Energy 162 (2018) 910e917 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Hierarchical Takagi-Sugeno fuzzy hyperbolic tangent static model control for a circulating ﬂuidized bed boiler thermal power unit Xusheng Zhuo a, *, Chun Lou b, Huaichun Zhou c, Jinxuan Zhuo a, Peifang Fu b a Hubei Research Center of Video Image and High Deﬁnition Projection Technology, School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China b State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China c Key Laboratory of Condition Monitering and Control for Power Equipment, Minstry of Education of China, School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 071003, China a r t i c l e i n f o a b s t r a c t Article history: Received 8 May 2018 Received in revised form 5 July 2018 Accepted 1 August 2018 Available online 4 August 2018 This paper proposed a novel two layer hierarchical Takagi-Sugeno fuzzy hyperbolic tangent static model control scheme for a circulating ﬂuidized bed (CFB) boiler thermal power unit to cope with the complex nonlinearity and large inertia performance which make its existing PI type load-fuel control loop not functioning normally. In the upper layer, a reference governor with Takagi-Sugeno fuzzy hyperbolic tangent static model control algorithm was developed to yield a compensation for the external load command of the existing PI type load-fuel control loop in the lower layer. By constructing a new quadratic integration Lyapunov function, the stability condition of proposed control system was derived. While implemented in the decentralized control system (DCS) of CFB boiler, the reference governor was constructed and adopted the cubic variables hyperbolic tangent function algorithm which can oppose effectively the nonlinearity and large inertia performance. The experimental results shown that the proposed hierarchical fuzzy hyperbolic tangent static model control scheme can improve the control performance of the PI type load-fuel control system obviously, weaken the ﬂuctuation in the main steam pressure and bed temperature apparently and make the controlled system more stable. © 2018 Elsevier Ltd. All rights reserved. Keywords: Circulating ﬂuidized bed boiler Hierarchical control Reference governor T-S fuzzy hyperbolic tangent static model Quadratic integration Lyapunov function 1. Introduction Circulating ﬂuidized bed (CFB) combustion technology, with excellent fuel ﬂexibility and cost-effective emission control, has been regarded as the best way for burning the fuels such as the low quality coal, washing coal waste, petcock and other solid combustible wastes [1e3]. Since coal is a major fuel in the thermal power plants in China and this situation unchanged in the near future, the CFB coal burning technology has been researched and developed most actively for half century . Today, over 10% of all coal-ﬁred generate units in China are the CFB boiler units , more than 370 CFB boilers with unit capacity over 410 t/h were in operation and the total installation capacity was up to 70 GW . However, extreme complexity, such as interactions between the gas and solid phases, chaotic nature of the heat transferred between the coal particles and water wall, and chemical reactions to * Corresponding author. E-mail addresses: Zhuo@wit.edu.cn, firstname.lastname@example.org (X. Zhuo). https://doi.org/10.1016/j.energy.2018.08.010 0360-5442/© 2018 Elsevier Ltd. All rights reserved. produce release of volatile materials [1e3,6,7], make it difﬁcult for the researchers and engineers to understand completely the dynamic mechanism of CFB boilers. Therefore, the modeling and control