A Comparative Study on Control Techniques of Non-square Matrix Distillation Column

Transcription

1 IJCTA, 8(3), 215, pp International Science Pre A Comparative Study on Control Technique of Non-quare Matrix Ditillation Column 1 S Bhat Vinayambika, 2 S Shanmuga Priya, and 3 I Thirunavukkarau* Abtract: The non-quare matrix control i very much important in proce indutry a mot of the plant tranfer function are non-quare in nature The controlling i challenging due to the complexity involved while olving for it performance and robutne The ditillation column tranfer function with right half plane zero i conidered here for the comparative tudy in control technique The peudo invere of the teady tate gain matrix i ued here to olve the coupling problem of non-quare proce Only few control technique like Davion - Tanttu and Lielethto method to control more manipulated and le number of control variable The Integral Square Error (ISE) performance i calculated to compare the controller deign method, ince the error i mall and exit for long time Alo ettling time, overhoot, interaction and robutne are tudied eyword: MIMO non-quare ytem; peudo invere; centralized controller 1 INTRODUCTION Majority of the eparation work in the chemical indutry, amounting to almot 95%, i carried out by ditillation and thee unit conume 3% of the total energy produced in the globe [1] The ditillation column control i important for energy aving and to yield increaed profit through improved product recovery Deigning everal control method for the ditillation column poe a great challenge in the proce control intrumentation field There are variou advantage and diadvantage for uing different control method in the proce control indutrie [2] In the lat two decade, the controller deign for high purity ditillation column ha een everal modification Thi i eential to achieve the deired product purity with minimum cot A tudy of the literature how that everal attempt have been made to deign a better controller taking into conideration different criteria In the chemical proce indutrie the mot commonly ued ytem are Multiple-Input-Multiple- Output (MIMO) ytem with multiple time delay or right half plane zero The control objective for multivariable ytem i to obtain a deirable behaviour of everal output variable by imultaneouly manipulating everal input channel [2] Thee ytem are further claified into quare and non-quare ytem baed on the number of manipulated and controlled variable [3] The proce with equal number of manipulated and controlled variable are referred to a quare ytem, while thoe with unequal number of manipulated and controlled variable are non-quare ytem Non-quare ytem are le enitive to modelling error, o it ha to be controlled in it original form to obtain robut tability and performance [4] A coupled ditillation column by Levein and Morari wa conidered for the tudy The genetic algorithm optimization technique wa ued here The imulation reult proved that in the preence of uncertainty, the two type of controller tructure achieved robut performance [5] Baed on internal model control for non-quare ytem baed on Smith delay compenator control technique alo dicued 1,3 Dept of Intrumentation and Control Engineering, Manipal Intitute of Technology, Manipal Univerity, arnataka-india 2 Dept of Chemical Engineering, Manipal Intitute of Technology, Manipal Univerity, arnataka-india * itarau@manipaledu

2 113 S Bhat Vinayambika, S Shanmuga Priya, and I Thirunavukkarau in literature Alo decoupling internal model control technique invetigated in literature to tet the tability and robutne of the multiple time delay ytem [6] The problem of coupling of non-quare procee wa olved by the peudo-invere of the teady tate gain matrix The propoed method dynamically overcame the drawback caued by the tatic decoupling Stability and performance of the ytem wa achieved [7] The controlling of uch MIMO ytem i challenging tak due interaction effect on proce output Thu, need to identify the control technique with leer interaction and better performance uch a overhoot, ettling time etc 2 DISTILLATION COLUMN To purify the end product, chemical and fuel indutrie generally ue ditillation a a eparation technology However, the ditillation column preent a whole array of control complication becaue they are the mot frequently ued proce in thee indutrie [1] Conider a typical column a hown in Fig 1, which i fed F mole/hr of a feed tream containing two major component The column eparate the feed into D mole/hr of overhead or ditillate product, which contain mot of the more volatile component and B mole/hr of bottom product, which contain mot of the le volatile component The main job of the control ytem i to adjut the plit between ditillate and bottom product by controlling the flow of one or the other of thee tream Many part make up the ditillation column, and each of thee either move the heat energy or augment ma tranfer Normally, a ditillation column i made up of a vertical column, wherein tray or plate are employed to improve the eparation of the component; a reboiler poitioned at the bae of the column, which upplie the heat needed for vaporization; a condener ituated at the top of the column, which cool and condene the vapor; and latly, a reflux drum which ave the vapor o condened, whereby it can be recycled to repeat the proce all over again Figure 1: Schematic diagram of ditillation column [1]

