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The Predictive Principle in Control Systems with Standard Lows
ScienceDirect ScienceDirect
Procedia Computer Science 00 (2019) 000–000 Procedia Computer Science 00 (2019) 000–000
Available online at www.sciencedirect.com
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
ScienceDirect Procedia Computer Science 150 (2019) 403–409
13th International Symposium “Intelligent Systems” (INTELS’18) 13th International Symposium “Intelligent Systems” (INTELS’18)
The Predictive Principle in Control Systems with Standard Lows The Predictive Principle in Control Systems with Standard Lows G.A.Pikinaa,a,*, F.F. Pashchenkobb G.A.Pikina *, F.F. Pashchenko
a National Research University “MPEI”, Krasnokazarmennaya str., 17, Moscow 111250, Russia a National Research University “MPEI”, Krasnokazarmennaya str., 17, Moscow 111250, RussiaRussia Institute of Control Sciences of Russian Science Academy, Profsoyuznaya str., 65, Moscow 117997, b Institute of Control Sciences of Russian Science Academy, Profsoyuznaya str., 65, Moscow 117997, Russia b
Abstract Abstract
Instead of the standard control principle on current state of controlled output, it offered to pass to the predictive control principle Instead of the standard principle on principle current state controlled output, it offered pass to the predictive control on future output. The control realization of this in of automatic control systems of to technological parameters with principle standard on future output. The realization of this quality principle in automatic systems technological parameters with given standard algorithms allows to increase significantly of regulation andcontrol at the same time of more fully using the opportunities by algorithms allows to increase significantly quality of regulation and at the timethat more using the opportunities given by programmable microprocessor equipment. The given in paper examples aresame proving thefully prediction allows to reduce the range programmable microprocessor equipment. The given in paper are proving thatoftheregulation predictionfor allows to reduce the of range of control output deviation twice – three times. Prediction canexamples use in coherent systems the best approach the of control output deviation to twice three times. Prediction can opportunities use in coherent systems ofalgorithms regulation can for the approach tuning of the real influence compensator the –ideal compensator. Potential of predictive use best at regulator’s real influence compensator the idealcharacteristics compensator.are Potential opportunities of predictive canlinear use at regulators regulator’sby tuning for cases when the object to dynamic unknown. The method of setup algorithms of predictive one for cases when the object parameter – predictive time dynamic – offered.characteristics are unknown. The method of setup of predictive linear regulators by one parameter – predictive time – offered. © 2019 The Author(s). Published by Elsevier B.V. © 2019 2019 The The Author(s). Authors. Published by Elsevier B.V. © Published Elsevier B.V. This is an open access article underbythe CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article underthe the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review Peer-review under under responsibility responsibility of of the scientific scientific committee committee of of the the 13th 13th International InternationalSymposium Symposium“Intelligent “IntelligentSystems” Systems”(INTELS’18) (INTELS’18). Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS’18) Keywords: principle on current state control; predictive control principle; automatic control systems; standard linear algorithms; setup of Keywords: principle on current state control; predictive control principle; automatic control systems; standard linear algorithms; setup of predictive regulators. predictive regulators.