still remain be one of the most challenging tasks [6e8,17]. Over the past two decades, many efforts have been taken to address these issues. The intelligence techniques such as fuzzy logic control and neural network etc had been adopted to deal with the nonlinearity or complexity of CFB boilers [9e14]. Other advance control strategies such as linear matrix inequalities (LMI) method  and H∞ robust control  had been reported to control effectively the bed temperature of CFB boilers. A linear parameter varying (LPV) model based model predictive control (MPC) method was reported to can yield a better control effect for an industrial CFB boiler . Even so, for a real CFB boiler thermal power unit, its control trouble still remain be unsolved well. The main reasons are that, on the one hand, many advance control algorithms like the above-mention were unable to be well integrated into the decentralized control system (DCS) of CFB boiler units. On the other hand, the power plant entrepreneurs are still reluctant to replace their existing PID-type (proportion and integration and differentiation) X. Zhuo et al. / Energy 162 (2018) 910e917 controllers because of needing a great deal investment. In the situations, other practical alternative schemes should be selected. The hierarchical control structures [18e21] and/or reference governor approaches [22e26] are the available schemes which both can make the existing traditional control structure unchanged and improve the control performance. In the power industries, the hierarchical control structure integrated with the MPC (model predictive control) technologies can yield the optimal operating trajectories for the traditional control system of a oil-ﬁred boilerturbine unit  or to achieve dynamic optimal control performance and guarantee the system stability . Like the hierarchical control technologies, the reference governor approaches were also the frameworks which can integrate with MPC technology  or intelligence scheme  to produce the optimal operating reference signals for the control system of the oil-ﬁred boiler units to improve their economical and control performances. However, compared with an oil-ﬁred boiler or pulverized coal ﬁred boiler, a CFB boiler has the different characteristics: 1. more difﬁcult to develop the mechanism model; 2. its combustion process response is much more slower, in other words, it is a large inertia process; 3. signiﬁcant difference in combustion mode and lower temperature ﬁring. Thus, it was difﬁcult to keep the original pattern ‘transplant’ above-mentioned hierarchical control technologies or reference governor approaches into the CFB boiler thermal power units. In this paper, a two layers hierarchical control structure based on an existing PI-type fuel-load control loop of the CFB boiler was developed. A reference governor in the upper layer was designed to supervise the CFB boiler's some important state variables and to yield timely the modiﬁed instruction signal fed to the PI controller loop in the lower layer. Because the fuzzy methods are suitable for solving the non-modeling problems [27,28] and fuzzy hyperbolic model (FHM) method can express a complex nonlinear process [29,30], a Takagi-Sugeno fuzzy hyperbolic static model (FHSM) method was selected as its supervised algorithm in the reference governor, so that the upper layer can yield theoretically a right compensation signal for the external load command to ask the fuel feed rate for CFB boiler under any operating conditions. Thus, the complex nonlinearity, large inertia performance in CFB boiler will be addressed. The remaining sections of this paper are organized as follows: First, a 480t/h coal fried CFB boiler and its control problems were described, and then a hierarchical structure on CFB boiler unit's load control loop was designed and the system stability was analyzed. Next, the supervisor's algorithm was implemented in the DCS of CFB boiler and the system regulations were shown. Fourthly, the experiment results were presented. Finally, some conclusions were drawn. 