3 A Comparative Study on Control Technique of Non-quare Matrix Ditillation Column METHODOLOGY The control block diagram of centralized PI (Proportional-Integral) controller applied to multivariable non-quare ytem i hown in Fig 2, where G p () i the tranfer function of the plant with m input and n output, G c () i the tranfer function of the controller with m output and n input where m > n The MIMO tranfer function matrix for G p () i conidered a Figure 2: Cloed loop multivariable control ytem [8, 9, 1] G pn, m () = G11 G12 G1 m G G G n1 Gn2 Gnm (1) Correpondingly, the controller matrix for the centralized PI controller i conidered a Gcm, n () = n m 1 m2 mn ij = cij + (2) (3) cij (4) = τ Where, in which cij i the controller gain and τ i the integral time of the PI controller 31 Comparion criterion for the performance of controller The performance of the controller on the proce can be meaure by Integral of Abolute Error (IAE), Integral Square Error (ISE) and Integral Time Abolute Error (ITAE) In MIMO ytem, baed on different criterion thee performance evaluation meaure have been conidered [5] The IAE hould be ued to uppre larger error, while ISE hould be ued to uppre mall error and error that lat for long time, ITAE criterion hould be ued In multivariable ytem, the election of performance criterion i alo baed on minimization of both the repone and the interaction

4 1132 S Bhat Vinayambika, S Shanmuga Priya, and I Thirunavukkarau IAE = r() t y() t dt [ ] ISE = r() t y() t dt ITAE = trt () y() t dt 2 (5) (6) (7) 4 CONTROLLER DESIGN The fully cro coupled multivariable controller i neceary for ytem with ignificant interaction [11] Since the interaction effect can be reduced along with maller overhoot and fater repone [7] The centralized control ytem have n m controller There are baically two claical model free tuning method for centralized multivariable PID controller They are i) Davion method and ii) Tanttu and Lielethto method Thee method are baed on the tranfer function matrix of the plant [4] 41 Diviion Method Davion method of centralized multivariable PI controller tuning method i applied for non-quare ytem There i no invere exit for non-quare ytem The Moore-Penroe peudo invere i ued For matrix A, it i given by A + = A H H ( A A ) 1 A H i the Hermitian matrix of A The PID controller gain for non-quare ytem i given by C [ G( = ] + = δ ) [ G( = ] + I = ε ) (1) Where [G(=)] + i called rough tuning matrix and fine tuning parameter ɛ and δ, uually range from to 1 42 Tanttu and Lielehto Method The tuning method for the deign of PI controller i baed on internal model control principle For a firt order time delay ytem ( 2τ ij + Lij ) cij = (11) 2λk τ ij ij ij (8) (9) = τ +5L (12) cij = τ (13) Where k ij and L ij are the gain and time delay of an element in the proce model for the i th output and j th input cij and τ are the proportional gain and integral time contant of the internal model controller of the ij th loop

5 A Comparative Study on Control Technique of Non-quare Matrix Ditillation Column 1133 Then the multivariable PID controller are deigned by taking the peudo-invere c I 1 = cij 1 = Where i the integral gain contant of the ij th loop + + (14) (15) 5 SIMULATION STUDIES To analyze the comparative tudy on the above control technique, we conidered a coupled ditillation column with 3-input and 2-output tudie by Levein and Morari i decribed by [5], ( ) ( ) 8 52e ) G p () = ( 1 56) Here the mole fraction of ethanol in ditillate (y 1 ) and mole fraction of water in bottom (y 2 ) are the controlled variable The ditillate flow rate (MV1), team flow rate (MV2), product fraction from the ide column (MV3) are the manipulated variable For the above plant tranfer function model, teady-tate gain matrix i given by: (16) G( ) = (17) The centralized PI controller for the peudo-invere of the above matrix i calculated uing the equation The tuning parameter ɛ= to 1 and δ=7 to 1, at which the ytem i table Thu, the centralized PI controller matrix baed on Davion method i obtained a: GC () = Similarly, uing Tanttu and Lielehto method the PI controller i obtained a: (18) GC () = It i oberved that, in both the control technique, the controller etting ign are different (eq (18) and (19)) The preence of zero in the plant tranfer function lead to change ign in ome of the individual controller (19)

