Automatic Control of Direct Reduction Iron Ore (DRI) Process

Automatic Control of Direct Reduction Iron Ore (DRI) Process

16th IFAC Symposium on Automation in Mining, Mineral and Metal Processing August 25-28, 2013. San Diego, California, USA Automatic Control of Direct ...

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16th IFAC Symposium on Automation in Mining, Mineral and Metal Processing August 25-28, 2013. San Diego, California, USA

Automatic Control of Direct Reduction Iron Ore (DRI) Process S. Guanin*, D. Pignattone**, A. Martinis*** * Research & Development Department Danieli & C. Officine Meccaniche S.p.A., Buttrio, 33043 UD, Italy (Tel:+39-0432-195-7246; e-mail: [email protected]). **L2 Department Danieli Automation S.p.A., Buttrio, 33043 UD, Italy (e-mail: [email protected]) *** DE-CM Department Danieli & C. Officine Meccaniche S.p.A., Buttrio, 33043 UD, Italy (e-mail: [email protected]) Abstract: An automatic control of a DRI plant has been performed in order to provide the best possible working point, to obtain the target level 2 process set points (DRI metallization, carburation, productivity) in function of Iron Ore and Reducing gas compositions. The target has been obtained by means of a Process Reconstruction Model (PRM) that provides continuous static estimation of plant measurements, efficiency analyses, virtual sensor and diagnostics. An Extended Kalman Filter (EKF) has been used to provide continuous robust dynamic estimations of the output process measurements. Finally the EKF feeds a Linear Quadratic Gaussian (LQG) regulator that performs, in real time, the calculation of Optimal Controls (minimum energy, maximum gas quality level 1 set points), in function of level 2 sets. The suite has been successfully applied to a DRI Energiron Plant. Keywords: Process Reconstruction Model, Extended Kalman Filter, LQG, Real time, DRI Energiron Plant, Automatic Process Control.

1.

measurements collected in the level 2 by the PRM are used in the EKF to correct the controlled variables estimation produced by the physical model; in this model the reduction process is described via a system of 7 differential equations, based on the mass/energy balance of the gas and solid flows inside the reducing reactor. The system is completed with 8 parametric equations used to define the kinetic working point of the reactor. The estimation of the process production data (DRI metallization, carburation and productivity) are used by the LQG regulator that describes their evolution in function of 7 main inlet variables. In this way, the outputs of the regulator are 7 controlled variables set points to be implemented directly in the level 1 control system (DCS).

INTRODUCTION

The Level 2 Automatic Process Control is an advanced technique, which includes various mathematical and empirical functions, with the final target to stabilize and optimize the overall process. The control is done pushing the Plant as close as possible to the theoretical optimum condition. The target is the minimization of variable standard deviations in order to obtain the highest production quality and yield. In the advanced control of an DRI plant a number of “virtual variables” (e.g. short simulation processes) are added to the traditional measurements, which are normally managed via control loops in level 1, in order to perform some local optimization functions. The suite has been realized via a Process Reconstruction Model (PRM) that is a grey box model which operates on line, in real time, as static virtual sensor applied to the system where the system is the complete set of process variables (Di Giorgio, 2011). An Extended Kalman Filter (EKF) performs the minimum variance estimation of a process variables subset (i.e. DRI metallization, and carburation). A Linear Quadratic Gaussian regulator (LQG) produces in real time the minimum energy optimal level 1 process variable set points (i.e. reducing, reformed, oxygen, natural gas flows (Nm3/h), reducing gas temperature (°C), productivity (t/h)). This paper considers the application of the whole level 2 structure described that is one of the most important features that characterizes the Energiron plant. The PRM collects and processes the measurements transmitted from instrumentation on field to the level 2 in order to monitorize the equipment efficiency, the adopted operating conditions in the various sections of the plant and the product quality as main final target. The 978-3-902823-42-7/2013 © IFAC

2.

