Evolutionary Based Optimisation of Multivariable Fuzzy Control System of a Binary Distillation Column

Transcription

1 2016 UKSim-AMSS 18h Inernaional Conference on Compuer Modelling and Simulaion Evoluionary Based Opimisaion of Mulivariable Fuzzy Conrol Sysem of a Binary Disillaion Column Yousif Al-Dunainawi Elecronic and Compuer Engineering Deparmen College of Engineering, Design and Physical Sciences Brunel Universiy London Uxbridge, London, UK yousif.al-dunainawi@brunel.ac.uk Maysam F. Abbod Elecronic and Compuer Engineering Deparmen College of Engineering, Design and Physical Sciences Brunel Universiy London Uxbridge, London, UK maysam.abbod@brunel.ac.uk Absrac Geneic Algorihms (GA), Simulaed Annealing (SA) and Paricle Swarm Opimisaion (PSO) are populaionbased sochasic search algorihms ha caegorised ino he axonomy of evoluionary opimisaion. These mehods have been employed independenly o une a fuzzy conroller for mainaining he produc composiions of a binary disillaion column. An analyical invesigaion has been conduced o disinguish he opimal uning approach of he conroller among hese echniques. Based on simulaion resuls, paricle swarm opimisaion approach combined wih he fuzzy logic conroller is idenified as a comparaively beer configuraion regarding o is performance index as well as compuaional efficiency. Keywords Fuzzy Logic Conrol; MIMO; Disillaion; Evoluionary Opimisaion; I. INTRODUCTION The pioneering sudies of Zadeh on he heory of fuzzy se, logic and approaches [1] [3], have moivaed many researchers o esablish a new discipline of he modern conrol sysem. Thus, Mamdani and his co-workers had proposed an innovaive fuzzy conrol sysem for various applicaions o model and conrol dynamic, nonlinear, illdefined and complex processes, based on fuzzy logic heory [4], [5] Laer, he concepion of fuzzy logic conrol FLC has been invesigaed and applied widely o he mos of he engineering and applied science realms [6] [9]. Addiionally, hybridisaion of he various of evoluionary-based algorihms, providing inelligen echniques ha gives FLC sysem a sep ahead o produce powerful and more efficien soluions for differen applicaions [10] [12]. Employing hese algorihms have been applied recenly o boh convenional and modern conrol sysem o find he opimal uning parameers of he differen configuraion conrollers [13], [14]. Insead of he radiional emphasis on accuracy and cerainy, sof compuing echniques can deal grealy wih imprecision and uncerainy o allow reasoning and compuaion usually required for pracical applicaions [11], as Zadeh saed Fuzzy logic is no fuzzy. Basically, fuzzy logic is a precise logic of imprecision and approximae reasoning [15]. This paper proposes an evoluionary-based muli-inpu muli-oupu fuzzy conrol sysem MIMO-FLC o mainain he produc composiions of a binary disillaion column as near as o desired requiremens. The disillaion process iself is considered a high nonlinear and characerised by uncerainy and he ill-defined relaionship beween he inpus and he oupus [16], [17]. The mos moivaed aim o inroduce a new conrol configuraion of he column is rying o find more robusness and effeciveness agains he process perurbaions, herefore, energy efficien columns. II. DISTILLATION COLUMNS I is well known ha disillaion columns are he mos uni ha used in oil refineries, chemical and perochemical plans. These columns are mainly used o separae mixures ino heir individuals componens depending, basically, on he difference of boiling poins. Disillaion is repored as a highly demanding energy process. A repor from he US Deparmen of Energy has indicaed ha disillaion column uni is he larges consumer of energy in he chemical indusry; ypically, i accouns for 40% of he energy consumed by perochemical plan [18]. Regardless of is hunger for energy, disillaion coninues o be a widely used process for separaion and purificaion. Therefore, efficienly operaing hese columns necessiaes a high degree of auomaic conrol [19]. A. Process Descripion The column has a number of rays (plaes) which are employed o enrich he componens separaion process. The mixure is usually fed in he middle (or around) in he column. Vapour is produced by a reboiler, which is supplied by enough hea. The seam ravels up hrough rays inside he column o reach he op and, hen, comes ou o be liquefied in a condenser. Liquid from he condenser, a ha poin, eners ino he reflux drum. As a final poin, he disillae produc is removed from his drum as a pure produc. In addiion, some liquid is fed back (reflux) close o he op, /16 $ IEEE DOI /UKSim

