbasis its capabilities, rate of specification, specification, The reasons for this popularity are simplicity construction control signal is formed on the of the parameter’s of regulators: 90-95% of them use the appropriate algorithm. deviation from the specification and its rate of specification, The reasons for this popularity are simplicity of construction control signal is formed on the basis of the parameter’s of regulators: 90-95% of them use the appropriate algorithm. deviation from the specification and its rate of specification, The reasons for this popularity are simplicity of construction without any predictive component. and industrial usage, clarity of functioning and suitability for control signal is formed on the basis of the parameter’s of regulators: 90-95% of them use the appropriate algorithm. without any any predictive component. suitability for and industrial usage, clarity of functioning andof deviation from the specification and its rate of specification, The reasons for this popularity are simplicity construction predictive component. and usage, clarity of for deviation from the and The reasons this are of construction without any predictive component. and industrial usage, clarity of functioning functioning and suitability for without solving mostfor practical problems. Amongand PID controllers, deviation from the specification specification and its its rate rate of of specification, specification, The industrial reasons for this popularity popularity are simplicity simplicity ofsuitability construction solving most practical problems. Among PID controllers, without any predictive component. and industrial usage, clarity of functioning and suitability for solving most practical problems. Among PID controllers, without any predictive component. and industrial usage, clarity of functioning and suitability for solving most practical problems. Among PID controllers, 64% are single-loop controllers and 36% are multi-circuit without any predictive component. and industrial usage, clarity of functioning and suitability for 64% are single-loop controllers and 36% are multi-circuit solving most practical problems. Among PID controllers, 64% are single-loop and 36% multi-circuit solving practical problems. Among PID controllers, 64% aremost single-loop controllers and 36% are are multi-circuit controllers (Denisenko, 2006). Instruments Instruments with feedback solving practicalcontrollers problems. Among PID controllers, controllers (Denisenko, 2006). with feedback 64% are aremost single-loop controllers and 36% are are multi-circuit controllers (Denisenko, 2006). Instruments with feedback 64% single-loop controllers and 36% multi-circuit controllers (Denisenko, 2006). Instruments with feedback control occupy 85% of the total number of controllers, with 64% are single-loop controllers and 36% are multi-circuit control occupy 85% of of the the total Instruments number of of controllers, controllers, with controllers (Denisenko, 2006). with feedback control occupy 85% total number with controllers (Denisenko, 2006). Instruments with feedback controlcontrol occupy 85% ofand the total Instruments number of Analogue-digital controllers, with direct 6%, cascaded 9%. controllers (Denisenko, 2006). with feedback direct control 6%, and cascaded 9%. Analogue-digital control occupy 85% of the total number of controllers, with direct --85% 6%, --allow 9%. Analogue-digital control occupy the total number of controllers, with direct control control 6%, of and cascaded 9%. Analogue-digital converters on microprocessor use control occupy ofand thecascaded totalbasis number of to controllers, with converters on aaa--85% microprocessor basis allow to use automatic automatic direct control 6%, and cascaded 9%. Analogue-digital converters on microprocessor basis allow to use automatic direct control 6%, and cascaded 9%. Analogue-digital converters on a- microprocessor basis-allow to use automatic parameter adjustment, adaptive algorithms, neural networks, direct control 6%, and cascaded 9%. Analogue-digital parameter adjustment, adjustment, adaptive algorithms, algorithms, neural networks, converters on a microprocessor basis allow neural to use automatic parameter adaptive networks, converters on basis to automatic parameter adjustment, adaptive algorithms, neural networks, genetic algorithms and fuzzy logic methods (Ahn, 2009, converters on aa microprocessor microprocessor basis allow allow to use use automatic genetic algorithms and fuzzy logic methods (Ahn, 2009, parameter adjustment, adaptive algorithms, neural networks, genetic algorithms and fuzzy logic (Ahn, 2009, parameter adjustment, algorithms, neural networks, genetic algorithms andadaptive fuzzy Bahgaat, logic methods methods (Ahn, 2009, Mohanty, 2014, Neath, 2014, 2014, Chiha et al., parameter adjustment, adaptive algorithms, neural networks, Mohanty, 2014, Neath, 2014, Bahgaat, 2014, Chiha et al., genetic algorithms and fuzzy logic methods (Ahn, 2009, Mohanty, 2014, 2014, Bahgaat, 2014, Chiha et al., genetic algorithms and fuzzy logic methods (Ahn, 2009, Mohanty, 2014, Neath, Neath, 2014, Bahgaat, 2014, Chiha et al., 2012). However, despite the long history of development and genetic algorithms and fuzzy logic methods (Ahn, 2009, 2012). However, despite the long history of development and Mohanty, 2014, Neath, 2014, Bahgaat, 2014, Chiha et al., 2012). However, despite the long history of development and Mohanty, 2014, 2014, Bahgaat, 2014, Chiha et al., However, despite the long history of development a2012). number of publications and the issues of Mohanty, 2014, Neath, Neath, 2014, Bahgaat, 2014, Chiha et and al., a great greatHowever, number of publications and patents, patents, the issues of 2012). despite the long long history of development and a2012). number of publications and the of despite the history of development and a great greatHowever, number of publications andofpatents, patents, the issues issues of expanding the limited functionality these devices remain 2012). However, despite the long history of development and the limited limited functionality ofpatents, these devices devices remain aaexpanding great number of publications and the issues of expanding the functionality of these remain great number of publications and patents, the issues of expanding the limited functionality these devices remain unresolved. aunresolved. great number of publications andof patents, the issues of expanding the limited functionality of these devices remain unresolved. expanding limited functionality of these devices remain Fig. unresolved.the expanding the limited functionality of these devices remain Fig. 1. 1. Dynamic Dynamic of of PID-controllers PID-controllers patenting. patenting. Fig. 1. Dynamic of PID-controllers unresolved. Fig. 1. Dynamic of PID-controllers patenting. patenting. unresolved. 1.1 Patent analysis unresolved. Fig. 1. Dynamic of PID-controllers patenting. 1.1 Patent analysis analysis Fig. 1.1 1.1 Patent Patent analysis Fig. 1. 1. Dynamic Dynamic of of PID-controllers PID-controllers patenting. patenting. 