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A Nonlinear Modelling Approach To The Sugar Cane Crushing Process ...
TP15 16:00 Proceedings of the 37th IEEEâ¨Conference on Decision & Controlâ¨Tampa, Florida USA* December 1998 A nonlinear modelling approach to the sugar cane crushing process Turker Ozkocak Minyue Fu Graham C. Goodwinâ¨Dept. of Elec. and Comp. Eng.,â¨The University of Newcastle, Callaghan 2308, Australia to the bagasse between the mills. Water isâ¨also added before the last mill to wash out anyâ¨remaining sugar. Measurements of bagasseâ¨mass and fedback juice flow between mills areâ¨often not available, making it difficult to esÂ¬â¨timate the mass balance. The first milling preparedâ¨cane _ Abstract Compaction of sugar cane varies all throughâ¨the milling train due to the preparation methÂ¬â¨ods and cane variety. Since compaction isâ¨the most crucial variable to influence torqueâ¨loads and therefore sugar extraction, an adeÂ¬â¨quate model for its estimation is needed. Inâ¨this paper we put forward a nonlinear dynamÂ¬â¨ical model based on a mass balance principle.â¨The model utilizes the fact that the density ofâ¨cane bagasse changes approximately linearlyâ¨with the exerted pressure over it in the operaÂ¬â¨tion regions significant to torque control. Theâ¨model is parametric in two variables whichâ¨need to be tuned according to the propertiesâ¨of the cane. Our model gives promising reÂ¬â¨sults on real plant data and is expected to beâ¨useful in nonlinear control of sugar mills. feedback juice f shredderâ¨and â¢sf*. \ added water ii entryâ¨conveyors !! "St,x pressuâ¨feedâ¨rolls 3D ;ib intercarriefei agasss \\ ** rr w no 3 First mill '3sher juice boot ofâ¨iurth mi fou fourth mill Figure 1: The milling train and related sensors unit is the major factor in the overall effiÂ¬â¨ciency of the train. This mill is controlled toâ¨maintain the throughput rate set by the speedâ¨of upstream belt conveyors. All the otherâ¨mills are controlled to achieve high overall exÂ¬â¨traction. What differs them from the firstâ¨mill is that they process bagasse delivered byâ¨a fixed speed inter-carrier from the previousâ¨mill. From the carrier the bagasse is fed intoâ¨a buffer chute where the volume and exit geÂ¬â¨ometry are changed via a flap. The free fallingâ¨bagasse or prepared cane for the first mill areâ¨gripped by pressure feed rolls and through anÂ¬â¨other short chute, pushed into crusher rolls.â¨At the exit of crusher rolls the bagasse divesâ¨into a boot where it absorbs fedback juice orâ¨water. From the boot the bagasse is carriedâ¨away via a fixed speed carrier into the bufferâ¨chute of the preceding mill. The pressure feedâ¨and crusher rolls are driven by steam turbines.â¨Gear boxes are coupled between the turbineâ¨and the rolls. There is one steam turbine per Key words: nonlinear modelling, sugarâ¨mills, sugar cane crushing 1 Introduction The function of a raw sugar factory is to proÂ¬â¨duce crystal sugar from the juice in sugarâ¨canes delivered to the factory. On arrival atâ¨the plant, the sugar cane is transported onâ¨belt conveyors to the shredder where it is preÂ¬â¨pared for the removal of juice by the extracÂ¬â¨tion station, see Fig. 1. The shredder preÂ¬â¨pares the cane by smashing it up into smallâ¨pieces. The extraction process in Australia isâ¨mostly done by crushing mills. The preparedâ¨cane from the shredder is passed through aâ¨series of mills (typically four to six) called theâ¨milling train as a whole. The mills squeezeâ¨or crush the cane to separate the juice whichâ¨contains the sugar from its fibrous part. Theâ¨fibrous material left after the juice is removedâ¨is called bagasse. To help the extraction ofâ¨juice, some of the produced juice is returned mill. The primary objective of mill control is toâ¨maximize the extraction at a determined proÂ¬â¨duction rate. On average 2.4% of sugar isâ¨not extracted. For a plant with a production 0-7803-4394-8/98 $10.00 Â© 1998 IEEE 3144 capacity of 550 tons/hr, the loss per hour isâ¨worth 700 AUD. The gross annual throughÂ¬â¨put of Australia is 5 million tons. Accordinglyâ¨the gross annual extraction loss of Australianâ¨Sugar Industry is around 40 million AUD. material property, which is the major disturÂ¬â¨bance, prevents the model from capturing theâ¨whole spectrum of operation. The nature of the model that we seek hasâ¨already been defined: It needs to be simÂ¬â¨ple enough for online purposes but complexâ¨enough to capture the key properties of theâ¨cane for extraction purposes. To achieve a high extraction, it is required toâ¨have a high average roll torque. Also smoothâ¨control must be maintained around the setâ¨point so that possible deviations at the torqueâ¨due to sudden changes in the cane varietyâ¨will not damage the machinery. In the curÂ¬â¨rent practice, torque control is achieved byâ¨changing the chute geometry via the flap whileâ¨height control is maintained by changing theâ¨turbine speed. The height of the material inâ¨the buffer chute must be at a level to enableâ¨an adequate degree of compaction of the maÂ¬â¨terial for efficient crushing . However, it isâ¨well-known that the chute height and torqueâ¨are closely coupled. The aforementioned "deÂ¬â¨coupled" control scheme is non-ideal. 3 A nonlinear compaction model : a-fiâ¨model Each mill consists of a buffer chute, a flap,â¨pressure feed rolls, a pressure feed chute,â¨crusher rolls and a boot that is the entry of theâ¨inter-carrier which feeds the preceding mill. Aâ¨diagram is given in Fig. 2 Sj bufferâ¨chute t Mass Input H â V. 2 Previous Efforts S(x) 61 (not in proportion) flap L The crushing process has been subject to aâ¨number of studies in the past. Works byâ¨Murry and Holt [5] and Loughran [3] areâ¨aimed at a better understanding of the processâ¨to improve the mill settings and cane preparaÂ¬â¨tion methods. The resultant models are nonÂ¬â¨linear, static, and based on parameters whichâ¨are difficult to estimate in practice. h Sl pressure h ; v i s feed rolls mas?â¨output bagasseâ¨to next mill The work carried out by Partanen [4] involvesâ¨iterative closed-loop black-box identificationâ¨in conjuction with LQG based controller deÂ¬â¨sign. Although more successful than the curÂ¬â¨rent practice the technique suffers from a sigÂ¬â¨nificant degree of complexity which makes itâ¨difficult to maintain efficiently in the lack of aâ¨highly skilled control expert. crusherâ¨rolls â¦ juice Figure 2: Diagram of Each Mill where For control purposes, a simple model whichâ¨can capture the gross dynamic behaviour isâ¨needed. This idea was the motivation forâ¨a masters' thesis submitted by Mark Westâ¨in our department in 1997, [2]. Well-knownâ¨physical behaviours coupled with informationâ¨gathered from step tests were combined forâ¨modeling. The resultant model is a linearâ¨two-input, two-output system that links theâ¨manipulating variables, flap position and millâ¨speed, to the controlled variables, torque andâ¨chute height. Although quite helpful for qualÂ¬â¨itative analysis, the lack of inclusion of the Height of the chuteâ¨Height of the material in the chuteâ¨Radius of the top two rollsâ¨Length at the topâ¨Length at height hiâ¨Roll gap between the top two rollsâ¨Width of the systemâ¨Surface speed of rollsâ¨Vertical angle of the fixed surfaceâ¨Vertical angle of the flap The static pressure-compression characterisÂ¬â¨tics of prepared canes <â nd bagasses are well H h hi Si Si s L V 0i 02 3145 The cross sectional area A(x) is known. The results of the experiments doneâ¨by Noel Deerr [1] are summarized in Fig 3.â¨The pressure drop across the chute is often lessâ¨than 1 atm. According to the figure, in theâ¨low pressure region, the relation between presÂ¬â¨sure and compression is approximately affine.