Modeling of a Steam Heated Rotating Cylinder A Grey-Box Approach

Transcription

1 Moeling of a Steam Heate Rotating Cyliner A Grey-Box Aroach Slätteke, Ola; Åtröm, Karl Johan Publihe in: Proceeing / American Control Conference DOI: 1.119/ACC Publihe: Link to ublication Citation for ublihe verion (APA): Slätteke, O., & Åtröm, K. J. (25). Moeling of a Steam Heate Rotating Cyliner A Grey-Box Aroach. In Proceeing / American Control Conference (Vol. 2, ). IEEE--Intitute of Electrical an Electronic Engineer Inc.. DOI: 1.119/ACC General right Coyright an moral right for the ublication mae acceible in the ublic ortal are retaine by the author an/or other coyright oner an it i a conition of acceing ublication that uer recognie an abie by the legal requirement aociate ith thee right. Uer may onloa an rint one coy of any ublication from the ublic ortal for the uroe of rivate tuy or reearch. You may not further itribute the material or ue it for any rofit-making activity or commercial gain You may freely itribute the URL ientifying the ublication in the ublic ortal Take on oli If you believe that thi ocument breache coyright leae contact u roviing etail, an e ill remove acce to the ork immeiately an invetigate your claim. L UNDUNI VERS I TY PO Box117 1L un

2 Donloa ate: 21. Jul. 218

3 25 American Control Conference June 8-1, 25. Portlan, OR, USA WeC9.4 MODELING OF A STEAM HEATED ROTATING CYLINDER A GREY-BOX APPROACH Ola Slätteke an Karl Johan Åtröm Abtract Drying i an imortant roce in aer manufacturing, here team heate liner are ue to ry aer. Control of the moiture content i accomlihe by ajuting the team reure in the liner. In reviou ork it ha been hon that the ynamic from team flo to team reure in the liner can be ecribe by a linear econ orer black box moel. Thi aer reent a firt rincile moel hich ha a tructure imilar to the black box moel. M I. INTRODUCTION oiture content i an imortant quality variable in aer manufacturing. There i a conierable economic incentive in keeing moiture ell regulate [1]. A moern aer machine make aroun 1 ton of aer er ay. With a aer rice of $9 er ton, a reuction of moiture variation by.1% correon to a aving of more than $3. er year. A goo moel of the ynamic of rying i eential for goo moiture control. A key element i the ynamic that relate team flo to reure in the rying liner. A black box moel i reente in [2]. Thi moel tructure ha alo been icue in [3]. The moel ha an integrator, a ole, an a zero, an i calle the IPZ-moel. A blackbox moel i aequate for controller tuning uroe but it oe not tell anything about the hyic behin the ynamic behavior an it cannot be ue for gain cheuling. In thi aer e ill reent a firt rincile moel, bae on ma an energy balance. The rimary moel i a nonlinear ifferential-algebraic equation hoe linearize verion ha the ame tructure a the IPZ-moel. It i convenient to chooe team reure an liner hell Manucrit receive Setember 15, 24. Thi ork a uorte by SSF (Seih Founation for Strategic Reearch) ithin the roject CPDC (Center for Proce Deign an Control) at Lun Intitute of Technology. O. Slätteke i an inutrial PhD-tuent at the Deartment of Automatic Control, Lun Intiutute of Technology, Seen, emloye by ABB Automation Technologie. (hone: ; fax: ; ola@control.lth.e). K. J. Åtröm, i Profeor Emeritu ince 2. Hi reviou oition a hea of the Deartment of Automatic Control, Lun Intiutute of Technology, Seen. temerature a tate variable, ince both variable can be meaure. A main uroe of thi grey-box moel i to gain inight into ho the hyical roertie influence the arameter of the IPZ moel. A imilar aroach for a rum boiler can be foun in [4]. The core of thi ork i reente in [5]. II. THE MODEL Let q be the ma flo rate of team into the liner, q c be the conenation rate, an q be the ihon flo rate. Alo, let V an V be the volume of team an ater in the liner, an let an be the enitie of team an ater. The ma balance for ater an team are then V q V qc q q here no blo-through team i aume. Sometime the blo-through team i moele a a fraction of q [6]. It then oe not affect the ynamic of the ytem, only the teay tate gain. The energy balance for team, ater an metal are uv qh qch uv qch qh m (2) T m here m i the oer ulie from the ater to the metal, i the oer ulie from the metal to the aer, h i the team enthaly, h i the ater enthaly, m the ma of the liner hell, C the ecific heat caacity of the hell, T the mean temerature of the metal, u an u are the ecific internal energie of team an ater. The oer flo to the metal i given by m c (1) A T T (3) /5/$ AACC 1449