1.1 Patent analysis Authors 1.1 Patent analysis Positive dynamic Authors of of the the patent patent (Verevkin (Verevkin et et al., al., 2006) 2006) proposed proposed an an 1.1 Patent analysisof Authors of the patent (Verevkin et al., 2006) proposed an is confirmed confirmed approach Positive dynamic of PID-controllers PID-controllers patenting patenting is Authors of the patent (Verevkin et al., 2006) proposed an Positive dynamic of PID-controllers patenting is confirmed of controlling dynamic objects with external Positive dynamic of PID-controllers patenting is confirmed by the analysis of more than 30 thousand international patents approach of controlling dynamic objects with external Authors of the patent (Verevkin et al., 2006) proposed an of controlling dynamic objects with external Authors of the patent (Verevkin et al., 2006) proposed an by the the analysis analysis of more more than 30 30 thousand thousand international patents approach Positive dynamic of PID-controllers patenting is confirmed approach of controlling dynamic objects with external by of than international patents perturbations by building a control signal based on the results Positive dynamic of PID-controllers patenting is confirmed Authors of the patent (Verevkin et al., 2006) proposed an by the analysis of more than 30 thousand international patents (granted in that develop this topic, such as China, Positive dynamic of PID-controllers is confirmed perturbations by building aa control control signal basedwith on the theexternal results of controlling dynamic objects perturbations building signal based on results approach of controlling dynamic objects external (granted in countries countries that develop thispatenting topic, such as patents China, approach by the analysis of more than 30 thousand international perturbations by buildingsignal a control signal basedwith on the results (granted in countries that develop this topic, such as China, of comparing specifies and an amount of measured by the analysis of more than 30 thousand international patents approach of by controlling dynamic objects with external (granted in countries that develop this topic, such as China, USA, Russia, Canada, Holland, UK and etc.) received by the analysis of more than 30 thousand international patents of comparing specifies signal and an amount of measured perturbations by building a control signal based on the results of comparing specifies signal and an amount of measured perturbations by building a control signal based on the results USA, Russia, Canada, Holland, UK and etc.) received (granted in countries that develop this topic, such as China, of comparing specifies signal and an amount of measured USA, Russia, Canada, Holland, UK and etc.) received values characterized an object’s technical condition. The (granted in that develop this topic, as China, perturbations byspecifies building aobject’s control signal based on the results USA, Russia, Canada, Holland, UK and such etc.) between 2006 and 2015 defined by using the of (granted in countries countries thatand develop this such asreceived China, values characterized ansignal technical condition. The comparing and an amount of measured values characterized an object’s technical condition. The of comparing specifies signal and an amount of measured betweenRussia, 2006 and 2015 and defined bytopic, using the method method of of USA, Canada, Holland, UK and etc.) received values characterized an object’s technical condition. The between 2006 and 2015 and defined by using the method of main drawback of this approach is measuring the object's USA, Russia, Canada, Holland, UK and etc.) received comparing specifies signal andis anmeasuring amount ofthemeasured between 2006 and 2015 and defined by using the 1). method of of semantic search in the Exactus Patent system (Fig. USA, Russia, Canada, Holland, UK and etc.) received main drawback of this approach object's values characterized an object’s technical condition. The main drawback of this approach is measuring the object's values characterized an object’s technical condition. The semantic search in the Exactus Patent system (Fig. 1). between 2006 and 2015 and defined by using the method of main drawback of this approach is measuring the object's condition variables behind the points of perturbation. semantic search in the Exactus Patent system (Fig. 1). between 2006 and 2015 and defined by using the method of values characterized an object’s technical condition. The semantic 2006 searchand in the Exactus Patent by system (Fig. 1). between 2015 and defined using theto method of condition condition variables behind the points points ofmeasuring perturbation. main drawback of behind this approach approach is of the object's object's variables the perturbation. main drawback of this is the semantic search in the Exactus Patent system (Fig. 1). A control method for dynamic objects subject external condition variables behind the points ofmeasuring perturbation. semantic search in the Exactus Patent system (Fig. 1). main drawback of this approach is measuring the (Vladov object's A control method for dynamic objects subject to external semantic search in the Exactus Patent system (Fig. 1). condition variables behind the points of perturbation. A control control method method for dynamic dynamic objects subject subject to external external The operational mode that is represented by a patent condition variables behind the points of perturbation. A for objects to perturbations of specific characteristics was proposed in The operational mode that is represented by a patent (Vladov condition variables behind the points of perturbation. operational mode is by (Vladov perturbations of specific characteristics was proposed in The A control method for dynamic objects subject to external Theal., operational modeonthat that is represented represented by aa patent patentparameter (Vladov perturbations of characteristics was in et 2011), measuring the A control for dynamic objects subject to perturbations ofal.,specific specific characteristics was proposed proposed in The (Tararykin et 2005). Its is A control method method for dynamic objectsdisadvantage subject to external external et al., al., 2011), based based onthat measuring the controlled controlled parameter operational mode is represented by aa patent (Vladov et 2011), based on measuring the controlled parameter The operational mode that is represented by patent (Vladov (Tararykin et of al.,specific 2005). Its basic basic disadvantage is that that perturbations characteristics was proposed in et al., 2011), based on measuring the controlled parameter (Tararykin et al., 2005). Its basic disadvantage is that and determining magnitude and speed of deviation of perturbations of specific characteristics was proposed in operational mode is represented by deviation a patentparameter (Vladov (Tararykin change et ofal.,specific 2005). Its basic disadvantage is that predictive in the state variables cannot be perturbations characteristics was proposed in The andal., determining magnitude and speed speed of of the the et al., 2011), based based onthat measuring the controlled controlled and determining magnitude and of deviation of et 2011), on measuring the parameter predictive change change in2005). the object’s object’s statedisadvantage variables cannot be (Tararykin et al., Its basic is that and determining magnitude and speed of deviation of the the predictive in the object’s state variables cannot be controlled parameter. Control signal is formed with a period, (Tararykin et al., 2005). Its basic disadvantage is that et al., 2011), based on measuring the controlled parameter predictive change the object’s state variables cannot be and taken into account if they are measured at the (Tararykin et al., in 2005). Its only basic disadvantage ispoints that controlled parameter. Controland