nonlinear model predictive control of walking beam · pdf filemiddle and tail of the slab are...

Advanced furnace control & heat recovery Session 4 1

Düsseldorf, 27 June – 1 July 2011

situation. In the example shown above the exit of the furnace is oriented to the reader.

Figure 6: main window of the simulator To visualize the calculated material temperatures the slabs are colorized corresponding to the anneal colors. The averaged material temperatures on head, middle and tail of the slab are shown as a hint when moving the mouse over the slab. The table on the left lower side contains information about the next slabs to be charged to the furnace. On the right lower side the annealing curve up to the actual moment can be seen for the slab chosen in the scheme (highlighted in green). The example shown in figure 6 shows the curve for a slab located in the first zone. Geometry and quality data of the selected slab are shown on the right upper side. The top line gives information about the program execution, the communication status, the chosen furnace configuration and buttons for offline operation. Additional windows are available to handle calculation parameters like furnace data or material properties. Future works For the future it is planned to extend the simulator by the dynamic behavior of the real furnace. With this option the response of the furnace to the change of furnace set points will be simulated. Advantages are expected for testing the optimization algorithm and for the commissioning of real plants. Conclusion A new concept for the control of reheating furnaces for slabs has been developed. It consists of three modules: Observer, prognosis and optimization. Observer and prognosis calculate the actual and estimated temperature distribution inside the slabs with high precision. The optimization generates

different future scenarios which are calculated by the prognosis and evaluated by a fitness function with variable terms. Parallelized algorithms reduce the calculation time on multiprocessor computers, which make the program suitable for the control of real production plants. Energy savings up to 6% have been estimated and sound promising for future investigations. Abbreviations λ heat conductivity ρ density T temperature t time cp heat capacity Acknowledgements We would like to express our gratitude to the Ministry of Economics and Technology which financially supported the development of the program celFcsRht by “ZIM: Supported by the Federal Ministry of Economics and Technology based on a decision by the German Bundestag”. References [1] Schupe W. : Vereinfachte Berechnung des Strahlungswärmeübergangs in Industrieöfen und Vergleich mit Messungen in einer Versuchsbrennkammer; Dr.-Thesis, (1974) [2] Kohlgruber, K.; Woelk, G.: Optimizing the energy input of industrial furnaces; Gas wärme international, vol. 36 (1987), p. 438-442 [3] Pederson, L.M.; Wittenmark, B.: On the reheat furnace control problem; American Control Conference (1998), p. 3811-3815 [4] Croce, L.; Grosse-Gorgemann, A.: New aspects in controlling a reheating furnace for slabs by a thermodynamic model; 2nd International Conference on Simulation and Modeling of Metallurgical Processes in Steelmaking, Graz (2007) [5] Schwefel, H.-P.: Evolutionsstrategie und numerische Optimierung. Dr.-Thesis, Technische Universität Berlin (1975) [6] Bäck, T. ; Schwefel, H.-P.: An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation, 1(1) (1993) p. 1-23 [7] Fogel, D. B.: An Introduction to Simulated Evolutionary Optimization. IEEE Trans. on Neural Networks: Special Issue on Evolutionary Computation, Vol. 5, No. 1 (1994), p. 3-14 [8] de Jong, Kenneth A.: Evolutionary Computation: A Unified Approach. MIT Press. 2006.

Abstract — VDL Weweler is a producer of air suspension systems. The base of these systems consists of spring steel. In order to reshape this spring steel component, it is heated in a walking beam furnace. Conventional control systems of such furnaces maintain the furnace temperature at target, while the furnace speed is fixed. These control strategies can function well under steady operations (continuous production at a fixed furnace speed), but they are less suitable in transients which arise after startup and stops. In practice, a furnace rarely operates in complete steady state conditions. In those transient situations, the furnace has to be controlled manually, since there is no information on the product temperature. This paper describes and evaluates the application of the DotX Nonlinear Predictive Controller (DNPC) to the VDL Weweler walking beam furnace. This controller belongs to the Nonlinear Model Predictive Controller (NMPC) family, in which control actions rely on on-line optimized model predictions. The model, used in DNPC, accurately predicts the temperature of all products in the furnace, depending on their geometry and the furnace’s speed and temperature. By adjusting the set points for furnace temperature and speed, DNPC is able to keep the product temperatures on target, while energy consumption is minimized, even during large transients. The DNPC controller runs on an external CPU which communicates with the furnace via an OPC server. Initial tests have shown that controlling the walking beam furnace at VDL Weweler by DNPC results in a reduction of CO2 and energy consumption of up to 10 % compared to the conventional furnace controller. Furthermore, the product temperature is maintained automatically at target by DNPC, even at startup and during transients. Moreover, the target product temperature can be changed online and is followed automatically. Key-words — Walking beam furnaces, Control Systems, Nonlinear Model Predictive Control, Reduction of Energy Consumption

I. Introduction ALKING beam furnaces are commonly used in the steel industry. These machines are able to heat

Manuscript received January 15, 2011 by the 1st International

Conference on Energy Efficiency and CO2 Reduction in the Steel Industry (EECR2011), Düsseldorf, Germany.