911 nozzles in the bottom of the furnace, and two secondary air fans to provide combustion air to the middle of the furnace. Its schematic diagram was shown in Fig. 1. Fuels of the CFB boiler were the mixtures such as coal, coal refuses and coal washing mud etc, and its low caloriﬁc value and high moisture in the mixtures led to a very long settling time in the transition process of parameters change. In other words, the CFB combustion was a nonlinear and large inertia process, which was backed up by an actual data gathered from a test in Fig. 2. In the test, when the fuel feed rate was step up form 74 to 90 t/h (tons per hour) by manual operation in 500 s, the process response data of the output power, main steam pressure, bed temperature, ﬂuidized air ﬂow rate and oxygen content were recorded and drawn: For the output power, it took about 1220 s to approach to the last stable point while the fuel feed rate being risen up. And for the main steam pressure and bed temperature, it was about 1300 s and 1100 s respectively. In addition, the ﬂuidized air rate was increased about 11000 Nm3/h (normal cubic meters per hour) to match the increment of the fuel feed rate which caused the oxygen content in ﬂue gas to decrease about 2.5%. Nevertheless, both the ﬂuidized air rate and oxygen content return almost to their previous values while the output power closed to the new stable point. 2.2. CFB boiler control problems For the complexity such as nonlinearity and large inertia performance etc in the combustion process, the existing PID-type control loops in the DCS of the CFB boiler were unable to do well Fig. 1. Schematic diagram of CFB boiler. 2. CFB boiler and control problems 2.1. CFB boiler description The considered CFB boiler was a 480t/h coal-ﬁred drum-type boiler in the thermal power plant of Ruiping in Henan Province, China. Such boilers were widely utilized to supply heating and electric power in China. Its speciﬁed steam mass ﬂow rate is 480t/h at a pressure of 13.7Mpa and in the bed temperature ranges from 800 C to 950 C. It included three key components: a membrane water-wall furnace, two steam-cooled cyclones and a heat recovery area housing the primary and secondary super-heater, re-heater and economizer. There are six fuel silos and three limestone silos positioned along the boiler front wall with a chain feeder under each one, which are controlled to drop the fuel and limestone mixtures onto a chain convey and to deliver the coal to drop chute/ screw feeder. There are two primary air fans to supply air from Fig. 2. Response to coal feed rate step up from 74 to 90 t/h. 912 X. Zhuo et al. / Energy 162 (2018) 910e917 as one would wish. In particular, the effect of the fuel-load control system was dissatisfactory: the serious ﬂuctuations of the main steam pressure and bed temperature of the CFB boiler can not be depressed while its output power was regulated into a neighbourhood of some set-points. Shown in Fig. 3. The ﬂuctuant amplitude values of the main steam pressure and bed temperature exceeded 3.5Mpa and 46 C respectively, which had seriously affected the lifetime of the CFB boiler. In addition, some factors such as the variety of fuel and time varying parameters