4 Paer eb T T V q qc T m q h q h m c A T T m (4) m Steam Conenate Dryer hell Fig. 1. A iece of the cro-ection of a rying liner, viualizing the aumtion on the temerature rofile an the energy flo to the metal, from (3). The aer eb i not inclue in the moel an conequently there i no aumtion on the aer temerature. The icture ha taken iniration from [9]. here i the heat tranfer coefficient from the teamconenate interface to the centre of the liner hell, A i the inner liner area, an T the team temerature. The outer urface area of the liner i aume to be equal to it inie area. The error i negligible (le than 5%), becaue the thickne of the liner hell i much maller than the outer liner iameter. For imlicity, all team ithin the liner cavity i aume to be homogeneou ith the ame reure an temerature. From (3) e make the aumtion of a temerature graient in the conenate layer an liner hell, a illutrate in Figure 1. The roertie of the aer eb are not inclue in the moel an the equation o not ay anything about the temerature in the aer. The energy flo to the aer,, varie loly comare to the teaman liner ynamic. For imlicity e aume that i a contant. The conequence of thi aumtion ill be icue in Section V. Equation (1), (2), an (3) i a crue nonlinear moel for the team an conenate ytem in the liner cavity. To obtain a linear econ-orer moel, e make a fe imlification. We aume that the team in the liner i aturate. Thi mean that the tate of the team can be characterize by one variable only an that it i ufficient to ue either the ma balance or energy balance. Therefore e leave out the energy balance. In aition, the thermal ynamic of the ater i very fat, o e relace it by a tatic moel. Oberving that the volume are contraine by V +V =V, here V i the total liner volume, the econ ma balance in (1) can be eliminate. Since the ater volume i mall e alo have V V. Summarizing, e fin that the ytem can be ecribe by the equation hich i a ma balance for the team, an energy balance for the metal, a tatic energy balance for the ater, an an algebraic equation for the energy flo. Eliminating the variable q c an m, the moel become h V q h q h A T T T A T T Auming that the team in the liner i aturate, enthalie h, h, enity an the temerature T, are all function of the reure. The moel can thu be ritten a h ( ) V qh ( ) q( ) h( ) A T ( ) T (6) T A T ( ) T here the tate are reure an mean metal temerature T. The team inlet flo, q, i the inut. The equilibrium i q A Hence h ( ) q ( T ( ) T ) h ( ) A T ( ) T T ( ) T q h ( ) q h ( ) (5) (7) A (8) Linearizing aroun the equilibrium give h ( ) V q h h q T q( ) h ( ) A A T h ( ) q T A T A T (9) 145

5 here the tate are exree in term of eviation. Auming that q h h q T q( ) h ( ) A the moel become h ( ) V A T h ( ) q A T A T T A T (1) (11) The inequality in (1) ill be commente an examine later in the imulation. Writing the ytem in tanar tate-ace form, e fin that here x T T an T A hv A T A C x Ax Bq y Cx Dq 1 D A hv A 1 V B (12) (13) The team roertie are here aume to be given in their equilibrium value. The matrix A ha an eigenvalue at the origin an one eigenvalue on the negative real axi. The tranfer function from team flo to reure i here z G b b z a a z b a 11 (14) 1 b V a 11 a z a A T A A hv The eential arameter of the moel are Cyliner volume V Cyliner ma m Secific heat of metal C Area of the liner urface A Steam roertie h,, T Heat tranfer coefficient (15) All arameter, excet the heat tranfer coefficient,, are knon beforehan, either by machine ecification or from a tanar chemical hanbook. The heat tranfer coefficient i ue to fit the moel to the meaure ata. Note that it i only the lat to item in the arameter lit that een on the oerating oint. The folloing aumtion have been mae in the eveloment of the moel No blo-through team The team in the liner i aturate Energy flo to aer i contant The thermal ynamic of the conenate i fat comare to the liner hell The conition (1) The ole an the zero z are both roortional to the heat tranfer coefficient. For large the tranfer function (14) i aroximate by b G( ) (16) here b oe not een on. For mall the tranfer function can be aroximate by here bz bz G( ) (17) h T Vh (18) 1451