1. Introduction 1. Introduction For improvement the quality of automatic control systems (ACS) with typical linear laws (PI, PID, etc.) in [1-4] For improvement quality of automatic control systemson (ACS) with typical (PI, PID, (t )into[1-4] offered to be passed the from the standard principle of control the current value linear of an laws regulation erroretc.) the (t ) offered to be passed from the standard principle of control on the current value of an regulation error to the principle of control according to the forecast (prediction) – the value (t pr ) expected through forecasting time principle of control according to the forecast (prediction) – the value (t pr ) expected through forecasting time
* Corresponding author. Tel.: +7-903-716-3577. * Corresponding Tel.: +7-903-716-3577. E-mail address:author. [email protected] E-mail address: [email protected]
1877-0509 © 2019 The Author(s). Published by Elsevier B.V. 1877-0509 © 2019 The article Author(s). by Elsevier license B.V. (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access underPublished the CC BY-NC-ND This is an open access article under CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS’18) Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS’18)
1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS’18). 10.1016/j.procs.2019.02.070
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G.A. Pikina et al. / Procedia Computer Science 150 (2019) 403–409
G.A.Pikina and F.F. Pashchenko / Procedia Computer Science 00 (2019) 000–000
pr in the future. The system of regulation in this case makes anticipatory impact therefore it is possible to
compensate partially an object lag effect, i. e. the lagging behind reaction of object to operations of the actuation device on object. The regulator which operating object according to the forecast of a regulation error we will call predictive regulator. Various laws can specify the transfer function of ideal (unrealizable) prediction Wpr ( p) exp p pr :
polynomial, exponential, exponential-harmoniously, auto regression models, etc. The conducted researches showed that increase the order of predictive algorithm poorly influences the accuracy of predictive regulation systems. We give the preference to the linear forecast. Unlike the exponential or auto regression forecast, it leaves the standard regulator in a class of linear systems. 2. Predictive control in one-loop ACS
The predictive regulator (Fig. 1) consists two parts – actually the regulator with the standard linear law Wr ( p) and the predictive element Pr with transfer function Wpr ( p ) . The predictive element together with a set-devise will transform a difference of the set s(t ) and output current value y (t ) to expect through time pr the error pr (t ) (t pr ) s (t ) y (t pr ).
We will carry out modeling the process of predictive control on the example of one-loop system of temperature regulation for primary steam overheat of a boiler TGMP-314 with PID regulator and object W ( p )
k e
p
(T1 p 1)(T2 p 1)(T3 p 1)
1.75 e 8 p . ( 40 p 1)(44 p 1)(10 p 1)
(1)
Results of calculations the processes of regulation at single step disturbance on the control channel and on a signal of a set presented at Fig. 2 and Table 1.
Fig. 1. Predictive regulator
Fig. 2. The processes for disturbance ( t ) 1( t ) : 1 – ordinary PID-controller; predictive PID-controller: pr 8 sec (2); 12 sec (3); 16 sec (4); 20 sec (5).
G.A.PikinaG.A. and Pikina F.F. Pashchenko / Procedia Computer Science150 00 (2019) (2019) 000–000 et al. / Procedia Computer Science 403–409
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Table 1. The quality properties of control processes for disturbance ( t ) 1(t )
pr
0
8
12
16
20
y din
0.399
0.325
0.29
0.261
0.235
I2
7.55
5.43
4.73
4.2
3.8
The graphs obtained with the optimal controller settings: k r 2.2 (kg /sec) / o C; Ti 41.2 sec; Td 23.3 sec . From data of table 1 consecutive reduction of values of a dynamic mistake ydin and integrated square criterion
I 2 in process of increase the prediction time is visible. On this basis, we conclude that by means of predictive algorithm it is possible to increase considerably the quality of regulation, having partially neutralized negative action not only pure delay, but an object capacitor inertia of also. At increase the prediction time to 20 sec a dynamic error of system decreases by 1.7 times for disturbance (t ) and by 6 times for a set-signal s (t ). The integrated square criterion I 2 decreases by 1.5–2 times in comparison with system without prediction. So the prediction time pr 18 20 sec considered as optimum for the system. Procedure of improvement the regulation quality in predictive systems we can continue if to perform optimization of the predictive regulator setup in compliance with the method offered in [4]. Process in system with optimal-tuning predictive PID regulator shows in Fig. 3 (curve 2). In the same place for comparison, process with usual PID regulator gives there (curve 1).
Fig. 3. The processes with ordinary (1) and optimal-tuning predictive (2) PID-controllers.
