Non Interacting Fuzzy Control System Design for Distillation Columns

Transcription

1 Non Interacting Fuzzy Control System Design for Distillation Columns A. MAIDI, 1, M. DIAF, A. KHELASSI, C. BOUYAHIAOUI Département Automatique, Faculté e Génie Electrique et Informatique, Université Moulou MAMMERI e Tizi-Ouzou, 15, Tizi-Ouzou, ALGERIE Laboratoire D automatique Appliquée, Faculté es Hyrocarbures et e la Chimie, Université M hame BOUGUERRA e Boumerès, 35 Boumerès, ALGERIE Abstract: - This paper proposes a fuzzy multiloop control esign for a istillation column. The interaction that occurs between the strategic istillation column variables, which represent a major constraint to construct the rules base when the fuzzy multivariable control of the istillation control is consiere, are reuce by introucing a compensator in cascae with the istillation column. The introuce compensator is esigne using an interaction analysis metho. Thus, a complete fuzzy rule base is generate for each loop inepenently without omain experts. The main avantage of the propose fuzzy multiloop strategy is that the etermination of the rule base is simplifie an facilitate; besies a weak level of interaction an the control stability are guarantee. Consequently, in comparison with the conventional multiloop control base on classical PI controllers, the fuzzy multiloop control achieves better control performance. Key Wors: - Multiloop control, interaction analysis, control configuration, compensator, Direct Nyquist Array (DNA), Relative Gain Array (RGA), PI fuzzy controller. 1 Introuction For many reasons, istillation remains the most important separation technique in the chemical process inustries aroun the worl. For these reasons, improve istillation control can have a significant impact on reucing energy consumption, improving prouct quality an protecting environmental resources. However, istillation control is a challenging problem, ue to the following factors [1]: process nonlinearity; substantial coupling of manipulate variables; severe isturbances; an nonstationary behavior. Accoringly, much research an evelopment in both the private an public sector has focuse on control methos that use moern computing power to cope with these control relate ifficulties [15]. Many methos have been suggeste to esign non interacting or ecoupling multivariable control systems [1], [7]. Weischeel an coworkers have stuie ecoupling of conventionally (energy balance) controlle istillation towers, an conclue that complete ecoupling is not feasible for many (high purity) columns ue to sensivity to moel error [17]. Ryskamp suggeste using implicit ecoupling rather than explicit ecoupling [13]. Ryskamp argue that by the proper selection of process measurements one coul obtain a naturally ecouple system. Georgakis evelope the extensive variable control metho to ecompose the process system into slow an fast ynamic moes, which are relate to the system or to the total energy or mass content of subsystem [3]. A simple structure for neural network control is propose by Ramchanran & Rhinehart [11]. Viel et al. evelope a Lyapunov base controller for the composition control of binary istillation columns [16]. Most avance control techniques are generally groune in the use of nonlinear multivariable moels [11]. The linear moels generally ten to become rigorous an computationally intensive as the process behavior become more complex. While control success has been emonstrate, it is often at the expense of computational power, operator frienly interaction or ease of controller evelopment an maintenance. Fuzzy logic offers an alternative approach to the control of processes, as they o not require a priori knowlege of the process phenomena. Fuzzy logic is capable of hanling complex