etc would make this PID controller loop be out of step with the coal feed rate required or even produce a reverse regulation. This would certainly lead to the sharpened ﬂuctuation of the main steam pressure and bed temperature, and ﬁnally the skilled technicians were asked to intervene and switch the operation to manual mode to avoid the system collapse. That was shown as Fig. 4. Therefore, the CFB boiler was basically operated under the PID controller loops with manual auxiliary mode. 3. Hierarchical structure on CFB boiler unit's load control loop In this section, a two layers hierarchical structure on the loadfuel control loop was presented to improve the control performance of the CFB boiler thermal power unit. Upper layer was supervisory level and lower layer was regulation level. Shown as Fig. 5. In the supervisory level, a reference governor as supervisor was designed to acquired real-time values of the CFB boiler's main steam pressure and bed temperature and produce a compensation signal for the external load command of the lower layer. Motivated by the ideas in the literature [29e32], a Takagi-Sugeno fuzzy hyperbolic tangent static model algorithm for the reference governor Fig. 5. The hierarchical control structure on CFB boiler unit's PI type fuel-load control loop. was developed to cope with the complex nonlinearity and large inertia performance in the dynamic response of CFB boiler. The regulation level was the existing load-fuel control loop with a traditional PI controller which can function only under the manual auxiliary. 3.1. Hierarchical structure expression 1. Supervisor's algorithm: a T-S fuzzy hyperbolic tangent static model was selected as following: The i-th rule: If z1 isFi1 , and … zg isFig . Then ri ðtÞ ¼ ci1 tanhðk1 x1 ðtÞÞ þ / þ cin tanhðkn xn ðtÞÞ i ¼ 1; 2; /; s (1) Herez1 /zg are the known premise variables which don't depend on the inputxðtÞ, Fij is the fuzzy set, ri ðtÞ2Ris the output variable of the supervisor, xðtÞ2Rn is the input vector andtanhðki xi ðtÞÞ ¼ eki xi ðtÞ eki xi ðtÞ , eki xi ðtÞ þeki xi ðtÞ cij is a coefﬁcient. By using the fuzzy inference method with a singleton fuzziﬁcation and product inference and center average defuzziﬁcation, the overall T-S hyperbolic tangent static model can be written as: rðtÞ ¼ s X wi ,ri ðtÞ ¼ H,tanhðkxðtÞÞ (2) i¼1 m Herewi ¼ Ps i ðzÞ , mi ðzÞ ¼ i¼1 Fig. 3. Control effect of CFB boiler's fuel-load loop with PI controller. mi ðzÞ g Y F~ij ðzÞ, F~ij ðzÞis the membership func- j¼1 P tion of fuzzy set Fij . His a 1 nmatric and H ¼ ½ si¼1 wi ,ci1 ; /; Ps tanhðkxðtÞÞ2Rn1 and tanhðkxðtÞÞ ¼ i¼1 wi ,cin , ½tanhðk1 ,x1 ðtÞÞ; /; tanhðkn ,xn ðtÞÞT , ki is a positive constant. 2. PI controller's expression Zt uðtÞ ¼ dP ,eðtÞ þ dI , eðtÞdt (3) 0 Here uðtÞ2Ris the output of PI controller, dP anddI are the proportion coefﬁcient and integration coefﬁcient respectively. The error eðtÞ ¼ Nref NE ðtÞ þ rðtÞ, Nref is the external load command andNE ðtÞis the output power of CFB boiler generation unit. 3. Pant's expression Fig. 4. A case that PID control loop was out of step with fuel required. The plant refers to a CFB boiler unit which has strong X. Zhuo et al. / Energy 162 (2018) 910e917 nonlinearity and complexity, in the section, we use a fuzzy hyperbolic tangent dynamic model describe it as follows: _ xðtÞ ¼ A,tanhðkxðtÞÞ þ B,uðtÞ (4) Here xðtÞ ¼ ½x1 ðtÞ; /; xn ðtÞ T , tanhðkxðtÞÞ ¼ ½tanhðk1 x1 ðtÞ Þ; /; 913 loop system (6) is globally asymptotically stable. Proof: Pn R t 2 Let VðtÞ ¼ i¼1 ð 0 tanhðki xi ðtÞÞdtÞ be a quadratic Lyapunov function andxi denotesxi ðtÞ for a brief description, then the time derivative of VðtÞ was: tanhðkn xn ðtÞ Þ T , A2Rnn , B2Rn1 , uðtÞ2R. _ VðtÞ ¼ 2, n X 0 ki ,sech ðki xi Þ,tanhðki xi Þ,@ i¼1 3.2. Stability analysis Zt 2 1 tanhðki xi Þdt A,x_i 0 (7) For the two layers hierarchical control system, when the output powerNE ðtÞ of CFB boiler unit was equal to its load commandNref , i.e. Nref ¼ NE ðtÞ, the output uðtÞ of PI controller's expression (3) was rewritten as: the Rt rðtÞ dt (5) tanhðxðtÞÞ dt 0 tanhðk1 x1 Þdt; /; tanhðkn xn Þ, Rt T tanhðkn xn Þdt and 2 _ can be the matrix PðxÞ ¼ diagðki ,sech ðki xi ÞÞnn , then VðtÞ expressed: 0 Zt ¼ dP H,tanhðxðtÞÞ þ dI H, XðxÞ ¼ ½tanhðk1 x1 Þ, Zt uðtÞ ¼ dP ,rðtÞ þ dI , Let vector- 0 _ VðtÞ ¼ XT ðxÞPðxÞx_ þ x_ T PðxÞXðxÞ (8) Substituting (6) into (8), we get: 0 Rt Here 0 tanhðkxðtÞÞdt ¼ Rt Rt T ½ 0 tanhðk1 x1 ðtÞÞdt; /; 0 tanhðkn xn ðtÞÞdt . Substituting (5) into (4), thus the overall closed loop system can be expressed as: _ xðtÞ ¼ ðA þ dP ,BHÞtanhðxðtÞÞ þ dI ,BH 2 _ ¼ XT ðxÞPðxÞ4ðA þ dP ,BHÞtanhðkxÞ þ dI ,BH VðtÞ Zt 0 2 þ4ðA þ dP ,BHÞtanhðkxÞ þ dI ,BH Zt Zt 3 tanhðkxÞdt 5 3T tanhðkxÞdt 5 PðxÞXðxÞ 0 tanhðxðtÞÞ dt (6) (9) 0 By transforming (9), we get: The asymptotic stability condition of this closed loop system can be summarized as follows: 8 0 1 > > > B C > > > B C > < B C 1 B C T _ VðtÞ ¼ X ðxÞ PðxÞðA þ dP ,BHÞ,diag BZ t C > B C > > B C tanhðk x Þdt > i i > @ A > 0 > : 0 B B B B þdiag BZ B B @ 0 nn 9 > > > > > > > = T T T , A þ dP ,H B PðxÞ XðxÞ > > > > > > > ; 1 C C C 1 C C t C tanhðki xi Þdt C A 1 þXT ðxÞ dI ,PðxÞBH,diag tanhðki xi Þ nn þ diag nn 1 tanhðki xi Þ nn Theorem: for the nonlinear system (4) with a PI control (5), if there exists a diagonal and positive deﬁnite matrixP > 0such as LMIPðxÞQ þ Q T PT ðxÞ < 0is satisﬁed, here matrixQ ¼ ðA þ dP ,BHÞ,L1 ðxÞ þ dI ,BH,L2 ðxÞ, dP and dI are the proportion and integration coefﬁcients of the PI controller respectively, L1 ðxÞ ¼ ! 1 1 R , L2 ðxÞ ¼ diag tanhðk , then the closed diag t xÞ 0 tanhðki xi Þdt i i nn nn ,dI ,HT BT PðxÞ XðxÞ 0 1 B C B C 1 LetL1 ðxÞ ¼ LT1 ðxÞ ¼ diagBR t C @ 0 tanhðki xi ÞdtA diag 1 tanhðki xi Þ , L2 ðxÞ ¼ LT2 ðxÞ ¼ nn _ , then VðtÞ can be expressed as: nn 914 X. Zhuo et al. / Energy 162 (2018) 910e917 o _ VðtÞ ¼ XT ðxÞfPðxÞ,ðA þ dP ,BHÞL1 ðxÞ þ L1 ðxÞ, AT þ dP ,HT BT PðxÞ XðxÞ o þXT ðxÞfdI ,PðxÞBHL2 ðxÞ þ L2 ðxÞ,dI ,HT BT PðxÞ XðxÞ T þ dP ,BHÞ,L 1 ðxÞ þ dI ,BH,L i 2 ðxÞ o h ¼ X ðxÞfPðxÞ½ðA þ LT1 ðxÞ, AT þ dP ,HT BT þ dI ,LT2 ðxÞ,HT BT PðxÞ XðxÞ trix PðxÞ is a diagonal and positive deﬁne matrix, i.e. PðxÞ ¼ that the derivativesp_ T ðtÞandT_ b ðtÞmade the another contribution torðtÞ. Hence, the algorithm of the reference governor can be expressed in (12) and its structure was shown in Fig. 7. PT ðxÞ > 0. ( Since PðxÞ ¼ diag If we ki sech2 ðki xi Þ let and ki > 0, sech2 ðki xi Þ > 0, mann matrixQ ¼ the ðA þ _ dI ,BH,L2 ðxÞ, then VðtÞ can be expressed as: dP ,BHÞ,L1 ðxÞ þ n o _ VðtÞ ¼ XT ðxÞ PðxÞQ þ Q T PT ðxÞ XðxÞ (10) roffs ðtÞ ¼ a1 , tanh k1 ,ðpT pT0 Þ3 þ b1 ,tanh k3 ,ðTb Tb0 Þ3 rdiff ðtÞ ¼ a2 , tanh k2 ,ðp_ T Þ3 þ b1 ,tanh k4 ,ðT_ b Þ3 (12) When the linear matrix inequality PðxÞQ þ Q T PT ðxÞ < 0 is _ < 0. It completes the proof. satisﬁed, then VðtÞ , P P P Here a1 ¼ si¼1 wi ci1 ; a2 ¼ si¼1 wi ci2 ; b1 ¼ si¼1 wi ci3 Ps 3.3. Reference governor construction in the DCS b2 ¼ wi ,ri ðtÞ i¼1 s X b To describe how to realize the system regulation by the reference governor in supervisory level. We deﬁne the two generalized variables: JðtÞ and vJðtÞ. Let JðtÞ ¼ tanh k1 ,ðpT pT0 Þ3 þ b # " s X tanh k1 $ðpT pT0 Þ3 wi ci1 wi ci2 wi ci3 ¼ þ 3 i¼1 tanh k2 $ðp_ T Þ i¼1 i¼1 # " #" " s s s X X tanh k1 $ðpT pT0 Þ3 P þ wi ci1 wi ci3 wi ci2 ¼ 3 i¼1 tanh k3 $ðTb Tb0 Þ i¼1 i¼1 ¼ roffs