The value of integrated square criterion I 2 appeared by 4.4 times, the dynamic mistake y din by 1.8 times, and regulation time by 3 times less than the corresponding indicators of usual system with usual PID regulator. Decrease in square criterion four times to equivalently the same decrease in dispersion at low-frequency disturbance, and it means, optimal adjusted predictive regulators allow reduce the deviation range of output practically twice. 3. Control according to the forecast in double-circuit ASR
At regulation of inertial parameters of power unit double-circuit schemes with an additional signal from quickresponse intermediate value z are used. As an example we will consider the regulation of a secondary steam overheat of boiler TGMP-314, and as a system of regulation – standard double-circuit ACS with the differentiator and PI regulator (Fig. 4). Transfer functions of the main and auxiliary channels of object have an appearance:
Wy ( p)
0.421 (49 p 1)
2
e 38 p
C C 0.62(298 p 1) ; Wz ( p ) . % (136 p 1)(41 p 1)(12 p 1) %
4406
G.A.F.F. Pikina et al. / /Procedia 150 (2019) 403–409 G.A.Pikina and Pashchenko ProcediaComputer Computer Science Science 00 (2019) 000–000
Fig. 4. Two-loops ACS with differentiator.
Fig. 5. The regulating processes in two-loop system: (a) object output, (b) movement of regulation devise.
The regulator PI and differentiator D optimum settings are equal k r 12.8 % C ; Ti 10.1 sec; k d 0.262 % C; Td 59 sec .
Processes of regulation at single step desturbance (t ) 1(t ) are presented in Fig. 5. As can see on Fig. 5, the effect from prediction in double-loop system is even stronger, than in one-loop system. It explained by possibility of installation of great values of prediction time . In comparison with usual system (a curve 0) value of a dynamic mistake ydin decreases by 4 times at increasing the prediction time to 100 sec, and integrated square criterion I 2 – almost by 10 times. At the same time at predictive control, the range of movement of regulation devise (t ) considerably decreases and the stability reserve in an external contour increases. Thus, realization of the principle of predictive control in systems with inertial objects and standard linear regulators allows reducing twice the range of an output deviation in one-loop and by 3 times ― in double-circuit systems at simultaneous reduction of regulator movement range. Potential opportunities of improvement of quality of regulation can be used for setup of standard regulators when dynamic characteristics of object are not known, i. e. it isn't possible to execute calculation of optimum settings. 4. Tuning of one-loop system by one parameter
We will carry out modeling of control process on the example of one-loop system for primary overheat of steam temperature with transfer function (1) and predictive PI regulator. We will recognize that transfer function of object to us it isn't known therefore originally we will establish the any settings of PI regulator, based on the most general ideas of object ― approximate time of its transition process (300 sec) and increasing coefficient ( k (1.5 2). Further gradual increase the predictive time we achieve the best regulation quality. We investigate influence of the PI initial settings on achievable quality. We choose initial regulator increasing coefficient from a ratio k r k 1 2, and an integration constant Ti – in (6 10) times less than time of object transition process. Results of control with the indication of optimum predictive time pr , a dynamic mistake ydin
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5
Fig. 6. The regulating processes in one-loop system.
