Benchmark for PID control based on the Boiler Control Problem

PID' Bresca (Italy), March 8-0, 0 ThA. Benchmark for PID control based on the Boler Control Problem F. Morlla Departamento de Informátca y Automátca, Escuela Técnca Superor de Ingenería Informátca, UNED, C/. Juan del Rosal 6, 8040 Madrd, Span, (Tel: 4+998756; fmorlla@da.uned.es) Abstract: Ths paper descrbes the benchmark proposed for the IFAC Conference on Advances n PID Controllers (PID ) at the end of july 0. It s expected that ths benchmark allows researchers to test ther recent developments n the desgn of PID controllers. Two approaches to the bolng process were provded; the frst ready to test a multvarable PID controller and the second ready to test PID controller, both wth or wthout feedforward. Nevertheless, the boler control systems descrbed n ths paper are ready to test other multvarable control strateges. The full documentaton about the benchmark was lnked from the webste PID and wll reman n www.da.uned.es/~fmorlla/benchmarkpid0. Keywords: boler control, bolng process, decentralzed control, PID control.. INTRODUCTION Steam generaton systems are a crucal part of most power plants. Therefore, boler control s an mportant problem for power plants that are frequently changng load or subject to sudden load dsturbances, whch are common n current market drven electrcty ndustry. In such crcumstances t s requred to keep the boler operatng well for large changes n the operatng condtons. One way to acheve ths s to ncorporate more process knowledge nto the control system (Aström and Bell, 000). In the boler area, nowadays many models exst rangng from complex knowledge based models to expermental models derved from specal plant tests. But, any model to be used for control system testng must take nto account the couplng between the ndvdual boler subsystems. Ths s satsfed by the control orented model proposed by Pellegrnett and Bentsman (996), that predcts the process response n terms of measurable outputs (drum pressure, drum water level, and excess oxygen n flue gas) to the major manpulated nputs (ar/fuel flow rates, feedwater flow rate) as well as the effect of dsturbances (changed steam demand, sensor nose), model uncertanty (e.g., fuel calorfc value varatons, heat transfer coeffcent varatons, dstrbuted dynamcs of the steam generaton), and constrants (actuator constrants, undrectonal flow rates, drum floodng). There s an extensve lterature related wth boler control systems. Tradtonally, they have been bult up as combnaton of conventonal sngle varable control loops, wth or wthout feedforward, and computaton of certan varables that cannot be measured drectly (Balchen and Mummé, 988). Other researchers propose to use advanced control technques, because they may gve better performance than a decentralzed one (Tan et al. 004, Lu et al. 005, Garrdo et. al. 009). More complex technques, LQG/LTR, H control, predctve control, and fuzzy control, have been also appled to mprove boler performance (Tan et al. 005). The advantage of usng PID controllers s ther ease of mplementaton and tunng, whle the advantage of other controllers s ther performance mprovement. There s always a tradeoff between ease to use and cost to mplement and tune (Tan et al. 004). The benchmark proposed n ths work wll allow researchers to approach an mportant control problem n order to test ther recent developments n the desgn of PID controllers. Ths paper s organzed as follows. The Boler Control Problem s presented n Secton. The attenton s frst addressed to the most general problem, and then, t s addressed to the MIMO and SISO problems selected for the benchmark. In addton, detals about the Boler Model are gven, payng specal attenton to the two open-loop bolng processes consdered n the benchmark. Secton descrbes how the testng and comparatve evaluaton of multvarable PID controllers can be carred out. The Secton 4 s dedcated to test the PID controller. Fnally, secton 5 summarzes the conclusons. All the examples mentoned n ths document can be checked downloadng the fles provded by the author n the webste: www.da.uned.es/~fmorlla/benchmarkpid0/. Full documentaton about the benchmark s also avalable n the webste.. THE BOILER CONTROL PROBLEM A schematc pcture of a typcal drum boler s shown n Fg.. The water that s to be evaporated s added to a drum. From the drum, the water goes down through the downcomers, whch are located outsde of the frebox. The water then goes nto the rsers, whch are located n the hottest part of the furnace. Here, the water evaporates, and the steam rses and flows back up to the drum. The combustble, fuel n ths case, s burned wth ar n the frebox. The functon of a boler s to delver steam of a gven qualty (temperature and pressure) ether to a sngle user, such as a steam turbne, or to a network of many users. Then, a

