PID Control of Heat Exchanger System

Transcription

1 Volume 8 No.6, October 00 PID Control of Heat Exchanger Sytem Yuvraj Bhuhan Khare Yaduvr Sngh Deartment of Electrcal & Intrumentaton Engneerng Thaar Unverty, Patala, 4700, Punjab, Inda ABSTRACT Heat exchanger ytem wdely ued n chemcal lant becaue t can utan wde range of temerature and reure. The man uroe of a heat exchanger ytem to tranfer heat from a hot flud to a cooler flud, o temerature control of outlet flud of rme mortance. To control the temerature of outlet flud of the heat exchanger ytem a conventonal PID controller can be ued. Due to nherent dadvantage of conventonal control technque, model baed control technque emloyed and an nternal model baed PID controller develoed to control the temerature of outlet flud of the heat exchanger ytem. The degned controller regulate the temerature of the outgong flud to a dered et ont n the hortet oble tme rreectve of load and roce dturbance, equment aturaton and nonlnearty. The develoed nternal model baed PID controller ha demontrated 84% mrovement n the overhoot and 44.6% mrovement n ettlng tme a comared to the clacal controller. Keyword Feed-forward controller, nternal model baed PID controller, PID Controller and heat exchanger.. INTRODUCTION In ractce, all chemcal roce nvolve roducton or aborton of energy n the form of heat. Heat exchanger commonly ued n a chemcal roce to tranfer heat from the hot flud through a old wall to a cooler flud. There are dfferent tye of heat exchanger ued n the ndutry but mot of the ndutry ued heat exchanger ytem []. Heat exchanger are robably the mot common tye of heat exchanger alcable for wde range of oeratng temerature and reure. They have larger raton of heat tranfer urface to volume than double e heat exchanger, and they are eay to manufacture n large varety of ze and confguraton. They can oerate at hgh reure, and ther contructon facltate daembly for erodc mantenance and cleanng. Heat exchanger fnd wderead ued n refrgeraton, ower generaton, heatng and ar-condtonng, chemcal roce, manufacturng, and medcal alcaton. A heat exchanger n an extenon of the double e confguraton. Intead of ngle e wthn a larger e, a heat exchanger cont of bundle of e or tube encloed wthn a cylndrcal hell. In the heat exchanger one flud flow through a tube and a econd flud flow through wthn the ace between the tube and the hell. Th aer reort a work that conder a heat exchanger and buld a ngle-nut ngle outut model of the ytem wth the hel of exermental data avalable. The outlet temerature of the heat exchanger ytem ha to be ket at a dered et ont accordng to a roce requrement. Frtly a clacal PID controller mlemented n a feedback control loo o a to acheve the control objectve. PID controller exhbt hgh overhoot whch underable. To reduce the overhoot and otmze the control erformance, a feed forward controller ued along wth a feedback controller. The combned effect of feedback and feed forward control cheme gve a much better reult than the feedback PID controller.. HEAT EXCHANGER SYSTEM A tycal nteractng chemcal roce for heatng cont of a chemcal reactor and a heat exchanger ytem. The roce flud whch the outut of the chemcal reactor tored n the torage tank. The torage tank ule the flud to the heat exchanger ytem. The heat exchanger heat u the flud to a dered et ont ung uer heated team at 80 C uled from the boler. The torage tank ule the roce flud to a heat exchanger ytem ung a um and a non returnng valve. The uer heated team come from the boler and flow through the tube, wherea the roce flud flow through the hell of the heat exchanger ytem. After the team heat u the roce flud, the condened team at 00 C goe out of the heat exchanger ytem. There alo a ath of non condened team to go out of the hell and heat exchanger ytem n order to avod the blockng of the heat exchanger. Dfferent aumton have been condered n th reearch aer. The frt aumton that the nflow and the outflow rate of flud are ame, o that the flud level mantaned contant n the heat exchanger. The econd aumton the heat torage caacty of the nulatng wall neglgble. In th feedback roce control loo, the controller revere actng, the valve ued of ar to oen (fal-cloe) tye. A thermocoule ued a the enng element, whch mlemented n the feedback ath of the control archtecture. The temerature of the outgong flud meaured by the thermocoule and the outut of the thermocoule (voltage) ent to the tranmtter unt, whch eventually convert the thermocoule outut to a tandardzed gnal n the range of 4-0 ma. Th outut of the tranmtter unt gven to the controller unt. The controller mlement the control algorthm, comare the outut wth the et ont and then gve neceary command to the fnal control element va the actuator unt. The actuator unt a current to reure converter and the fnal control unt an ar to oen (fal-cloe) valve. The actuator unt take the controller outut n the range of 4-0 ma and convert t n to a tandardzed reure gnal,.e. n the range of 3-5 g. The valve actuate accordng to the controller decon. Fgure how the bac feedback control cheme mlemented n a heat exchanger ytem. There can be two tye of dturbance n th roce, one the flow varaton of nut flud and the econd the temerature varaton of nut flud. But n ractce the flow varaton of nut flud a more romnent dturbance