and square criterion I 2 present in Table 2. In the last lines the optimum settings for the PI and PID regulators, calculated on transfer function (1), are given. Transition processes of considered in the Table 2 variants for step disturbance show in Fig. 6. Table 2. The tuning results of control system Marks on Fig. 6
kr
Ti
pr
Td
y din
I2
1
0.6
50
100
23.3
0.42
19.9
2
0.8
50
80
23.3
0.4
14
3
0.8
30
70
23.3
0.39
8.2
4
1.25
40
40
23.3
0.41
7.9
PID (opt)
2.2
41
―
23.3
0.4
8
PI (opt)
0.79
61.5
―
―
0.82
55.3
Analyzing processes and table 2 we may give the following conclusions: Predictive PI regulator is much better than usual, even optimal-tuning adjusted (see curves PI and 1–4) Tuning the predictive PI algorithm by one parameter – prediction time – is quite possible (see curves PID, 3, 4 on Fig. 6 and value of quality indicators of table 2) The integration time Ti determined originally has strong impact on the achievable accuracy of stabilization (see curves 1 and 2). Similarly it is possible to adjust and not one-loop systems, changing only one parameter – prediction time [1,2]. 5. Using the prediction at realization of compensators
Transfer functions of ideal compensators in regulation schemes with disturbance compensation or in coherent systems are receiving from a condition of absolute invariance. Often such transfer functions contain a prediction element e p . Here it is possible as well to use the prediction. We investigated the double-coherent standard system of efficiency combustion for boiler BKZ-320. The system includes a PI fuel regulator stabilizing steam pressure before the turbine and PI regulator of air, stabilizing oxygen O2 in the boiler gases. Connection from the fuel to oxygen in boiler decreased compensator K. Ideal compensator has physically impossible properties of accurate predictions. For the practical implementation of it applied two ways: simple drop component predictions or using linear prediction input signal compensator for linear prediction that corresponds to the first two components of the Taylor series decomposition of exhibitors. All three variants of the compensator transfer function in coherent systems of fuel and air supply for boiler are: K id ( p)
9,2 p 9,2 p 9,2 p (1 3 p) e 3 p , K1 ( p ) , K 2 ( p) . 19,96 p 0.935 19,96 p 0,935 19,96 p 0,935
(2)
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6
Fig. 7. Oxygen content with compensator K1 ( p ) and conventional PI regulators.
Fig. 8. Oxygen content with compensator K 2 ( p ) : 1 – with conventional PI regulators, 2 – with predictive PI regulators.
Fig. 7 shows the process of regulation of oxygen content in flue gases in step variation on fuel in the system with fractional-rational compensator K1 ( p) and conventional PI regulators of fuel and air. To compare Fig. 8 given processes with prognostic compensator K 2 ( p ) and conventional PI regulators (curve 1) and predictive regulators and compensator. If the implementation of fractional-rational compensator allows 7 times to reduce the value of quadratic criterion in normal communication system control, application of fractional-rational compensator with a forecast by lower quadratic criterion in 25 times (from 8.4 to 0.33). If in addition to the compensator to apply the principle of control by the prediction, the value of the quadratic criterion can reduced 60 times (from 8.4 to 0.14) compared with typically in practice systems. 6. Conclusion
Realization of the predictive control principle in systems with inertial objects and standard linear regulators allows to reduce the deviation range of a controlled output (by 2–3 times) with reduction the range of control action and to increase the stability reserve. Using the predictive algorithm as a part of standard regulators does possible control of one- circuit and doublecircuit systems only by one parameter – forecast time, having refused expensive procedure of object identification and optimum parameters calculation of regulation. Owing to simplicity of realization on programmable microprocessor equipment, the predictive algorithms constructed based on typical laws can be very perspective for real control systems of technological processes. Acknowledgements
The work performed with assistance of the Russian scientific fund (project no. 14-19-01772).
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References [1] Pikina GA. Realization of the predictive control principle in automatic systems of regulation. In: Proceedings of the XII All-Russian meeting on control problems. 2014, June 16-19, Moscow, Russia. Moscow: ICS RSA Publishing; 2014. [2] Pikina GA. The predictive control principle and possibility the regulation systems tuning by one parameter. J. New in Russian Electro-energy 2014;3:3-13. [3] Pikina GA, Pashchenko FF, Pashchenko AF. Methods to improve accuracy of typical controllers based on predictive algorithms. In: Proceedings of the IEEE 8th Conference on Industrial Electronics and Applications: 2013 June 19-21, Melbourne, Australia. Melbourne: ICIEA; 2013, p. 613-616. [4] Pikina GA, Kuznetsov MS. Tuning methods for typical predictive control algorithms. J. Thermal Engineering 2012;59:2:154-158.