PID' Bresca (Italy), March 8-0, 0 ThA. properly functonng boler must satsfy the followng basc requrements: ) The rato of ar to fuel must be carefully controlled n order to obtan good, safe, and effcent combuston. ) The level of water n the drum must be controlled at the desred level n order to prevent overheatng of drum components or floodng of steam lnes. ) A desred steam pressure must be mantaned at the outlet of the drum despte varatons n the quantty of steam demanded by users. Wth the prevous assumptons, the Benchmark provdes two boler control systems. The system of Fg. 4, that s ready to test a multvarable PID Controller wth or wthout feedforward. And the system of Fg. 5, that s ready to test a PID Controller wth or wthout feedforward. Nevertheless, any type of controller can be tested. Y U Fuel flow Water flow Load lev el Oxygen level BOILER wth ar control setponts Y U MIMO PID CONTROLLER nputs loadlevel From outputs Workspace Fg. 4. MIMO PID Boler Control System. Y U Fuel f low Oxygen lev el setpo nt PID CONTROLLER Load level BOILER wth ar and water control Fg.. Schematc pcture of an ndustral drum boler. To fulfl the control objectves lsted above, the control system for a drum boler s usually dvded nto several subsystems. Therefore, assumng that ar flow rate s regulated properly by the ar control subsystem, we can approach the bolng process as the x system shown n Fg.. In ths system, two varables (steam pressure and water level) can be controlled by two manpulated varables (fuel flow and water flow) takng nto account the measured dsturbance varable (load level). In addton, the ndrect controlled varable (oxygen level) can be used as qualty performance varable. Fuel flow Water flow Load lev el Oxygen level BOILER wth ar control Fg.. Bolng process approached as a x system. Moreover, assumng that the water flow rate s regulated properly by the feedwater control subsystem, we can approach the bolng process as the x system shown n Fg.. Now the steam pressure can be controlled by the fuel flow takng nto account the load level, and the ndrect controlled varable (oxygen level) and the controlled varable (water level) can be used as qualty performance varables. Fuel flow Load lev el Oxygen level BOILER wth ar and water control Fg.. Bolng process approached as a x system. loadlevel From Workspace Fg. 5. SISO PID Boler Control System.. About the controllers nputs outputs The multvarable controller needs to be a 5x Smulnk block; however, t could be a contnuous, a dscrete or a hybrd block. There s also total freedom to decde the structure of the block; the controller can use the fve nput sgnals or only some of them. The fve nput sgnals are: the steam pressure (Y), ts setpont (), the water level (Y), ts setpont () and the load level (). The two output sgnals are the fuel flow (U) and the water flow (U). Fg. 6 shows the multvarable controller ncluded by default n the Benchmark. It s a decentralzed PID controller, the smplest structure, wth two dscrete PID controllers (PID and PID) wthout feedforward compensaton. Y Y U U MIMO PID CONTROLLER Y 4 Y 5 Setpont Process value Setpont PID Process value PID Termnator Fg. 6. The decentralzed PID controller ncluded by default n the MIMO PID Boler Control System. Control Control U U

PID' Bresca (Italy), March 8-0, 0 ThA. The PID controller needs to be a x Smulnk block; however, t could be a contnuous, a dscrete or a hybrd block. There s also total freedom to decde the structure of the block; the controller can use the three nput sgnals or only some of them. The three nput sgnals are: the steam pressure (Y), ts setpont () and the load level (). The output sgnal s the fuel flow (U). Fg. 7 shows the PID controller ncluded by default n the benchmark. Y U PID CONTROLLER Y Setpont Process value PID Termnator Fg. 7. The PID controller ncluded by default n the SISO PID Boler Control System.. About the Boler Model The control systems of Fg. 4 and 5 use the same nonlnear model proposed by Pellegrnett and Bentsman (998). The model has been developed n Smulnk ncludng some changes: several coeffcents have been slghtly modfed, restrcted ranges for the nputs and outputs have been selected and normalzed n percentage. However, the followng man features of the model have been preserved: ) It has a relatvely low complexty whle fathfully capturng the essental plant dynamcs and ts nonlneartes over a wde operatng range. Control U The open-loop features of the x bolng process are the followng: the steam pressure response s stable for the two nputs. The oxygen level s only slghtly affected by the fuel flow. The water level n the drum shows now the selfregulatng behavour for the two nputs. The level control loop s hdng some dffcultes mentoned before, but they are present because the process s the same.. TESTING MULTIVARIABLE PID CONTROLLERS The MIMO PID Boler Control System of Fg. 4 s ready to test any multvarable controller operatng the boler n dfferent scenaros. The Matlab program Test_Boler_ MIMOControl.m s provded to help ths testng. The only requrement s that all experments should start