6 oe not een on. Therefore neither the initial art of a te reone nor the loe of the aymtote een on the heat tranfer coefficient. A can be notice, the grey-box moel oe not exlain the time elay often een in the black-box moel. It i imortant to remember that e are ealing ith amle meaurement an it ha, in ractice, been oberve that the time elay of the ytem often i cloe to the amling time. Moreover, e have een from the erivation of the greybox moel that there are neglecte ynamic in the IPZtructure, hich may oibly give rie to an etimation of the ea-time that i larger than the true value. Magnitue (ab) Phae (eg) III. FREUENCY RESPONSE To invetigate the ynamic behavior of the linearize moel, given by (12), e ill look at it frequen reone. The machine eenent arameter are taken from a team grou of a fluting machine, running at an oerating oint ith a team reure of 9 kpa (gauge reure), a nominal ee of 45 6 m/min an a bai eight beteen 11 2 g/m 2. Simulation value are Cyliner volume: V = 12.6 m 3 Cyliner ma: m = 761 kg Cyliner area: A = 37.2 m 2 Heat caacity for cat iron: C = 5 J/(kgC) Steam roertie for the given oerating oint The nominal team ma flo rate to each liner i aroximately.25 kg/. Thi value i obtaine from a team flo gauge, meauring the total machine team conumtion. Figure 2 ho the Boe lot of the ytem, here the gain i normalize by 4 kpa. The gain i ineenent of, both at high an lo frequencie, a hon in (16) an (17). The heat tranfer coefficient ha a conierable influence on both the gain an hae in the mi-frequen range. For the uroe of eigning a PI-controller, thi ifference in gain an hae influence the controller arameter. It can alo be een that, a higher heat tranfer coefficient yiel a loer team reure gain, ince there i a larger heat tranfer through the liner an a higher conenation rate. Thi ha alo been ointe out in [2]. In (1) an inequality, that een on the oerating oint an liner imenion, a utilize to make a ignificant imlification. Uing value from thi examle, e can examine it jutification. Aart from the team roertie, e alo nee an exreion for the erivative of ihon flo rate, q, ith reect to the liner reure. Some exerimental value are given in [7] an uing thoe e fin that the right han ie of (1) i 1 to 2 time larger than the left han ie. The next ection ho that the moel ha a goo fit to exerimental ata Frequen (ra/) Fig. 2. Frequen roertie for ifferent value of the heat tranfer coefficient = 5 (otte), 1 (ahe), an 2 (oli). IV. COMPARISIONS WITH PLANT DATA To evaluate the accura of the grey-box moel it ha been calibrate an valiate againt meaurement from a team- an conenate ytem. The exeriment have been carrie out on a aer boar machine an ignal have been meaure ith a amling time of 1. The liner ata i Cyliner volume: V = 18.4 m 3 Cyliner ma: m = 83 kg Cyliner area: A = 45.5 m 2 Since the inut ignal (team inut flo) i not maniulate irectly, neither meaure, a moel for a team valve ha to be ae to (12). A imle aroach i to aume a linear relationhi beteen the controller ignal, u, an the team inut flo, q, namely q u (19) here i a valve contant hich ill be a econ calibration arameter together ith the heat tranfer coefficient,. Uing thi valve ecrition e kee the linearity an IPZ-tructure in the moel, given in (12). In orer to calibrate the moel, the function igrey.m an em.m in Sytem Ientification Toolbox for Matlab, ere ue to fin the otimal calibration arameter. The otimization metho i bae on minimizing the reiction error, ee [8]. Figure 3 ho an oen loo te reone together ith the calibrate moel, here the moel outut i bia correcte. The calibration arameter obtaine are = 182 W/(m 2 K); =.38 kg/(%) (2) To comare the reult ith nominal value cite in 1452

7 (kpa) u (%) t () Fig. 3. Calibration of moel (otte) an meaure ata (oli). literature, e nee a heat tranfer coefficient through only the conenate film, c. From [9] the relationhi 1 1 c (21) i given, here i the itance into the liner here the temerature i equal to the mean liner temerature, an i the thermal conuctivity of the liner hell. In thi examle, the liner thickne i 25 mm (the mean temerature, T, occur in the mile of the liner hell), an the thermal conuctivity i 5 W/(mK). The heat tranfer coefficient through the conenate i then c = 334 W/(m 2 K) In [9], tyical value of the heat tranfer coefficient, c, are given. They een trongly on the conenate thickne an activity, an can vary beteen 5 an 4 W/(m 2 K), here 2 i a nominal value. Neverthele, the fact that our etimate value from the moel i ithin that range, give uort for the legitima of the moel. The total ma flo rate of team, uring the exeriment, to the rying ection i 85 ton/h. The machine ha 93 liner, o the average team flo er liner i.254 kg/. The arameter, in (2), an the average valve oening give the team flo to the articular liner in the moel, namely.154 kg/. The team flo i likely to vary a great eal beteen ifferent rying grou but by comaring the to value e kno that alo the econ calibration arameter i realitic. In () the grey-box moel i comare ith the correoning black-box moel, ajute on the ame ata et. The velocity gain in the moel i normalize ith the (kpa) u (%) t () Fig. 4. Valiation of moel (otte) an meaure ata (oli). meauring range of the reure gauge. The black-box moel i not hon in the figure but it give a lightly better fit to the ata, ince it ha more egree of freeom (three arameter to ajut intea of to). There i alo a ifference in the arameter of the tranfer function. The time elay come from the ientification roceure an i equal to the amling time. G G grey black e e () The grey-box moel ha alo been valiate grahically by uing the meaure control ignal value to imulate an outut. The moel outut i then comare ith the meaure team reure. Figure 4 ho uch an evaluation. The excitation in the control ignal i generate by a erie of te in the et oint (cloe loo), hich i not hon in the figure to kee it clear. V. A MODIFIED MODEL It ha reviouly been oberve that in ome occaional cae the IPZ-tructure i not ufficient to ecribe the reure ynamic in a team liner. Thi can be reolve by changing the integrator to a real ole [5]. In the greybox moel thi can be accomlihe by changing the aumtion that the energy flo i contant to A T T (23) here i the heat tranfer coefficient from the center of the liner to the aer-liner interface, i the fraction of ryer urface covere by the aer eb, an T i the aer temerature. By letting T be contant, (13) become 1453