â¨From the above observation, we propose the (6) A{x) = S{x)L where S(x) is the width of the cross sectionâ¨at x which depends on the flap angle : (x - hi) S(x) = 5i + (Si - Sx) (7) H and static pressure versus compression - Tests of Noel Deerr 10 Si = Si + H(tan(02) - tan(0i)) (8) Then, the expression for r(x) reads: r\j .Â§ 6 r(x,a,P,h,62) =â¨L0 h^St-Si) (Si -Si)(ah- l) + 104S(h)Ljâ¨hi(Si-Si) !â eah ) + H a Lp 3 â¢ region for buffer a2H 2 - chute Lp -(Si- ) + ax e H a Â°0 LP compression ratio - initial Volume / Compressed Volume (Si - Si)(ax - 1) ,hi<x<h (9) a2H Next, we derive a dynamic model for the chuteâ¨height. To this end, we first note that theâ¨output mass flow is approximately given by: Figure 3: Operation region at low pressure following relationship for pressure versus denÂ¬â¨sity along the chute height. M0 = SxLVd(hi) (10) d(x) = aP(x) + P (1) Denoting by M(t) the total mass in the chuteâ¨at time t The static pressure at any height through theâ¨chute is the sum of the weight of the mateÂ¬â¨rial and atmospheric force acting on its crossâ¨section. Denoting by A(x) the cross-sectionalâ¨area of the chute at height x, we have fh â d(x)A(x)dx J hi M(t) (11) the mass balance for the buffer chute may beâ¨written as: P(x)A(x) = f J X â¢ (12) dt ah dt 062 dt A(v)d(v)dv + PaA(h) (2) The partial derivative of chute mass with reÂ¬â¨spect to height is: where h is the height of the material in theâ¨chute and Pa = 10Akgf /m2 is the atmosphericâ¨pressure. Solving this with respect to presÂ¬â¨sure, we get : 9M T < ssr = L(e (.Si-S1) â ah (S(h)(10*a + P) + (Si-Si) ) - 104 104 e axr(x,a,P,h,62)â¨P(x) = - (3) H H A(x) (13) and the partial derivative of chute mass withâ¨respect to 02'- where r(x, a, P, h, d2) is to be explained later.â¨It follows that the density at any height x isâ¨given by: dM PL H (eah ~ 1)( â(1 d02 COS(62) e axr(x) d(l> = a~sW + " a (4) (b-h,) , i) + {1_(Â±zMlw,})â¨aH H H Subsequently, the density of material at theâ¨exit of the chute is: (h - hi) or hi H a + H e ahlr(hi) (hi - h) PL + 77))) + ~(1 + a h\ Li (5) d(h\) = a + P (14) SiZ, H a 3146 By now, our nonlinear compaction model isâ¨completely described. Since our model inÂ¬â¨volves two major parameters a and ft, we willâ¨refer to it as the a-ft model. These parametersâ¨depend on the cane properties and must be esÂ¬â¨timated for each variety. To verify our model,â¨Eqn. (12) is solved with respect to height andâ¨a comparison between the calculated and acÂ¬â¨tual heights is taken to be a measure for theâ¨verification of our model. sity variations in the chute well enough to beâ¨extended further into the analysis of torqueâ¨and extraction where material compaction isâ¨shown to be important. A correct expressionâ¨of mass balance is essential. The closeness beÂ¬ tween the calculated and actual heights is theâ¨main evidence of a good model. Accordingly Eqn. (12) was implemented in MATLAB for selected data groups from mill 1 and 4. a andâ¨ft values which would give the least square erÂ¬â¨ror between the real and calculated heightsâ¨were searched over a space. The search spaceâ¨was limited by an upper bound on the possibleâ¨material density. It is known that preparedâ¨cane has density values around 300-400 kg/m3â¨whereas the no-void density of the materialâ¨is approximately 1130 kg/m3. Fibre densityâ¨may be taken as constant at 1530 kg/m3. Soâ¨search space for a was defined to be [0.0001Â¬â¨0.2] where ft changed over the region [0-500].â¨Finding a and 0 values which would estimateâ¨the height with a reasonable LSE was thoughtâ¨to be the measure of how good the a-ft modelâ¨explains the process in terms of material charÂ¬â¨acteristics. It must be noted that a and ftâ¨values depend on the cane variety and prepaÂ¬â¨ration methods which are subject to changeâ¨all through the operation. 4 Experiments The mill considered for the tests is at the CSRâ¨Macknade Mill on the Herbert River north ofâ¨Townsville, Queensland, Australia. The millâ¨is a sensor weak case from the multivariableâ¨control point of view. The only continuousâ¨weight measurement is done on conveyor beltsâ¨via a belt weigher before the chute entry of theâ¨first mill. The mass flow measurements of exÂ¬â¨tracted juice at mill no 1 and the added waterâ¨before the entry of mill no 4 are continuous.