from the same operatng pont mentoned n Secton.. They can nclude step changes n the steam pressure setpont, n the water level setpont and tme varant load level condtons. Three types of experments have been consdered n the benchmark. The standard experment ncludng a step change n the load level, the experment type ncludng a profle of load level, and the experment type ncludng a sngle step n the steam pressure setpont. The MAT-fles dat_n_boler_ mmo, dat_n_boler_mmo and dat_n_boler_mmo are prepared to generate the correspondng smulaton condtons. These experments or any others experments can be also used to explore the boler operatng ponts. The model s able to attend load level between 0% and 70% wth steam pressures between 0% and 70%. ) The model s control orented n that the manpulated varables, the controlled varables and the sgnfcant dsturbance are explctly shown. ) The model s realstc n that the constrants on the manpulated varables are known, and the measurement nose and tme delays are present on the outputs. The boler model accepts nput varables n the range 0-00%. And addtonally, a rate lmt of ±%/s has been ncorporated for the fuel flow and ndrectly for the ar flow. The model s ready to be controlled wth a samplng perod greater than 0. s, startng always n the same operatng pont gven by: Fuel flow 5.%, Water flow 57.57%, Load level 46.6%, =60%, Oxygen level=50%, =50%. The open-loop features of the x bolng process are the followng: The steam pressure response s stable for the three nputs (the two flows and the load level). The oxygen level s only slghtly affected by the fuel flow. The water level n the drum shows non-mnmum phase behavour for the fuel flow and the load level, n addton to an ntegratng response for the three nputs. The tme delays are not sgnfcant n ths process. The man control dffcultes n ths multvarable process are caused by the couplng, the non-mnmum phase, the ntegraton and the load dsturbance. More nformaton about the bolng process s avalable n the benchmark webste. Fg. 8. Example of standard test wth the MIMO PID Boler Control System. Fg. 8 s an example of standard test. A new operatng pont has been reached due to a 0% load level step change at

PID' Bresca (Italy), March 8-0, 0 ThA. t=00 s. It has been possble ncreasng the fuel flow and the water flow, whle the steam pressure and the water level recover ther setponts after about 800 s. Durng the experment the oxygen level remans ndrectly controlled by the fuel/ar rato, affected only by the nose. Ths example can be checked wth the m-fle Test_Boler_MIMOControl loadng the MAT-fle dat_n_boler_mmo. The benchmark ams also to facltate the comparatve evaluaton of controllers provdng the Matlab program Boler_MIMOControl_Evaluaton.m. Two controllers, whch have been prevously tested n the same experment, can be compared each tme. One of them plays the role of controller of reference (C r ) and the other one plays the role of controller to evaluate (C e ). For the multvarable boler control problem seven ndvdual performance ndexes and one combned ndex have been proposed n the comparatve evaluaton. shows two decentralzed PID controllers that are canddates for the next comparatve evaluatons. The table only shows the control parameters that have been modfed: the samplng perod for control t c, the proportonal gan (K P ) and the ntegral tme (T I ). The other common features are: no dervatve acton (T D =0), proportonal acton wth the error sgnal, 0-00% control range, %/s rate lmt n controller. Table. Decentralzed PID controllers for the next comparatve evaluatons t c K P T I Case of Controller 0 s.5 50 s reference Controller 0 s.5 50 s Case to Controller 5 s 5.0 5 s evaluate Controller 5 s.5 5 s The frst three ndexes are the Ratos of Integrated Absolute Error (RIAE) takng nto account that the steam pressure and the water level have ther respectve setponts and that the oxygen level must reman n the 50%. The fourth and ffth ndexes are the Ratos of Integrated Tme multpled Absolute Error (RITAE) for the two controlled varables, the steam pressure and the water level. The varable typechange s used to dsplay the RITAE ndex only when the respectve setpont has changed. The sxth and seventh ndexes are the Ratos of Integrated Absolute Varaton of Control sgnal (RIAVU) for the two manpulated varables, the fuel flow and the water flow. The combned ndex J M s obtaned as the mean value of the seven ndvdual ndexes usng a weghtng factor (w) for the RIAVU ndexes. The followng expressons, whch summarze these ndexes, have been programmed n the Matlab functon JBolerMIMO.p. IAE = ITAE = IAVU = tme e (t) dt () 0 tme ( t-tchange ) e (t) dt () tchange d u (t) tme 0 dt dt () IAE (C ) e RIAE (C e,c r) = (4) IAE (C r ) ITAE (C ) e RITAE (C e,c r) = typechange (5) ITAE (C r ) IAVU (C ) e RIAVU (C e,c r) = (6) IAVU (C r ) ( ) J C,C,w = M e r = + RIAE (C,C ) + RITAE (C,C ) + RITAE (C,C ) + = e r e r e r w RIAVU (C,C ) e r + typechange +typechange + w Note