2 while he impure produc is produced a he boom oule. The disillaion column diagram is depiced in Fig. 1. Above he feed sage i = NF +1: M i = L i+1 x i+1 + V i 1 y i 1 L i x i V i y i + F V y F (2) Below he feed sage i = NF: M i = L i+1 x i+1 +V i 1 y i 1 L i x i V i y i +F L X F (3) In he reboiler and column base i =1, x i = xb: M B = L i+1 x i+1 V i y i + Bx B (4) In he condenser, i = N +1, xd = xn +1: Figure 1. Schemaic represenaion of a binary disillaion column B. Model Represenaion The model of a binary disillaion column simulaed in his research is considered under he following assumpions: 1) No chemical reacions occur inside he column 2) Consan pressure 3) Binary mixure 4) Consan relaive volailiy 5) No vapour hold-up occurs a all sages 6) Consan hold-up liquid a all rays 7) Perfec mixing and equilibrium for vapour-liquid on all sages Hence, he mahemaical expression of he model can be represened by he following equaions: On each ray (excluding reboiler, feed and condenser sages): M i = L i+1 x i+1 + V i 1 y i 1 L i x i V i y i (1) M D = V i 1 y i 1 L i x D Dx D (5) Vapour-liquid equilibrium relaionship for each ray [20]: y i = The flow rae a consan molar flow: since αx i 1+(α 1)x i (6) L i = L, V i = V + F V (7) F L = q F F (8) F v = F + F L (9) The flowrae of boh condenser and reboiler as: Reboiler: B = L + F L V (10) Condenser: D = V + F V L (11) The feed composiions xf and yf are found from he flash equaion as: F zf = F L x F F V y F (12) The nominal and operaion condiions of he column are shown in he appendix in he end of his paper, and he schemaic diagram of a heoreical sage of he column is shown in he Fig. 2. Figure 2. Schemaic diagram of ih sage of a binary disillaion column