E. Nederkoorn and J. Schuurmans are with DotX Control Solutions BV, James Wattstraat 23, 1817 DC Alkmaar, The Netherlands, www.dotxcontrol.com, (email: [email protected], [email protected]).

P. van Wilgen is with VDL Weweler BV, Kayersdijk 149, 7332 AP Apeldoorn, The Netherlands, www.vdlweweler.nl, (email: [email protected]).

steel products by moving them through a gas heated furnace. Once these products have been heated, their shapes are able to be modified (by forging or hot rolling). Walking beam furnaces transport all products at discrete time steps over a fixed distance. By altering the time between consecutive steps, the furnace speed can be varied. Fig. 1 shows a schematic view of the furnace and its semi-discrete motion. From a control point of view, a furnace preferably operates at a fixed furnace speed, and is loaded with one type of product only. However, in practice, both vary: furnaces need to stop regularly due to process interruptions downstream, and the product types to be produced change frequently. During such a stop, it is important that the furnace temperature is dropped quickly in order to reduce oxidation, decarburization and energy losses. Moreover, the product temperature, at the end of the furnace, should be reached with minimal heat input. There are several complications in this control problem. First, the target temperature, dictated by downstream processing, varies per product. Secondly, the furnace speed should vary as little as possible, and may not exceed an upper limit which depends on the last product in the furnace. Third, the furnace‟s temperatures should remain below an upper limit (to avoid damaging the furnace). Finally, burner variations should be minimized, since variations cause thermal fatigue of the furnace lining.

The conventional control strategy of walking beam furnaces typically boils down to controlling the furnace temperature(s) and furnace speed at predetermined set points. These set points can be determined by experiments, steady state calculations, or a combination of both. This strategy works fine during steady state conditions, but not during transients, since the actual product temperatures are not controlled. In practice, the control must be switched to manual operation frequently, which makes the quality of the end product strongly dependent on human intervention. In [13] an improved control technique is presented

Nonlinear Model Predictive Control of Walking Beam Furnaces

Eelco Nederkoorn, Peter van Wilgen, Jan Schuurmans

W

Fig. 1. Schematic view of a walking beam furnace. Products are moved periodically through the furnace by the rotation of the beam. At such a “step”, the doors open and the beam moves all products a fixed distance to the right.



which strives for a fixed target temperature profile (temperature versus location in furnace) for the products in the furnace. An on-line model is deployed to estimate the product temperatures. PI controllers adjust the burners such that the model temperatures approach the prefixed temperature target. This strategy is an improvement over the fixed furnace temperature control method. However, PI controllers have difficulties satisfying all the requirements and constraints optimally. For complicated control problems with nonlinear interacting dynamics and multiple constraints, such as walking beam furnaces, Model Predictive Control is much better suited. Linear Model Predictive Control (LMPC) is widely applied to the control of petrochemical plants. In LMPC, control actions are calculated online, and are based on model predictions. This technique requires a linear model of the process to be controlled. Constraints on manipulatable inputs and outputs are systematically dealt with. However, the model dynamics of a walking beam furnace are inherently nonlinear which makes standardized LMPC not applicable. The DotX Nonlinear Predictive Controller (DNPC, [6], [12]), a member of the class of Nonlinear Model Predictive Controllers (NMPC), is able to cope with the nonlinearities in the underlying model ([2], [3], [4], [5], [11]). Only recently, NMPC methods have been developed in such way that they have guaranteed stability ([2], [3], [11]). This essential feature enables DNPC to operate safely in real-life applications. This work discusses and evaluates the actual application and implementation of DNPC to a walking beam furnace at VDL Weweler, which has been up and running for several months at time of writing. VDL Weweler, a company based in The Netherlands, is a producer of air suspension systems. The base of the suspension systems is made of spring steel and needs to be heated in a walking beam furnace in order to obtain its characteristic shape. Although this paper restricts itself to the furnace at VDL Weweler, the results apply to walking beam furnaces in general. In this specific implementation, DNPC is programmed as a stand alone external controller. Communication with the PLC of the walking beam furnace is realized through an OPC (Object Linking and Embedding for Process Control) connection.

This paper is organized as follows. In section two the underlying nonlinear model is presented. Section three explains how this model can be used in DNPC as well as how the entire solution can be implemented. In its final section, the performance of DNPC is presented, using measured data of the VDL Weweler implementation.

II. Process Modeling Model predictive controllers base their control actions on online computed model predictions. At discrete sample times the control inputs are updated by optimizing a cost function based on these model

predictions. Hence, it is of vital importance that the model represents the process dynamics accurately. Recall that the control objective is to maintain the product temperature at the furnace‟s exit at target as closely as possible using minimal heat input. Therefore, the core component of the model represents the temperature of the products inside the furnace.

