Pass Balancing Switching Control of a Four-passes Furnace System

Transcription

1 Pass Balancing Switching Control of a Four-passes Furnace System Xingxuan Wang Department of Electronic Engineering, Fudan University, Shanghai 004, P. R. China (el: ; wxx07@fudan.edu.cn) Abstract: Pass balancing control of industrial multi-passes furnace systems, which are widely used in petroleum refineries, is very necessary to improve the product quality, economic efficiency, and plant safety. From considerations of reducing the time of the flowrate valves being regulated and hence prolonging their lifespan, a switching based control technique has been suggested to address the related problems for multi-passes furnace systems. his paper further studies the SDC technique, with an emphasis on the balanceability of the switching control policy. he principle of the technique and a switching control policy are first introduced, the balanceability problems, which concerns whether or not a furnace system could be balancing controlled by a switching policy, are then elaborated, and finally a sufficient condition for the balanceability of the control policy for four-passes systems is obtained. Keywords: Pass balancing control, Multi-passes furnace systems, Outlet temperature control, Algebraic constraint, Generalized switching control, Balanceability.. INRODUCION An industrial furnace with multiple passes is commonly used in petroleum refineries to improve the heat transfer efficiency and to reduce the possibility of coke formation (Cheng et al, 999, Friedman 994, Garg 999, Herzog 004, Li et al 994, Wang & Zheng 005, 006, 007, Zhang et al 008). As shown in Fig., the crude oil enters the furnace through N parallel passes, and the oil flowrates f to f N come from the same source F, total oil inlet flowrate, and hence they satisfy the algebraic constraint N f i i F. () For the product quality, economic efficiency, and plant safety considerations, the control measures are needed to keep the outlet temperatures of multiple parallel passes as identical as possible. It can be found from () that, in order to obtain a uniform outlet temperature, regulating the inlet flowrate of certain pass must regulate that of some other pass or passes simultaneously to keep () satisfied, that is to say, control loops among the multiple passes are seriously coupled. he difference control technique (DC) has been proposed to dynamically distribute the inlet flowrates among the passes to maintain the outlet temperatures uniformity (Li et al, 994, Wang & Zheng, 005) and applied to a furnace with four passes successfully (Wang & Zheng, 005). he basic idea of the DC technique is that, the difference of the two outlet temperatures is controlled to be zero, and the output of the single input single output (SISO) controller is the flowrate deviation, which is added to the flowrate setvalue of one pass whose outlet temperature is high and at the same time subtracted from that of another whose temperature is low. hus, the two outlet temperatures can be controlled using just one SISO controller, and its output does not change the sum of the two flowrates, which resolves the flowrate algebraic constraint () effectively and conveniently. he DC technique transforms the pass balancing control problem for a furnace system with two parallel passes to a conventional single variable control problem. However, for a furnace with N parallel passes, there would need reiteratively employing the DC technique N times to realize the pass balancing control, which is boring especially when N is large. In addition, in some cases where N or N n, n,,, such reiterative employment of the DC technique might result in the problem that the inlet flowrate coupling cannot be decoupled properly. In order to overcome the mentioned shortcomings of the DC technique, Wang & Zheng (006, 007) have proposed a generalized version of the difference control technique, called differences control technique (DsC). For both of the DC and the DsC techniques, all the N inlet flowrate valves are regulated through the whole time horizon, which is disadvantageous for the lifespan of the flowrate valves. Considering that, in recent years, the study of switched systems has obtained many research results and the related switching control techniques have been widely applied to engineering practices (Lennartson et al 996, Morse 997, Engell et al 007, Li & Guan 00, El-Farra & Christofides 00, Wang et al 00, Jin & Huang 00), a switching control technique, called SDC technique, has been suggested to control the N parallel passes in a time sharing manner to reduce the regulation time of the flowrate valves and hence to help prolong their lifespan (Wang et al 008). his paper further studies the SDC technique, with an emphasis on the balanceability of the switching control policy for the four-passes systems. he rest of the paper is organized as follows. In Section, the SDC technique related problems are introduced. Section Copyright by the International Federation of Automatic Control (IFAC) 078