3 III. CONTROL SYSTEM CONFIGURATION In he presen work, MIMO configuraion is invesigaed o conrol he produc composiions of a binary disillaion column. One of he mos common conrol loops of he binary column is so-called (L V ) configuraion [19]. Where, he reflux flow (L) is seleced o conrol he mole fracion of he op produc (xd), while he reboiler seam flow (V ) is chosen o conrol he composiion of he boom produc, as expressed in Eq. 13. [ ] [ ] xd = G LV L (13) xb V where G LV is he column s ransfer funcion. As i is known, he performance of any conroller depends as much on is design as on is uning. Tuning mus be applied by operaors o fi he conroller o he process. Therefore, here are many differen approaches for uning, based on he paricular performance crieria seleced. Therefore, evoluionary algorihms are employed as an opimal uner of he conrol parameers; geneic algorihm, simulaed annealing and paricle swarm opimisaion in his paper for his purpose. The conrol sysem aims o mainain he produc composiions as close o he desired ones as possible despie he expeced disurbances. A. Fuzzy logic conrol A conrol sysem, based on fuzzy heory, simply ransforms a linguisic conrol sraegy ino auomaic capabiliies for managing he nonlineariies and uncerainies of he process. The proposed FLC srucure has Mamdani inference sysem and he cenroid defuzzificaion mechanisms. The universe of discourse of he inpus and oupu were normalised in he inerval [1, 1]. Thus, acual sysem values were convered hrough scaling parameers (gains). Gaussian,he mos common membership funcion was used o defined he inpus and oupu of he fuzzy conroller. he relaionship of he inpus as error and change in error, and he oupu as conrol signal is shown in he surface viewer of FLC in Fig. 3 as well as he if-hen rules are deailed in Table I. Linguisic expressions demonsraed o hese fuzzy ses are: PB: posiive big, PM: posiive medium, PS: posiive small, ZE: zero, NS: negaives small, NM: negaive medium and NB: negaive big. The Gaussian membership membership funcion is expressed as: y(x) =e (x c)2 α (14) where c and α are he mean and deviaion of a Gaussian membership funcion, respecively. The resuling fuzzy se mus be convered o a signal ha can be sen o he process as a conrol inpu. Cenroid of he area has been used here for he defuzzificaion process. B. Geneic algorihms Naural evoluion inspired procedure as known geneic algorihms GAs, can search for opimal or close-opimal soluions for an opimizaion problem over he search space. I generaes an iniially random populaion of candidae soluions oward he opimal finess (objecive funcion) by performing specific echniques, which are mimic he naural selecion processes, such as reproducion, crossover, and muaion. The procedures are repeaed unil he prescribed finess is acceped, or he predeermined number of ieraions (generaions) is implemened. The research opic of uning various conrol sysems via GAs has already been invesigaed in many researches [9], [21], [22]. C. Simulaed Annealing Simulaed annealing is a heurisic opimisaion mehod, which is mimicking he process of meals annealing o find he opimum soluion via conrolling he emperaure. SA iniialises a candidae emperaure, in opimizaion and searches for opimal global finess by slowly reducing he emperaure alike o he physical annealing process. Is TABLE I RULESBASEDOFTHEFLC. Change in Error Error NB NM NS SS PS PM PB NB SS NS NM NM NB NB NB NM PS SS NS NM NM NB NB NS PM PS SS NS NM NM NB SS PM PM PS SS NS NM NM PS PB PM PM PS SS NS NM PM PB PB PM PM PS SS NS PB PB PB PB PM PM PS SS Figure 3. conroller. The relaionship beween inpus and oupu of he fuzzy

4 advanages are repored as he considerable abiliy o find he minimal finess funcion in specific condiions as well as i can deal wih any objecive funcion [23]. D. Paricle Swarm Opimisaion Paricle swarm opimisaion (PSO) has been proposed by Kennedy and Eberhar in 1995 [20] and 2001 [24], PSO algorihm urned o be vasly successful. The several of researchers have presened he meri of he implemenaion of PSO as an opimiser for various applicaions [25], [26]. In PSO procedure, all paricles are locaed randomly and heoreical o move arbirarily in a defined direcion in he search domain. Each paricle direcion is hen changed seadily o ravel along he direcion of is bes previous posiions o discover a new beer posiion according o predefined objecive funcion (finess). IV. SIMULATION AND RESULTS In his paper, MIMO FLC has been designed of a binary disillaion column. EAs such as GA, SA and PSO were employed o find he opimal scaling facors of he conroller. The inegral of he ime-weighed absolue error (ITAE) was seleced as he quaniaive crierion for measuring conrol performance. Minimisaion of his index expressed in Eq. 15 is considered as finess or objecive funcion of EAs ha is used in his research. 3) Design of MIMO PID conroller uned by convenional Ziegler-Nichols mehod [27] Exensive simulaions were carried ou o find he opimal iniial parameers of EAs like he populaion size, he iniial condiion, weigh, ec. Due o he randomness of EAs a iniialisaion sage, 20 imes of runs had been done independenly of each algorihm. MATLAB R and Simulink R R2014b plaform were used for simulaion via processor 3.6 GHz, wih 8 GB of RAM. The FLC configuraion wih and wihou compensaor are shown in Fig. 5. The performance index of he differen conrollers wih various uning mehod is given in Table II. Clearly, all of he conrollers designed using differen approaches pass he ransien response requiremens. Neverheless, he performance of he PSO-base FLC wih compensaor indicaed beer achievemen regarding he performance index and ransi response. In addiion, PSO ouperformed he oher EAs echniques wih minimum compuaion ime. ITAE = T =0 T E d (15) where, E is he error beween he desired value and oupu of he produc composiions of he column and T is a simulaion ime, he schemaic diagram of he designed conrol sysem is depiced in Fig. 4. To compare he performance of he various EAs for he FLC conroller design, hree simulaion experimens were performed as follows: 1) Design of MIMO FLC conroller wihou a compensaor 2) Design of MIMO FLC conroller wih a compensaor (a) (b) Figure 4. EA-based FLC design Figure 5. MIMO FLC (a) wihou compensaor, (b) wih compensaor