A. Heat Equations Modeling the heating process starts with defining the product‟s geometry. Let the spatial x -axis be aligned with the beam‟s moving direction. Define 0x to be the furnace‟s entrance and Lx the furnace‟s exit. The products have known thickness ),( xtDS inside the furnace (i.e. known for ],0[ Lx ). At a point x , the steel product temperature is defined by ),( xtTS and the furnace‟s combustion gas temperature by ),( xtTF . Heat exchange between the furnace‟s combustion gas and the steel surface is defined by:

)),(),(()( 44 xtTxtTTQ SFS , (1) where is the Stefan Boltzmann constant and the steel emission index [13]. In our case, the steel product is so thin that uniform temperature distribution may be assumed, and therefore, the product‟s temperature dependence on heat input can be modeled as:

xT

txtDTcT

TQtT S

SS

SS )(),()()(

)(2 . (2)

where )( ST is the characteristic steel density, )( STc the heat capacity of steel [1], and )(t is the furnace‟s speed. A model with a non-uniform distribution should be applied in situations where the product is thick enough so internal heat diffusion cannot be neglected.

The steel density and heat capacity are nonlinear functions of the product temperature. Fig. 2 illustrates

Fig. 2. Combined nonlinear function )()( SS TcT . The peak at about 750-800 degrees Celsius corresponds to the phase change of steel. At this temperature the molecular structure changes from ferrite into austenite which implies a low heat intake.



which strives for a fixed target temperature profile (temperature versus location in furnace) for the products in the furnace. An on-line model is deployed to estimate the product temperatures. PI controllers adjust the burners such that the model temperatures approach the prefixed temperature target. This strategy is an improvement over the fixed furnace temperature control method. However, PI controllers have difficulties satisfying all the requirements and constraints optimally. For complicated control problems with nonlinear interacting dynamics and multiple constraints, such as walking beam furnaces, Model Predictive Control is much better suited. Linear Model Predictive Control (LMPC) is widely applied to the control of petrochemical plants. In LMPC, control actions are calculated online, and are based on model predictions. This technique requires a linear model of the process to be controlled. Constraints on manipulatable inputs and outputs are systematically dealt with. However, the model dynamics of a walking beam furnace are inherently nonlinear which makes standardized LMPC not applicable. The DotX Nonlinear Predictive Controller (DNPC, [6], [12]), a member of the class of Nonlinear Model Predictive Controllers (NMPC), is able to cope with the nonlinearities in the underlying model ([2], [3], [4], [5], [11]). Only recently, NMPC methods have been developed in such way that they have guaranteed stability ([2], [3], [11]). This essential feature enables DNPC to operate safely in real-life applications. This work discusses and evaluates the actual application and implementation of DNPC to a walking beam furnace at VDL Weweler, which has been up and running for several months at time of writing. VDL Weweler, a company based in The Netherlands, is a producer of air suspension systems. The base of the suspension systems is made of spring steel and needs to be heated in a walking beam furnace in order to obtain its characteristic shape. Although this paper restricts itself to the furnace at VDL Weweler, the results apply to walking beam furnaces in general. In this specific implementation, DNPC is programmed as a stand alone external controller. Communication with the PLC of the walking beam furnace is realized through an OPC (Object Linking and Embedding for Process Control) connection.

This paper is organized as follows. In section two the underlying nonlinear model is presented. Section three explains how this model can be used in DNPC as well as how the entire solution can be implemented. In its final section, the performance of DNPC is presented, using measured data of the VDL Weweler implementation.

II. Process Modeling Model predictive controllers base their control actions on online computed model predictions. At discrete sample times the control inputs are updated by optimizing a cost function based on these model

predictions. Hence, it is of vital importance that the model represents the process dynamics accurately. Recall that the control objective is to maintain the product temperature at the furnace‟s exit at target as closely as possible using minimal heat input. Therefore, the core component of the model represents the temperature of the products inside the furnace.

A. Heat Equations Modeling the heating process starts with defining the product‟s geometry. Let the spatial x -axis be aligned with the beam‟s moving direction. Define 0x to be the furnace‟s entrance and Lx the furnace‟s exit. The products have known thickness ),( xtDS inside the furnace (i.e. known for ],0[ Lx ). At a point x , the steel product temperature is defined by ),( xtTS and the furnace‟s combustion gas temperature by ),( xtTF . Heat exchange between the furnace‟s combustion gas and the steel surface is defined by:

)),(),(()( 44 xtTxtTTQ SFS , (1) where is the Stefan Boltzmann constant and the steel emission index [13]. In our case, the steel product is so thin that uniform temperature distribution may be assumed, and therefore, the product‟s temperature dependence on heat input can be modeled as:

xT

txtDTcT

TQtT S

SS

SS )(),()()(

)(2 . (2)

where )( ST is the characteristic steel density, )( STc the heat capacity of steel [1], and )(t is the furnace‟s speed. A model with a non-uniform distribution should be applied in situations where the product is thick enough so internal heat diffusion cannot be neglected.