8 A T A h V T A A h V A ( ) (24) an the other matrice are unchange. By examining ata et here the IPZ-tructure i ufficient ith cae here i i not, an exlanation to the moeling roblem i foun. If >> then moel (13) i aequate an mean that (24) i a better tructure. Thi ha alo been verifie by imulation of the rimary DAE ytem (1)(3) in Moelica. An brief overvie of Moelica i foun in [1]. Cloer examination of (24) ho that >> give a ytem ith one fat ole an one cloe to the origin. When i increae, the lo ole move along the real negative axi toar the other ole, an it can then no longer be regare a an integrator. It can be hon, knoing that all factor in the element of (24) are oitive, that the eigenvalue of A' are real an negative. The characteritic equation of (24) i 2 ( a a ) a a a a (25) 11 Ientification of the arameter give T A A A a11 a h V T A A a11a a12a21 hv (26) an Routh criterion ho tability. The root of (25) are 1,2 a11 a ( a11 a) a12a21 (27) 2 4 an ince both a 12 an a 21 are oitive, the olution ha no comlex art. The relation beteen the oition of the ole an the hyical arameter i a bit more comlicate than in (15). It can alo be hon that the initial ynamic of the moifie moel in (24) are equal to (16). The lo frequen roertie ill be ifferent for the to moel though ince (12) contain an integrator an ha no teay tate gain. For mall the moifie moel become 2 h ( A A ) G( ) (28) T A A VI. CONCLUSIONS Thi aer ha reente a grey-box moel for the reure ynamic in a rotating rying liner. The moel a erive from firt rincile. It ha been evaluate ith real lant ata an comare ith a correoning black-box moel. The main uroe of the grey-box moel i to gain inight into the hyical la behin the blackbox moel. Thi can have effect on the mechanical eign of the ryer ection, uch a the ihon hae an form, ryer bar, liner imenion etc. It i alo ueful for the controller eign. There i alo a otential to make a recurive ientification of the heat tranfer coefficient for fault etection ith reect to conenate evacuation. It oul then be beneficial to have a earate reure meter an ma flo meter intalle at the rying liner of interet, to acquire an accurate etimate. An imortant thing to remember here i that the moel i an aroximation of the real roce. Moel error ill therefore be inclue in the calibration arameter an it abolute value might be uncertain. The relative value i a ueful arameter though. ACKNOWLEDGMENT The author acknolege Lar Jonhe at AiDomän Frövi for hi uort ith the exerimental ork. REFERENCES [1] B. Bialkoki, The roce variability challenge in In critical conition but ome hoe remain, The Entech Reort, vol. 14, no. 2,. 18, Nov.. [2] D. Nelon an T. Garner, Otimizing aer machine control a cae tuy, Pul & Paer Canaa, vol. 97, no. 11,. 4349, [3] O. Slätteke, K. Forman, T. Hägglun, an B. Wittenmark, On ientification an control tuning of liner ryer, In Proceeing Control Sytem, , Stockholm, Seen,. [4] K. J. Åtröm an R. D. Bell Drum boiler ynamic, Automatica, vol. 34, no. 5, , 2. [5] O. Slätteke, Steam an conenate ytem control in aer making, Licentiate thei, Deartment of Automatic Control, Lun Intitute of Technology, Seen, 23. [6] M. Karlon, O. Slätteke, B. Wittenmark, an S. Stentröm, Evaluation of moel for the team uly ytem, In Tai Sring Technical Conference & Trae Fare, Chicago, Illinoi, 23. [7] S. Stentröm, an T. Svanquit, A general moel for calculating reure ro in ihon an ihon rier tube art 2: exerimental reult, Tai Journal, vol. 74, no. 12, , [8] L. Ljung, Sytem ientification theory for the uer, econ eition, Prentice Hall, [9] M. Karlon (e), Paer making art 2, rying, Tai Pre, 2. [1] S. E. Matton, H. Elmqvit, an M. Otter, Phyical ytem moeling ith Moelica, Control Engineering Practice, Vol. 6,. 5151,