2 formulates the balanceability problems for balancing control of furnace systems with multiple parallel passes, investigates the balanceability of a switching control policy, and obtains a sufficient condition for the policy being balanceable. Finally, some concluding remarks are presented in Section 4.. SDC ECHNIQUE AND SWICHING POLICY. SDC echnique Considering that the DC technique can be employed for balancing control of the two parallel passes (Wang & Zheng 005) and it is hoped to reduce the regulation time of the flowrate valves for prolonging their lifespan, a switching control scheme is suggested as follows: at any given instant, just some two passes are selected from the N passes for balancing control using the DC technique, leaving the other passes in no control status temporarily. With time evolving and based on certain feedback policy, different passes are dynamically chosen for balancing control so that all the N passes can be controlled in a time sharing manner. hus, at any given time interval there are two and only two passes being controlled, and hence the regulation times of all the N flowrate valves are reduced significantly as a whole. he related technique is here called the switching difference control technique (SDC) (Wang et al 008). he SDC control system is a switched system, where the basic switching unit is a subsystem, denoted as DC, that consists of two parallel passes and an SISO controller. A schematic diagram of the DC subsystem that is composed of Passes and, and controller C is given in Fig.. he controller in the subsystem can be called server, and when the subsystem consists of Passes i and j, the location of the sever is said to be Loc(i, j). Once one or two passes leave the subsystem, it is said that the location of the server switches, and hence the SDC system is a generalized switched server (GSS) system (Wang & Zheng 006, 009, Wang 008). An SDC control system with the server location being Loc(, ) is shown in Fig.. For a subsystem DC, the difference of the two outlet temperatures D is controlled by a continuous time controller with the reference input being zero, and the control objective is to make the two temperatures identical. he output of the controller is added to and subtracted from the two input setvalues simultaneously, which makes the sum of the two inputs do not change with the controller output. Fig. shows a subsystem DC, where the inputs of the two passes are given by f f Δf s. () f f Δf s Fig.. A schematic diagram for an industrial furnace system with N parallel passes, where the N inlet flowrates come from the total flowrate F. Fig.. A schematic diagram of the DC subsystem, where the D is controlled to be zero, and the f is added to the f s and subtracted from the f s simultaneously. switching policy, the FRR (first balancing control for some two passes and then round-robin switching) policy is briefly reviewed as follows: the current subsystem switches when it reaches the pass balancing status, and the subsystem switches in a round-robin manner when it switches. hat is, at initial time t 0 0, some two adjacent passes, say Passes and, are selected for balancing control. At time n, n,,, assume that the indices of the two parallel passes that are selected for control are i and i respectively. From the time n, the regulation run for the parallel passes i and i continues to the time when the subsystem reaches to the. Switching Control Policy Wang & Zheng (006, 009) have proposed some switching control policies for the SDC control systems. For convenience of narration for the balanceability analysis of the Fig.. A schematic diagram of the SDC control systems, where at any given time interval, just two passes are selected for balancing control using the DC technique. 079

3 pass balancing status. At the time, the basic switching unit is switched to be the subsystem that consists of parallel passes i and i for i,,, N-; or parallel passes N and for i N-; or parallel passes and. he regulation and the evolution procedures of the basic switching unit are repeated like this.. BALANCEABILIY PROBLEMS. Problem Formulation As shown in Fig. 4, the balanceability problem is formulated as that, under a zero system input (F 0), for any given initial outlet temperature 0 [ 0, 0,, 0N ], where the 0i is the initial outlet temperature of the parallel pass i, i,,, N, whether or not the given switching control policy could drive the N parallel passes to have identical outlet temperatures. Denote () t () t t () M () N t () Fig. 4. A schematic diagram showing the balanceability problem formulation, where the φ i is the oil inlet flowrate of parallel pass i, and the ω i is the holding value of the φ i when the switch takes place, i,,, N. as the system load status at time t, where the i (t) is the outlet temperature of the parallel pass i, i,,, N. Definition : A switching control policy is said to be balanceable, if the limit of () () t 0 () t 0 limt () lim U, for 0 M, (4) M N () t 0N where the U is a uniform vector whose components are all identical.. Constraint Decoupling heorem : For the FRR switching control policy, the system structural algebraic control input constraint can be decoupled, if it can be at the initial time t 0. Proof: From (), it can be found that, for the basic switching unit DC, the sum of the task inputs of the two parallel units is given by f f f f, (5) s s and it does not change with the output of the continuous time controller. In addition, for the FRR policy, only some adjacent two parallel passes are selected for balancing control during any given time slot, keeping the other N- oil flowrate f to f N be constant temporarily. hus, the sum of the N oil flworate Fig. 5. A schematic diagram for the performance analysis of the basic switching unit subsystem. N f i i (6) does not change with the time. So, if the value of (6) is set to be the total inlet flowrate F at initial time t 0, Equation () holds, that is, the system structural algebraic control input constraint is decoupled.. Balanceability of FRR Switching Policy Denote DC ij { kk, } as the basic switching unit subsystem which is composed of parallel passes i and j, i j, i, j,,, N, during the time interval (kh, (k)h), k0,,,, where the h is the control time slot. For a four-passes furnace system and FRR policy, the evolution of the basic switching unit (7), can be given by DC DC DC DC {4 n, 4 }, {4n, 4 } {4n, 4 } 4 {4n, 4 4} 4 (7) t (4 nh,(4 ) h), t ((4 ) h, (4 ) h), (8), t ((4 ) h,(4 ) h), t ((4 ) h, (4 4) h) 080