Procedia Computer Science 00 (2019) 000–000 Procedia Computer Science 00 (2019) 000–000
Available online at www.sciencedirect.com
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
ScienceDirect Procedia Computer Science 150 (2019) 403–409
13th International Symposium “Intelligent Systems” (INTELS’18) 13th International Symposium “Intelligent Systems” (INTELS’18)
The Predictive Principle in Control Systems with Standard Lows The Predictive Principle in Control Systems with Standard Lows G.A.Pikinaa,a,*, F.F. Pashchenkobb G.A.Pikina *, F.F. Pashchenko
a National Research University “MPEI”, Krasnokazarmennaya str., 17, Moscow 111250, Russia a National Research University “MPEI”, Krasnokazarmennaya str., 17, Moscow 111250, RussiaRussia Institute of Control Sciences of Russian Science Academy, Profsoyuznaya str., 65, Moscow 117997, b Institute of Control Sciences of Russian Science Academy, Profsoyuznaya str., 65, Moscow 117997, Russia b
Abstract Abstract
Instead of the standard control principle on current state of controlled output, it offered to pass to the predictive control principle Instead of the standard principle on principle current state controlled output, it offered pass to the predictive control on future output. The control realization of this in of automatic control systems of to technological parameters with principle standard on future output. The realization of this quality principle in automatic systems technological parameters with given standard algorithms allows to increase significantly of regulation andcontrol at the same time of more fully using the opportunities by algorithms allows to increase significantly quality of regulation and at the timethat more using the opportunities given by programmable microprocessor equipment. The given in paper examples aresame proving thefully prediction allows to reduce the range programmable microprocessor equipment. The given in paper are proving thatoftheregulation predictionfor allows to reduce the of range of control output deviation twice – three times. Prediction canexamples use in coherent systems the best approach the of control output deviation to twice three times. Prediction can opportunities use in coherent systems ofalgorithms regulation can for the approach tuning of the real influence compensator the –ideal compensator. Potential of predictive use best at regulator’s real influence compensator the idealcharacteristics compensator.are Potential opportunities of predictive canlinear use at regulators regulator’sby tuning for cases when the object to dynamic unknown. The method of setup algorithms of predictive one for cases when the object parameter – predictive time dynamic – offered.characteristics are unknown. The method of setup of predictive linear regulators by one parameter – predictive time – offered. © 2019 The Author(s). Published by Elsevier B.V. © 2019 2019 The The Author(s). Authors. Published by Elsevier B.V. © Published Elsevier B.V. This is an open access article underbythe CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article underthe the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review Peer-review under under responsibility responsibility of of the scientific scientific committee committee of of the the 13th 13th International InternationalSymposium Symposium“Intelligent “IntelligentSystems” Systems”(INTELS’18) (INTELS’18). Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS’18) Keywords: principle on current state control; predictive control principle; automatic control systems; standard linear algorithms; setup of Keywords: principle on current state control; predictive control principle; automatic control systems; standard linear algorithms; setup of predictive regulators. predictive regulators.