THE PRM MODEL

The PRM mathematical model used for data analysis is a grey box type; its structure is based on the concept of the process static reproducer. Empirical equations based on measurements and physical equations, are applied at the same time to a defined data set, with the chosen degree of freedom between variables, in order to obtain the desired analysis for the observed section of the plant. Some sets of instrumentation signals coming from PLCs are processed via physical equations to complete with non-measurable values all the process data of system, to provide a full description of its status. In addition, some redundancies have been applied inside the model in order to have a double validation between measurements and calculations: it means that reliability of instrumentation and plant conditions/productivity can be continuously monitored.

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2.1 The PRM Virtual Sensor

Iron Ore In

The software can envisage, through variation of degrees of freedom on a selected and isolated system, the possible presence of inconsistencies. For this reason, the first result of this kind of analysis is the detection of incorrect response from instrumentation installed in the field. In that case the incorrect measurement can be substituted, corrected or completed with a virtual one. The figure 1 represents the reality of a Direct Reduction Plant: the measurements transmitted from instrumentation on field are collected and processed in level 2 in order to keep monitored equipment efficiency, operating conditions in the various sections of the plant and product quality (productivity, carbon content, metallization, DRI temperatures, etc.).

Top Pre Red Area Red & AR Area Cracking Area

- Fe 2 O3 ® ¯ Fe 2 O3 - FeO ® ¯ FeO

H 2 l 2 FeO

H 2O

CO l 2 FeO

CO 2

H 2 l Fe

H 2O

CO l Fe

CO 2

-CH 4 H 2 O l CO 3 H 2 ® ¯CO H 2 O l CO 2 H 2 2CO l C

CO 2

CH 4 l C

2H 2

(1) (2) (3) (4) (5)

(1) Pre Reduction (PreRed) (2) Reduction (Red) Bottom (3) Auto Reforming (AR) (4) Boudouard DRI out (5) Cracking Fig. 2 Shaft reactor scheme and main chemical reactions As shown in the figure, three main chemical areas characterize the evolution of the process. From Top to Bottom of the shaft following the downstream of the pellets inside the reactor, we can find the Pre Reduction Area (Pre Red Area), where the reduction species change all the iron oxides in Wustite oxide (FeO). Then there is the Reduction and Auto Reforming Area (Red & AR Area) where the reduction to metallic Iron of the pellets is completed and where the reduction gas changes its species distribution, with a contribution of Auto Reforming Reactions (3) Boudouard (4) and methane Cracking too (5). The thermodynamic equilibrium is not reached. To evaluate the distance from the equilibrium of each reaction it’s necessary to calculate the reaction kinetics for the whole reaction system. Finally the iron pellets find the Cracking Area where the Cracking of methane (5) take place to enrich the pellets in carbon, the most in the Fe3C form.

Fig. 1 Level 2 application: Schematic architecture of the PRM installed on level 2 at a DRI Energiron plant. Overall plant condition is continuously under control to optimize the production and minimize the consumptions. In fact several indexes (e.g. energy yield, equivalent metallization, minimum carbon, etc.) have been set up in order to rationalize the plant performance and properly evaluate the process yield. 3.

Main Chemical Reactions

ENERGIRON PROCESS

3.1 The Shaft Reactor Chemical Process The iron ore reduction process takes place in a gas-solid reactor. The ore pellets are charged from the top of the reactor and moves downstream to the bottom for the DRI extraction. The reducing gas is a mixture of H2, CO, H2O, CO2, CH4 and moves upstream from the middle of the reactor to the top. The chemical mechanism of the process consists in a continuous migration of atomic oxygen contained in the ore pellets (bond in form of iron oxides wustite FeO, hematite Fe2O3) to the reducing gas. The gas species that take place in the reduction reactions (1) and (2) are (Fig. 2): hydrogen H2, carbon monoxide CO, carbon dioxide CO2, water H2O. The atomic oxygen is captured by the reductive species (H2, CO) to form oxidant species (H2O, CO2). The addition of methane CH4 is done in order to enrich the reducing gas and to carburize the product (when the injection is done in the shaft bottom). The relevant reactions are the Cracking of the methane (5) in equilibrium with the Boudouard reaction (4) and the Methane Reforming (3) (Fig. 2). Reactions (3), (4) and (5) bring the gas mix to a continuous changing equilibrium during his track inside the reactor. The main reaction space distribution is shown in figure 2.

