Integration of Systems Engineering-based Paradigms for the Scheduling and Control of an Experimental Hot-Rolling Mill

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This paper presents research work associated with the integration of systems engineering-based paradigms for implementing state-of-the-art mechanisms of scheduling and control on an experimental laboratory-scale hot-rolling mill located at Sheffield University (UK). A comprehensive hybrid model for metal processing was combined with a Genetic Algorithm (GA)-based optimisation method to calculate the optimal rolling schedule, hence realising the concept of right-first-time production of steel alloys. Furthermore, the mill used Model-based Predictive Control (MPC) to guarantee optimal control performance during its real time operations. Results from hot-rolling experiments are presented to provide a proof-of-concept about the use of integrated model-based systems to solve complex metallurgical problems.
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  1.Introduction Modelling the correlation between the processing and themechanical properties of the rolled product, especially after experimental substantiation of the predictions, is a veryuseful tool for adding valuable information to the currentunderstanding of the thermomechanical processing of met-als. Significant successes have been achieved in this areaduring the last years, particularly when combining physi-cally-based models with those associated with ‘intelli-gence’ such as Neural Networks (NN) or Neural–Fuzzy(NF) systems, which are known for being capable of ex-tracting useful knowledge from industrial or experimentaldata-sets. 1)  Nevertheless, although modelling for predictionis evidently an important part of the ethos relating to metaldesign, the ‘acid test’ rests with the exploitation of suchmodels by driving them in such a way as to identify the ‘op-timal’ routes (recipes) for process optimisation. This is tan-tamount to identifying a systematic route for the optimaldesign and production of metals which should ensure ahigh quality of the final product and a consistent and repeatable production process.The aim of systems integration is to link the differentaspects of the thermomechanical processing to analyse thetransactions of energy between them and the effect of the chemistry, microstructure, and temperature gradients(among others) on the metal final mechanical properties. Inhot-rolling, such an integration takes place when the stock is passed through the work rolls. During this precise mo-ment, complex phenomena of microstructural and mechani-cal natures do occur. For instance, the granular microstruc-ture of the metal is flattened and elongated such that eachgrain, in its austenitic phase, undergoes a dimensionalchange followed by restoration processes such as dynamicor static recrystallisation. Meanwhile, the metal tries to push the work rolls apart as a result of the stress generated  by the deformation producing a force whose componentsare associated with the rolling torque (mechanical load) and the roll ‘separating’ force. The mechanics of such a forcedepend on the rolls geometry, the stock dimensions, and therolling schedule parameters, particularly the rolling speed,the amount of deformation, and the metal temperature. Therolling torque directly affects the speed regulation duringrolling, therefore, the mill control system has to provide op-timal control actions so as to counteract such a load inorder to keep the rolling speed at the desired value. Recentstudies have demonstrated that the various constituents of complex metallurgical processes should not be treated sepa-rately, but dealt as single elements (models) of an inte-grated system. 2) Although extensive research work hasalready been successfully undertaken in this area, there areyet few examples of the exploitation of such models withinreal processing scenarios and their subsequent implementa-tion to develop the idea of ‘optimal’ mill scheduling. Fur-thermore, integrated strategies should be implemented toredress the current dichotomies, both in academy and in-dustry, between the approach used by metallurgists who tryto understand and optimise the process, and the mill tech-nologists who may only be interested in control problems.The aim of this paper is to design an integrated frame-work for the ‘optimal’ control and scheduling of hot-rollingmills using, as a test bed, an experimental laboratory-scalemill located at the Engineering Materials Laboratory of theUniversity of Sheffield (UK). This mill, also known as the‘Hille’ mill (see Fig. 1 ), is used by the Institute for Mi-crostructural and Mechanical Process Engineering: TheUniversity of Sheffield (IMMPETUS) for the investigationof steel, aluminium, and titanium microstructures and prop-erties through real-time hot-rolling experiments. The pro- posed approach can be seen in Fig. 2 which shows a block diagram of the integrated system for the model-based scheduling and control of the Hille mill. Such a system is based on a comprehensive modelling structure that includesmicrostructural and property models