2 Volume 8 No.6, October 00 than the temerature varaton n nut flud. So, n feed forward control loo, the nut flud flow meaured and the dturbance n the flow controlled ung a feed forward controller. The outut of the feedback and the feed forward controller added and the reultant outut gven to the control valve. Wth the addton of feed forward controller the control erformance further otmzed. Fgure : Heat Exchanger Sytem Control Scheme 3. MATHEMATICAL MODELLING Fgure how conventonal control block dagram contng of roce, controller, actuator, fnal control element, enor, et ont and dfferent knd of roce dturbance. From the exermental data, the tranfer functon and gan are obtaned a below: Tranfer functon of roce Gan of valve 0.3 Tranfer functon of valve T 50e d Fgure : Block dagram for feedback control of heat exchanger ytem. Gan of I/P converter 0.75 Tranfer functon of dturbance varable (flow and temerature dturbance reectvely) 3, Tranfer functon of thermocoule 0 To control the ext temerature of the heat exchanger ytem a clacal feedback controller ued. The PID control algorthm reman the mot oular aroach for ndutral roce control dete contnual advance n control theory. Th not only due to the mle tructure whch concetually eay to undertand and, whch make manual tunng oble, but alo to the fact that the algorthm rovde adequate erformance n the vat majorty of alcaton. The charactertc equaton (+G() H() =0) n th cae obtaned a below k c +=0 () Routh tablty crteron gve kc a 3.8 () Auxlary Equaton k c +=0 =0.8 and T=8.79 PID controller n contnuou tme gven a de( t) u( t) kc e( t) e( t) dt d dt The tranfer functon of PID controller u () Gd () k e() c t 0 d u () d Gd () kc e( ) f (3) (4) (5) u () d Gd () kc e( ) (6) Mot of the PID tunng rule develoed n the lat xty year ue frequency-reone method [6,8]. Examle nclude, Zegler Nchol rule, ymmetrc otmum rule, Zegler Nchol comlementary rule, ome-overhoot rule, no-overhoot rule, refned Zegler Nchol rule, ntegral of quared tme weghted error rule, and ntegral of tme abolute error rule [7]. Thee method are traghtforward to aly nce they rovde mle tunng formulae to determne the PID controller arameter. However, nce only a mall amount of nformaton on the dynamc behavour of the roce ued, n many tuaton they do not rovde good enough tunng or roduce a atfactory cloed-loo reone. In ractce, the Zegler Nchol rule often lead to a rather ocllatory reone to et ont change. From t nventon n 940 Zegler-Nchol tunng rule ued extenvely n ndutre to tune the PID controller. Accordng to Zegler-Nchol frequency reone tunng crtera K 0.6Kc, 0.5T and d 0.5T For the PID controller n the heat exchanger, the value of tunng arameter obtaned are K =4.8, τ =4.395, τd=3.59 and P= 3.8, I=.65, D=85.44 Uually, ntal degn value of PID controller obtaned by all mean need to be adjuted reeatedly through comuter mulaton untl the cloed loo ytem erform or comrome a dered. In order to have a good cloedloo tme reone, the followng erformance functon are condered durng the degn of a PID controller. f 3