â¨For every mill actual values for flap position,â¨roll speeds and chute height are available. EvÂ¬â¨ery mill is driven by a dedicated steam turÂ¬â¨bine. The total torque generated at each ofâ¨those turbines is calculated based on turbineâ¨chest, exhaust pressures and speeds. For millâ¨1 and mill 4 the torque measurements for presÂ¬â¨sure feeder and crusher roll groups are availÂ¬â¨able. The loads on the electrical drives of allâ¨three intermediate carriers are also availableâ¨as current measurements. Data was loggedâ¨during both open and closed loop operation. Experimental Results for Mill No 1 For mill no 1, the parameter search was doneâ¨over three data sets: 1. Group Ml-STA includes 800 seconds ofâ¨mill no 1 measurements where a totalâ¨startup and stop sequence in closed loopâ¨is captured. Open loop tests for a particular mill were doneâ¨while the height and speed were controlledâ¨manually by the operator. In that mode,â¨speed and flap position were changed in stepsâ¨around the operating point. Due to the couÂ¬â¨plings and persistent disturbances it was veryâ¨difficult to apply steps for long. As being theâ¨most critical stand, mill 1 could not be held inâ¨open loop more than 12 minutes, much shorterâ¨than for downstream mills. Due to the slowâ¨nature of the process a sampling period of 0.5â¨sec was chosen. 2. Group Ml-Gl includes 200 seconds ofâ¨mill no 1 measurements in manual opÂ¬â¨eration. 3. Group Ml-OL includes 1250 seconds ofâ¨mill no 1 measurements mainly in autoÂ¬â¨matic mode everywhere but the regionâ¨covered by Ml-Gl. The results are summarized in Figures 4, 5, 6.â¨The parameters found are reasonably close toâ¨each other. The density of the prepared caneâ¨is estimated to be changing around 450 kg/m3â¨which is reasonable in practice. The model isâ¨shown to be adequate enough to predict theâ¨density variations provided that the correctâ¨mass input flow rate is used. Since the critical mills, no 1 and no 4, wereâ¨equipped with more adequate sensors includÂ¬â¨ing separate torque measurements for crusherâ¨and feeder roll assemblies, we decided to startâ¨our analysis with them. Our model must be able to estimate den- 3147 Experimental Results for Mill No 4 For mill no 4, the parameter search was doneâ¨over three data sets where all three wereâ¨logged in manual mode. the material provided a correct kicz is used.â¨At correct kicz the input density of the mateÂ¬â¨rial, a 104 + /3, must also be the actual value.â¨For wrong kicz the same rational relation inâ¨input densities is preserved as in gains. Thisâ¨was verified by search for optimum parameÂ¬â¨ters at different gains:â¨kicz 20 1. Group M4-G1 includes 2000 seconds ofâ¨mill no 4 measurements. 70 110 40 Gla 0.05 0.095 0.155 0.21 G1/3 10 0 G2a 0.049 0.095 0.1515 0.197 G2@ 0 G3a 0.045 0.095 0.165 0.22 G30 100 70 0 2. Group M4-G2 includes 250 seconds ofâ¨mill no 4 measurements. 20 230 20 0 300 3. Group M4-G3 includes 1000 seconds ofâ¨mill no 4 measurements. 230 The inter-carrier load measurements provedâ¨to be efficient in estimating the mass inputs. The major problem for mill no 4 was theâ¨lack of measurement of input mass flow. Theâ¨only continuous mass flow rate is measuredâ¨30 sees before the chute entry of mill 1. HowÂ¬â¨ever loads on the electrical drives of the inter-â¨carriers were available as current measureÂ¬â¨ments. The inter-carrier feeding mill no 4â¨causes a transport lag of 40 sees. If the toÂ¬â¨tal mass over the conveyor at any time is Mc,â¨the power need to pull this mass at constantâ¨speed, v, is: 5 Conclusions It is shown that our nonlinear model for sugarâ¨mill can adequately estimate the compactionâ¨of sugar cane in the buffer chute . With anâ¨online estimation scheme, it can be