Sborník vědeckých prací Vysoké školy báňské - Technické univerzity Ostrava číslo 2, rok 2006, ročník LII, řada strojní článek č.

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1 Sborník vědekýh praí Vysoké školy báňské - Tehniké univerzity Ostrava číslo 2, rok 2006, ročník LII, řada strojní článek č Abstrat Sanda MIHALACHE *, Marian POPESCU ** and Alina BĂIEŞU ** PROPYLENE ISTILLATION COLUMN COMPOSITION CONTROL ŘÍZENÍ PROPYLENOVÉ ESTILAČNÍ OLONY In petrohemial industry, distillation olumns are great energy onsumers, their onsumption usually representing more than 40% of total plant onsumption. Therefore, the investigation of these olumns is an important tool in finding solutions to this problem. This paper presents the results of simulating the propylene separation proess when best ontrol onfiguration is used. First a simplified model of the propylene/propane distillation olumn (PPC) is proposed. A deoupler is designed for the hosen onfiguration. Also, a multivariable internal model ontrol (IMC) system is designed and applied to ideal PPC. Simulation results prove that IMC ontroller an deal with the interative nature of ideal PPC more effetively than PI ontrollers, indiating that the IMC ontroller ould provide a better solution for ideal PPC if high ontrol performane is required. Abstrakt V petrohemikém průmyslu destilační kolony jsou velkými spotřebiteli energie, jejih spotřeba představuje obvykle víe než 40 % elkové spotřeby podniku. Výzkum těhto kolon je tedy důležitým nástrojem pro nalezení řešení tohoto problému. Tento příspěvek presentuje výsledky simulae proesu separae propylenu, kdy je používána nejlepší konfigurae řízení. Nejdříve je navržen jednoduhý model propylenové/propanové destilační kolony (PPC). Pro danou konfigurai je navržen kompenzátor (korekční člen) zajišťujíí autonomnost. Pro ideální PPC je také navrženo mnohorozměrové řízení s vnitřním modelem (IMC). Výsledky simulae potvrdily, že regulátory IMC jsou shopny poradit si se vzájemnými interakemi ideálníh PPC efektivněji než PI regulátory a ukazují, že IMC regulátory mohou zajistit lepší řešení, pokud je vyžadován vysoký výkon. 1 INTROUCTION The propylene-propane distillation olumn is part of atalyti raking unit, from hydroarbon distillation plant. The goal of the plant is to reover as muh C3 C4 frations as possible from FCCU rih gas and gasoline. The PPC is one of the final olumns with valuable produts and 0.90-mole fration purity is required in distillate produt. The ontrol struture for PPC an be hosen following steady state and dynami riteria. The steady state RGA riterion leads to the results presented in Table 1. The best onfigurations from RGA point of view are L/B, V/B and SV/B. LV onfiguration leads to a gain greater than 20 whih makes this struture not suitable for ontrolling PPC [2], [3]. * Leturer Ph Eng, Control Engineering and Computers epartment, Mehanial and Eletrial Engineering Faulty, Petroleum-Gas University of Ploiesti, Bd. Buuresti 39, Ploiesti, Romania, tel. (+40) , e- mail ** Assist. Let. Eng, Control Engineering and Computers epartment, Mehanial and Eletrial Engineering Faulty, Petroleum-Gas University of Ploiesti, Bd. Buuresti 39, Ploiesti, Romania, tel. (+40) , e- mail 9

2 Tab. 1 Steady state RGA Λ V Λ L/B Λ V/B Λ L Λ LV Λ LL/B Λ LV/B Λ S Λ SV Λ SL/B Λ SV/B Λ S The dynami riteria must be used, as well. In PPC ase, dynami behavior was the best riterion for this seletion. The seleted struture was SV/B (see Figure 1); it has the smallest effet on produts omposition for hanges in feed rate, whih is the most frequent disturbane for PPC [3]. Fig. 1 SV/B struture The struture has the advantage of a faster dynami response of bottom omposition ontrol and Λ SV / B is smallest within larger than 1 relative gains. From auray point of view, the best manipulated variable for distillate omposition ontrol is /V. 2 THE PROPOSE CONTROL SYSTEM The simulations for ideal PPC were made using a simplified model from [6]. The model has 140 states, but it an be redued to about 20 states without any notieable differene in the response. Small hanges in operating onditions allow the use of a linearized model. Although the SV/B onfiguration has the biggest deoupling feature, a deoupler must be designed in order to improve ontrol performanes. The deoupling problem is solved by ompensating the effets of two parallel-opposite hannels, with the same gain, deadtime and almost equal transient time, expressed by relations [4]: where: T ij deoupler time onstants. 4T 4T t t 4T 4T t t, (1) 0

3 After identifiation, the following parameters (gain ij, deadtime eah input output hannel will be used to design the assoiated deoupler: with ' [ / V / B as inputs, L ] [ ] ' (0.9, 7 min,0min) (0.2, 9min, 300min) x as outputs. x B The resulted deoupler has the following struture where deoupler gains are alulated with 1 ( s) Ts + 1 τ s ke k k / / ( 0.76, 8min, 400min) ( 0.83, 7min, 400min) τ, transient time ) for dij T tij (2) τs k e Ts + 1, (3) (4) The new deoupled proess will have the following steady state gains: + k + k (5) 0.66 This leads to a simpler design of multivariable IMC ontroller that onsists of the deoupler and two monovariable IMC ontrollers (for the two distint produt omposition ontrol loops). The deoupled proess ontains the PPC, the deoupler, all valves and omposition transduers. The transfer matrix of deoupled proess is: () H s e 2m1 0 Td 1s ( T s + 1) 2 0 Td 2s ( + ) 2 T s 1 2m2 e. (6) The model (6) will be used to design the IMC ontrollers. If the model desribes perfetly the real proess dynamis, the ommand has a step evolution, and the variation form of ontrolled variable is similar to the step response of the proess [1]. An IMC ontroller has the transfer funtion: T T where: 2 mi p e, i 1, 2, τ pi l mi T 3 SIMULATION RESULTS 1 2 pz + p z H (7) R RS ( z) l (1 ) m pm pz p z p z, T sample time. The deoupler with the struture from (3) and the parameters from (4) improves deoupling features of L x and V B xb hannels as shown in Figure 2. The PPC model without deoupler has the oupling oeffiient CC : CC %, (8) where ij are proess gains. The deoupler will redue these oupling features to the value: 1