2 an nonlinear problems, process information rapily an can reuce the engineering effort require in controller moel evelopment [], [1], [18]. Fuzzy logic has been successfully applie to variety of inustrial processes such as cemetery, paper prouction, control of the chemical reactor temperature an ethylene prouction. In the area of process control, a few applications have been reporte. In this paper, the fuzzy control of istillation column is presente an the performances of this control approach are compare in simulation with that provie by the classical PID controllers. The outline of this paper is as follows. Section eals with fuzzy logic an its relevance to process control an the encountere ifficulties when it is applie for istillation control whereas section 3 presents the consiere control strategy for the istillation column. A comparison between the use of fuzzy an the classical PID controllers in the multiloop strategy consiere is reporte in section 4 followe by a final conclusion. Fuzzy logic an its relevance to process control The fuzzy logic control is interesting for the following reasons: Simple to realize, an aaptable to the working prouction conitions; The synthesis of several expert acknowlege is easily feasible; It s a robust control technique; The users juge that it permits a high accuracy an generally the energy economy; It has proven its efficiency in many applications [1]. The application of the fuzzy logic to control the istillation column stumbles to the following problems: The choices of the fuzzifie variables, since, there are several control variables an variables to be controlle; Moeling ifficulties of the operators acknowlege, so the eterminations of the rules base, since the istillation phenomenon is complex; consuming to generate the control actions seen the number of the rules. Power integrity. In aition the interaction that occurs between the istillation column variables poses a serious problem to esign a fuzzy control system. In this work, we esign a fuzzy multiloop control for a istillation column. This control strategy simplifies an facilitates the esign of the fuzzy control since the rules base is etermine for each loop inepenently. Besies the fuzzy multiloop esign, also a comparison with the multiloop control using the classical controllers is presente to show the contribution of the fuzzy control. 3 Control strategy In esigning a multiloop control, the key ecision is the selection of the best control configuration. The most encountere problem while esigning the multiloop control is the interactions that occur between system variables. Many techniques to analyze interaction have been evelope to esign more effective control system [5], [9]. However there are many cases where the interaction measures show the absence of an aequate control configuration (the system is highly interactive). The Decoupling metho (simplifie, ieal or inverte ecoupling) is relatively complex task since all techniques have their avantages an limitations [8], [9]. Seen the interaction that occurs between the istillation control variables, the multiloop control o not provie the esire control performance for expecte isturbances an set point changes. In orer to apply the fuzzy control of istillation columns, the control strategy given in Figure 1 is consiere. As shown in Figure 1, a compensator is introuce in cascae with the istillation column that reuces the interaction c + - Multiloop controller u Compensator u Distillation column Fig.1 The consiere multiloop control structure. y

3 between the consiere control configuration loops. 4 Fuzzy an classical multiloop control of istillation column 4.1 Distillation column moel The example consists of a two prouct istillation tower separating a binary fee. Both top an bottom prouct compositions are of equal importance, an the major isturbance is a change in fee composition. The consiere process shown in Figure, has the istillate an reflux pairings interchange; this calle material balance an has the following moel [8]: Where G x x b f = G + G f v x..747 e 1 s e 9 s + 1 s.8 e 5 s e 3 s + 1 = s s G p 5 s.7 e = 14.4 s s 1.3 e 1. s + 1 f s (1) Where x is the istillate, x b is the bottoms, f is the istillate flow, f v is the reboile vapor an x f is the fee composition. Note that the reflux flow f v are potential manipulate variables, an the fee composition x f is a isturbance, because it epens on upstream operations an is assume not free to PC ajust. The units are mole fractions of the light key components for the composition, Kmole/min for the flows, an min for time. 4. Interactions analysis The Direct Nyquist Array in Figure 3 is use to analyze the interaction in the consiere istillation column. Thus, Figure 4 gives the iagonal elements superpose by the Gershgorin circles [5], [9]. It shows that the manipulate variable f affects strongly the controlle variable x an x b. Therefore, the two possible control configurations are interactive. Thus, the control strategy given in Figure 1 is inicate to control correctly the istillation column using the multiloop control system. 4.3 Compensator esign To reuce the interaction between the istillation column variables, the compensator K ( s) is introuce. The compensator K is esigne using the metho propose in [6] to control highly interactive system. The application of the Direct Nyquist Array (DNA) as an interaction Fig. 3. The Direct Nyquist Array of the stuy istillation column x f fee LC f f v LC istillate AC AC x bottom prouct x b Imaginary Axis g 11 ( s) g ( s) Real Axis Fig.. Schematic iagram of material balance energy. Fig. 4. The iagonal elements of the istillation column superpose by the Gershgorin circles.