signal is formed formed with aa period, period, determining magnitude and speed of deviation deviation of the the controlled parameter. Control signal is with and determining magnitude speed of of taken into account if they are only measured at the points predictive change in the object’s state variables cannot be controlled parameter. Control signal is formed with a period, taken into account if they are only measured at the points equals to the sum of the time lag and the time constant of the predictive change in the object’s state variables cannot be and determining magnitude and speed of deviation of taken into account theyobject’s are applied. onlystate measured at the points where the perturbations are A different control predictive inif the variables cannot be controlled equals to to the the sum of of the the time lag lag andis the time constant constant of the the parameter. Control signal formed with a period, equals sum time and time of controlled parameter. Control signal formed with where into the change perturbations are applied. A different control taken account if they are only measured at the points equals toThe the sum of the timeislag andis the time constant of the where the perturbations are applied. A control object. disadvantage limited functionality, since taken account if they are only measured at the points controlled parameter. Control signal isthe formed with aa period, period, where into the perturbations are applied. A different different control method was proposed in (Kostogryz, 1994): in that approach, taken into account if they are only measured at the points object. The disadvantage is limited functionality, since equals to the sum of the time lag and the time constant of the object. The disadvantage is limited functionality, since equals to the sum of the time lag and the time constant of the method the was perturbations proposed in in (Kostogryz, (Kostogryz, 1994): in that that approach, approach, where are applied. A different control object. The disadvantage is limited functionality, since method was proposed 1994): in where the perturbations are applied. A different control equals to the sum of the time lag and the time constant of the method the was perturbations proposed in (Kostogryz, 1994): in that approach, where are applied. A different control object. The disadvantage is limited functionality, since object. disadvantage is limited method was proposed in (Kostogryz, 1994): in that approach, method proposed in 1994): in that object. byThe The disadvantage isreserved. limited functionality, functionality, since since 2405-8963 © IFAC (International Federation Control) Elsevier Ltd. All rights method was was proposed in (Kostogryz, (Kostogryz, 1994): of in Automatic that approach, approach, Copyright © 2018, 2018 IFAC 712Hosting Copyright 2018 IFAC 712 Copyright © 2018 IFAC 712 Peer review© of International Federation of Automatic Copyright ©under 2018 responsibility IFAC 712Control. Copyright © 2018 IFAC 712 10.1016/j.ifacol.2018.11.464 Copyright © 2018 IFAC 712 Copyright © 2018 IFAC 712
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control action does not take into account the forecast component, describing future changes of the controlled parameter. Method of identifying an object with test signals bases upon control actions summarizing two components. The first of them depends on the values of output variables of an object, and the second depends on errors of regulation. Test signals help to fix a trajectory of output variables and to evaluate dynamic performance of the controlled object [6]. The disadvantage of this method is the necessity of test signals. It severely limits the possibilities of this approach for most varieties of technological objects that do not permit additional influences. Another problem is the dependence one of the components from control errors. 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. 2. TECHNICAL SOLUTION
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 Fig. 2a, we show 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.
In the functional diagram of the system for determining trends in the technological 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:
The weighting factor of the predictive term Apc is calculated on a polynomial dependency of the coefficient of variability ν of the controlled parameter with coefficients of approximation b0, b1, b2, b3, specified for the object:
Apc = b0 + b1v + b2v2 + b3v3.
y0 ti
(1)
where y0(ti) is the normalized value of the controlled parameter at time ti; y(ti) is the current value of the controlledl 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 control signal Ak from PID controller could be found according to the expression: Ak = 1 – Apc.
(2)
Calculating the weights, we took into account the condition 2
A 1. i 1
y ti y t0 , yn y t0
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:
i
t2 lg 1 y01 t1 lg 1 y02 , lg 1 y01 lg 1 y02
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:
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T
Module (20) for determining the discrepancy between the predicted xpr and specified values of the controlled parameter xz:
t2 . 2,3lg 1 y02
dxpr = xpr – xz.
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.
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
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:
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.
n
mx
x t i 1
i
n
,
where xi (t) is the measured value of the controlled parameter; n – a number of measurements. Module (14) 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.
3. VERIFICATION The proposed method is verified for the reactor that processes the waste gases in sulphur production. The reactor operates in two stages.
(15) - the module for determining the trend k*, from the formula
(1) Adsorption. Regeneration gases heated in (7) a tube array pass to the reactor at 120–140°С, at a rate of at least 25000 m3/h.
k* = mx/dТi. (7) 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 sx, taking account of the measured values of the controlled parameter: n
sx
x t m i 1
i
x
n 1
(2) Catalyst regeneration, which itself consists of two stages. (2.1) Heating of the catalyst to 260°С, with sulphur desorption from its surface at 200–250°С. (2.2) Catalyst cooling.
2
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.
,
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. 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.
tpr = a0 + a1v + a2v2 + a3v3.
Fig. 3. Chart of temperature variation during the first and second stages of the workflow
Module (19) for calculating the predicted value tpr of the controlled parameter from the formula:
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.
xpr = k*tpr.
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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 quality criterion amounted J12 .
Table 1. Heating characteristic of an object No
y(ti), оС
yо(ti)
1 2 3 … 59 60 61
535 537 545 … 656 657 658
0.00 0.02 0.08 … 0.98 0.99 1.00
715
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 (table 2). Table 2. Temperature of gas regeneration in heaters
For normalized values of temperature y01= 0.12 and y02 = 0.8 we identify appropriate moments: t1 = 24 m and t2 = 83 min.
Time 2:33 2:34 2:35 2:36 2:37 2:38 2:39
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. 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. Base 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.