The steel density and heat capacity are nonlinear functions of the product temperature. Fig. 2 illustrates

Fig. 2. Combined nonlinear function )()( SS TcT . The peak at about 750-800 degrees Celsius corresponds to the phase change of steel. At this temperature the molecular structure changes from ferrite into austenite which implies a low heat intake.

the nonlinear product )()( SS TcT for steel. At the phase change of heated steel, around 750 degrees Celsius, the function peaks; which is one of the contributions to the severe nonlinearity (along with the fourth order of temperature dependence in the heat flow formula in (1)). Eventually we wish to have a (system) of equations which is not dependent on the spatial variable x . Therefore, we introduce discretization NLkxk / for

Nk ,,1,0 . By defining the approximation of the product temperature by

),()( kSkS xtTtT ,

we can use a first order approximation of the partial derivative:

xtTtT

xtT k

SkS

kS )()()( 1

.

Hence, the lumped heat equation (3) is reduced to the following system of ordinary differential equations:

1)(),()()(

)(2 kS

kS

kkS

kS

kS

kS TT

xt

xtDTcTTQ

dtdT ,

(4) for Nk ,,2,1 . The furnace temperature ),( xtTF is modeled by a curve H which is fitted through a set of discrete temperatures M,,1 . These temperatures are said to correspond to „zones‟ of the furnace. The temperature value at a any location x in the furnace equals the fit value

),,,(),( 1 xHxtT MF .

Fig. 3 illustrates such a curve for 2M . In conventional furnace control systems, the temperatures },,{ 1 M are controlled by feedback controllers that adjust the burners (typically PI controllers). The tuning of these controllers is relatively simple. In this work this control structure is unchanged, but instead of manual adjustments of the target temperatures, they are changed online by DNPC. Denoting these target temperatures by },,{ 1 Muu , the furnace model is completed by a first order model that relates the furnace temperature j to ju :

jjj u

dtd (5)

where is a fixed time constant. The reason why such a simple model can be used, is that the response of furnace air temperature to burner alterations is fast, and

almost independent of the products inside the furnace. This model has its limitations due to the fact that furnace temperatures cannot be controlled completely freely of any bounds. Hence, the model must be extended with some physically determined constraints. These constraints can be effectively taken into account by MPC. The model given in (4) and (5) is continuous and nonlinear. In order to apply model-predictive control, we need a method that is able to cope with these nonlinearities. As mentioned, in this work we have used DNPC, a commercial package based on nonlinear model-predictive control.

III. DNPC The walking beam‟s control variables are the furnace‟s zone target temperatures },,{ 1 Muu and the furnace speed . In model-predictive control, at a time nt , we seek to find set-points for these quantities such that the solution of the model )(tT k

S exhibits optimal behavior for Nk ,,2,1 and ntt . This optimality of model predictions is defined in a so-called cost-function.

A. Cost function The cost-function is a functional G , which depends on the product temperature at the furnace‟s exit )(tT N

S and control efforts },,{ 1 Muu and . Using this function as the objective function of a minimization problem yields:

01 ),,,,(

21mint

MNS dtuuTtG , (6)

Fig. 3. Furnace and product temperature at a fixed time in a walking beam furnace. A fitted curve through the measurement values of two sensors (for zone 1 and 2) determine the gas temperature of the furnace at all locations. Note how the profile of the product temperature has a dip at about 750 degrees Celsius, caused by the steel phase transition (Fig. 2).



where )(tT NS must be a solution to (4). This is the

exact problem that DNPC is build to solve. All that is left now is to design a cost function G for the walking beam furnace application. Recall the main objective, keeping the product temperature at the end of the furnace )(tT N

S on a given set-point )(t with the smallest possible energy usage. This last point is equivalent to choosing Muu ,,1 as low as possible. These two points (temperature on target and minimal heat input) are reflected by

2

212

2

21 ),,,()()( xHttTG MNS

where 1 and 2 are penalty parameters, )(tT N

S is a solution to (4) and M,,1 are solutions of (5). The penalty parameters can be used to fine tune the balance between the, sometimes conflicting, optimization goals of DNPC. This control problem formulates the optimization calculations at a time nt . In model-predictive control these control updates have to be made at a predetermined sample rate. Hence, at times

tnttn 0 , where t is the time between two updates, problem (6) is solved and the controls set-points Muu ,,1 and , computed for 1nt , are returned to the walking beam furnace. The model (4)-(5) is implicitly solved in these computations. However, for the model to be well-posed, it needs additional conditions.