3.2 The Shaft Physical Model The mechanism described in the previous section is a simplification of the real chemical mechanism of the process, the scheme in figure 2 lets to the following simplified physical model: qin - x °CH 2 V ˜ CinH 2 ° x qin °C ˜ CinCH 4 ° CH 4 V ° x qin ° ˜ CinCO ®CCO V ° x qin ° °CCO2 V ˜ CinCO2 ° x qin °C ˜ CinH 2O H O V ¯° 2

qout ˜ CH2 Wgs 3 ˜ St 2 ˜ Cr PH 2 RH 2 V qout ˜ CCH4 St Cr V qout ˜ CCO Wgs St 2 ˜ Bou PCO RCO V qout ˜ CCO2 Wgs Bou PCO RCO V qout ˜ CH2O Wgs St PH 2 RH 2 V

(6)

The dynamic system (6) calculates the volumetric concentration trajectory of the chemical species that take part to the chemical reaction (1)..(5). In (6) the qin and qout represent the gas volume flow inlet and outlet the reactor [m3/s], Cj and Cinj are the chemical species concentrations 341

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[kmol/m3] outlet and inlet respectively, V the reactor volume [m3], Wgs represents the Water Gas Shift Reaction, St is the Steam Reforming reaction (Wgs and St are the AR reactions), Cr represents the Cracking reaction, PH2 and PCO are the Pre Reduction reactions, RH2 and RCO represent the Reduction Reactions and finally, Bou is the Boudouard reaction, all reaction in [kmol/m3s]. To complete the dynamic system (6) we need now the calculation of the reaction chemical contributions, by means of the calculation of their kinetics: Ki ˜ e

Rkin

Ei R˜TR

§ ˜ ¨¨ (Ca ) a ˜ (Cb ) b ©

(Cc ) c ˜ (Cd ) d Keqi TR

· ¸¸ ¹

temperatures of the gas, and finally by 8 parametric equations, referred to the kinetics Kj of the 8 reactions that take place in continuous process to follow the trajectory of the reaction kinetic gains. 3.3 The EKF Estimator The Kalman Filter theory brings to a solution of the optimal state estimation problem, for a linear discrete time dynamic system described by the following equation: - x(k 1) f ( x(k ), u (k )) w(k ) ® ¯ y (k ) h( x(k ), u (k )) v(k )

(7)

With f and h linear function of states and inlets; w, v additives gaussian noise of states and measurements respectively with known covariance matrix W = E(wwT) and V = E(vvT) respectively. For nonlinear systems a closed solution for the same problem doesn’t exists. In this case, a classical method to solve the problem is to linearize the system around the actual estimation and to apply the Kalman Filter to the linearized system (Voros 2008).

In (7) the Keqi(TR) terms represent the equilibrium constants of the reactions calculated at the reaction temperature TR [adim.] (for reactions with no mole production), Rkin are the reaction contribution [kmol/m3s], Ei represent the Arrhenius coefficients of the reactions [kJ/kmol], (Ca)a are the chemical species concentration rising to the power of its mole contribution [kmol/m3]a, TR is the reaction temperature, or the temperature of both gas and solid flows at the Red & AR Area [K], R is the gas Constant 8.314 [kJ/kmolK] and finally Ki are the Kinetic Constants to estimate [1/s]. The physical model finally has been completed with the energy balance equations, taking in consideration the energy equilibrium at the inlet (Red & AR Area) and outlet (Top) of the shaft for both gas and solid flows: D ˜ A ˜ TR Tin V ˜ U ˜ CP ( 'H Wgs ˜ Wgs 'H Cr ˜ Cr 'H St ˜ St 'H Bou ˜ Bou x

TR

Qin ˜ Tin V

Qout ˜ TR V

'H RH 2 ˜ RH 2

'H RCO ˜ RCO 'H PH 2 ˜ PH 2 x

TTop

Qin ˜ TR V

C pox ˜ qDRI

Qout ˜ TTop V DO ˜ Tox

CP ˜V ˜ U

Let f and h be nonlinear function of the states, F(k), B(k) and H(k) be the jacobian matrices of f and h, respectively, denoted by (Yang, 2011): F (k )