Q(ti), °С 658 660 657 661 657 657 645
mx(ti), °С 658.00 659.00 658.33 659.00 658.60 658.33 656.43
% 1.23 1.38 1.28 1.38 1.32 1.28 0.99
6. CONCLUSIONS 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., 2011, 2012). This research is a part of a project on the smart control of high-tech systems (Vladov et al., 2018).
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.
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%.
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.
REFERENCES Ahn K.K., Truong D.Q. (2009), Online tuning fuzzy PID controller using robust extended Kalman filter/ Journal of Process Control. Vol. 19. Iss. 6. pp. 1011–1023. Bahgaat, N.K., El-Sayed, M.I., Moustafa Hassan, M.A. and F.A. Bendary (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. pp. 1–24. DOI: 10.4018/ijsda.2014070101 Chiha, I., Liouane, N. and P. Borne Tuning PID controller using multiobjective ant colony optimization (2012). 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., 2006, Vol. 4, pp. 66–74. Kostogryz, P.V. (1994), RU Patent 2017196.
Fig. 4. A fragment of the simulation results 715
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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. pp. 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. pp. 1523–1531. 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., Pavlova, Yu.S., Vladova, A.Yu., and Turkov, V.V. (2011), RU Patent 2450303. Vladov, Yu.R., Pavlova, Yu.S., Vladova, A.Yu., and Kalmykov, A.V. (2012), RU Patent 2459255. Vladov, Yu.R. and Vladova, A.Yu. (2013), Control signals of a predictive industrial PID controller/ Russian Engineering Research, 2018, Vol. 38, No. 5, pp. 399– 402.
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Two-stage workflow control with aa predictive component Two-stage workflow control with component Two-stage workflow control with aa predictive predictive component Two-stage workflow control with predictive component Two-stage workflow control with a predictive component Two-stage workflow control with a predictive Yury control R. Vladov*.with Alla Yu. Vladova** component Two-stage workflow a predictive component
Yury R. Vladov*. Alla Yu. Vladova** Yury Yu. Yury R. R. Vladov*. Vladov*. Alla Alla Yu. Vladova** Vladova** Yury R. Vladov*. Alla Yu. Vladova** Yury R. Vladov*. Alla Yu. Vladova** Yury R.Ural Vladov*. Alla Yu. Vladova** *Orenburg Scientific Centre of the Branch of the Russian *Orenburg Scientific Scientific Centre Centre of of the the Ural Ural Branch Branch of of the the Russian Russian Academy Academy of of Sciences, Sciences, Orenburg, Orenburg, *Orenburg Academy *Orenburg Scientific Centre of+7 the(353) Ural 277-54-17; Branch of the Russian Academy of of Sciences, Sciences, Orenburg, Orenburg, Russia (Tel: e-mail: [email protected]). Russia (Tel:of +7 (353) 277-54-17; e-mail: [email protected]). *Orenburg Scientific Centre the Ural Branch of the Russian Academy of Sciences, Orenburg, 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, Russia (Tel:of+7 (353) 277-54-17; e-mail: [email protected]). **Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia (e-mail: *Orenburg Scientific Centre the Ural Branch of the Russian Academy of Sciences, **Institute of of Control Control Sciences of(353) the Russian Russian Academy of [email protected]). Sciences, Moscow, Moscow, Russia RussiaOrenburg, (e-mail: Russia (Tel: +7 277-54-17; e-mail: **Institute Sciences of the Academy of Sciences, Russia (Tel: +7 (353) 277-54-17; e-mail: [email protected]). **Institute of Control Sciences of(353) [email protected])} Russian Academy of [email protected]). Sciences, Moscow, Russia (e-mail: (e-mail: Russia (Tel: +7 277-54-17; e-mail: [email protected])} **Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia (e-mail: **Institute Russian Academy of Sciences, Moscow, Russia (e-mail: [email protected])} **Institute of of Control Control Sciences Sciences of of the [email protected])} Russian Academy of Sciences, Moscow, Russia (e-mail: [email protected])} [email protected])} [email protected])} Abstract: Abstract: Background. Background. Despite Despite the the wide wide use use of of controllers controllers with with proportional-integral-differential proportional-integral-differential control control Abstract: Background. Despite the wide controllers with control Abstract: Background.the Despite theexpanding wide use use of of controllers with proportional-integral-differential proportional-integral-differential control law (PID controllers), issue of the limited functionality of not taking into account the trend law (PID controllers), the issue of expanding the limited functionality of not taking into account the trend Abstract: Background. Despite the wide use of controllers with proportional-integral-differential control law (PID the issue of expanding the limited functionality of into account the trend Abstract: Background. Despite the wide use of controllers with proportional-integral-differential control law (PID controllers), controllers), the issue of expanding the limited The functionality of not notistaking taking into account the trend of changing technological parameters is open. Methods. control action formed taking into account Abstract: Background. Despite the wide use of controllers with proportional-integral-differential control of changing technological parameters is open. Methods. The control action is formed taking into account law (PID controllers), the issue of expanding the limited functionality of not taking into account the trend of changing technological parameters is open. Methods. The control action is formed taking into account law (PID controllers), the issue of expanding limited functionality of not into account trend of changing technological parameters is parameter. open.the Methods. The control action istaking formed taking intothe account the predicted value of technological Verification. The proposed method is verified for the law (PID controllers), the issue of expanding the limited functionality of not taking into account the trend the predicted value of the technological parameter. Verification. The proposed method is verified for the of changing technological parameters is open. Methods. The control action is formed taking into account the predicted value of the technological parameter. Verification. The proposed method is verified for the of changing technological parameters is open. Methods. The control action is formed taking into account the predicted value of the technological parameter. Verification. The proposed method is verified for the reactor that processes waste gases in sulfur production. Conclusions. Using a PID controller with aa of changing technological parameters is open. Methods. The control action is formed taking into account reactor that processes waste gases in sulfur production. Conclusions. Using a PID controller with the predicted value of the technological parameter. Verification. The proposed method is verified for the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller with a the predicted value of technological parameter. Verification. The proposed method is verified for the reactor that processes the waste gases in sulfur production. Conclusions. Using a PID controller with a predictive component significantly improves the quality of control, reduces the maximum deviations of the predicted value of the technological Verification. Thereduces proposed verified for predictive component significantly improves theproduction. quality of control, control, themethod maximum deviations ofaa reactor