1. Introduction 1. Introduction For improvement the quality of automatic control systems (ACS) with typical linear laws (PI, PID, etc.) in [1-4] For improvement quality of automatic control systemson (ACS) with typical (PI, PID, (t )into[1-4] offered to be passed the from the standard principle of control the current value linear of an laws regulation erroretc.) the (t ) offered to be passed from the standard principle of control on the current value of an regulation error to the principle of control according to the forecast (prediction) – the value (t pr ) expected through forecasting time principle of control according to the forecast (prediction) – the value (t pr ) expected through forecasting time
* Corresponding author. Tel.: +7-903-716-3577. * Corresponding Tel.: +7-903-716-3577. E-mail address:author. [email protected] E-mail address: [email protected]
1877-0509 © 2019 The Author(s). Published by Elsevier B.V. 1877-0509 © 2019 The article Author(s). by Elsevier license B.V. (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access underPublished the CC BY-NC-ND This is an open access article under CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS’18) Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS’18)
1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS’18). 10.1016/j.procs.2019.02.070
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G.A. Pikina et al. / Procedia Computer Science 150 (2019) 403–409
G.A.Pikina and F.F. Pashchenko / Procedia Computer Science 00 (2019) 000–000
pr in the future. The system of regulation in this case makes anticipatory impact therefore it is possible to
compensate partially an object lag effect, i. e. the lagging behind reaction of object to operations of the actuation device on object. The regulator which operating object according to the forecast of a regulation error we will call predictive regulator. Various laws can specify the transfer function of ideal (unrealizable) prediction Wpr ( p) exp p pr :
polynomial, exponential, exponential-harmoniously, auto regression models, etc. The conducted researches showed that increase the order of predictive algorithm poorly influences the accuracy of predictive regulation systems. We give the preference to the linear forecast. Unlike the exponential or auto regression forecast, it leaves the standard regulator in a class of linear systems. 2. Predictive control in one-loop ACS
The predictive regulator (Fig. 1) consists two parts – actually the regulator with the standard linear law Wr ( p) and the predictive element Pr with transfer function Wpr ( p ) . The predictive element together with a set-devise will transform a difference of the set s(t ) and output current value y (t ) to expect through time pr the error pr (t ) (t pr ) s (t ) y (t pr ).
We will carry out modeling the process of predictive control on the example of one-loop system of temperature regulation for primary steam overheat of a boiler TGMP-314 with PID regulator and object W ( p )
k e
p
(T1 p 1)(T2 p 1)(T3 p 1)
1.75 e 8 p . ( 40 p 1)(44 p 1)(10 p 1)
(1)
Results of calculations the processes of regulation at single step disturbance on the control channel and on a signal of a set presented at Fig. 2 and Table 1.
Fig. 1. Predictive regulator
Fig. 2. The processes for disturbance ( t ) 1( t ) : 1 – ordinary PID-controller; predictive PID-controller: pr 8 sec (2); 12 sec (3); 16 sec (4); 20 sec (5).
G.A.PikinaG.A. and Pikina F.F. Pashchenko / Procedia Computer Science150 00 (2019) (2019) 000–000 et al. / Procedia Computer Science 403–409
4053
Table 1. The quality properties of control processes for disturbance ( t ) 1(t )
pr
0
8
12
16
20
y din
0.399
0.325
0.29
0.261
0.235
I2
7.55
5.43
4.73
4.2
3.8
The graphs obtained with the optimal controller settings: k r 2.2 (kg /sec) / o C; Ti 41.2 sec; Td 23.3 sec . From data of table 1 consecutive reduction of values of a dynamic mistake ydin and integrated square criterion
I 2 in process of increase the prediction time is visible. On this basis, we conclude that by means of predictive algorithm it is possible to increase considerably the quality of regulation, having partially neutralized negative action not only pure delay, but an object capacitor inertia of also. At increase the prediction time to 20 sec a dynamic error of system decreases by 1.7 times for disturbance (t ) and by 6 times for a set-signal s (t ). The integrated square criterion I 2 decreases by 1.5–2 times in comparison with system without prediction. So the prediction time pr 18 20 sec considered as optimum for the system. Procedure of improvement the regulation quality in predictive systems we can continue if to perform optimization of the predictive regulator setup in compliance with the method offered in [4]. Process in system with optimal-tuning predictive PID regulator shows in Fig. 3 (curve 2). In the same place for comparison, process with usual PID regulator gives there (curve 1).
Fig. 3. The processes with ordinary (1) and optimal-tuning predictive (2) PID-controllers.