ª wf x ( k ), u ( k ) º « » wx ( k ) ¬ ¼

H (k )

(8)

'H PCO ˜ PCO ) /( U ˜ C P )

D ˜ A ˜ TTop Tox V ˜ U ˜ CP C pDRI ˜ q DRI ˜ TR CP ˜V ˜ U

(10)

, B (k ) xÖ ( k ), u ( k )

ª wf x ( k ), u ( k ) º « » wu ( k ) ¬ ¼

ª wh x ( k ), u ( k ) º « » wx ( k ) ¬ ¼

, xÖ ( k ), u ( k )

(11) xÖ ( k ),u ( k )

The solution is given by a recursive algorithm (table 1) that can be easily described in the following steps: - Time update step that brings to the estimation of the current state and the state error covariance matrix P. The evaluation is an ‘a priori’ estimation for the next step. - Measurement update step that brings to the feedback correction. The evaluation is an ‘a posteriori’ estimation for the current step.

(9)

In (8) the Tin term represents the gas temperature at the inlet (Red & AR Area) [K], Qin and Qout are the gas mass flow inlet and outlet the reactor [kg/s], . is the heat transfer coefficient between gas and solid bed at inlet point [W/m2K], A represents the equivalent area for the heat exchange [m2], ! is the gas inlet density [kg/m3], Cp represents the gas heat capacity [kJ/kgK], û+i represent the heat of reactions [kJ/kmol], In (9) the TTop is the gas temperature at the Top [K], Tox is the iron ore pellets temperature at inlet (Top) [K], Cpox and CpDRI represent the heat capacity of the solid bed at the inlet (for pellets the inlet is the Top zone) and at the Red & AR Area [kJ/kgK], qDRI is the solid flow [kg/s], DO represents the oxygen mass flow, passing from solid to gaseous phase during the reduction process [kg/s].

The following scheme represents the previous algorithm: Table 1. Predictor - Corrector Time Update (step k) - Predictor - xÖ ( k 1) f ( xÖ (k ), u (k )) Future (12) ® state ¯ yÖ (k ) h( xÖ (k )) Future P ( k 1) F ( k ) ˜ P ( k ) ˜ F ( k )T W (13) covariance Measurement Update (step k+1) – Corrector K ( k ) P (k ) ˜ H (k )T ˜ Kalman (14) Filter Gain ( H (k ) ˜ P(k ) ˜ H (k )T V ) 1 Innovation K (k ) ˜ ( y(k ) h( xÖ(k ))) (15) estimation xÖ (k 1) f ( xÖ (k ), u (k )) (16) K (k ) ˜ ( y ( k ) h( xÖ (k ))) correction covariance P ( k ) ( I K ( k ) ˜ H ( k )T ) ˜ P ( k ) (17) correction The next predicted state and state error covariance matrix at step k, xÖ(k+1) and P(k+1) respectively, are computed in the first step and then in the measurement update at step k+1, the

The physical model of the shaft finally has been synthesized using a system of 15 dynamic equations that represent the complete evolution of the shaft state, considering both the field measurements and the estimated reaction kinetics. The system is composed by 5 dynamic chemical equations that describe the complete evolution trajectory of the 5 chemical gas species concentrations Cj, 2 dynamic energy equation referred to the energy balance of the mass/gas system at the shaft inlet/outlet that describe the tracking of the TR and TTop 342

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next estimated step xÖ(k+1), is obtained by means of the corrective term called innovation, calculated by the Kalman Filter Gain K(k).

- A Reformer Unit that converts Steam and Natural gas into Reducing (Bustle) gas, a gas mix rich in H2 and CO. - A Dewatering Unit that removes H2O from the recirculating process gas. - A Compressor Unit that rises up the pressure of the recirculating process gas. - A CO2 Removing Plant Unit that removes the CO2 from the recirculating process gas. - A Heater Unit that rises the Process Gas temperature up to the process request value before entering the Reactor Unit. - A Flare Unit that bursts the bleed to maintain the pressure in the circuit when regulations take place and to keep in control the Inert gas specie concentration (Nitrogen N2) in the process gas loop (minimum bleed required).