thatcomponent processes waste gases gases inparameter. sulfur production. Conclusions. Using a PID PID iscontroller controller withthe predictive significantly improves the quality of reduces the maximum deviations of reactor that processes the waste in sulfur Conclusions. Using a with predictive component significantly improves the quality of control, reduces the maximum deviations of process parameters from specified values, contributing to additional energy saving and a significant reactor processesfrom the waste gases in sulfur Conclusions. Using a PID and controller withofa process that parameters specified values, contributing to control, additional energy saving significant predictive component significantly improves theproduction. quality of of control, reduces thesaving maximum deviations process from specified values, contributing to additional energy and aaa mechanical significant predictive component significantly improves the quality reduces the maximum deviations of process parameters parameters from specified values,process contributing to additional energy saving and significant increase in the efficiency of automated units in the oil and gas industry and predictive component significantly improves the quality of control, reduces the maximum deviations of increase in the efficiency of automated process units in the oil and gas industry and mechanical process parameters parameters from specified specified values,process contributing to additional energy saving and and a mechanical significant increase in the efficiency of automated units in the oil and gas industry and process from values, contributing to additional energy saving a significant increase parameters in the efficiency of automated process units to in additional the oil and gas industry anda mechanical engineering. process from specified values, contributing energy saving and significant engineering. increase in the efficiency of automated process units in the oil and gas industry and mechanical engineering. increase in the of automated process units the and industry engineering. increase inOptimal the efficiency efficiency of automated process units in inRobust the oil oil and gas gas industry and and mechanical mechanical Keywords: Control; Real-Time Control Problems; Control and Stabilization engineering. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. engineering. Keywords: Optimal Control; Real-Time Control Problems; Robust Control and Stabilization Keywords: Optimal Control; Real-Time Control Problems; Robust Control and Stabilization engineering. Keywords: Optimal Control; Real-Time Control Problems; Robust Control and Stabilization Keywords: Optimal Control; Real-Time Control Problems; Robust Control and Stabilization Keywords: Robust Keywords: Optimal Optimal Control; Control; Real-Time Real-Time Control Control Problems; Problems; Robust Control Control and and Stabilization Stabilization aa specification is formed, specification is is formed, formed, the the controlled controlled parameter parameter is is 1. INTRODUCTION a specification the controlled parameter is a specification is formed, the controlled parameter is 1. INTRODUCTION measured, and the deviation of the parameter from 1. measured, and the the deviation the of the the parameter parameter from the the 1. INTRODUCTION INTRODUCTION ameasured, specification is formed, controlled parameter is and deviation of from the a specification is formed, the controlled parameter is measured, and the deviation of with the the parameter from the 1. INTRODUCTION is along rate of The controller controller with with proportional-integral-differential aspecification specification is formed, the controlled is 1. specification is determined, determined, along with the rate parameter of deviation. deviation. The aaa proportional-integral-differential measured, and the deviation of the parameter from the 1. INTRODUCTION INTRODUCTION specification is along with the rate The controller with measured, and the deviation of the parameter from the specification is determined, determined, along with the rate of of deviation. deviation. The controller with a isproportional-integral-differential proportional-integral-differential Its disadvantage is its limited functional capabilities, since the control law (PID controller) one of the most common types measured, and the deviation of the parameter from Its disadvantage disadvantage is its its limited limitedalong functional capabilities, since the the control law (PID controller) one of the most common types specification is determined, with the rate of deviation. The controller with a is proportional-integral-differential is functional capabilities, since control law controller) is one most types specification is determined, along with the rate of deviation. The controller with Its disadvantage is formed its limited functional capabilities, since the control law (PID (PID controller) isproportional-integral-differential one of the most common common types Its control signal on the basis of the of regulators: 90-95% of aathem them use of thethe appropriate algorithm. specification is is determined, along with the rate ofparameter’s deviation. The controller withof proportional-integral-differential control signal is formed on the basis of the parameter’s use the appropriate algorithm. of regulators: 90-95% Its disadvantage is its limited functional capabilities, since the control law (PID controller) is one of the most common types control signal is on the of parameter’s of 90-95% of use the appropriate algorithm. disadvantage its limited capabilities, since control law controller) is the most common types control signal isis formed onfunctional theandbasis basis of the the parameter’s of regulators: 90-95% of them them use the appropriate algorithm. deviation from specification its rate of Theregulators: reasons for this popularity areof simplicity of construction Its disadvantage is formed its limited functional since the the control law (PID (PID controller) is one one of the most of common types Its deviation from the the specification andbasis its capabilities, rate of specification, specification, The reasons for this popularity are simplicity construction control signal is formed on the of the parameter’s of regulators: 90-95% of them use the appropriate algorithm. deviation from the specification and its rate of specification, The reasons for this popularity are simplicity of construction control signal is formed on the basis of the parameter’s of regulators: 90-95% of them use the appropriate algorithm. deviation from the specification and its rate of specification, The reasons for this popularity are simplicity of construction without any predictive component. and industrial usage, clarity of functioning and suitability for control signal is formed on the basis of the parameter’s of regulators: 90-95% of them use the appropriate algorithm. without any any predictive component. suitability for and industrial usage, clarity of functioning andof deviation from the specification and its rate of specification, The reasons for this popularity are simplicity construction predictive component. and usage, clarity of for deviation from the and The reasons this are of construction without any predictive component. and industrial usage, clarity of functioning functioning and suitability for without solving mostfor practical problems. Amongand PID controllers, deviation from the specification specification and its its rate rate of of specification, specification, The industrial reasons for this