4 where n0,,,. Lemma : For a basic switching subsystem with zero input, if the subsystem can be balancing controlled by its continuous time controller, then, the identical outlet temperatures of the two parallel passes would be given by 0 0, (9) where the 0 and 0 are the two initial outlet temperatures. Proof: Consider a subsystem with zero input (as shown in Fig. 5). From the condition, it is known that the two outlet temperatures (t) and (t) would be identical at and after the time t s when the subsystem reaches to a pass balancing status, that is, (t) (t) for time t > t s. It can be found from Fig. 5 that f (t) -f (t) and () t y() t 0. (0) () t y() t 0 In addition, for time t > t s, the following holds. y () t K f () t, () i i where the K is the steady gain of parallel passes i, i,. Considering (0), (), and that (t) (t), it can be found that 0 0 t () () t () for time t > t s. his completes the proof of the lemma. heorem : For a four-passes furnace system, if the basic switching unit subsystems can be balancing controlled by the continuous time controller during the control time slot h, then, for the evolution procedures presented by (8), the system outlet temperature () at switching time t kh (k 4, 4, 4, 44, where n 0,,, ) t () t kh ( k) 4 can be given respectively by ) for n 0, () () 0 / 0 / () (), (4-) () 0 () 4 04 () 0 / 0 / () 0/ 0 / 0/, (4-) () () () 4 04 () 0 / 0 / () 0/ 0/ 0/, (4-) () 0/ 0 / 0/ 04 / () () 4 (4) / 0 / 0 / 0 / 0 / 04 / (4) 0/ 0/ 0/ (4) 0/ 0/ 0/ 04/ (4) (4) 4 or ) for n, ; (4-4) (4 ) ( f gn/ c) 0 ( f gn/ c) ( f 9 / ) gn c 0 ( fn 5 gn/ c) , (4 ) (4 ) (4n ) ( fn 5 gn/ c) 0 ( fn 5 gn/ c) ( f / ) n gn c 0 ( f gn/ c) (4 ) 4 ( f 9 gn/ c) 0 ( f 9 gn/ c) ( f 5 / ) n gn c 0 ( fn gn/ c) (5-) where 6 c, fn cos( n arctan c n ). gn n sin( n arctan c ) 08

5 (4 ) (4n ) (4 ) (4 ) (4n ) (4 ) (4 ) 4 4 (4 ) (4 ) (4 ) (4 ) (4 ) (4 ) (4n ) (4 ) (4 ) 4 (4 ) (4 ) 4 (4 4) (4 4) (4 ) (4 4) (4n ) (4 4) (4 5) 4 (4 ) (4 ) 4 ; (5-) ; (5-) ; (5-4) Proof: he proof can be finished by using the mathematical induction approach, however, due to the page limit, the proof is omitted. heorem : For a four-passes furnace system, the FRR switching control policy is balanceable, if the basic switching unit subsystems can be balancing controlled by the continuous time controller during the given switching time slot h. Proof: Consider the series of the system outlet temperature () at the switching time t kh, k0,,, () t t kh ( k) ( k ). (6) ( k ) 4 From (8), Equation (6) can be completely disassembled into the following four sub-series. ( k) (4 ) SS () (4 ) (4 ) (4 ) (4 ) ; (7-) ( k) (4 ) SS () ( k) (4 ) SS () ( k) (4 4) SS (4) (4 ) (4 ) (4 ) (4 ) (4 ) (4 ) (4 ) (4 ) (4 4) (4 4) (4 4) (4 4) ; (7-) ; (7-) ; (7-4) where the n 0,,,. From heorem, the above four sub-series can be given by (5-) to (5-4) respectively for n,,, if the basic switching unit subsystems can be balancing controlled by the continuous time controller during the given switching time slot h. It can be found from (5-) that sub-series (7-) is convergent when the n approaches to infinity, and its limit is given by lim n (4 ) lim n (4 ) lim (4n ) n (4 ) lim n (4 ) lim n 4 μ where the μ is a constant, and it is given by μ ( )/4., (8) Similarly, it can be easily verified from (5-) to (5-4) that the sub-series (5-) to (7-4) are also convergent, and they have the same limits as that of the sub-series (7-). So, the system outlet temperature series (6) is convergent when the k goes to infinity, and its limit is given by lim k ( k) μ, (9) 08