3.4 EKF with Parametric Estimation In this application we need to estimate not only the state trajectory but also parameters represented by the reaction kinetics. This kinetics must be represented as state variable too (Voros 2008), with no dynamic (constant states). The dynamic states represented by 5 chemical concentration trajectory and by 2 temperature trajectory have been augmented by 8 static parametric equations representing the kinetics. Kj 0 (18) Introducing the parameters in the state equation (10): - x( k 1) f ( x (k ), u (k ),T ( k )) w(k ) ® ¯ y (k ) h( x (k ), u ( k ),T (k )) v( k )

(19)

Brings to the final state that has been obtained in the following form: -ª x(k 1) º ª f ( x(k ), u (k ),T (k ))º °« » °¬T (k 1)»¼ «¬ T (k ) ¼ ® ° °¯ y (k ) >h( x(k ), u (k ),T (k )) 0@

ª w(k )º « 0 » ¼ ¬

(20)

(a)

v( k )

The final state dimension is 15 and the dimensions of the matrices used applying the Extended Kalman Filter are: F • R15 x15 ; B • R 15 x 7 ; H • R 7 x15 ; W • R15 x15 ; V • R 7 x 7 ; K • R15 x 7 ; P • R15 x15

3.5 EKF with Augmented Measurement The EKF estimation is not as consistent as the Kalman Filter estimation for linear problems (Simon 2006). To check if the solution is consistent the method of augmented measurement has been applied on the boundary conditions of the process. The boundary conditions are the mass/energy balance equations of the system. If the EKF solution brings to a deviation from 0 of the mass/energy balances, a corrective measurement has been added to the state, as correction. The gain has been calculated to maintain the deviation as low as possible, to minimize the estimation error in any status of the plant. Using the consistency criteria on balances, the final result for estimation has the following form: xÖ ( k 1)

f ( xÖ ( k ), u ( k ), T ( k ))

K ( k ) ˜ ( y ( k ) h ( xÖ ( k )))

(b) Fig. 3: (a) Plant configuration scheme: the defined control inlets are signed with an increasing number inside a circle. (b) Configuration of the discrete-time LQG scheme for the DRI Plant. The process needs many gas inlets to be managed. In figure 3a all the main gas inlets of the process are reported: the Fuels for Reformer and Heater to control the heating system, the Natural gas for Reformer, process and shaft to control gas composition, process gas heating (with oxygen inlet too) and carburation of DRI and finally Water for the production of Steam in the Reformer. To manage the process it’s necessary to control the flow, temperature and composition of the gas entering the reactor. To do this it’s necessary to control the flows reported with an increasing numeration from 1 to 7.

(21)

With H • R11x15 the new jacobian measurement matrix function of mass/energy balance deviation equations from PRM. 4.

CONTROL DESCRIPTION

4.1 Energiron Process and Inlets choice

4.2 The LQG solution for the Energiron Process

The figure 3a reports a general plant configuration scheme of a DRI Energiron plant. The main equipment of the plant required to drive the process gas in the process loop are:

The LQG control problem is to find the optimal control law which minimizes the following cost function (Skogestad, 2001):

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IFAC MMM 2013 August 25-28, 2013. San Diego, USA

f

¦ >x

J

T

(k ) ˜ Q ˜ x (k ) u T (k ) ˜ R ˜ u (k )

@

PRM user interface has 5 forms that represent in real time an overview for the main plant equipment (Shaft, Cooler, Reformer, Heater, CO2 plant). The operators have a powerful software instrument that let them easily manage the whole plant, taking in account both the quality of the product and the real time efficiencies of the equipment, with the possibility to diagnose the instruments too. The EKF uses some of the PRM estimation as inlets and outlets of the shaft and builds up an optimal estimation of the process targets in function of the process inlets. In figure 5 it’s represented an on line comparison between the EKF response vs. the PRM estimation and the DRI metallization Laboratory measurement [%]. The laboratory takes more or less 6 hours to realize a measurement of the DRI produced at the Red & AR Area. The reason is that the DRI resident time in the reactor cone is more or less 3 hours (and vary in function of the productivity) and takes about 2 hours to cool up to environment temperature. During this period, the information at disposal about DRI (both metallization and carburation) coming from PRM and EKF. The frequency of the laboratory measurement is about 3 hours (circle in Fig. 5) that is the DRI Sampling Bin frequency pick up. This means 2 or 3 measurements to know what was going on at Red & AR Area.