3 Volume 8 No.6, October 00 J( K, K, Kd ) ( r( t) y( t)) dt (7) 0 J( K, K, Kd ) t ( r( t) y( t)) dt (8) 0 Thu, the otmal PID controller degn tated a mn J (K, K, Kd ) The dturbance nut ntroduce error n the ytem erformance. In everal ytem the dturbance can be redcted and t effect can be elmnated wth the hel of feed forward controller before t can change the outut of the Sytem. In feedback control cheme the enor detect the roce outut and gve the error to the controller, whch n turn take arorate controllng acton. But tll the controllng acton reache the roce, the outut ha been changed. So a feed forward controller along wth the feedback controller ha been mlemented. A feed forward control etmate the error and change the manulatng varable before the dturbance can affect the outut. To further mnmze the overhoot a feed-forward controller ntroduced n the forward ath of the roce along wth the feedback controller. The combned effect of feedback and feedforward controller reduce the overhoot value. Fgure 4 how the tranfer functon rereentaton of ytem wth feedback and feed-forward controller. Ste reone of heat exchanger ytem wth feedback controller. T 5e G ( ), G ( ) d The tranfer functon of the feed-forward controller G cf () Gd () G () (9) (0) Fgure 4: Feed forward and feedback control block dagram of heat exchanger ytem. INTERNAL MODEL BASED PID CONTROLLER The mot common ndutral controller PID controller and nternal model control cheme hown n fgure 7 can be ued to degn a tandard feedback PID controller. The tandard feedback controller a functon of the nternal model and nternal model controller Q(). The tranfer functon of feedback controller equvalent to nternal model controller hown n eq. (). G () c Q (). () G ( ) Q( ) Subttutng the value n eq. () the tranfer functon of the feedback controller baed on nternal model controller obtaned a hown n eq. (3). G () c ( ). (3) Equatng the term of eq. (5) and eq. (3), the value of PID arameter are obtaned. PID controller for mroved dturbance rejecton can be acheved by changng the nternal model controller flter. For mroved dturbance rejecton the flter n the form of F() = ( ) n (4) Here γ elected to acheve good dturbance rejecton. It elected to cancel low dturbance tme contant. Several method of tunng of nternal model controller and effcent calculaton of flter arameter have been rooed n lterature []. 4. SIMULATION AND TESTING The mulaton for the dfferent control mechanm dcued above were carred out n Smulnk and the mulaton reult have been obtaned. Fgure 5 rereent the Smulnk modellng of the heat exchanger ytem wth PID a a feedback controller. G cf () () 4

4 Volume 8 No.6, October 00 Fgure 5: Smulnk model of heat exchanger ytem wth feedback PID controller. A hown n fgure 5 for auto-tunng of PID controller, a relay block connected n arallel wth the PID controller wth the hel of a manual wtch. When the auto-tune functon requred, the manual wtch et to the relay block. The relay block rereent a nonlnear behavour. In auto-tune mode, the cloed loo ytem ocllate and the manulated varable acton ON-OFF. From the auto-tune mode, two arameter are obtaned. Thee arameter are ultmate gan and ultmate frequency. Ultmate gan and ultmate frequency are gven a Ultmate gan (5) Ultmate frequency (6) K cu u 4h a Here P the erod between the ucceve eak a the amltude of roce outut h the heght of controller outut The behavour obtaned from auto tunng mode very mlar to the behavour obtaned from Zegler- Nchol cloed loo cyclng method. Fgure 6 how the te reone of the heat exchanger ytem wth PID controller wth and wthout tranortaton delay. Ste reone of heat exchanger ytem wth feedback controller. Fgure 7 how the Smulnk model of heat exchanger ytem wth both feedback and feed-forward controller. The advantage of feed-forward control trategy that a dturbance varable meaured and a manulated varable changed before the outut affected. But the man dadvantage of th knd of control trategy entvty to uncertanty. If the nlet flow rate not erfectly meaured or the team nut can t be manulated erfectly, then the outlet temerature of heat exchanger wll not be erfectly controlled. Wth any mall dturbance the outut temerature can t be controlled n an effectve manner. Fgure 7: Smulnk model of heat exchanger ytem wth feedback and feed forward controller. To mlement a feed-forward control trategy ror knowledge of the roce dturbance and mathematcal model of the roce mut be known to the roce engneer. Fgure 8 how the te reone of the heat exchanger ytem wth feedback and feed forward controller. The combned effect of feedback and feed forward controller reduce the overhoot and alo decreae the ettlng tme by %. Fgure 8: Ste reone of heat exchanger ytem wth feedback and feed forward controller. Fgure 9 how the Smulnk model of heat exchanger ytem wth nternal model baed PID controller. Internal model baed PID controller carre a gnfcant advantage over conventonal PID controller a there only one tunng arameter where a there are three tunng arameter n 5

