Multi-region fuzzy logic controller with local PID controllers for U-tube steam generator in nuclear power plant

Transcription

1 Archive of Control Science Volume 25(LXI), 2015 No. 4, page Multi-region fuzzy logic controller with local PID controller for U-tube team generator in nuclear power plant BARTOSZ PUCHALSKI, KAZIMIERZ DUZINKIEWICZ and TOMASZ RUTKOWSKI In the paper, analyi of multi-region fuzzy logic controller with local PID controller for team generator of preurized water reactor (PWR) working in wide range of thermal power change i preented. The U-tube team generator ha a nonlinear dynamic depending on thermal power tranferred from coolant of the primary loop of the PWR plant. Control of water level in the team generator conducted by a traditional PID controller which i deigned for nominal power level of the nuclear reactor operate inufficiently well in wide range of operational condition, epecially at the low thermal power level. Thu the team generator i often controlled manually by operator. Incorrect water level in the team generator may lead to accidental hutdown of the nuclear reactor and conequently financial loe. In the paper a comparion of propoed multi region fuzzy logic controller and traditional PID controller deigned only for nominal condition i preented. The gain of the local PID controller have been derived by olving appropriate optimization tak with the cot function in a form of integrated quared error (ISE) criterion. In both cae, a model of team generator which i readily available in literature wa ued for control algorithm ynthei purpoe. The propoed multi-region fuzzy logic controller and traditional PID controller were ubjected to broad-baed imulation tet in rapid prototyping oftware Matlab/Simulink. Thee tet proved the advantage of multi-region fuzzy logic controller with local PID controller over it traditional counterpart. Key word: nuclear power plant, U-tube team generator, PID control, fuzzy logic, multiregion PID controller, advanced control ytem. 1. Introduction The main objective of team generator control ytem deigned for preuried water nuclear reactor i to maintain water level within the NRL (Narrow Range water The Author are with Gdańk Univerity of Technology, Faculty of Electrical and Control Engineering, G. Narutowicza 11/ Gdańk, Poland. bartoz.puchalki@pg.gda.pl, kazimierz. duzinkiewicz@pg.gda.pl, tomaz.adam.rutkowki@pg.gda.pl Received Revied Thi work wa upported by the National Centre for Reearch and Development under Strategic Reearch Project No. SP/J/10/176450/12. The author wih to expre their thank for the upport.

2 430 B. PUCHALSKI, K. DUZINKIEWICZ, T. RUTKOWSKI Level) by changing flow rate of feed water from team condener and heat exchanger. It i a difficult tak due to [6,12]: the controlled plant i non-linear and it characteritic depend on thermal power tranferred from the primary coolant loop, efficiency of commonly ued water level controller i inufficient due to complex thermal and hydraulic procee taking place in the team generator i.e. riing and falling water level depending on the feed water and the team flow rate (hrink and well phenomena). Inufficient heat tranfer between primary and econdary coolant loop may occur when water level in the team generator goe below minimum lower limit poing a afety hazard to the entire nuclear power tation. On the other hand, water level exceeding the upper limit increae the threat of feed water tranfer to the team turbine potentially cauing it blade to erode [2]. Incorrectly controlled water level in the team generator, either dropping below or exceeding permiible limit may caue frequent unforeeen reactor hutdown entailing unneceary financial penaltie [7]. At the tart-up phae water level controller fail to aure atifactory control performance, therefore in many nuclear power tation water level during the tart-up i controlled manually [7, 12]. Thi problem may be eliminated by deigning a control ytem which would provide atifactory control performance both at the tage of reactor tart-up and alo during daily operation. Outcome of reearch into jut uch a olution, namely multi-region fuzzy logic controller with local PID controller are preented in thi paper. The reearch to date into advanced technique of water level control in team generator come to algorithm baed on gain cheduling control [1,6,12] artificial neural network [4,6,11], fuzzy logic [5,6,11,13], adaptive control [8, 11], Model Predictive Control [9,10] and combination of aforementioned. Compared to above-mentioned, the propoed multi-region fuzzy logic control ytem i baed on PID controller which are commonly ued acro the indutry. The multi-region fuzzy controller conit of everal local PID controller tuned for it operating point and one Takagi-Sugeno fuzzy interface module. That fuzzy inference module combine local control ignal produced by local PID controller into one global control ignal. The main advantage of propoed control algorithm i implicity of implementation in modern digital control device (e.g. programmable controller PLC). Thi tem from the fact that the PID control algorithm i available practically in every programmable controller and fuzzy logic module may be implemented by uing imple IF-THEN function. Fig. 1 preent analyzed in the paper water level control tructure for the team generator [6,9,12].