that the comparatve evaluatons are not restrcted to very dfferent controllers. For nstance, the comparatve evaluatons of controllers whch only dffer n the control parameters can be useful to fnd the best tunng. The Table (7) Fg. 9. Example of comparatve test type for the MIMO PID controllers of Table. Case of reference n blue. Case to evaluate n green. Fg. 9 s an example of comparatve test type for the controllers of Table. Startng at the operatng pont, the system had to attend a tme varant load level. Frst, the load ncreased n ramp from 46.6% at t=00 s untl 70% n t=500 s; second, the load remaned constant; thrd, the load decreased n ramp at t=000 s untl reachng the ntal operatng pont at t=400 s, where t remaned untl t=400 s. The change of control parameters has brought two drect benefts: the steam pressure and the water level show mnor devatons from ther setponts. However, that was possble wth more actvty n the fuel flow and the water flow. Durng the experment the oxygen level remans ndrectly controlled by the fuel/ar rato, affected only by the nose. The Table shows the numercal comparatve evaluaton. The change of

PID' Bresca (Italy), March 8-0, 0 ThA. control parameters has drastcally reduced the error ndexes RIAE and RIAE. It comes at the expense of ncreasng the control ndexes RIAVU and RIAVU. The global beneft s apparent by a J M ndex less than the unt, from 0.56 wth w=0 to 0.9574 wth w=. The value 0.68 corresponds to w=0.5. Ths example can be checked wth the m-fle Boler_MIMOControl_Evaluaton loadng the MAT-fles testbolermimo_cl and testbolermimo_cl. Table. Indexes correspondng to the test of Fg. 9 RIAE RIAE RIAE RITAE 0.645 0.9996 0.4 - RITAE RIAVU RIAVU J M (0.5) -.58.6868 0.680 table shows that J M s near the unt for w=0.5. Ths example can be checked wth the m-fle Boler_MIMOControl_ Evaluaton loadng the MAT-fles testbolermimo_cl and testbolermimo_cl. Table. Indexes correspondng to the test of Fg. 0 RIAE RIAE RIAE RITAE 0.50.540.98 0.696 RITAE RIAVU RIAVU J M (0.5) -.660 4.4489.0985 4. TESTING THE PID CONTROLLER The SISO PID Boler Control System of Fg. 5 s prepared to test any controller for step change n the steam pressure setpont and for tme varant load level condtons. The procedure to follow s smlar to the multvarable case and three types of experments have been consdered. For the sngle-loop boler control problem, fve ndvdual ndexes and one combned ndex have been proposed n order to compare the controllers. The Matlab program Boler_SISOControl_Evaluaton.m and the functon JBolerSISO.p are provded to help ths testng. The combned ndex s gven now by (8). ( ) J C,C,w = S e c = RIAE (C,C ) + RITAE (C,C ) + w RIAVU(C,C ) e r e r e r + typechange + w (8) Table 4 shows the two PID controllers that are canddates for the next comparatve evaluaton. The table only shows the control parameters that have been modfed: the samplng perod for control t c, the proportonal gan (K P ) and the ntegral tme (T I ). Others common features are: no dervatve acton (T D =0), proportonal acton wth the error sgnal, 0-00% control range, %/s rate lmt n the controller. Table 4. PID controllers for the next comparatve evaluatons Fg. 0. Example of comparatve test type for the MIMO PID controllers of Table. Case of reference n blue. Case to evaluate n green. Fg. 0 s an example of comparatve test type for the same decentralzed PID controllers. Startng at the operatng pont, the system had to attend a sudden change of 5% n the steam pressure setpont at t=00 s. The change of control parameters has brought only benefts about the steam pressure response. The water level showed great oscllatons and there was more actvty n the fuel flow and the water flow. Durng the experment, the oxygen level showed a greater transtory devaton. The Table shows the numercal comparatve evaluaton. The change of control parameters has drastcally reduced the error ndexes RIAE and RITAE. It comes at the expense of ncreasng the other ndexes. There s not apparent global beneft, because the J M ndex goes from 0.796 wth w=0 to.708 wth w=. The t c K P T I Case of reference 0 s.5 50 s Case to evaluate 5 s 5.0 5 s Fg. s an example of comparatve test type wth the controllers of Table 4. The change of control parameters has brought a drect beneft: the steam pressure show mnor devatons from ts setpont. Nevertheless that was possble wth more actvty n the fuel flow. Durng the experment, the water level showed smlar devatons and the oxygen level remaned ndrectly controlled by the fuel/ar rato, affected only by the nose. The Table 5 shows the numercal comparatve evaluaton. The change of control parameters has drastcally reduced the error ndex RIAE. It comes at the expense of ncrease the control ndex RIAVU. The global beneft s apparent by a J ndex less than the unt. The value 0.870 corresponds to a weghtng factor w=0.5. Ths example can be checked wth the m-fle Boler_SISOControl_Evaluaton loadng the MAT-fles testbolersiso_cl and testbolersiso_cl.