ðtÞ þ rdiff ðtÞ " i¼1 wi ci2 4. System regulation tiveT_ b ðtÞ, the expression (2) can be written as follows: s X i¼1 wi ci4 b Letx1 ðtÞ ¼ ðpT ðtÞ pT0 Þ3 denotes the cube of deviation of main 3 _ denotes its cube of derivasteam pressure andx2 ðtÞ ¼ ðpðtÞÞ 3 tivep_ T ðtÞ; x3 ðtÞ ¼ ðTb ðtÞ Tb0 Þ denotes the cube of deviation of bed temperature and x ðtÞ ¼ ðT_ ðtÞÞ3 denotes its cube of deriva- rðtÞ ¼ , Ps Ps ; Remark: in expression (12), the coefﬁcientsa1 anda2 were negative values so that the compensation signalsroffs ðtÞandrdiff ðtÞwere opposite to the change direction of the pressurepT ðtÞand temperatureTb ðtÞ. the coefﬁcients b1 2½ 0; 1 and b2 2½ 0; 1 were the weight factors which describe the proportions occupied byT ðtÞandT_ ðtÞ. In this subsection, a reference governor was constructed so that the supervisor's algorithm (2) can be implemented in the DCS of CFB boiler. To cope with the complex nonlinearity and large inertia performance in CFB boiler effectively, the hyperbolic tangent function of cubic state variables were selected as supervisor's algorithm. This kind functions can be expressed by y ¼ tanhðk,x3 Þ shown in Fig. 6. 4 i¼1 wi ci1 s P #" # tanh k3 $ðTb Tb0 Þ3 wi ci4 i¼1 tanh k4 $ðT_ b Þ3 # #" s tanh k2 $ðp_ T Þ3 P wi ci4 i¼1 tanh k4 $ðT_ b Þ3 s P #" (11) b1 ,tanh k3 ,ðTb Tb0 Þ3 , which integrate the main steam pressure " In " expression (11), roffs ðtÞ ¼ s X wi ci1 s P # wi ci3 i¼1 i¼1 # tanh k1 ,ðpT pT0 Þ3 described that the errors pT ðtÞ pT0 and tanh k3 ,ðTb Tb0 Þ3 Tb ðtÞ Tb0 made the contribution to the compensation signal rðtÞ, # " s #" s X tanh k2 ,ðp_ T Þ3 P described wi ci2 wi ci4 and rdiff ðtÞ ¼ i¼1 tanh k4 ,ðT_ b Þ3 i¼1 errorpT ðtÞ pT0 with the bed temperature error Tb ðtÞ Tb0 to reﬂect the drift away from their set points. Let vJðtÞ ¼ tanh k2 ,ðp_ T Þ3 þ b2 ,tanh k4 ,ðT_ b Þ3 , which integrate the one order derivativep_ T ðtÞ of main steam pressure with the one order derivativeT_ b ðtÞ of bed temperature to reﬂect their change directions. Then, the system regulation can be classiﬁed into ﬁve cases, and each case corresponding to one regulation region of the reference governor in the supervisor level. The ﬁve regulation regions were numbered as A, B, C, D and O region and shown in Fig. 8. X. Zhuo et al. / Energy 162 (2018) 910e917 915 In the ﬁve cases of system regulation, Case 1 corresponding to O Region and Case 2 corresponding to A Region and Case 3 corresponding to B Region and Case 4 corresponding to C Region and Case 5 corresponding to D Region. The regulation process as follows: Fig. 6. Curve of y ¼ tanhðk,x3 Þ with k ¼ 0:1 Fig. 7. Block diagram of reference governor in supervisory level. Fig. 8. Regulation regions of reference governor in supervisory level. Case 1: when the regulation of reference governor in the supervisory level was located in O Region, the generalized variables JðtÞ/0 and vJðtÞ/0. This shown that the main steam pressurepT ðtÞ and bed temperatureTb ðtÞ almost approach to their set-points respectively, i.e. pT ðtÞypT0 and Tb ðtÞyTb0 , meanwhile, their one order derivatives were very small, almost zero, i.e. p_ T ðtÞy0and T_ b ðtÞy0. According to the expression (11) or (12) the compensation signal rðtÞy0. Hence, the coal feed rate of CFB boiler will remain almost unchanged. Case 2: when the regulation of reference governor was located in A Region, the generalized variables JðtÞ < 0 and vJðtÞ 0. This shown that the main steam pressurepT ðtÞ and/or bed temperatureTb ðtÞ were less than their set-point values respectively, i.e. pT ðtÞ < pT0 and/or Tb ðtÞ < Tb0, and their one order derivative were greater than or equal to zero. i.e.p_ T ðtÞ 0 and/or