encompassed in a sin-gle hybrid model, rolling force and torque models describ-ing the mechanics of the stock during deformation, and anoff-line systematic optimisation mechanism aimed at calcu-lating the suitable rolling parameters for the mill set-up. 64 © 2009ISIJISIJ International, Vol. 49 (2009), No. 1, pp. 64–73 Integration of Systems Engineering-based Paradigms for theScheduling and Control of an Experimental Hot-rolling Mill Miguel A. GAMA and Mahdi MAHFOUF Institute for Microstructural and Mechanical Process Engineering, The University of Sheffield, Mappin Street, Sheffield, S13JD, UK. E-mail: Received on July 28, 2008; accepted on October 15, 2008  )This paper presents research work associated with the integration of systems engineering-based para-digms for implementing state-of-the-art mechanisms of scheduling and control on an experimental labora-tory-scale hot-rolling mill located at Sheffield University (UK). A comprehensive hybrid model for metal proc-essing was combined with a Genetic Algorithm (GA)-based optimisation method to calculate the optimalrolling schedule, hence realising the concept of right-first-time  production of steel alloys. Furthermore, themill used Model-based Predictive Control (MPC) to guarantee optimal control performance during its real-time operations. Results from hot-rolling experiments are presented to provide a proof-of-concept  about theuse of integrated model-based systems to solve complex metallurgical problems.KEY WORDS:hot-rolling; GA-based optimisation; hybrid modelling; Neural–Fuzzy paradigms; predictivecontrol.  The mill uses robust control algorithms, such as Gener-alised Predictive Control (GPC) for the speed control, aswell as a Proportional-Integral-Derivative (PID) controller with mill spring compensation for the thickness control. Itis worth noting that both the input and the output of the proposed approach are based on achieving a set of user-defined requirements in terms of the mechanical propertiesof the final product.The remainder of this paper is structured as follows: Sec-tion 2 will present the modelling paradigms adopted for describing the dynamics of the microstructure and the me-chanical properties of the steel alloy, as well as the assem- bly of the hybrid model; Section 3 will describe how such amodel can be exploited to solve the scheduling (optimisa-tion) problem in the multi-objective sense. Section 4 willreview the strategy for the optimal control of the rollingspeed to guarantee a good performance of the mill duringexperiments. The results from hot-rolling experiments and laboratory analyses will be presented in Section 5. Finally,Section 6 will draw some concluding remarks with respectto the overall study. 2.The Hybrid Model for Hot-rolling It has been almost 30 years since Sellars and co-workersat Sheffield University developed the basis for the currentunderstanding of the thermomechanical processing. 3) Theresulting model, also known as the physically-based model,includes equations for the critical microstructural eventssuch as recrystallisation, grain growth, and phase transfor-mation. The combination of these equations aims at pre-dicting the evolution of the steel microstructure in itsaustenite phase and its quantitative features at room tem- perature ( i.e. ferrite grain size and volume fractions). Ex-amples of such equations are summarized in Table 1 whenconsidering the C–Mn steel alloy (Mild Steel). The use of these equations has demonstrated the high degree of sensi-tivity of the microstructure to the operating conditions,where the determining variables are normally characterised  by the stock temperature ( T  ), the strain ( e  ), and the strainrate ( ˙ e  ), with flow stress being the measurable response of the microstructure to such conditions. Furthermore, the de-termination of the ferrite grain size ( d  a  ), which is the criti-cal parameter that defines the metal mechanical propertiesfor room-temperature applications, depends significantly onthe processing history and the microstructure conditions prior to the austenite–ferrite transformation. 4) 2.1.Neural–Fuzzy Modelling of Mechanical Proper-ties The concept of systems integration can be described bythe assembly of a hybrid model which combines the physi-cally-based model with a set of NF models describing addi-tional aspects of the rolling process, including the dynamicsof hot-rolling and cooling, as well as the final product char-acteristics. For instance, consider the NF paradigm com-monly known as Adaptive Network-based Fuzzy InferenceSystem (ANFIS) proposed by Jang. 5) The power of such astructure lies in the combination of the human-like reason-ing and interpretability of Fuzzy Inference Systems (FIS)with the learning and generalizing abilities of Neural Net-works (NN) to extract knowledge from a set of industrialdata. A NF model with n inputs and 1 output, assuming thateach input space is partitioned using  p fuzzy partitions, can ISIJ International, Vol. 49 (2009), No. 165 © 2009ISIJ Fig.2. A block diagram of the proposed integrated system for the optimal scheduling and the control of the ‘Hille’ mill. Fig.1. The hot-rolling ‘Hille’ mill located at Sheffield Univer-sity. Table1. Equations of the microstructure model for C–Mnsteels. 