6 1134 S Bhat Vinayambika, S Shanmuga Priya, and I Thirunavukkarau 51 Simulation Reult The imulation tudy i carried out uing Simulink For a unit tep change in r 1 Fig 3 how the repone in y 1 Alo, for a unit tep change in r 2 Fig 4 how the repone in y 2 The Fig 5 and Fig 6 how the interactive repone in y 2 or y 1 The ettling time and ISE value are compared for both the method It i found that the Tanttu and Lielehto control technique need more time to ettle compare to Davion method Alo Tanttu and Lielehto method give luggih repone and ISE value are 2-3 time a compared to Davion method The um of the ISE value correponding to the repone in y 1 and y 2 for the tep change in r 1 and r 2 are given in Table 1 The um of ISE for both perfect parameter and perturbed ytem i noted It i oberved that the Davion method give ISE value cloer to that of the perfect parameter ytem 52 Robutne Studie for the Ditillation Column The robutne of ditillation column i carried out by changing the individual element time contant by ±1% Alo by changing the ytem proce gain by ±1% [12] In both the cae the ame controller i ued which i obtained for original proce tranfer function The Davion method i found to be more robut than Tanttu and Lielehto method a tabulated in Table 2 Table 1 ISE value for the ditillation column uing centralized PI controller Technique Step Change in ISE value of y1 ISE value of y2 Sum of ISE Davion Tanttu & Lielehto r r r r Table 2 ISE value for robutne comparion for the ditillation column Technique Step change in Sum of ISE for original plant +1% change in proce gain +1% change in time contant Davion r r Tanttu & Lielehto r r Proce output T&L D Proce output T&L D Time (ec) Figure 3: The unit tep repone of y1 for a tep in r 1 =1 and r 2 = Time (ec) Figure 4: The unit tep repone of y2 for a tep in r 1 = when r 2 =1

7 A Comparative Study on Control Technique of Non-quare Matrix Ditillation Column Proce output y1 of T&L y2 of T&L y1 of D y2 of D Proce output y1 of T&L y2 of T&L y1 of D y2 of D Time (ec) Figure 5: The interactive repone for r 1 =1 and r 2 = Time (ec) Figure 6: The interactive repone for r 1 = and r 2 =1 6 CONCLUSIONS The Moore-Penroe peudo-invere method i ued to find the invere of the non-quare ytem The Davion method i having the benefit of mall overhoot, fater tracking feature, and le interaction compared to Tanttu and Lielethto method Better robutne could be achieved when the proce plant mimatched with the proce tranfer function model The imulation reult alo howed better operational tability and performance than the conventional control trategy in the literature There i a ign change in the individual controller deigned due to the zero in the proce tranfer function But the controller ign etting i different in both the method for the ame proce tranfer function Alo the Davion method fail when the ytem ha integral term Alo with load diturbance the repone need to be controlled to attain robutne and performance Further reearch required to be done in thi direction ACNOWLEDGEMENT Vinayambika S Bhat to acknowledge the Mangalore Intitute of Technology and Engineering, Moodabidri, for ponoring her PhD programme Reference [1] Vu Trieu Minh and Ahmad Majdi Abdul Rani, Modeling and control of ditillation column in petroleum proce, Mathematical Problem in Engineering, pp , 29 [2] Ether Monika Baumann, Modeling and control of an indutrial ditillation plant, Doctoral Thei, Swi Federal Intitute of Technology, Zurich, Bael, Switzerland, 21 [3] Peter H, I Peter, H 1998, New York: T Proce Dynamic and Control, Tata McGraw Hill, 1998 [4] L N Sharma and M Chidambaram, Centralized PI/PID controller for non-quare ytem with RHP zero, Journal Indian Intitute of Science, pp , 25 [5] P Ganeh and M Chidambaram, Multivariable Controller Tuning for Non-quare Sytem with RHP Zero by Genetic Algorithm, Chemical and Biochemical Engineering, Vol 24, pp 17-22, 21 [6] Haung Can, Gui Wei Hua, Yang Chun Hua and Xie Yong Fang, Deign of decoupling mith control for multivariable ytem with time delay Vol 18, pp , 211, J Cent South Univ,, vol 18, pp , 211 [7] Jian Chang Liu, Nan Chen, Xia Yu and Shubin Tan, Modified internal model control for non-quare ytem baed on Smith delay compenator control, Senor and Tranducer, Vol 165, pp 96-11, 214

8 1136 S Bhat Vinayambika, S Shanmuga Priya, and I Thirunavukkarau [8] Shehagiri Rao and M Chidambaram, Decoupled Smith predictor for multivariable non-quare ytem with multiple time delay, 86, , Journal Indian Intitute of Science, Vol 86, pp , 26 [9] Shahagiri Rao and M Chidambaram, Smith delay compenator for multivariable non-quare ytem with multiple time delay, Computer and Chemical Engineering, Vol 3, pp , 26 [1] Juan Chen, Ze-Fang He and Xin Qi, A new control method for MIMO firt order time delay non-quare ytem, Journal of Proce Control, pp , 211 [11] Qing-Guo Wang, Yu Zhang, Min-Sen Chiu, Non-interacting deign for multivariable indutrial procee, Journal of Proce Control, Vol 13, pp , 23 [12] Sigurd Skogetad and Ian Potlethwaite, Multivariable Feedback Control Analyi and Deign, 2 ed, John Wiely and Son, 25