PID' Bresca (Italy), March 8-0, 0 ThA. controller, ncludng or not PID controllers, operatng the boler n dfferent scenaros. Fg.. Example of comparatve test type for the PID controllers of Table 4. Case of reference n blue. Case to evaluate n green. Table 5. Indexes correspondng to the test of Fg. RIAE RIAE RIAE RITAE RIAVU J S (0.5) 0.646.000.0747 -.54 0.870 Fg. s an example of comparatve test type, where the two PID controllers have the same K P =5 and T I =5 s, and dfferent samplng perods; t c =0 s and t c =5 s respectvely. The change of the samplng perod has brought great benefts. The oscllatons n the steam pressure response have almost dsappeared. The Table 6 shows that all ndexes have been drastcally reduced. Ths example can be checked wth the m- fle Boler_SISOControl_Evaluaton loadng the MAT-fles testbolersiso_cl and testbolersiso_cl. Table 6. Indexes correspondng to the test of Fg. RIAE RIAE RIAE RITAE RIAVU J S (0.5) 0.504 0.69 0.799 0.655 0.5745 0.654 5. CONCLUSIONS The benchmark provdes two approaches to the bolng process n order that researchers can test ther recent developments n the desgn of PID controllers. It provdes also ndvdual and combned performance ndexes for usng n the comparatve evaluaton of controllers. Three types of experments are used to llustrate the decentralzed or sngleloop PI control of the bolng process. Nevertheless, the benchmark can be very useful to test any multvarable Fg.. Example of comparatve test type for two PID controllers wth dfferent samplng perod. Case of reference n blue. Case to evaluate n green. ACKNOWLEDGEMENTS Ths work was supported by the Spansh CICYT under grant DPI 007-605. The author wshes to express hs grattude for the support and suggestons durng the preparaton of the benchmark to R. González from Petronor, F. Vazquez and J. Garrdo from Unversty of Córdoba, S. Dormdo from UNED, and A. Vsol from Unversty of Bresca. REFERENCES Aström K. J., and Bell, R. D. (000). Drum-boler dynamcs. Automatca, Vol. 6, pp. 6-78. Balchen, J. G., and Mummé, K. I. (988). Process Control: Structures and Applcatons. Van Nostrand Renhold Company Inc., NewYork. Garrdo, J., Morlla, F., and Vázquez, F. (009). Centralzed PID Control by Decouplng of a Boler-Turbne Unt. 0th European Control Conference, Budapest. Lu, C. X., Rees, N. W., and Donaldson, S. C. (005). The use of the Aström-Bell model for the desgn of drum level controllers n power plant bolers. 6th IFAC World Congress, Prague. Pellegrnett, G., and Bentsman, J. (996). Nonlnear Control Orented Boler Modellng - A Benchmark Problem for Controller Desgn. IEEE Transactons on Control Systems Technology, Vol. 4, No., pp 57-64. Tan, W., Lu, J., Fang, F., and Chen, Y (004). Tunng of PID controllers for boler-turbne unts. ISA Transactons Vol. 4, pp. 57 58. Tan, W., Marquez, H. J., Chen, T., and Lu, J. (005). Analyss and control of a nonlnear boler-turbne unt. Journal of Process Control. Vol. 5, No. 8, pp. 88-89.