3 MULTI-REGION FUZZY LOGIC CONTROLLER WITH LOCAL PID CONTROLLERS FOR U-TUBE STEAM GENERATOR IN NUCLEAR POWER PLANT 431 Fig. 1. Steam generator water level control tructure. The following ymbol are ued, repectively: q v (t) team flow rare, q e (t) feed water flow rate, u(t) multi region fuzzy logic controller control ignal, u * (t) valve control ignal, y(t) team generator water level (controlled variable), y ref (t) team generator water level reference value, e(t) team generator water level control error, P(t) nuclear reactor thermal power. The tructure of thi paper i a follow: ec. 2 decribe model of the team generator ued for analyi and ynthei of the propoed multi-region fuzzy logic controller with local PID controller, ec. 3 preent the proce of deigning the multi-region fuzzy logic controller including tuning of the local PID controller a well a the fuzzy logic ued for witching between them, ec. 4 compare the multi-region fuzzy logic controller baed on the local PID controller with traditional, ingle PID controller tuned for two different operation point. In concluion, ec. 5, the paper i briefly ummarized. 2. Steam generator and feed water control valve model A mathematical model of U-tube team generator commonly ued in water level control ytem deign [6,8,12] ha been applied in thi paper alo. Accurate model of a team generator are intricate and complex for ynthei of water level control ytem [2,3]. Therefore linear model of team generator with changeable parameter depending on output thermal power P(t) wa ued. It i the tranfer function with input: Q e () [kg/] flow rate of feed water, Q v () [kg/] flow rate of team, and output Y() [mm] relative water level: where: i the Laplace operator. K1 K 2 Y ( ) = ( Qe( ) Qv( ) ) + 1+ τ 2 K + τ π τ T Q e ( ) (1)

4 432 B. PUCHALSKI, K. DUZINKIEWICZ, T. RUTKOWSKI Parameter K 1, K 2, K 3, τ 1, τ 2, T and Q v depend on thermal power output and are hown in Tab. 1. All variable from equation (1) are poitive. All term ued in model (1) atify the following function [6,7]: K1 ma accumulation in econdary coolant loop of U-tube team generator, thi term integrate flow rate difference (Q e () Q v ()) thu it determine change in water level, K 2 ( 1+ τ ) 2 negative heat effect caued by hrink and well phenomena primarily occurring when either team or feed water change their flow rate at low-power, K 3 τ1 + 4π T + 2τ1 + feed water ocillatory change of water ma caued by inlet Sytem of differential and algebraic equation i derived from model (1) in order to decribe the controlled plant in tate pace. Hence, new tate variable X A, X B, X C are introduced: Y = X + X + X (2) Then, by invere Laplace tranform into time domain: A B C K1 X A( ) = ( Qe( ) Qv( ) ) (3) X K Q Q 2 = B e v 1+ τ 2 K XC Qe τ + 4π T + 2τ + 3 = (4) (5) 1, the tate variable X A and X B are tranformed 1 X = K Q Q (6) A 1 e v / dx A dt ( t) 1 ( e v) = K q t q t (7) 2 B B e v τ2 τ2 ( ) 1 K X X = Q Q / (8) B dx t x t ( e v) 2 2 K2 q t q t B = (9) dt τ τ