used forâ¨height control. Extension of it towards theâ¨behaviour of the material inside the rolls mayâ¨be interesting for better torque control andâ¨extraction optimization especially for sensorâ¨weak plants. Power = Mc x g x (sin(7) -t- ficos(-f)) x vâ¨= kx IL (15) where g is acceleration due to gravity, 7 is theâ¨inclination of the conveyor, p is the frictionâ¨coefficient, k is a constant and II is the meaÂ¬â¨sured current. Accordingly at any time the toÂ¬â¨tal mass on the carrier must be proportionallyâ¨related to current load. The delay introducedâ¨by the carrier is 40 sees. The average massâ¨input flow rate was thought to be Mc/40. Soâ¨Mi for mill no 4 is written as: References [1] Hugot, E. (1972), "Handbook of cane sugar engineering," Elsevier Publishing ComÂ¬ pany,new York, pp. 144-149. [2] West, M. (1997), "Modelling and conÂ¬ trol of a sugar cane crushing mill", MEECEâ¨Thesis, Electrical and Computer EngineerÂ¬â¨ing, The University of Newcastle, New Southâ¨Wales, Australia. (16) Mi = kicz x II where II is the net current after subtractingâ¨the load current at idle run. The best resultâ¨was obtained when 40 sees delay was introÂ¬â¨duced from the load to the mass input.For ourâ¨purposes proof of the existence of a-/3 valuesâ¨for any kjcz values would be enough. AccordÂ¬â¨ingly kicz is chosen to be 70. All three groupsâ¨minimized the LSE at very similar a-/3 values.â¨Results are summarized in Figures 7, 8, 9. [3] Loughran, J.G. (1990), "Mathematical and experimental modelling of the crushing ofâ¨prepared sugar cane," PhD thesis, MechanÂ¬â¨ical Engineering, University of Queensland,â¨Queensland, Australia. [4] Partanen, A. G. (1995), "Controller reÂ¬â¨finement with application to a sugar caneâ¨crushing mill," PhD thesis, Systems EngiÂ¬â¨neering, Research School of Information SciÂ¬â¨ences and Engineering, The Australian NaÂ¬â¨tional University. Since M4 G1 and M4 G2 were logged withinâ¨an hour, their a parameters were much closerâ¨compared to M4 G3 which belonged to a batchâ¨of another day. The search results demonÂ¬â¨strate the adequacy of our model in estimatÂ¬â¨ing the mass balance, hence the compaction of [5] Murry, C. and Holt, J. (1967) "The MeÂ¬ chanics of crushing sugar cane," Elsevier PubÂ¬â¨lishing Company, New York . 3148 Ml STA Real & Predicted Height M4 G1 Real & Predicted Height on IC3 Load 2.5 ;"i n â /.j: Â« i to i u i fi a> T\ r u, ;v M / Iffâ¨) i' i/1' v V 3 â¢ J' ll -w :: f v A | ; /a t i 1.5 E 2- alpha = 0.0059 V'.' alpha = 0.155 beta = 395 beta = 20 LSE = 19.72 gain = 70 â Model rv Real 0.5 - LSE = 20.23 0 - â- model real -1(- 0 800 200 400 600 1000 1200 1400 1600 2000 2500â¨samples - 0.5 sees 3000 3500 4000 4500 500 1000 1500 samples - 0.5 sees Figure 7: Model performance at best parameÂ¬â¨ters for Mill No 4, group M4-G1 Figure 4: Model performance at best parameÂ¬ ters for Mill No 1, group Ml-STA M1 G1 Real & Predicted Height M4 G2 Real & Predicted Height on 1C3 Load 2.8 alpha = 0.0095 3.8 alpha = 0.1515 2.6 3.6 beta = 360 S beta = 0 2.4 LSE = 4.935 3.4 LSE = 5.668 2.2 3.2 V gain = 70 e 3 - / ' it; I ' 1.8 â model real 1.6 2.6 r .' â Model Real 2.4 i 1.4 (*: height measurement is erratic) 2.2 1.2 0 1o 200 300 50 100 150 250 350 400 100 200 300â¨5-0 400 500 600 samples - 0.5 sees samples .5 sees Figure 5: Model performance at best parameÂ¬â¨ters for Mill No 1, group Ml-Gl Figure 8: Model performance at best parameÂ¬â¨ters for Mill No 4, group M4-G2 M1 OL Real & Predicted Height 4.5 M4 G3 Real & Predicted Height on IC3 Load 2.6 J Model 2.4 Real 3.5 & P 2.2 fa 2.5 : U 1.8 V 'I' alpha = 0.0072 I 1.5 Al ii k beta = 390 1.4 LSE = 22.47 0.5 1.2 alpha = 0.165 gain = 70 model real beta = 0 LSE = 9.447 -0.5 0.8L 2000 1000 1500 2500 500 1000 2000 2500 500 1500â¨samples - 0.5 sees samples - 0.5 sees Figure 9: Model performance at best parame- Figure 6: Model performance at best parameÂ¬ ters for Mill No 4, group M4-G3 ters for Mill No 1, group Ml-OL 3149