4 analysis metho gives the following compensator K (see Appenix) K = () The contribution of the compensator is illustrate by Figure 5, which shows that the cascae (compensator istillation column) is much more iagonally ominant. Therefore, interactions between the control loop configuration efine by the cascae iagonally elements ; [ ] x f v xb are insignificant, which permits to apply multiloop control. 4.4 Stability analysis The stability of the consiere control strategy is guarantee if the control configuration loops verify the Bristol s conition, that means, the corresponent relative gain to the control configuration pairs must be positive [5], [8-9], [14]. The values of the cascae s RGA below, inicate that the stability of this column using the control strategy shown in Figure 1 is assure, since the iagonally elements correspons to the consiere control configuration pairs are positives RGA = (3) Conventional an fuzzy PI controllers esign The conventional PI controllers are esigne using the metho evelope by Issaksson an Graeb [4], which gives the parameters epicte in Table 1. The consiere PI fuzzy controller for each loop is shown in Figure 6. Where G e, G e an G u Imaginary Axis ĝ 11 ĝ Real Axis Fig. 5 The iagonal elements of the istillation column superpose by the Gershgorin circles. are gains scaling factors an heir values are reporte in Table 1. The membership functions of inputs (error e an erivative error e) an output of each controller are triangular with five sets. The fuzzy rules escribing the controller structure are shown in Table. The inference engine use for fuzzy rules processing is sum pro metho. The center of gravity metho is use to fuzzify the overall subset representing output control variable. Loops Table 1 Controllers parameters Fuzzy controllers Conventional controllers Ge Ge u K c T i x v x b e u Where: c i N B Table Rule base e NB NS ZE PS PB NB NB NB NB ZE NS PB NB NB NB PB ZE NB NB ZE PB PB PS PS PB PB PB PB PB ZE NB PB ZE PB NB: negative big. NS: negative small. ZE: zero. PS: positive small. PB: positive big. + - y i Ge ii Ge ii Fig. 5. PI Fuzzy controller. FLC ii Gu ii Σ u i

5 4.5 Simulation results The transient responses for well tune feeback control in response to a fee composition upset are given in Figure 6, an the control performances are summarize in the IAE values in Table 3. Note that both fuzzy an conventional control assures the set point tracking. Base on the total IAE values (.791 for the conventional controllers an.139 for the fuzzy controllers) an the response time, the performances obtaine with the fuzzy multiloop control are better than those obtaine using the conventional multiloop control for the fee composition isturbance. The ynamic responses for a set point change in the top composition controller of +.5 mole fraction, with the other set point an all isturbances constant, are given in Figure 7. The results summarize in Table 3, show that the total IAE values are.55 for the conventional control an.8783 for the fuzzy control. In this case, the former system control gives the better results, but the controlle variable x b is more affecte in relation to the fuzzy control case an note that the transient responses for x present the oscillations Distillate, x Bottoms, x b Fig. 6. Transient response to a change in light key in fee of.4. Fuzzy control ; Conventional control Distillate, x Bottoms, x b Fig. 7. Transient response of istillation control to +.5 istillate light key set point change. Fuzzy control ; Conventional control Loops Table 3 IAE values Fuzzy controllers Set point change Perturbation rejection IAE Conventional controllers Set point change Perturbation rejection x v x b 5 Conclusion In this paper, a systematic esign proceure to obtain a fuzzy multiloop control for istillation column is presente. The key iea of the esign proceure is to introuce a compensator in cascae with the istillation column in orer to reuce the interaction that occurs between their strategic variables. The main avantage of the consiere multiloop control strategy is the simplicity in etermining the control rules an controllers parameters since each loop is treate inepenently both in fuzzy an conventional control. The valiity of the propose strategy, in which a compensator is introuce an esigne using an interaction analysis metho, is confirme through simulations results an emonstrates the superior performance of the fuzzy multiloop control scheme since it permits attaining esire responses to changes in set point an achieving sufficient feeback properties (isturbance rejection). Appenix The application of the metho to control a highly interactive system propose by Khelassi, et al. [6] gives: G ( s) K ( s) = G ( s) (3) Where G ( s) is the istillation column moel, ( s) G s is the cascae K the compensator an () moel. The Direct Nyquist Array (DNA) is use as an interaction metho to esign K, an the consiere control configuration is efine by the iagonally elements of G.