4 ' 2 pm CC %. (9) The deoupled proess is sensitive to very large input hanges, but it performs well for medium input hanges. eoupling operation quality an be experimentally validated through the suitable tuning of deoupler parameters, espeially of the two lag time onstant. Tuning multivariable IMC ontroller is redued to tuning two distint monovariable omposition ontrol loops. The omposition analyzer imposes sample time of the system (5 min) (Figures 3 and 4). Fig. 2 SV/B open loop mode: the x B omposition hanges to 5% inrease of manipulated variable for (, L ) x 1 The IMC ontroller has three model parameters (the gain pm, the deadtime τ d and the time onstant T 2 m ) and one tuning parameter (the gain R ). The inrease/derease of model gain leads to the derease/inrease of the ommand intensity that is made by the inrease/derease of gain. R Fig. 3 tuning of IMC1: response to a mole fr. step inrease of x setpoint Fig. 4 tuning of IMC1: x response to a 0.02 mole fr. step inrease of setpoint x 1

5 The standard value R 1 of IMC algorithm does not provide speial dynami performane, but a relatively simple and robust ontrol ( R 1 R 2 1 were used). As stated before, if the model perfetly desribes the real proess dynamis, the ommand has a step evolution, and the variation form of ontrolled variable is similar to the step response of the proess (Figures 3 and 4). This is the main idea in tuning this ontroller. The best tuning parameters obtained for omposition ontrollers were: IMC1: IMC2: R1 R2 1, 1, 0.66, T 2m1 0.9, T 2m2 45 min, T m1 35 min, T 7 min. (8) 7 min IMC performane is ompared to PI one as shown in Figures 5 and 6. Composition ontrol loops usually use PI algorithm; the output signal generated by omposition analyzer is step type (if PI algorithm is used this signal should first be filtered with a seond order lag element). The best tuning parameters for PI ontrollers are k 1, T 50min. P i As shown in Figure 5, IMC responds better than PI to a omposition bellow setpoint speifiation means loss). m2 x setpoint hange (any produt Fig. 5 IMC/PI: x response to a 0.02 mole fr. step derease of x setpoint Fig. 6 IMC/PI: of x F response to a step derease feed flowrate As for x response to a hange of the main disturbane, the feed flowrate F it an be stated that IMC has a better response than PI (the gain response for IMC is slightly smaller than PI one). 4 CONCLUSIONS An appropriate struture for a redued-order model of transfer funtion type is first proposed for an ideal propylene/propane distillation olumn (PPC) based on the proess dynamis. The redued-order model ould well represent the proess not only in steady state but in dynami state as well. A multivariable internal model ontrol (IMC) system is designed and applied to the ideal PPC. The multivariable IMC ontroller onsists of a deoupler and two monovariable IMC ontrollers. One of the important advantages of using deoupler is that tuning multivariable IMC ontroller is redued to tuning two distint IMC monovariable omposition ontrol loops. The deoupler improves deoupling features of SV/B onfiguration for PPC, whih is the best ontrol onfiguration (from RGA and CLG riteria). The simulation results demonstrates that the IMC ontroller an deal with the interative nature of the ideal PPC more effetively than PI ontrollers, indiating the IMC ontroller ould be 3

6 a better solution for the ideal PPC operation in ases where high system performane is required. However, the ideal PPC is extremely sensitive to great hanges in operating onditions and this makes it neessary to adopt an online model adaptation mehanism. An appropriate approah for highly non-linear distillation olumns is the use of logarithmi ompositions, whih makes the response of distillation olumns more linear [5]. Nevertheless, for medium hanges in operating onditions IMC ontrollers perform better than PI ontrollers. ACNOWLEGMENTS This work was supported in part by the Romanian National Authority for Sientifi Researh under Grant 3145/ REFERENCES [1] CÎRTOAJE, V., FRÂNCU, S. and GUŢU, A. Valenţe noi ale reglării u model intern. In Buletinul Universităţii Petrol-Gaze din Ploieşti, Romania: Vol. LIV, Nr. 2, 2002, pp ISSN [2] FRÂNCU, S. and MARINOIU, V. Advaned ontrol struture analysis of propylene separation proess. In Proeedings of International Symposium on System Theory Craiova, Romania: 2000, pp. A4-A7. [3] FRÂNCU, S. Hierarhial ontrol system of a gas proessing unit. Ph Thesis. Petroleum- Gas University of Ploiesti, Romania, [4] FRÂNCU, S. eoupling in distillation. In Control Engineering and Applied Informatis, Vol.7, No.1, 2005, pp , ISSN [5] SHINSEY, G.F. Proess Control Systems. MGraw-Hill, New York, [6] SOGESTA, S. and POSTLETHWAITE, I. Multivariable Feedbak Control. John Wiley&Sons, Reviewer: prof. Antonín Víteček, CS., r.h.., VŠB-Tehnial University of Ostrava 4

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