T_ b ðtÞ 0. According to the expression (11) or (12), the compensation signalrðtÞin A Region will make the coal feed control signal changed appropriately to drive the main steam pressure pT ðtÞand/or bed temperature Tb ðtÞto approach to their set-points at an appropriate speed. The regulation process was shown in Fig. 9. Case 3: when the regulation of reference governor was located in B Region, the generalized variables JðtÞ < 0 and vJðtÞ 0. This shown that the main steam pressurepT ðtÞ and/or bed temperatureTb ðtÞ were less than their set-point values respectively, i.e. pT ðtÞ < pT0 and/or Tb ðtÞ < Tb0, and their one order derivative were less than or equal to zero. i.e.p_ T ðtÞ 0 and/or T_ b ðtÞ 0. According to the expression (11) or (12), the compensation signalrðtÞin B Region will make the coal feed control signal increased rapidly to reverse the variables' tend further away from their set-points, and to drive them to approach to their set-points at an appropriate speed. The regulation process was shown in Fig. 10. Case 4: when the regulation of reference governor was located in C Region, the generalized variables JðtÞ > 0 and vJðtÞ 0. This shown that the main steam pressurepT ðtÞ and/or bed temperature Tb(t) were greater than their set-point values respectively, i.e. pT(t) >pT0 and/or Tb(t) >Tb0, and their one order derivative were less than or equal to zero. i.e. dpT(t)/dt 0 and/or dTb(t)/dt ≤0. According to the expression (11) or (12), the compensation signal r(t) in C Region will make the coal feed control signal changed appropriately to drive the main steam Fig. 9. Curve of main steam pressure (or bed temperature) in Case 2. 916 X. Zhuo et al. / Energy 162 (2018) 910e917 Fig. 10. Curve of main steam pressure (or bed temperature) in Case 3. pressure pT(t) and/or bed temperature Tb(t) to approach to their set-points at an appropriate speed. The regulation process was shown in Fig. 11. Case 5: when the regulation of reference governor was located in D Region, the generalized variables JðtÞ > 0 and vJðtÞ 0. This shown that the main steam pressure pT ðtÞ and/or bed temperatureTb ðtÞ were greater than their set-point values respectively, i.e. pT ðtÞ > pT0 and/or Tb ðtÞ > Tb0, and their one order derivative were less than or equal to zero. i.e. p_ T ðtÞ 0 and/ or T_ b ðtÞ 0. According to the expression (11) or (12), the compensation signal rðtÞ. in D Region will make the coal feed control signal decreased rapidly to reverse the variables' tend further away from their set-points, and to drive them to approach to their set-points at an appropriate speed. The regulation process was shown in Fig. 12. 5. Experiment results To examine the practicability of the proposed hierarchical control structure for the PID control loop of CFB boiler unit, as the supervisor, the reference governor with a T-S fuzzy hyperbolic static model (T-S FHSM) algorithm was implemented on the DCS of CFB boiler unit in Ruiping thermal power plant. The parameters' values in reference governor were decided as follows: According to the actual data, the deviation value of main steam pressure pT ðtÞ pT0 2½ 2:0; þ2:0 .Mpa and the derivative p_ T ðtÞ2½ 0:0006; þ0:0006 . Mpa/sec, and the deviation value of bed temperature Tb ðtÞ Tb0 2½ 50; þ50 . Centigrade and the derivative T_ ðtÞ2½ 0:01; þ0:01 . Centigrade/sec. If these regions b were translated into the interval ½ 3:0; þ3:0 , the values of parameters will be decided as a1 ¼ a2 ¼ 0:02., b1 ¼ b2 ¼ 0:3 and k1 ¼ k2 ¼ k3 ¼ k4 ¼ 0:1. Fig. 11. Curve of main steam pressure (or bed temperature)in Case 4. Fig. 12. Curve of main steam pressure (or temperature) in Case 5. The veriﬁcation