5 MULTI-REGION FUZZY LOGIC CONTROLLER WITH LOCAL PID CONTROLLERS FOR U-TUBE STEAM GENERATOR IN NUCLEAR POWER PLANT 433 Next, the ancillary tate variable X D i introduced into tate pace model: ( ) XC τ π T + XC 2τ1 + XC = K3Qe XD ( ) (10) ( ) ( τ1 4π ) X = + (11) C XD T Then, the tate variable X C (10) i tranformed into time domain: ( τ ) X = K Q X 2 X / (12) 1 1 C 3 e C 1 D dx C dt ( t) 1 ( 2τ ) = Kq t x t x t (13) 3 e C 1 D and finally, the ancillary tate variable X D (11) i tranformed into time domain: D C( τ1 4π ) X = X + T (14) x D ( t) dt C ( τ1 4π ) = x t + T (15) The above tranformation give the ytem of firt order differential equation and the ytem of algebraic equation, which denote the team generator model in tate pace a follow: x A() t = K1 qe() t qv() t xb() t K2 x B() t = ( qe() t qv() t ) τ2 τ2 1 x C() t = xc()(2 t τ1 ) xd() t + K3qe() t x D() t = xc()( t τ1 + 4 π T ) y() t = xa() t + xb() t + xc() t (16) Model (16) i linear and non-tationary ince it parameter depend on change in reactor thermal output. Tab. 1 how parameter of the model (16) in five elected operating point which are characterized by thermal power of nuclear reactor. Thu, five linear model of team generator are obtained.

6 434 B. PUCHALSKI, K. DUZINKIEWICZ, T. RUTKOWSKI Tab. 1. Parameter of the team generator model relative to thermal power output [6]. Reactor power [%] K 1 [mm/kg] K 2 [mm /kg] K 3 [mm/kg] τ 1 [] τ 2 [] T [] q v [kg/] In order to derive parameter of the team generator model within interval between elected five operating point (Tab. 1) and extend it utility the linear interpolation i ued. The following interval are ubjected to linear interpolation: interval I 5% < power 15%, interval II 15% < power 30%, interval III 30% < power 50%, interval IV 50% < power 100%. Furthermore, linear extrapolation wa ued for interval from 0% to 5% and above 100% of thermal power. Fig. 2 preent chart howing known and interpolated parameter relative to reactor thermal output for interval I to IV. In Fig. 2 the parameter K 1 wa omitted becaue it i contant acro all interval. Fig. 2. Parameter of the team generator model relative to thermal power tranferred by primary ide.

7 MULTI-REGION FUZZY LOGIC CONTROLLER WITH LOCAL PID CONTROLLERS FOR U-TUBE STEAM GENERATOR IN NUCLEAR POWER PLANT 435 Fig. 3 and 4 preent tep repone of the team generator model both in operating point defined by Tab. 1 a well a in interval between thee point. Parameter of the team generator model in thee interval are derived through linear interpolation preented on Fig. 2. Fig. 3 how repone of the team generator model to unit tep of feed water Q e with zero team flow rate Q v. While, the Fig. 4 how repone of the model to unit tep of team flow rate Q v with zero flow rate of feed water Q e. Familie of tep repone characteritic preented in Fig. 3 and 4 are viualiing the impact of change in the reactor thermal output on the team generator dynamic. Fig. 3. Family of unit tep repone Q e of the team generator model. Fig. 4. Family of unit tep repone Q v of the team generator model.

8 436 B. PUCHALSKI, K. DUZINKIEWICZ, T. RUTKOWSKI The feed water control valve, which i an integral part of the team generator water level control tructure (Fig. 1), i modelled with imple tranfer function in Laplace domain a follow [12]: ( ) Qe 1 = (17) * U + 1 where: Q e () i Laplace tranform of feed water flow rate ignal and U * () i Laplace tranform of valve control ignal. 3. Multi-region fuzzy logic controller with local PID controller 3.1. Controller tructure The tructure of multi-region fuzzy logic controller with local PID controller, preented in thi paper (Fig. 5), i compoed of: five local PID controller; and Takagi- Sugeno fuzzy logic interface module. Fig. 5. Structure of the multi-region fuzzy logic controller with local PID controller. The local PID controller ha a tandard form, which can be decribed in Laplace domain a follow: / PID = K + K + K (18) p i d where: K p, K i and K d are proportional, integral and derivative gain of PID controller, Takagi-Sugeno fuzzy logic interface module i the econd main element of the propoed controller. The main purpoe of thi module i to oftly witch between control ignal of local PID controller and derive ingle control ignal, depending on current thermal power output P(t). Fig. 6 how five memberhip function µ i (P(t)) ued in