B. State Estimation The system of differential equations (4) needs a boundary condition at the furnace‟s entrance. This is the temperature of the products entering the furnace:

nS tttT ,)(0 . (7)

A typical assumption is that the products enter the furnace with a temperature equal to the outside temperature of the production facility (for instance

o20 ). Furthermore, the model needs to be initiated at

ntt . Hence, we need }{ k such that

NktT kn

kS ,,2,1,0,)( . (8)

The initial state of the system N,,, 10 is not known (besides 0 ), and needs to be estimated based on measurements of the furnace temperatures. Though such state estimation typically is non-trivial, we will explain a remarkably simple approach. Estimating the initial state (8), at a time nt can be done by using actual measurements M,,1 to

solve equation (4) on the interval ],[ 1 nn tt . However, this does not solve the problem, since again we need an initial condition for this sub-problem at time 1nt .

Repeating this process for 01 ,, ttn shifts the problem to finding an initial condition at 0t , the moment the entire observation process is started. In order to compute this absolute initial state estimate properly, a few strategies can be deployed. Firstly, one can pick a moment t that the states )(tT k

S are completely known, and use this known state as initial condition. For instance, when the furnace is empty and has been turned off for a while, one can assume the state is equal to the furnace‟s temperature. Another method is to pick a random guess and keep DNPC idle for a while. In such cases the state estimation will catch up to the furnace‟s steady state. When this has happened, DNPC can be safely activated.

C. Process Interruptions By using the predictive nature of DNPC, it is possible to obtain additional energy savings, by responding to special circumstances. One of such situations is the so-called operator stop. Typically, the walking beam furnace is part of a larger production line, which could have other (un)foreseen stops downstream from the furnace. In many cases the operator will stop the entire process, including the walking beam, and later, release the hold. By measuring the operator stop, DNPC can respond by lowering the furnace‟s temperature. This immediately results in a reduction of energy usage as well as a reduction of oxidation and decarburization. When an operator restarts the furnace, DNPC uses its model prediction to place an extra hold on the furnace, and releasing it only when the products have regained the target temperature. As shown in the results section, the energy saving modes typically result in a 50% reduction of energy consumption when compared to the normal production mode.

D. Implementation of DNPC Implementing DNPC requires either the controller to be embedded in the PLC of the furnace, or to run externally and exchange data with the PLC. For this application we have chosen to do the latter, and communicate through an OPC (Object Linking and Embedding for Process Control) connection. Such protocols allow cross-application data communication. The key idea in OPC is to have a server running at all times, which can communicate with all desired applications. In our situation both the PLC and the computer where DNPC is running on, have access to the OPC server. Fig. 4 illustrates the data exchange between the components of the DNPC software solution, the OPC server and the PLC of the furnace. The DNPC solution consists of a Control Monitor, an optional Web – Interface and a computation core. The Monitor acts as an OPC client and collects data from the server and Web – Interface and passes it through to



where )(tT NS must be a solution to (4). This is the

exact problem that DNPC is build to solve. All that is left now is to design a cost function G for the walking beam furnace application. Recall the main objective, keeping the product temperature at the end of the furnace )(tT N

S on a given set-point )(t with the smallest possible energy usage. This last point is equivalent to choosing Muu ,,1 as low as possible. These two points (temperature on target and minimal heat input) are reflected by

2

212

2

21 ),,,()()( xHttTG MNS

where 1 and 2 are penalty parameters, )(tT N

S is a solution to (4) and M,,1 are solutions of (5). The penalty parameters can be used to fine tune the balance between the, sometimes conflicting, optimization goals of DNPC. This control problem formulates the optimization calculations at a time nt . In model-predictive control these control updates have to be made at a predetermined sample rate. Hence, at times

tnttn 0 , where t is the time between two updates, problem (6) is solved and the controls set-points Muu ,,1 and , computed for 1nt , are returned to the walking beam furnace. The model (4)-(5) is implicitly solved in these computations. However, for the model to be well-posed, it needs additional conditions.

B. State Estimation The system of differential equations (4) needs a boundary condition at the furnace‟s entrance. This is the temperature of the products entering the furnace:

nS tttT ,)(0 . (7)

A typical assumption is that the products enter the furnace with a temperature equal to the outside temperature of the production facility (for instance

o20 ). Furthermore, the model needs to be initiated at

ntt . Hence, we need }{ k such that

NktT kn

kS ,,2,1,0,)( . (8)

The initial state of the system N,,, 10 is not known (besides 0 ), and needs to be estimated based on measurements of the furnace temperatures. Though such state estimation typically is non-trivial, we will explain a remarkably simple approach. Estimating the initial state (8), at a time nt can be done by using actual measurements M,,1 to

solve equation (4) on the interval ],[ 1 nn tt . However, this does not solve the problem, since again we need an initial condition for this sub-problem at time 1nt .

Repeating this process for 01 ,, ttn shifts the problem to finding an initial condition at 0t , the moment the entire observation process is started. In order to compute this absolute initial state estimate properly, a few strategies can be deployed. Firstly, one can pick a moment t that the states )(tT k

S are completely known, and use this known state as initial condition. For instance, when the furnace is empty and has been turned off for a while, one can assume the state is equal to the furnace‟s temperature. Another method is to pick a random guess and keep DNPC idle for a while. In such cases the state estimation will catch up to the furnace‟s steady state. When this has happened, DNPC can be safely activated.