popularity popularity are simplicity simplicity ofsuitability construction solving most practical problems. Among PID controllers, without any predictive component. and industrial usage, clarity of functioning and suitability for solving most practical problems. Among PID controllers, without any predictive component. and industrial usage, clarity of functioning and suitability for solving most practical problems. Among PID controllers, 64% are single-loop controllers and 36% are multi-circuit without any predictive component. and industrial usage, clarity of functioning and suitability for 64% are single-loop controllers and 36% are multi-circuit solving most practical problems. Among PID controllers, 64% are single-loop and 36% multi-circuit solving practical problems. Among PID controllers, 64% aremost single-loop controllers and 36% are are multi-circuit controllers (Denisenko, 2006). Instruments Instruments with feedback solving practicalcontrollers problems. Among PID controllers, controllers (Denisenko, 2006). with feedback 64% are aremost single-loop controllers and 36% are are multi-circuit controllers (Denisenko, 2006). Instruments with feedback 64% single-loop controllers and 36% multi-circuit controllers (Denisenko, 2006). Instruments with feedback control occupy 85% of the total number of controllers, with 64% are single-loop controllers and 36% are multi-circuit control occupy 85% of of the the total Instruments number of of controllers, controllers, with controllers (Denisenko, 2006). with feedback control occupy 85% total number with controllers (Denisenko, 2006). Instruments with feedback controlcontrol occupy 85% ofand the total Instruments number of Analogue-digital controllers, with direct 6%, cascaded 9%. controllers (Denisenko, 2006). with feedback direct control 6%, and cascaded 9%. Analogue-digital control occupy 85% of the total number of controllers, with direct --85% 6%, --allow 9%. Analogue-digital control occupy the total number of controllers, with direct control control 6%, of and cascaded 9%. Analogue-digital converters on microprocessor use control occupy ofand thecascaded totalbasis number of to controllers, with converters on aaa--85% microprocessor basis allow to use automatic automatic direct control 6%, and cascaded 9%. Analogue-digital converters on microprocessor basis allow to use automatic direct control 6%, and cascaded 9%. Analogue-digital converters on a- microprocessor basis-allow to use automatic parameter adjustment, adaptive algorithms, neural networks, direct control 6%, and cascaded 9%. Analogue-digital parameter adjustment, adjustment, adaptive algorithms, algorithms, neural networks, converters on a microprocessor basis allow neural to use automatic parameter adaptive networks, converters on basis to automatic parameter adjustment, adaptive algorithms, neural networks, genetic algorithms and fuzzy logic methods (Ahn, 2009, converters on aa microprocessor microprocessor basis allow allow to use use automatic genetic algorithms and fuzzy logic methods (Ahn, 2009, parameter adjustment, adaptive algorithms, neural networks, genetic algorithms and fuzzy logic (Ahn, 2009, parameter adjustment, algorithms, neural networks, genetic algorithms andadaptive fuzzy Bahgaat, logic methods methods (Ahn, 2009, Mohanty, 2014, Neath, 2014, 2014, Chiha et al., parameter adjustment, adaptive algorithms, neural networks, Mohanty, 2014, Neath, 2014, Bahgaat, 2014, Chiha et al., genetic algorithms and fuzzy logic methods (Ahn, 2009, Mohanty, 2014, 2014, Bahgaat, 2014, Chiha et al., genetic algorithms and fuzzy logic methods (Ahn, 2009, Mohanty, 2014, Neath, Neath, 2014, Bahgaat, 2014, Chiha et al., 2012). However, despite the long history of development and genetic algorithms and fuzzy logic methods (Ahn, 2009, 2012). However, despite the long history of development and Mohanty, 2014, Neath, 2014, Bahgaat, 2014, Chiha et al., 2012). However, despite the long history of development and Mohanty, 2014, 2014, Bahgaat, 2014, Chiha et al., However, despite the long history of development a2012). number of publications and the issues of Mohanty, 2014, Neath, Neath, 2014, Bahgaat, 2014, Chiha et and al., a great greatHowever, number of publications and patents, patents, the issues of 2012). despite the long long history of development and a2012). number of publications and the of despite the history of development and a great greatHowever, number of publications andofpatents, patents, the issues issues of expanding the limited functionality these devices remain 2012). However, despite the long history of development and the limited limited functionality ofpatents, these devices devices remain aaexpanding great number of publications and the issues of expanding the functionality of these remain great number of publications and patents, the issues of expanding the limited functionality these devices remain unresolved. aunresolved. great number of publications andof patents, the issues of expanding the limited functionality of these devices remain unresolved. expanding limited functionality of these devices remain Fig. unresolved.the expanding the limited functionality of these devices remain Fig. 1. 1. Dynamic Dynamic of of PID-controllers PID-controllers patenting. patenting. Fig. 1. Dynamic of PID-controllers unresolved. Fig. 1. Dynamic of PID-controllers patenting. patenting. unresolved. 1.1 Patent analysis unresolved. Fig. 1. Dynamic of PID-controllers patenting. 1.1 Patent analysis analysis Fig. 1.1 1.1 Patent Patent analysis Fig. 1. 1. Dynamic Dynamic of of PID-controllers PID-controllers patenting. patenting. 1.1 Patent analysis Authors 1.1 Patent analysis Positive dynamic Authors of of the the patent patent (Verevkin (Verevkin et et al., al., 2006) 2006) proposed proposed an an 1.1 Patent analysisof Authors of the patent (Verevkin et al., 2006) proposed an is confirmed confirmed approach Positive dynamic of PID-controllers PID-controllers patenting patenting is Authors of the patent (Verevkin et al., 2006) proposed an Positive dynamic of PID-controllers patenting is confirmed of controlling dynamic objects with external Positive dynamic of PID-controllers patenting is confirmed by the analysis of more than 30 thousand international patents approach of controlling dynamic objects with external Authors of the patent (Verevkin et al., 2006) proposed an of controlling dynamic objects with external Authors of the patent (Verevkin et al., 2006) proposed an by the the analysis analysis of more more than 30 30 thousand thousand international patents approach Positive dynamic of PID-controllers patenting is confirmed approach of controlling dynamic objects with external by of than international patents perturbations by building a control signal based on the results Positive dynamic of PID-controllers patenting is confirmed Authors of the patent (Verevkin et al., 2006) proposed an by the analysis of more than 30 thousand international patents (granted in that develop this topic, such as China, Positive dynamic of PID-controllers is confirmed perturbations by building aa control control signal basedwith on the theexternal results of controlling dynamic objects perturbations building signal based on results approach of controlling dynamic objects external (granted in countries countries that develop thispatenting topic, such as patents China, approach by the analysis of more than 30 thousand international perturbations by buildingsignal a control signal basedwith on the results (granted in countries that develop this topic, such as China, of comparing