5 TABLE II PERFORMANCE INDEX OF CONTROLLERS TUNED BY VARIOUS APPROACHES Conroller Tuning mehod ITAE Time (hour) PID Z-N GA FLC SA PSO FLC-compensaor PSO The compensaor slighly improved he performance by eliminaing he ineracing of loops, wih more ime cos due o he number of parameers involved. For he convenience, he comparisons of he ime response behaviour of he PID and PSO-based FLC wih and wihou compensaor is presened in Fig. 6. A. Robusness of he opimal conroller To check he robusness of he PSO-based FLC wih compensaor agains exernal disurbances, he desired composiions of he column were se o change asynchronously as follows; The desired composiions of disillae and booms producs are changing every 100 minues for a housand minues. I can be observed ha he conrol acions of he conroller were successfully adaped o eliminae he effec of he exernal disurbances, where he convergence of he desired responses was achieved afer he adapaion of he conrol oupu. The process oupu responses o sepoins changes in he disillae and booms composiions. Beer performance is achieved wih fuzzy logic conroller ha uned by PSO wih a compensaor o eliminae he effec of inpus variance as shown in Fig. 7. This resul gives an indicaion ha he proposed conroller can cope efficienly wih disurbances PID PSOFLC PSOFLC wih Compensaor xd Time(min) (a) PID PSOFLC wih Compensaor PSOFLC (a) xb Time (min) (b) Figure 6. Time Response of sep sepoins of differen conrol configuraions (a) disillae and (b) booms produc. (b) Figure 7. Time response of changed-sep sepoins of he produc composiions of he column (a) disillae and (b) booms produc

6 V. CONCLUSIONS In his research, hree of he common echniques of EA were performed independenly as a uner o FLC. GA, SA and PSO had been combined wih FLC o conrol a binary disillaion column. The resuls showed ha PSO ouperformed GA and SA by achieving improvemen o he performance of he conroller as well as compuaional efficiency. For comparison purposes, he convenional PID conroller was also simulaed and applied o he same column. PSO-based FLC wih compensaor proved is feasibiliy and superioriy by handling disurbances wih minimal ITAE performance index. Differen conrol configuraions could be applied o disillaion columns wih various uning mehod like Graviaional Search Algorihm, which is o be he subjec of fuure work. ACKNOWLEDGMENT The corresponding auhor is graeful o he Iraqi Minisry of Higher Educaion and Scienific Research for supporing he curren research. REFERENCES [1] L. A. Zadeh, Fuzzy ses, Informaion and conrol, vol. 8, no. 3, pp , [2] L. 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Symbol Descripion Value Uni N Number of rays 20 - N F Feed sage locaion 11 - F Typical inle flow rae o he column 1 kmol/min D Typical disillae flow rae 0.5 kmol/min B Typical booms flow rae 0.5 kmol/min zf Ligh componen in he feed (mole fracion) q F Mole fracion of he liquid in he 1 - feed L Typical reflux flow rae 1.28 kmol/min V Typical boil-up flow rae 1.78 kmol/min α Relaive volailiy 2 - xd Disillae composiion (mole fracion) xb Booms composiion (mole fracion) i Sage number during disillaion - - x Mole fracion of ligh componen - - in liquid y Mole fracion of ligh componen - - in vapour M Tray hold-up liquid 0.5 kmol MD Condenser hold-up liquid 0.5 kmol MB Reboiler hold-up liquid 0.5 kmol