3)   be represented by fuzzy implications or sub-models (one ineach sub-space), which can be written as follows:............................(1)where  x n is the model input and   y i is the output of each i sub-space, whereas  A in is a linguistic value ( e.g. low,medium, high) characterised using membership functions,while the c ’s are real-valued parameters. Using the aboveformulation, a complex high-dimensional nonlinear model-ling problem can be decomposed into a set of simpler linear models valid within certain operating regions defined byfuzzy boundaries. Fuzzy inference is then used to interpo-late the output of the local models in a smooth fashion tolead to an overall data-based model. The formulation of Eq.(1) represents a Takagi–Sugeno–Kang (TSK) Fuzzy modelwhere the grade of membership of the input  x in the fuzzyset  A , as described by the Gaussian membership function, iscalculated by the following equation:..................(2)where a and  b are the centre and the width of the Gaussianfunction respectively. In addition, the ratio of the i -th impli-cation’s firing strength to the sum of all implications’ firingstrengths can be calculated according to the following for-mula:......(3)The implications’ firing strengths are now normalised, suchthat ∑  pi ϭ 1 b  i ϭ 1.The method for calculating the membership parametersis based on the subtractive clustering method proposed byChiu, 6) where the input–output data is partitioned into ho-mogeneous groups of data or clusters whose centres and ra-dius of influence are associated with the membership func-tion parameters of Eq. (2). On the other hand, if such pa-rameters remain fixed, the overall fuzzy model output can be expressed as follows:..................................(4)where...............(5).......(6)Using this formulation, the ‘consequent’ parameters of thefuzzy rules can be calculated by a linear regression method,such as the least-squares algorithm.With the above modelling technique, along with a set of industrial data associated with the C–Mn steel alloy, a NFmodel for the prediction of the metal Tensile Strength (TS)was developed. Such a set contains 536 measurements of TS as a result of using different weights for the main chem-ical constituents, i.e. carbon (C), manganese (Mn), silicon(Si), and nitrogen (N). The data-set also includes the ferritegrain size ( d  a  ) as a means to correlate the microstructurewith the chemistry and the final properties. The data-setwas split into two sub-sets to be used for training and test-ing respectively. The aim was to extract knowledge fromsuch data in order to create a model which can provide ac-curate predictions of TS within an interest range. After training, the resulting model was comprised of 5 inputs( i.e. C, Mn, Si, N, and the ferrite grain size expressed asD ϭ ( d  a  /1000) Ϫ 1/2 with 4 Gaussian membership functions per input, 4 fuzzy rules, and 1 output ( i.e. TS). After train-ing a sample of the resulting TSK fuzzy rules can be ex- pressed as follows:  R 1 :If C is Low and Si is High and Mn is Very Highand N is High and D is Very High, Then TS ϭ 302.32 ϩ 577.66C ϩ 446.94Si Ϫ 13.35Mn Ϫ 1838.50N ϩ 9.00D  R 2 :If C is High and Si is Medium and Mn is Mediumand N is Medium and D is Medium, TS ϭ 139.89 ϩ 915.79C ϩ 218.69Si ϩ 125.54Mn Ϫ 10341N ϩ 7.06D  R 3 :If C is Very High and Si is Very High and Mn isHigh and N is Low and D is High, Then TS ϭϪ 55.37 ϩ 713.68C ϩ 202.34Si ϩ 4758.5Mn ϩ 4758.5N ϩ 5.61D  R 4 :If C is Medium and Si is Low and Mn is Low and  N is Very High and D is Low, Then TS ϭ 78.898 ϩ 647.44C ϩ 652.58Si ϩ 151.05Mn ϩ 2149.7N ϩ 19.48D. The parameters of the membership functions can be found in Ref. 7). Figure 3  presents the model surfaces using selected  input–output relationships along with a comparison between the measured and the predicted data. All predictions werereasonably accurate considering a Ϯ 10 confidence band. Aquantitative analysis between the NF model and the con-ventional model used in current literature 8,9) revealed a re-duction of the Root Mean Square Error (RMSE) in the pre-dictions given by the proposed model which was 32.46MPafor the training data and 24.96MPa for the testing data,whereas using the conventional model the RMSE for thetraining data was 47.98MPa and 38.17MPa for the testingdata.In addition to the TS model, two NF models were devel-oped to estimate the rolling force and load torque of theC–Mn steel alloy using a similar modelling procedure. For these models, measurements obtained from hot-rolling ex- periments using the Hille mill, along with data generated bya Finite-Element (FE)-based model, were used for trainingand testing. The obtained data-set included measurementsof the rolling speed, the deformation temperature, and the percentage of reduction, which were considered as the ϕ β β β β β β  ϭ [] 11111  x x x x n p p p nT  L L L θ  ϭ [] c c c c c c n p pn p 0101101 L L L  y m ϭ θ ϕ  ⋅ β µ µ µ µ  i A i A n A i A ni p iniini  x x x xi p ϭϫ ϫϫ ϫϭ ϭ 11 1 1()()()(),,, LLL ∑ µ   A x x ab ()exp ϭ ϪϪ 12 2   y c c x c x i p ii inin ϭ ϩ ϩ ϩ ϭ 011 1 L L ,,,If is and and is then  x A x A in ni 11 L , ISIJ International, Vol. 49 (2009), No. 166 © 2009ISIJ Fig.3. Selected input–output surfaces associated with the TS Neural–Fuzzy model.  