The value of integrated square criterion I 2 appeared by 4.4 times, the dynamic mistake y din by 1.8 times, and regulation time by 3 times less than the corresponding indicators of usual system with usual PID regulator. Decrease in square criterion four times to equivalently the same decrease in dispersion at low-frequency disturbance, and it means, optimal adjusted predictive regulators allow reduce the deviation range of output practically twice. 3. Control according to the forecast in double-circuit ASR
At regulation of inertial parameters of power unit double-circuit schemes with an additional signal from quickresponse intermediate value z are used. As an example we will consider the regulation of a secondary steam overheat of boiler TGMP-314, and as a system of regulation – standard double-circuit ACS with the differentiator and PI regulator (Fig. 4). Transfer functions of the main and auxiliary channels of object have an appearance:
Wy ( p)
0.421 (49 p 1)
2
e 38 p
C C 0.62(298 p 1) ; Wz ( p ) . % (136 p 1)(41 p 1)(12 p 1) %
4406
G.A.F.F. Pikina et al. / /Procedia 150 (2019) 403–409 G.A.Pikina and Pashchenko ProcediaComputer Computer Science Science 00 (2019) 000–000
Fig. 4. Two-loops ACS with differentiator.
Fig. 5. The regulating processes in two-loop system: (a) object output, (b) movement of regulation devise.
The regulator PI and differentiator D optimum settings are equal k r 12.8 % C ; Ti 10.1 sec; k d 0.262 % C; Td 59 sec .
Processes of regulation at single step desturbance (t ) 1(t ) are presented in Fig. 5. As can see on Fig. 5, the effect from prediction in double-loop system is even stronger, than in one-loop system. It explained by possibility of installation of great values of prediction time . In comparison with usual system (a curve 0) value of a dynamic mistake ydin decreases by 4 times at increasing the prediction time to 100 sec, and integrated square criterion I 2 – almost by 10 times. At the same time at predictive control, the range of movement of regulation devise (t ) considerably decreases and the stability reserve in an external contour increases. Thus, realization of the principle of predictive control in systems with inertial objects and standard linear regulators allows reducing twice the range of an output deviation in one-loop and by 3 times ― in double-circuit systems at simultaneous reduction of regulator movement range. Potential opportunities of improvement of quality of regulation can be used for setup of standard regulators when dynamic characteristics of object are not known, i. e. it isn't possible to execute calculation of optimum settings. 4. Tuning of one-loop system by one parameter
We will carry out modeling of control process on the example of one-loop system for primary overheat of steam temperature with transfer function (1) and predictive PI regulator. We will recognize that transfer function of object to us it isn't known therefore originally we will establish the any settings of PI regulator, based on the most general ideas of object ― approximate time of its transition process (300 sec) and increasing coefficient ( k (1.5 2). Further gradual increase the predictive time we achieve the best regulation quality. We investigate influence of the PI initial settings on achievable quality. We choose initial regulator increasing coefficient from a ratio k r k 1 2, and an integration constant Ti – in (6 10) times less than time of object transition process. Results of control with the indication of optimum predictive time pr , a dynamic mistake ydin
G.A. Pikina et al. / Procedia Computer Science 150 (2019) 403–409
407
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5
Fig. 6. The regulating processes in one-loop system.