5 Volume 8 No.6, October 00 conventonal PID controller. Fgure 0 how the te reone of heat exchanger ytem when an nternal model baed PID controller ued to control the controllng varable. The maxmum overhoot only 5% and the controller meet both teady tate and tranent tate crtera. Fgure 9: Smulnk model of nternal model baed PID controller. Fgure 0: Ste reone of controller. nternal model baed PID To evaluate the erformance of the dfferent controller th aer ha condered two vtal arameter of the te reone of the ytem. The frt arameter the maxmum overhoot and the econd arameter the ettlng tme. 5. RESULT AND DISCUSSION In the tme doman, ecfcaton for a control ytem degn nvolve certan requrement aocated wth the tme reone of the ytem. The requrement are often exreed n term of the tandard quantte on the re tme, ettlng tme, overhoot, eak tme, and teady tate error of a te reone. In all the four controller thee two arameter are evaluated. A comaratve tudy of ther erformance ha been n the table below. From the above obervaton t clear that n conventonal PID controller n feedback loo the heat exchanger roduce an overhoot 38.38%. To comenate th knd of hgh overhoot a feed forward controller n conjuncton wth the conventonal PID n feedback loo mlemented. By mlementng th method the ytem overhoot wa reduced to 30%, an mrovement of %. Though the overhoot ha ome what decreaed, t can be further decreaed by mlementng nternal model baed controller and nternal model baed PID controller. By mlementng nternal model baed PID controller the overhoot reduce to 5% reectvely. In feedback controller the ettlng tme wa 5. ec where a n feed forward lu feedback controller the ettlng tme decreae to 9.34 ec, an mrovement of 0.7%. By mlementng nternal model baed PID controller the ettlng tme decreae by 63.8 ec. From thee obervaton t clear that nternal model baed PID controller a much better oton for control rather than conventonal feedback and feedback lu feed forward controller. 6. CONCLUSIONS Th aer take a cae tudy of heat exchanger ytem and evaluate dfferent method to control the outlet flud temerature. Four dfferent knd of controller are degned to control the outlet temerature of flud and the erformance of thee controller are evaluated by two dfferent method. One of the method for erformance evaluaton the tme doman analy of overhoot and ettlng tme and other method calculaton of erformance Indce. Frtly a clacal PID controller degned to acheve the control objectve. But due to the unatfactory erformance of the PID controller a feed forward controller degned and laced n the forward ath of the ytem. To further ncreae the effcency of the ytem the nternal model baed PID controller degned and mlemented. The nternal model baed PID controller gve atfactory erformance n both teady tate and tranent tate n tme doman analy. The erformance ndce of all the controller are alo evaluated. Th aer take the roce model to be the ame a the roce, whch ractcally moble to acheve. So a a further work we can mlement drect model and nvere model baed controller and aly ytem dentfcaton a well a neural network concet for etmaton of roce model. 6

6 Volume 8 No.6, October REFERENCES [] Fernando G. Martn, Tunng PID Controller U ng the ITAE Crteron, Internatonal Journal of Engneerng Educaton, vol., no. 3, 005. [] G.K.I. Mann, B. G. Hu and R.G Gone, Tme- Doman Baed Degn and Analy of New PID Tunng Rule, IEEE Proceedng of Control Theory Alcaton, vol. 48, no. 3,, 00,. 5-6 [3] G.P. Lu, S. Daley, Otmal Tunng PID Control for Indutral Sytem, Control Engneerng Practce, 9, 00, [4] Ian G Horn et.al, Imroved Flter Degn n In ternal Model Control, Indutral Engneerng Chemtry Reearch, 35, 996, [5] Ibrahm Kaya and Nuret Tan, Controller Degn for Stable Procee Ung Uer Secfed Gan and Phae Margn Secfcaton and Two Degreeof-Freedom IMC Structure, n Proceedng of th Medterranean Conference on Control and Automaton, 003 [6] Kam Heong Ang, Gregory Chong and Yun L, PID Control Sytem Analy, Degn, and Technology, IEEE tranacton on control ytem technology, vol. 3, no. 4, 005, [8] Orlando Duran et.al, Neural Network for Cot Etmaton of Shell and Tube Heat Exchanger, n Proceedng of Internatonal Mult Conference of Engneer and Comuter Scentt, vol II, 008. [9] R. Vlanova et.al, A Framework for Dturbanc e Attenuaton on SISO Stable/Untable Sytem, n Proceedng of 7 th World Congre on Intellgent Control and Automaton, 008, [0] Satean Tunyarrut et.al, The Auto-Tunng PID Controller for Interactng Water Level Proce, n Proceedng of World Academy of Scence, Engneerng and Technology, vol., 006, [] T N Luan et.al, Degn of Mult-Loo PID Controller Baed on the generalzed IMC-PID Method wth M Crteron, Internatonal Journal of Control, Automaton, and Sytem, vol. 5, no., 007,. -7. [] Wen Tan et.al, Comaron of Some well-known PID Tunng Formula, Comuter and Chemcal Engneerng, 30, 006, [7] Myungoo Jun and Mchael G. Sofonov, Automatc PID Tunng: An Alcaton of Unfalfed Control, IEEE Symoum on CACSD, 999,