model inputs. Overall, 3 new models were developed whichallows for an accurate prediction of (1) TS, (2) the rollingtorque, and (3) the rolling force. 2.2.The Assembly of the Hybrid Model For modern industries concerned with the thermome-chanical processing of metals, off-line modelling and on-line control techniques based on physical knowledge arehighly desirable in order to improve the quality of the final product, the time and cost efficiency, and to develop newmaterials. Artificial Neural Network (ANN) based modelsare popular tools, but they do not necessarily and inherentlyembed physical knowledge. On the other hand, current physically-based models are too complex for industrial ap- plications and are less efficient than ANN. A combinationof intelligent systems-based paradigms and physically- based models leads to a ‘hybrid model’. While the physi-cally-based models ensure that the results are physically ac-ceptable, Neuro–Fuzzy (NF) models can be used to in-crease the accuracy of fitting the experimental results. Ini-tial modelling results showed that the hybrid approach can be a successful tool for modelling nonlinear relationships between the mechanical properties, the chemical composi-tion and the microstructure of materials. This modelling ap- proach represents an attractive approach to compromise be-tween accuracy and model interpretability, hence leading torobust as well as transparent models for better modelling of thermomechanical processing.The overall hybrid model associated with the C–Mn steelalloy is illustrated in Fig. 4 . Additionally, an empirical tem- perature model was also implemented to calculate the tem- perature gradients during heating, rolling, and cooling. 7) Itis worth noting that although the prediction of TS using a NF model is considered here, no special assumptions aremade to preclude the use of this methodology for other  properties such as Yield Strength (YS) or the Impact Tran-sition Temperature (ITT), the latter being a measure of themetal Toughness. 3.The Optimisation of the Mill Schedule This section will describe how to control the behaviour of the metal processing by ‘inverting’ the above hybrid model. However, instead of explicitly calculating the in-verse model, optimisation techniques are used in order toidentify the ‘optimal’ routes for systematic design of metals via the microstructure and the metal processing. This con-cept is illustrated in Fig. 5 where two nonlinear functionsare used to represent the relationships between (1) the me-chanical properties of the steel with its microstructure, and (2) the microstructure with a set of rolling parameters. Thiscan be expressed as follows:.................(7)where  f  (·) is a function that defines the metal propertiesand whose arguments are the quantitative elements of themetal microstructure, such as the ferrite grain size and thevolume fraction of pearlite, whereas  g  (·) is a function rep-resenting the microstructure described in terms of the de-formation parameters, such as the temperature, the strain,and the strain rate applied to the stock during the rolling pass. The aim of this formulation is to find correlating points or solutions that satisfy a defined criterion. In other words, given the desired mechanical properties  p , one canoptimise  f  (  p ) to find the best microstructural parameters,which are also the components of the solution m ; the rolling parameters can then be found by using m and   g  ( m ) alongwith a set of optimality criteria. Such criteria can be repre-sented by a set of ‘cost’ functions to be minimised. Con-sider the following cost functions which constitute the opti-mality criteria for the microstructure and the rolling sched-ule optimisation:........(8)where  P  i is the property considered in the optimisation problem, l  i is a user-defined   priority factor  for each prop-erty, and   N  is the number of properties contributing to thecost  J   M  ; the superscript  F  refers to the requirements on thefinal state of the mechanical properties ( i.e. at room temper-ature). On the other hand, the cost  J  S  includes two main ob- jectives associated with two critical microstructure parame-ters; the first term minimises the variance between the re-crystallised austenite grain size ( d  g  ) and a grain size targetfor the rolling pass. The second objective establishes thatfull recrystallisation has to be achieved before the onset of  Minimise: target  J  P  P i N  JS d i d id i X ii N   M iii F i N  ϭ Ϫ ϭϭϪϩ Ϫϭ ϭ λ  γ γ  112112 122 ,,,()()()[()],,, max LL ∑   f p m M M M  g m r R R R nmnr  ()[,,,]()[,,,] ϭ ϭϭ ϭ 1212 LL  ISIJ International, Vol. 49 (2009), No. 167 © 2009ISIJ Fig.4. The assembly of the hybrid model associated with theC–Mn steel alloy. Fig.5. ‘Through-Process’ modelling and ‘Reverse Engineering’for calculating the ‘optimal’ rolling schedule.
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