6 where the μ is as in (8). In addition, for a basic switching unit subsystem DC ij, the two outlet temperatures satisfy that () t () t, (0) i j for time t ( κh, ( κ ) h), if i (t) j (t) at switching time t κh, where i j, i, j,,, and κ is some positive integer. It can be found from (9) and (0) that () t () t lim t () lim μ, () t 4 () t where the μ is as in (8). hus, from Definition, it is known that the FRR switching control policy is balanceable for a four-passes furnace system. his completes of the proof. 4. CONCLUSIONS his paper has investigated the balancing control problems for industrial multi-passes furnace systems, which is widely used in petroleum refineries. For considerations of reducing the time of the flowrate valves being regulated and hence prolonging their lifespan, a switching control based technique has been introduced to address the related problems for a four-passes industrial furnace system. hrough an analysis of the basic switching subsystem and the switching sequence, a sufficient condition for the balanceability of the FRR policy for the four-passes systems is obtained. It should be pointed that further studies, e.g., how to extend the number of passes N4 to an arbitrary N, the analysis for dynamical performances, etc., are needed to be done, and the corresponding problems are being researched. ACKNOWLEDGMEN he author would like to thank his mother, Lady Huai-Ying Ma, for her unselfish helps for completing of this work, and also thank Prof. Da-Zhong Zheng from singhua University for his valuable contributions. his work is supported in part by the Shanghai Municipal Natural Science Foundation (No. 0ZR404500), the Specialized Research Fund for the Doctoral Program of Higher Education ( ), the open funds from the State Key Laboratory of Industrial Control echnology at Zhejiang University (No. IC09), and in part by the National High echnology Research and Development Program of China (No. 007AA04Z95). REFERENCES Cheng, G., He, M., and Li, D.L. (999). Model-free coking furnace adaptive control. Hydrocarbon Processing (International edition), 78 (), pp El-Farra NH, and Christofides PD. (00). Coordinating feedback and switching for control of hybrid nonlinear processes. AIChE Journal.49, pp Engell S, Kowalewski S, Schulz C, Stursberg O. (000). Continuous-discrete interactions in chemical processing plants. Proceedings of the IEEE. 88, pp Friedman,Y.Z. (994). Model based control of crude product qualities, available at Garg, A. (999). Improve vacuum heater reliability. Hydrocarbon Processing, 78 (), pp Herzog, C. (004). Heat and material balance method of process control for petrochemical plants and oil refineries. available at Jin X, and Huang B. (00). Robust identification of piecewise/switching autoregressive exogenous process. AIChE Journal. 6, pp Lennartson B, ittus M, Egardt B, Pettersson S. (996). Hybrid systems in process control. IEEE Control Systems Magazine.6, pp Li HX, and Guan S. (00). Hybrid intelligent control strategy - supervising a DCS-controlled batch process. IEEE Control Systems Magazine., pp Li, S., Wu, F., Chen, H., Chen, Z., and Qing, Z. (994). Refinery furnace feed-branches outlet temperatures balancing control (in Chinese), Information and Control, (4), pp Morse AS. (997). Control using logic-based switching. Springer-Verlag, Secaucus, NJ. Wang W, Li HX, Zhang J. (00). A hybrid approach for supervisory control of furnace temperature. Control Engineering Practice., pp Wang, X. and Zheng, D.-Z. (005). Difference control of parallel streams temperatures. Journal of Process Control, 5 (5), pp Wang, X. and Zheng, D.-Z. (006). Generalized difference control of parallel streams temperatures. Journal of Process Control, 6 (5), pp Wang X, and Zheng DZ. (006). Generalized switched server systems and task balancing. Proceedings of the American Control Conference. pp Wang, X. and Zheng, D.-Z. (007). Load balancing control of furnace with multiple parallel passes. Control Engineering Practice, 5 (5), pp Wang X. (008). On switching policies for generalized switched server systems. Proceedings of the 7th Chinese Control Conference. pp Wang X, Zheng DZ. Zhang J, Zhang L. (008). Switching difference control of parallel streams temperatures. Proceedings of the 7th International Federation of Automatic Control World Congress. pp Wang X, and Zheng DZ. (009). Fuzzy scheduling strategy for generalized switched server systems and its robustness over system heterogeneity. International Journal of Intelligent Systems. 4, pp Zhang, W., Huang D., Wang, Y., and Wang, J. (008). Adaptive state feedback predictive control and expert control for a delayed coking furnace. Chinese Journal of Chemical Engineering, 6 (4), pp