6 Accoring to the DNA of the G in Figure 3, the compensator will be esigne in orer to reuce the effect of f v on the controlle variable x, hence, the iea consist to etermine, using the DNA plot of G, a linear combination between columns or lines of the DNA so that the effect of f v on x will be negligible, this is achieve by the subtraction of line from line 1 witch gives the following cascae. g g11 1 G = α g () () () () 11 s g 1 s α g1 s g s (4) Where α is terminate so that the interaction transmittances are almost reuce an G ( s) will be iagonally ominant. The parameter α is etermine as follow. an K g g 11 ( ) ( ) 1 α = (5) 1 G ( s) G ( s) = (6) In orer to simplify the compensator structure an to assure the physical realization of the compensator given in (6), K is taken as: K ( ) G ( ) 1 = G (5) References [1] B. W. Bequette, T. F. Egar. Non Interacting Control System Design Methos In Distillation. Computers Chem. Engng, Vol. 13, No. 6, 1989, pp [] D. Driankov, H. Hellenoorn, M. Reinfranf. An Introuction to Fuzzy Control. Spinger Verlag, Berlin, Germany, [3] C. Georgakis, D. H. Kint, M. Kasotaki. Extensive Variable Control Structures for Binary Distillation Columns. AIChe Annl Mtg, San Francisco, [4] A. J. Issaksson, S. F. Graebe. Analytical PID Parameter Expressions for Higher Orer Systems. Automatica, Vol. 35, No. 6, 1999, pp [5] N. Jensen, D. G. Fisher, S. L. Shah. Interaction Analysis in Multivariable Control Systems. AIChE Journal, Vol. 3, N. 6, 1986, pp [6] A. Khelassi, A. Maii, A. Benhalla. A General Metho to Control Highly Interactive Systems. Preprints of the 1 st IFAC / IEEE Symposium on System Structure an Control, 9 31 August 1, Prague, Czech Republic. [7] W. L. Layben. Distillation Decoupling. In. Engng Chem. Funum, Vol. 16, 197, pp [8] T. E. Marlin. Process Control, Designing Processes an Control Systems for Dynamic Performance. McGraw Hill International Eitions, Singapore, [9] J. T. McAvoy. Interaction Analysis. Instrument Society of America, USA, [1] B. B. Meunier. La Logique Floue et Ses Applications. Eition Aison Wesley, France, [11] S. Ramchanran, R. Russell Rhinehart. A Very Simple Structure for Neural Network Control of Distillation. J. Proc. Cont., Vol. 5, No., 1995, pp [1] J. B. Riggs. Improve Distillation Column Control. Chemical Engineering Progress, Vol. 94, N. 1, [13] C. J. Ryskamp. Explicative Implicit Decoupling in Distillation Control. Chemical Process Control II. Engineering Founation. [14] S. Skogesta, I. Postlethwaite. Multivariable Feeback Control, Analysis an Design. John Wiley & Sons, Chichester, [15] K. V. Waller. Distillation Control System Structures. IFAC Control Of Distillation Columns An Chemicals Reactors, Bournemouth, UK, 1986, pp [16] F. Viel, E. Busvelle, J. P. Gauthier. A Stable Control Structure for Binary Distillation Columns. Int. J. Control, Vol. 67 No. 4, 1997, pp [17] M. F. Weischeel, T. J. McAvoy. Feasibility of Decoupling in Conventionally Controlle Distillation Columns. In. Engng Chem. Funum, Vol. 19, 198, pp [18] R. R. Yager, D. G. Filev. Essentials of Fuzzy Moeling an Control. John Wiley & Sons, 1994.