C. Process Interruptions By using the predictive nature of DNPC, it is possible to obtain additional energy savings, by responding to special circumstances. One of such situations is the so-called operator stop. Typically, the walking beam furnace is part of a larger production line, which could have other (un)foreseen stops downstream from the furnace. In many cases the operator will stop the entire process, including the walking beam, and later, release the hold. By measuring the operator stop, DNPC can respond by lowering the furnace‟s temperature. This immediately results in a reduction of energy usage as well as a reduction of oxidation and decarburization. When an operator restarts the furnace, DNPC uses its model prediction to place an extra hold on the furnace, and releasing it only when the products have regained the target temperature. As shown in the results section, the energy saving modes typically result in a 50% reduction of energy consumption when compared to the normal production mode.

D. Implementation of DNPC Implementing DNPC requires either the controller to be embedded in the PLC of the furnace, or to run externally and exchange data with the PLC. For this application we have chosen to do the latter, and communicate through an OPC (Object Linking and Embedding for Process Control) connection. Such protocols allow cross-application data communication. The key idea in OPC is to have a server running at all times, which can communicate with all desired applications. In our situation both the PLC and the computer where DNPC is running on, have access to the OPC server. Fig. 4 illustrates the data exchange between the components of the DNPC software solution, the OPC server and the PLC of the furnace. The DNPC solution consists of a Control Monitor, an optional Web – Interface and a computation core. The Monitor acts as an OPC client and collects data from the server and Web – Interface and passes it through to

the computation core. This core is a set of optimization routines, combined with a programmed model (including equations (4) to (8)), and is contained in a dynamically linked library (DLL). The Control Monitor has access to this library and is able to exchange data through shared memory. The control updates computed by the core find their way back to the PLC through the monitor and OPC server. When implementing an external controller through such a connection protocol, it is essential that error handling is done carefully. That is, both PLC and Control Monitor need to adequately respond to connection failures. In order to achieve this, both applications have a reserved OPC item they use as a life-beat. When a control or measurement update is missed, the PLC automatically switches to the conventional furnace control strategy and notifies the operator. The Control Monitor sends a message to the Web-Interface and waits for the connection to be re-established.

IV. Results VDL Weweler, a Dutch company, produces air suspension systems. The base of these systems are made of spring steel. In order to form them into different shapes, the bases need to be reheated in a walking beam furnace. At the moment of writing VDL Weweler has two of these furnaces solely designated to reheating these components. DNPC has been installed on an external computer which communicates with one of the furnaces by OPC. This section will demonstrate,

by means of actual measurement data, that DNPC is able to maintain the product temperatures at target, while at the same time realizes a significant energy saving.

A. Furnace at VDL Weweler There are two sensors inside the furnace )2(M , which leads to measurements 21 , . This reduces the optimal control problem to finding a set-point for both sensors and a walking beam velocity ],,[ 21 uu . The two sensors are said to measure different zone‟s of the furnace, i.e. 1 defines the temperature of zone 1 and

2 of zone 2. The computed set-points are maintained by PI controllers which control the gas burners. The walking beam furnace is part of a larger manufacturing process. Down the production line, products need to be cooled down rapidly in order to keep the hardening property gained by heating it. Such cooling is done in an oil bath, and products need to be in there for a minimum amount of time. Hence, besides the desired product temperature , the operator needs to set a maximum velocity . This leads to an extra condition for the optimal control problem (6) at time nt :

nttt ,)( . At all times the operator is able to change the settings

],[ ; DNPC will use the new parameters in the next control update. In order to obtain an indication of the controller‟s performance, we need to study actual measurement data. The next section contains such an analysis.

B. Model Verification Recall that DNPC aims to maintain it‟s modeled product temperature at the furnace‟s exit )(tT N

S on a target )(t . The model can be verified by comparing the

computed values to actual measurements of the product temperature. Such a measurement is not easy to obtain, because a sensor needs to be placed at a critical location and can easily break down or give corrupted data. Fig. 5 shows the temperature computed by the model and the actual measured temperature. In

Fig. 4. Schematic view of the DNPC implementation using OPC connections. The PLC of the walking beam furnace communicates through designated OPC items with the server, which in its turn passes that information to the control monitor. The monitor retrieves user data from the Web-Interface and requests DNPC to update the controller setpoints. Those setpoints are send back to the server which passes it on to the PLC of the furnace.