9 MULTI-REGION FUZZY LOGIC CONTROLLER WITH LOCAL PID CONTROLLERS FOR U-TUBE STEAM GENERATOR IN NUCLEAR POWER PLANT 437 Takagi-Sugeno fuzzy logic block (one memberhip function for each local PID controller). Propoed fuzzy logic interface i baed on typical triangular and trapezoidal memberhip function atifying the partition of unity condition. In the operating point, where parameter of the team generator are exact (Tab. 1) memberhip function are equal 1. When thermal power i below 5% or exceed 100%, the memberhip function are equal 1 a well. Figure 6. Memberhip function ued in Takagi-Sugeno fuzzy logic interface module. Finally, the global control ignal u(t) generated by the multi-region fuzzy logic controller (Fig. 1 and 5) i combined from local PID controller ignal by Takagi-Sugeno fuzzy logic interface module. It i done with following weighted mean formula (19): µ 5% ( Pt ()) µ 5% () t + µ 15% ( Pt ()) µ 15% () t µ 100% ( P()) t µ 100% () t u() t = µ ( Pt ()) + µ ( Pt ()) µ ( Pt ()) 5% 15% 100% 3.2. Controller tuning procedure The local PID controller parameter are determined baed on the olving of tatic and nonlinear programming problem with ingle, quadratic objective function in the form of ISE criterion (Integral of the Square value of the Error). It i done in order to minimize the team generator water level control error e in appropriate operating point i (20). The team generator operating point are related to the thermal power of nuclear reactor (Tab. 1). Hence, mentioned optimization problem (20) i olved individually for each local PID controller: (19) according to: Kp, Ki, Kd t end t0 i min { f = e( Kp, Ki, Kd ) dt} (20) ISE [0; 0; 0] T [K p ; K i ; K d ] T [10; 10; 10] T 2 i where: f ISE ingle-objective function; e team generator water level control error; t 0, t end beginning and end of the analyzed period of time; t time.

10 438 B. PUCHALSKI, K. DUZINKIEWICZ, T. RUTKOWSKI The olver with hybrid tructure i propoed to olve preented tatic mathematical programming problem (20). The value of objective function i evaluated baed on the numerical imulation [14], in imulation phae, of the team generator water level control tructure with multi-region fuzzy controller (Fig. 1 and Fig. 5) with team generator model (16). Notice, that during imulation phae the reference trajectory wa a tep change from 0 [mm] to +100 [mm] of deired relative water level in team generator. During optimization phae, the optimization problem (20) i olved by SQP (Sequential Quadratic Programming) algorithm [14] and the optimal value of the deciion variable K p, K i, K d are determined. For the cae tudy purpoe, 5 operating point were elected, within wide range of nuclear reactor thermal power. The PID controller parameter obtained via olving optimization problem (20) for elected operating point are preented in the Tab. 2. Tab. 2. Optimal parameter of local PID controller according to ISE criteria in optimization tak (20). Local PID controller 5% 15% 30% 50% 100% K p K i K d [t 0 t end ] [0; 1500] [0; 1000] [0;200] [0;200] [0;100] [K p ; K i ; K d ] 0 [1; 0; 0] [0.0662; 0; 0] [0.13; 0; 0] [0.2972; 0; 0] [0.5287; 0; 0] In Tab. 2, the [K p ; K i ; K d ] 0 denote initial condition for optimization procedure [14] that i local PID controller parameter and t 0, t end denote time range conidered for objective function calculation during optimization problem (20) olving. 4. Simulation tet reult Comparion between PID controller tuned for 100% and 50% of nuclear reactor thermal power and the propoed multi-region fuzzy logic controller wa performed. Tet imulation were done with the Matlab/Simulink [14] environment. Three different tet were propoed to verify controller effectivene: the poitive tep of nuclear reactor thermal power from 0% to 100% (tart time 10 ec.), the negative tep of nuclear reactor thermal power from 100% to 5% (tart time 110 ec.),