specifies and an amount of measured by the analysis of more than 30 thousand international patents approach of by controlling dynamic objects with external (granted in countries that develop this topic, such as China, USA, Russia, Canada, Holland, UK and etc.) received by the analysis of more than 30 thousand international patents of comparing specifies signal and an amount of measured perturbations by building a control signal based on the results of comparing specifies signal and an amount of measured perturbations by building a control signal based on the results USA, Russia, Canada, Holland, UK and etc.) received (granted in countries that develop this topic, such as China, of comparing specifies signal and an amount of measured USA, Russia, Canada, Holland, UK and etc.) received values characterized an object’s technical condition. The (granted in that develop this topic, as China, perturbations byspecifies building aobject’s control signal based on the results USA, Russia, Canada, Holland, UK and such etc.) between 2006 and 2015 defined by using the of (granted in countries countries thatand develop this such asreceived China, values characterized ansignal technical condition. The comparing and an amount of measured values characterized an object’s technical condition. The of comparing specifies signal and an amount of measured betweenRussia, 2006 and 2015 and defined bytopic, using the method method of of USA, Canada, Holland, UK and etc.) received values characterized an object’s technical condition. The between 2006 and 2015 and defined by using the method of main drawback of this approach is measuring the object's USA, Russia, Canada, Holland, UK and etc.) received comparing specifies signal andis anmeasuring amount ofthemeasured between 2006 and 2015 and defined by using the 1). method of of semantic search in the Exactus Patent system (Fig. USA, Russia, Canada, Holland, UK and etc.) received main drawback of this approach object's values characterized an object’s technical condition. The main drawback of this approach is measuring the object's values characterized an object’s technical condition. The semantic search in the Exactus Patent system (Fig. 1). between 2006 and 2015 and defined by using the method of main drawback of this approach is measuring the object's condition variables behind the points of perturbation. semantic search in the Exactus Patent system (Fig. 1). between 2006 and 2015 and defined by using the method of values characterized an object’s technical condition. The semantic 2006 searchand in the Exactus Patent by system (Fig. 1). between 2015 and defined using theto method of condition condition variables behind the points points ofmeasuring perturbation. main drawback of behind this approach approach is of the object's object's variables the perturbation. main drawback of this is the semantic search in the Exactus Patent system (Fig. 1). A control method for dynamic objects subject external condition variables behind the points ofmeasuring perturbation. semantic search in the Exactus Patent system (Fig. 1). main drawback of this approach is measuring the (Vladov object's A control method for dynamic objects subject to external semantic search in the Exactus Patent system (Fig. 1). condition variables behind the points of perturbation. A control control method method for dynamic dynamic objects subject subject to external external The operational mode that is represented by a patent condition variables behind the points of perturbation. A for objects to perturbations of specific characteristics was proposed in The operational mode that is represented by a patent (Vladov condition variables behind the points of perturbation. operational mode is by (Vladov perturbations of specific characteristics was proposed in The A control method for dynamic objects subject to external Theal., operational modeonthat that is represented represented by aa patent patentparameter (Vladov perturbations of characteristics was in et 2011), measuring the A control for dynamic objects subject to perturbations ofal.,specific specific characteristics was proposed proposed in The (Tararykin et 2005). Its is A control method method for dynamic objectsdisadvantage subject to external external et al., al., 2011), based based onthat measuring the controlled controlled parameter operational mode is represented by aa patent (Vladov et 2011), based on measuring the controlled parameter The operational mode that is represented by patent (Vladov (Tararykin et of al.,specific 2005). Its basic basic disadvantage is that that perturbations characteristics was proposed in et al., 2011), based on measuring the controlled parameter (Tararykin et al., 2005). Its basic disadvantage is that and determining magnitude and speed of deviation of perturbations of specific characteristics was proposed in operational mode is represented by deviation a patentparameter (Vladov (Tararykin change et ofal.,specific 2005). Its basic disadvantage is that predictive in the state variables cannot be perturbations characteristics was proposed in The andal., determining magnitude and speed speed of of the the et al., 2011), based based onthat measuring the controlled controlled and determining magnitude and of deviation of et 2011), on measuring the parameter predictive change change in2005). the object’s object’s statedisadvantage variables cannot be (Tararykin et al., Its basic is that and determining magnitude and speed of deviation of the the predictive in the object’s state variables cannot be controlled parameter. Control signal is formed with a period, (Tararykin et al., 2005). Its basic disadvantage is that et al., 2011), based on measuring the controlled parameter predictive change the object’s state variables cannot be and taken into account if they are measured at the (Tararykin et al., in 2005). Its only basic disadvantage ispoints that controlled parameter. Controland signal is formed formed with aa period, period, determining magnitude and speed of deviation deviation of the the controlled parameter. Control signal is with and determining magnitude speed of of taken into account if they are only measured at the points predictive change in the object’s state variables cannot be controlled parameter. Control signal is formed with a period, taken into account if they are only measured at the points equals to the sum of the time lag and the time constant of the predictive change in the object’s state variables cannot be and determining magnitude and speed of deviation of taken into account theyobject’s are applied. onlystate measured at the points where the perturbations are A different control predictive inif the variables cannot be controlled equals to to the the sum of of the the time lag lag andis the time constant constant of the the parameter. Control signal formed with a period, equals sum time and time of controlled parameter. Control signal formed with where into the change perturbations are applied. A different control taken account if they are only measured at the points equals toThe the sum of the timeislag andis the time constant of the where the perturbations are applied. A control object. disadvantage limited functionality, since taken account if they are only measured at the points controlled parameter. Control signal isthe formed with aa period, period, where into the perturbations are applied. A different different control method was proposed in (Kostogryz, 1994): in that approach, taken into account if they are only measured at the points object. The disadvantage is