Fig. 5. Model and measurement values of the temperature of products leaving the furnace. Note that the computed values match the actual measurements both in characteristic shape and quantity. The vertical lines indicate an operator stop.



this situation DNPC is not actively controlling the furnace. Note how the modeled and measured data closely match. Moreover, after an operator stop the products exit the furnace with a relative low temperature. This characteristic behavior, which can be observed in both model as measurement data, is due to the fact that the furnace temperature at the exit of the furnace is hardly influenced by the burners. It is too close to the furnace exit. As shown in later sections, this cooling cannot be prevented, however it can be mitigated by DNPC. This result indicates that controlling the modeled temperature corresponds to controlling the factual product temperature at the furnace‟s exit. Now let us evaluate the situation where DNPC is actively controlling the furnace.

C. Data Analysis First we will look at a small transient caused by the operator placing a hold on a short time interval. Fig. 6 shows how DNPC adjusts the temperature set-points in zone 1 and zone 2 during and after two short stops. While the stop is still happening, DNPC reduces the furnace‟s temperature in both zones. Note that during

this time the gas flow drops by approximately 10%. This energy reduction is a direct result of this advanced control strategy. As in the conventionally controlled situation, the first products leave the furnace somewhat colder. However, this is still within quality margins.

Recall that the biggest saver is the energy savings mode, in which set-points are lowered drastically when a stop lasts more than a predetermined threshold. Fig. 7 illustrates the behavior of the furnace‟s measured and target temperature, its gas flow and product temperature during such an event. Ten minutes after the stop has been initiated, the setpoints for zone 1 and zone 2 are reduced to about 700 degrees Celsius. This results in a sudden drop of gas consumption from about 140 m3/hr to 70 m3/hr. The energy savings mode lasts for about fifty minutes. When the operator ends the stop, DNPC holds the furnace in order to reheat it until the products are hot enough. For about 7 minutes, DNPC heats up the furnace at full „throttle‟. After this time period, the product temperature (computed by the internal model) has reached a desired threshold and normal production starts again. In total the controller saved about 20% during the stop, and has not caused any products to be heated excessively, as can also be

Fig. 6. Two consecutive short furnace stops. The vertical lines indicate the intervals where the operator has placed a hold. Note that during the stops itself DNPC automatically reduces the set-points for zone 1 and zone 2. Moreover, during the stop all products receive more energy than intended in a steady state situations. This results in lower set-points for a longer period of time after the stops, and therefore a reduction of energy usage. This can be observed by the dip in the gas flow graph. Moreover, besides a slight cooling after a stop, DNPC is able to keep the product temperature on target.

Fig. 7. An operator stop illustrated by temperatures of zone 1 and zone 2, their set points and the energy usage. Note how the temperature set points are lowered drastically when the stop has lasted ten minutes. This energy savings mode last for about 45 minutes. After the operator releases the hold, DNPC reheats the furnace by a sharp increase in the temperature set points. Moreover, it stops the furnace for about 7 minutes, until the products regain a desired temperature threshold, and after that initiates normal production. Again, the released products are quickly steered towards the target temperature.



this situation DNPC is not actively controlling the furnace. Note how the modeled and measured data closely match. Moreover, after an operator stop the products exit the furnace with a relative low temperature. This characteristic behavior, which can be observed in both model as measurement data, is due to the fact that the furnace temperature at the exit of the furnace is hardly influenced by the burners. It is too close to the furnace exit. As shown in later sections, this cooling cannot be prevented, however it can be mitigated by DNPC. This result indicates that controlling the modeled temperature corresponds to controlling the factual product temperature at the furnace‟s exit. Now let us evaluate the situation where DNPC is actively controlling the furnace.

C. Data Analysis First we will look at a small transient caused by the operator placing a hold on a short time interval. Fig. 6 shows how DNPC adjusts the temperature set-points in zone 1 and zone 2 during and after two short stops. While the stop is still happening, DNPC reduces the furnace‟s temperature in both zones. Note that during

this time the gas flow drops by approximately 10%. This energy reduction is a direct result of this advanced control strategy. As in the conventionally controlled situation, the first products leave the furnace somewhat colder. However, this is still within quality margins.

Recall that the biggest saver is the energy savings mode, in which set-points are lowered drastically when a stop lasts more than a predetermined threshold. Fig. 7 illustrates the behavior of the furnace‟s measured and target temperature, its gas flow and product temperature during such an event. Ten minutes after the stop has been initiated, the setpoints for zone 1 and zone 2 are reduced to about 700 degrees Celsius. This results in a sudden drop of gas consumption from about 140 m3/hr to 70 m3/hr. The energy savings mode lasts for about fifty minutes. When the operator ends the stop, DNPC holds the furnace in order to reheat it until the products are hot enough. For about 7 minutes, DNPC heats up the furnace at full „throttle‟. After this time period, the product temperature (computed by the internal model) has reached a desired threshold and normal production starts again. In total the controller saved about 20% during the stop, and has not caused any products to be heated excessively, as can also be

Fig. 6. Two consecutive short furnace stops. The vertical lines indicate the intervals where the operator has placed a hold. Note that during the stops itself DNPC automatically reduces the set-points for zone 1 and zone 2. Moreover, during the stop all products receive more energy than intended in a steady state situations. This results in lower set-points for a longer period of time after the stops, and therefore a reduction of energy usage. This can be observed by the dip in the gas flow graph. Moreover, besides a slight cooling after a stop, DNPC is able to keep the product temperature on target.