11 MULTI-REGION FUZZY LOGIC CONTROLLER WITH LOCAL PID CONTROLLERS FOR U-TUBE STEAM GENERATOR IN NUCLEAR POWER PLANT 439 the thermal power change according to the riing and falling lope of the thermal power curve. Figure (Fig. 8 14),that illutrate obtained imulation reult are preented in each ubparagraph in following order: the reactor power, the water level in the team generator, the feed water flow rate. In all preented figure (Fig. 8 14) the olid line repreent multi-region (PID MR ) controller, dah-dotted line repreent the ingle, PID controller tuned for 100% thermal power output (PID 100% ) and dotted line repreent typical PID controller tuned for 50% thermal power output (PID 50% ). The water level in the team generator wa et to relative level according to reference water level denoted a 0 [mm]. During the tet imulation the following contraint related to control ignal value u(t) and feed water flow rate q e (t) were taken into conideration: [ kg ] u ( t) [ kg ] 500 / 500 / (21) qe ( t) 0 (22) 4.1. Poitive tep change of thermal power from 0% to 100% Reult of poitive tep change tet are hown in Fig.8 and Fig. 9. Fig. 8. Water level in the team generator poitive tep change of thermal power.

12 440 B. PUCHALSKI, K. DUZINKIEWICZ, T. RUTKOWSKI Fig. 9. Flow rate of feed water into team generator poitive tep change of thermal power. The firt tet howed that the PID 100% controller tuned for the 100% of the thermal power output operated identically to the multi-region controller PID MR. At thi point, the multi-region controller generate control ignal by olely uing the PID 100% controller thi action i jutified. The control ytem with PID 50% controller et up for 50% thermal power output ha lower repone and an ocillatory nature compared to the PID MR and PID 100% Negative tep change of thermal power from 100% to 5% Reult of negative tep tet are preented in Fig. 10 and Fig. 11. Fig. 10. Water level in the team generator negative tep change of thermal power.

13 MULTI-REGION FUZZY LOGIC CONTROLLER WITH LOCAL PID CONTROLLERS FOR U-TUBE STEAM GENERATOR IN NUCLEAR POWER PLANT 441 Fig. 11. Flow rate of feed water into team generator negative tep change of thermal power. The econd tet proved that the multi-region controller preent better control quality than it traditional counterpart. PID controller et up for 100% and 50% thermal power output are incapable to maintain the reference water level in the team generator. The multi-region controller PID MR through Takagi-Sugeno fuzzy logic oftly witche between local PID controller depending on the operating condition. In thi way appropriate continuou control ignal i alway derived. The water level in team generator i tabilized to a atifactory level at low power output and conequently equal the reference water level Thermal power change poitive and negative lope of power curve Reult concerning power change at riing and falling lope of power level reference ignal are preented in Fig. 12, 13 and Fig 14. Fig. 12. Thermal power change poitive and negative lope of power curve.

14 442 B. PUCHALSKI, K. DUZINKIEWICZ, T. RUTKOWSKI Fig. 13. Water level in team generator poitive and negative lope of power curve. Fig. 14. Flow rate of feed water into team generator poitive and negative lope of power curve. The third tet proved once more that the multi-region controller i better than it traditional counterpart. The tet wa devied to how controller performance at lowly changing thermal power output a well a to verify whether fuzzy logic baed PID controller witching operate correctly. The multi-region controller howed atifactory control performance during power change and at low thermal power output. Traditional PID controller provide inferior control performance in both cenario. At low power output, the traditional PID controller fail to guarantee good control performance a portrayed already in tet no 2 and confirmed by the third tet.