limited functionality, since equals to the sum of the time lag and the time constant of the object. The disadvantage is limited functionality, since equals to the sum of the time lag and the time constant of the method the was perturbations proposed in in (Kostogryz, (Kostogryz, 1994): in that that approach, approach, where are applied. A different control object. The disadvantage is limited functionality, since method was proposed 1994): in where the perturbations are applied. A different control equals to the sum of the time lag and the time constant of the method the was perturbations proposed in (Kostogryz, 1994): in that approach, where are applied. A different control object. The disadvantage is limited functionality, since object. disadvantage is limited method was proposed in (Kostogryz, 1994): in that approach, method proposed in 1994): in that object. byThe The disadvantage isreserved. limited functionality, functionality, since since 2405-8963 © IFAC (International Federation Control) Elsevier Ltd. All rights method was was proposed in (Kostogryz, (Kostogryz, 1994): of in Automatic that approach, approach, Copyright © 2018, 2018 IFAC 712Hosting Copyright 2018 IFAC 712 Copyright © 2018 IFAC 712 Peer review© of International Federation of Automatic Copyright ©under 2018 responsibility IFAC 712Control. Copyright © 2018 IFAC 712 10.1016/j.ifacol.2018.11.464 Copyright © 2018 IFAC 712 Copyright © 2018 IFAC 712
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control action does not take into account the forecast component, describing future changes of the controlled parameter. Method of identifying an object with test signals bases upon control actions summarizing two components. The first of them depends on the values of output variables of an object, and the second depends on errors of regulation. Test signals help to fix a trajectory of output variables and to evaluate dynamic performance of the controlled object [6]. The disadvantage of this method is the necessity of test signals. It severely limits the possibilities of this approach for most varieties of technological objects that do not permit additional influences. Another problem is the dependence one of the components from control errors. 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. 2. TECHNICAL SOLUTION
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 Fig. 2a, we show 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.
In the functional diagram of the system for determining trends in the technological 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:
The weighting factor of the predictive term Apc is calculated on a polynomial dependency of the coefficient of variability ν of the controlled parameter with coefficients of approximation b0, b1, b2, b3, specified for the object:
Apc = b0 + b1v + b2v2 + b3v3.
y0 ti
(1)
where y0(ti) is the normalized value of the controlled parameter at time ti; y(ti) is the current value of the controlledl 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 control signal Ak from PID controller could be found according to the expression: Ak = 1 – Apc.
(2)
Calculating the weights, we took into account the condition 2
A 1. i 1
y ti y t0 , yn y t0
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:
i
t2 lg 1 y01 t1 lg 1 y02 , lg 1 y01 lg 1 y02
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:
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T
Module (20) for determining the discrepancy between the predicted xpr and specified values of the controlled parameter xz:
t2 . 2,3lg 1 y02
dxpr = xpr – xz.
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.
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
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:
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.
n
mx
x t i 1
i
n
,
where xi (t) is the measured value of the controlled parameter; n – a number of measurements. Module (14) 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.
3. VERIFICATION The proposed method is verified for the reactor that processes the waste gases in sulphur production. The reactor operates in two stages.
(15) - the module for determining the trend k*, from the formula
(1) Adsorption. Regeneration gases heated in (7) a tube array pass to the reactor at 120–140°С, at a rate of at least 25000 m3/h.
k* = mx/dТi. (7) 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 sx, taking account of the measured values of the controlled parameter: n
sx
x t m i 1
i
x
n 1
(2) Catalyst regeneration, which itself consists of two stages. (2.1) Heating of the catalyst to 260°С, with sulphur desorption from its surface at 200–250°С. (2.2) Catalyst cooling.
2
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.
,
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. 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.
tpr = a0 + a1v + a2v2 + a3v3.
Fig. 3. Chart of temperature variation during the first and second stages of the workflow
Module (19) for calculating the predicted value tpr of the controlled parameter from the formula:
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.
xpr = k*tpr.
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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 quality criterion amounted J12 .
Table 1. Heating characteristic of an object No
y(ti), оС
yо(ti)
1 2 3 … 59 60 61
535 537 545 … 656 657 658
0.00 0.02 0.08 … 0.98 0.99 1.00
715
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 (table 2). Table 2. Temperature of gas regeneration in heaters
For normalized values of temperature y01= 0.12 and y02 = 0.8 we identify appropriate moments: t1 = 24 m and t2 = 83 min.
Time 2:33 2:34 2:35 2:36 2:37 2:38 2:39
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. 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. Base 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.
Q(ti), °С 658 660 657 661 657 657 645
mx(ti), °С 658.00 659.00 658.33 659.00 658.60 658.33 656.43
% 1.23 1.38 1.28 1.38 1.32 1.28 0.99
6. CONCLUSIONS 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., 2011, 2012). This research is a part of a project on the smart control of high-tech systems (Vladov et al., 2018).
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.
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%.
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.
REFERENCES Ahn K.K., Truong D.Q. (2009), Online tuning fuzzy PID controller using robust extended Kalman filter/ Journal of Process Control. Vol. 19. Iss. 6. pp. 1011–1023. Bahgaat, N.K., El-Sayed, M.I., Moustafa Hassan, M.A. and F.A. Bendary (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. pp. 1–24. DOI: 10.4018/ijsda.2014070101 Chiha, I., Liouane, N. and P. Borne Tuning PID controller using multiobjective ant colony optimization (2012). 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., 2006, Vol. 4, pp. 66–74. Kostogryz, P.V. (1994), RU Patent 2017196.
Fig. 4. A fragment of the simulation results 715
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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. pp. 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. pp. 1523–1531. 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., Pavlova, Yu.S., Vladova, A.Yu., and Turkov, V.V. (2011), RU Patent 2450303. Vladov, Yu.R., Pavlova, Yu.S., Vladova, A.Yu., and Kalmykov, A.V. (2012), RU Patent 2459255. Vladov, Yu.R. and Vladova, A.Yu. (2013), Control signals of a predictive industrial PID controller/ Russian Engineering Research, 2018, Vol. 38, No. 5, pp. 399– 402.
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