Fig. 7. An operator stop illustrated by temperatures of zone 1 and zone 2, their set points and the energy usage. Note how the temperature set points are lowered drastically when the stop has lasted ten minutes. This energy savings mode last for about 45 minutes. After the operator releases the hold, DNPC reheats the furnace by a sharp increase in the temperature set points. Moreover, it stops the furnace for about 7 minutes, until the products regain a desired temperature threshold, and after that initiates normal production. Again, the released products are quickly steered towards the target temperature.

seen from Fig. 7.

D. Key Performance Indicators At time of writing, DNPC has been actively controlling the furnace at VDL Weweler for several months. Measurements on the energy consumption of the furnace has indicated that DNPC has a energy savings over the conventional control system of up to 10 %, depending on circumstances as product type, etc. These savings include both steady state and transient energy consumption. Moreover, during the DNPC controlled situation, products have been produced within sharp quality margins.

V. Conclusion Accurate models of the heating dynamics of walking beam furnaces contain nonlinear terms. Hence, using the systems in model-predictive requires specialized solving techniques. We demonstrated that DNPC, a commercial NMPC controller which can cope with these nonlinearities, can be used in practice to obtain high performing, robust and stable control of walking beam furnaces. DNPC enables the operator to directly steer the product temperature rather than the furnace temperature. As a result, products not only exit the furnace at a desired temperature, they also have not been heated excessively. Moreover, the predictive nature of DNPC makes it possible to deal with large transients caused when the operator places a hold on the furnace. The DNPC controlled production results in a reduction of energy consumption of up to 10 % over a conventionally controlled situation.

VI. Acknowledgements The authors wish to thank the AgentschapNL of the Dutch Ministry of Economic Affairs for financial support.

VII. References [1] Y. Jaluria and K.E. Torrance, “Computational heat transfer”, in

Series in computational methods in mechanics and thermal sciences, 2nd ed., Taylor & Francis, 2003, pp. 180-189.

[2] R. Findeisen, L. Imsland, F. Allgöwer and B. Foss, “Stability conditions for observer based output feedback stabilization with nonlinear model predictive control”, in Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii USA, 2003, pp. 1425-1430.

[3] R. Findeisen and F. Allgöwer, “An introduction to nonlinear model predictive control”, in 21st Benelux Meeting on Systems and Control, Veldhoven, 2002, pp.1-23.

[4] B. Kouvaritakis, M. Cannon and J.A. Rossiter, “Non-linear model based predictive control”, in Int. J. Control, vol. 72(10), 1999, pp. 919-928.

[5] M. Bacic, M. Cannon and B. Kouvaritakis, “Extension of efficient predictive control to the nonlinear case”, Int. J. of Robust Nonlinear Control, vol. 15. 2005, pp. 219 – 231.

[6] J. Schuurmans, “DotX nonlinear predictive controller (DNPC)”, url: www.dotxcontrol.com, 2009, Retrieved on 27-08-2010.

[7] H.E. Pike, and S.J. Citron, “Optimization studies of a slab reheating furnace”, in Automatica, vol. 6, Pergamon Press, 1970, pp. 41-50.

[8] B. Zhang, Z. Chen, L. Xu, J. Wang, J. Zhang, and H. Shao, “The modeling and control of a reheating furnace”, in Proc. Of the American Contr. Conf., Anchorage, USA, May 8-10, 2002, pp. 3823-3828.

[9] H.S. Ko, J.S. Kim, T.W. Yoon, M. Lim, D.R. Yang, and I.S. Jun, “Modeling and predictive control of a reheating furnace”, ”, in Proc. Of the American Contr. Conf., Chicago IL, USA, June, 2000, pp. 2725-2729.

[10] Z. Chen, C. Xu, B. Zhang, H. Shao, and J. Zhang, “Advanced control of a walking-beam reheating furnace”, in J. of Univ. Sc. and Tech. Beijing, vol. 10, nr. 4, August 2003, pp. 69-74.

[11] M. Tenny, J. Rawlings, and S. Wright, “Closed-loop behavior of nonlinear model predictive control”, AIChE Journal, doi: 10.1002/aic.10177, vol. 15, 2005, pp. 219-231.

[12] E.A. Nederkoorn, J. Schuurmans, and W. Schuurmans, “Continuous Model Predictive Control of a Hybrid Water System – Application of DNPC to a Dutch Polder”, in Proceedings of the 8th IEEE Int. Conf. on Netw., Sens. and Contr., Delft NL, 2011.

[13] D. Staalman, “The funnel model for accurate slab temperature control in reheating furnaces”, Rev. Met. Paris, DOI: 10.1051/metal:2004187, nr 6, June 2004, pp. 453-459.

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