15 MULTI-REGION FUZZY LOGIC CONTROLLER WITH LOCAL PID CONTROLLERS FOR U-TUBE STEAM GENERATOR IN NUCLEAR POWER PLANT 443 Baed on waveform characteritic of control ignal (feed water fed into the team generator a in Fig. 11 and Fig. 14) obtained in econd and third tet, the multi-region controller again dominate over it traditional counterpart. Control ignal generated by the multi-region controller doe not change abruptly a oppoed to the traditional controller. It i a welcomed effect for econdary loop element e.g. feed water pump and feed water piping ytem. During abrupt flow rate change thoe element are expoed to ubtantial load and may potentially utain damage over hort period of operation. 5. Summary The multi-region controller deigned for controlling feed water flow rate into the team generator ha many advantage. It i capable of tabiliing water level in the team generator at the reference level acro a wide operating range of thermal power output whilt maintaining atifactory control performance a oppoed to traditional PID controller et up for a pecific deign point (100% and 50% reactor power). The multi-region controller generate better characteritic of the control variable in contrat to a typical controller. The generated control ignal i free of abrupt flow rate change expanding expected lifetime of econdary loop ytem element. The operating principle, tructure and ynthei of the multi-region fuzzy logic controller deigned for control of feed water in the team generator in order to tabilie water level at pre-determined reference level wa preented in thi paper. Baed on imulation tet, the multi-region controller proved to generate better control ignal (feed water flow rate) than the traditional controller and to obtain overall better control ytem performance. Traditional PID controller or manual control commonly ued in nuclear power tation today may be replaced by a imple to implement multi-region fuzzy logic controller preented in thi paper. Reference [1] G.R. Anarifar, H.A. Talebi and H. Davilu: Adaptive etimator-baed dynamic liding mode control for the water level of nuclear team generator. Progre in Nuclear Energy, 56 (2012), [2] R.N. Banavar and U.V. Dehpande: Robut controller deign for a nuclear power plant uing H optimization. Proc. of the 35th IEEE Conf. on Deciion and Control, 4 (1996), [3] J. Doboz, K. Duzinkiewicz, A. Michalak and K. Wąek: Technical report: Static and Dynamic Simulation Model of Steam Generator of VVER-440 Nuclear Reactor. Gdańk Univerity of Technology, Intitute of Electroenergetic and Automatic, Gdańk, 1989, (in Polih).

16 444 B. PUCHALSKI, K. DUZINKIEWICZ, T. RUTKOWSKI [4] A. Fakhrazari and M. Borouhaki: Adaptive critic-baed neurofuzzy controller for the team generator water level. IEEE Tran. on Nuclear Science, 55(3), (2008), [5] Gee Yong Park and Poong Hyun Seong: Application of a fuzzy learning algorithm to nuclear team generator level control. Annal of Nuclear Energy, 22(3-4), (1995), [6] H. Habibiyan, S Setayehi and H. Arab-Alibeik: A fuzzy-gain-cheduled neural controller for nuclear team generator. Annal of Nuclear Energy, 31(15), (2004), [7] A.M. Haanul Baher and J. March-Leuba: Report No.: ORNL/TM-2001/166 Development of a Robut Model-Baed Water Level Controller for U-Tube Steam Generator. Oak Ridge National Laboratory, Oak Ridge, Tenneee, [8] E. Irving and C. Bihoreaux: Adaptive control of non-minimum phae ytem Application to the P.W.R. team generator water level control. 19th IEEE Conf. on Deciion and Control, including The Symp. on Adaptive Procee, (1980), [9] Ke Hu and Jingqi Yuan: Multi-model predictive control method for nuclear team generator water level. Energy Converion and Management, 49(5), (2008), [10] M.V. Kothare, B. Mettler, M. Morari, P. Bendotti and C-M. Falinower: Linear parameter varying model predictive control for team generator level control. Computer & Chemical Engineering, 21 (1997), Supplement, [11] S.R. Munainghe, Min-Soeng Kim and Ju-Jang Lee: Adaptive neurofuzzy controller to regulate UTSG water level in nuclear power plant. IEEE Tran. on Nuclear Science, 52(1), (2005), [12] Myung-Ki Kim, Myoung Ho Shin and Myung Jin Chung: A gain-cheduled L 2 control to nuclear team generator water level. Annal of Nuclear Energy, 26(10), (1999), [13] Shou-Yu Cheng and Xin-Kai Liu: A new control trategy baed on fuzzy-pid and water ma inventory for Nuclear Steam Generator Int. Conf. on Machine Learning and Cybernetic (ICMLC), (2011), [14]