experiments were conducted in two respects: (1). Test1 was to compare the control performances between the existing PI control loop with manual auxiliary and the proposed hierarchical T-S FHSM control scheme. (2). Test2 was to evaluate the control effect of the proposed hierarchical T-S FHSM control scheme in a long period operation. Test1 was a comparison experiment in which the CFB boiler ﬁrst was operated more than 2 h under the existing PI type load-fuel control loop with manual auxiliary, then switched to the proposed hierarchical T-S FHSM control mode. The result was shown in Fig. 13. Under the existing PI control system with manual auxiliary mode, the main steam pressurepT ðtÞ was in the range 8.75e10.0 Mpa and its maximum peak-valley deviation DpTmax ¼ pTmax pTmin was 1.25 Mpa; and the bed temperature Tb ðtÞwas in the range 854e887 C and its maximum peak-valley deviation wasDTbmax ¼ 330 C. However, while the CFB boiler was controlled by the proposed hierarchical T-S FHSM control system, the pressurepT ðtÞwas in the range 9.1e9.6Mpa and its maximum peak-valley deviation wasDpTmax ¼ 0:5Mpa; the bed temperature Tb ðtÞwas in the range 865e878 C and its maximum peak-valley deviation wasDTbmax ¼ 130 C. By comparison, the proposed hierarchical T-S FHSM control system can improve the control performance of the load-fuel control loop in CFB boiler obviously. Test2 was an evaluation experiment in which the CFB boiler was operated more than 12 h under the proposed hierarchical T-S FHSM control system. The result was shown in Fig. 14. During the experiment, the output power was kept around 107 MW. For the main steam pressurepT ðtÞand bed temperature Tb ðtÞ, their maximum peak-valley deviations were DpTmax ¼ 2:4Mpaand Fig. 13. Comparison of PI control with manual auxiliary mode vs. hierarchical T-S FHSM control mode. X. Zhuo et al. / Energy 162 (2018) 910e917 917 References Fig. 14. Operation of CFB boiler unit under hierarchical T-S FHSM control mode. DTbmax ¼ 550 C respectively in the ﬁrst 2 h, but in the next 10 h, the maximum peak-valley deviations were DpTmax ¼ 1:3Mpa and DTbmax ¼ 390 C respectively. Compared with the result in Fig. 3 which was controlled by the existing PI control loop with manual auxiliary, the proposed hierarchical T-S FHSM control scheme can weaken the ﬂuctuation of the main steam pressure and bed temperature apparently in a long period and make the controlled system more stable. In addition, the proposed control system can also bear some short-time coal chocking phenomenon in the operation. 6. Conclusions In this paper, we proposed a two layers hierarchical control structure for the existing PID type load-fuel control loop of CFB boiler thermal power unit. In the upper layer, a reference governor with Takagi-Sugeno fuzzy hyperbolic tangent static model control algorithm was developed as the supervisor to yield the compensation for the external load command of the existing PI type loadfuel control loop in the lower layer, which regulated the coal feed rate to meet the demand of output power of the thermal power unit. To overcome the large inertia performance and complex nonlinearity of CFB boiler, the reference governor in the upper layer take the hyperbolic tangent function of cubic of the state variables as the core of the algorithm so that the calculated compensation was both timely and appropriate for the dynamic control in the lower layer. After construction, the proposed hierarchical control scheme can be implemented in the DCS of the CFB boiler thermal power unit and some experiments had been conducted. 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