and square criterion I 2 present in Table 2. In the last lines the optimum settings for the PI and PID regulators, calculated on transfer function (1), are given. Transition processes of considered in the Table 2 variants for step disturbance show in Fig. 6. Table 2. The tuning results of control system Marks on Fig. 6
kr
Ti
pr
Td
y din
I2
1
0.6
50
100
23.3
0.42
19.9
2
0.8
50
80
23.3
0.4
14
3
0.8
30
70
23.3
0.39
8.2
4
1.25
40
40
23.3
0.41
7.9
PID (opt)
2.2
41
―
23.3
0.4
8
PI (opt)
0.79
61.5
―
―
0.82
55.3
Analyzing processes and table 2 we may give the following conclusions: Predictive PI regulator is much better than usual, even optimal-tuning adjusted (see curves PI and 1–4) Tuning the predictive PI algorithm by one parameter – prediction time – is quite possible (see curves PID, 3, 4 on Fig. 6 and value of quality indicators of table 2) The integration time Ti determined originally has strong impact on the achievable accuracy of stabilization (see curves 1 and 2). Similarly it is possible to adjust and not one-loop systems, changing only one parameter – prediction time [1,2]. 5. Using the prediction at realization of compensators
Transfer functions of ideal compensators in regulation schemes with disturbance compensation or in coherent systems are receiving from a condition of absolute invariance. Often such transfer functions contain a prediction element e p . Here it is possible as well to use the prediction. We investigated the double-coherent standard system of efficiency combustion for boiler BKZ-320. The system includes a PI fuel regulator stabilizing steam pressure before the turbine and PI regulator of air, stabilizing oxygen O2 in the boiler gases. Connection from the fuel to oxygen in boiler decreased compensator K. Ideal compensator has physically impossible properties of accurate predictions. For the practical implementation of it applied two ways: simple drop component predictions or using linear prediction input signal compensator for linear prediction that corresponds to the first two components of the Taylor series decomposition of exhibitors. All three variants of the compensator transfer function in coherent systems of fuel and air supply for boiler are: K id ( p)
9,2 p 9,2 p 9,2 p (1 3 p) e 3 p , K1 ( p ) , K 2 ( p) . 19,96 p 0.935 19,96 p 0,935 19,96 p 0,935
(2)
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Fig. 7. Oxygen content with compensator K1 ( p ) and conventional PI regulators.
Fig. 8. Oxygen content with compensator K 2 ( p ) : 1 – with conventional PI regulators, 2 – with predictive PI regulators.
Fig. 7 shows the process of regulation of oxygen content in flue gases in step variation on fuel in the system with fractional-rational compensator K1 ( p) and conventional PI regulators of fuel and air. To compare Fig. 8 given processes with prognostic compensator K 2 ( p ) and conventional PI regulators (curve 1) and predictive regulators and compensator. If the implementation of fractional-rational compensator allows 7 times to reduce the value of quadratic criterion in normal communication system control, application of fractional-rational compensator with a forecast by lower quadratic criterion in 25 times (from 8.4 to 0.33). If in addition to the compensator to apply the principle of control by the prediction, the value of the quadratic criterion can reduced 60 times (from 8.4 to 0.14) compared with typically in practice systems. 6. Conclusion
Realization of the predictive control principle in systems with inertial objects and standard linear regulators allows to reduce the deviation range of a controlled output (by 2–3 times) with reduction the range of control action and to increase the stability reserve. Using the predictive algorithm as a part of standard regulators does possible control of one- circuit and doublecircuit systems only by one parameter – forecast time, having refused expensive procedure of object identification and optimum parameters calculation of regulation. Owing to simplicity of realization on programmable microprocessor equipment, the predictive algorithms constructed based on typical laws can be very perspective for real control systems of technological processes. Acknowledgements
The work performed with assistance of the Russian scientific fund (project no. 14-19-01772).
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References [1] Pikina GA. Realization of the predictive control principle in automatic systems of regulation. In: Proceedings of the XII All-Russian meeting on control problems. 2014, June 16-19, Moscow, Russia. Moscow: ICS RSA Publishing; 2014. [2] Pikina GA. The predictive control principle and possibility the regulation systems tuning by one parameter. J. New in Russian Electro-energy 2014;3:3-13. [3] Pikina GA, Pashchenko FF, Pashchenko AF. Methods to improve accuracy of typical controllers based on predictive algorithms. In: Proceedings of the IEEE 8th Conference on Industrial Electronics and Applications: 2013 June 19-21, Melbourne, Australia. Melbourne: ICIEA; 2013, p. 613-616. [4] Pikina GA, Kuznetsov MS. Tuning methods for typical predictive control algorithms. J. Thermal Engineering 2012;59:2:154-158.