(22)

k 0

The term Q is nonnegative definite state weighting matrix, R a positive definite control weighting matrix. The optimal state-feedback law for zero reference sets is given by: L ˜ x( k )

u(k ) L

B ˜ T ˜ B Vp T

1

(23)

˜ BT ˜ T ˜ F

The L • R 7 x15 matrix gain is the optimal gain calculated by means of the T • R15 x15 matrix that is the unique symmetric nonnegative definite solution for the following Discrete Algebraic Riccati Equation (DARE): T

F T ˜T ˜ F

>

F T ˜ T ˜ F ˜ B T ˜ T ˜ B Vp

@

1

˜ BT ˜ T ˜ F

W

(24)

The Vp • R 7 x 7 matrix is the optimal solution cost matrix. Finally in the figure 3b, has been reported the automatic control configuration, the N • R 7 x15 matrix has been used to fit the regulation for a non-zero reference set points. 5.

APPLICATION RESULTS

An Energiron plant has been controlled by a suite with three main components: a grey box model (section 2), an optimal estimator (section 3) and a LQG regulator (section 4). The control lets the optimal fitting of the product quality with the minimum energy consumption.

Fig. 5 Comparison between PRM, EKF and laboratory measurement for DRI metallization [%] on 1 week operation. The figure 6 reports the EKF response for the kinetic gains. A bounded parameter value performed by the EKF means that the maximum likelihood estimation for parameters has been correctly calculated during the observation period (1 month).

(a)

Fig. 4: The PRM data generation for both process variables and process indicators to drive the plant The PRM executes the first estimation with both physical and statistical expressions from level 1 data; the figure 4 represents an example of the PRM user interface with estimations and virtual data production for the shaft unit. The

(b) Fig. 6 One month Constant Kinetics EKF evaluation: (a) Pre Reduction (with H2, CO). (b) Reduction (with H2, CO). 344

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laboratory measurements (circles) before and after regulation (regulation time: 2012, September 23, 1:00am). The regulator let to the stability of the plant response reducing the mean error of lab measurements and estimation from set required. Finally in figure 7d is reported the energy consumption comparison: Natural gas consumption (upper line) and the whole specific energy consumption (lower line), before and after the regulation. As we can expect from the theory, the LQG regulates the process following both the management requests (for the variation of metallization in this case) the different response time of the equipment and the minimum transformation cost (medium saving 0.1Gcal/t on 2.4Gcal/t total consumption). The correct estimation of the shaft states lets the control loop to act on the main gas flows, taking in accounts the process time response.

The dynamic system model aided by the PRM (for the effective quantities of reactants and plants indicators) and the EKF (with the estimation of kinetics and anti-windup for state correction) lets to the determination of the whole shaft state trajectory (Fig. 5, Fig. 7a). The formalization of the state trajectory lets the application of the LQG controller. The figure 7 shows the response in closed loop of the plant applying the LQG controller to track a new plant working point. The example reports a variation in the product quality requests by the plant management: the request was the augment of metallization +1[%] maintaining carburation and productivity.

6.

CONCLUSIONS

This paper presents the first automatic process controller realized for a DRI Energiron plant, developed on level 2 by means of a Grey Box model (PRM) an optimal state estimator (EKF) and an optimal regulator (LQG). The process control variables (level 1 set points) are automatic calculated on line in function of the process target requests (level 2 set points: DRI metallization, DRI carburation and DRI productivity). The input/output plant values and the mass/energy balances are calculated in real time by the PRM, in function of accessible plant measurements. The EKF use the physical shaft model and the PRM measurements, virtual measurements and balances to generate an optimal estimation of the shaft state. The LQG regulator performs the calculation of the optimal level 1 set point input trajectories to manage the plant from the current working point to a new one, to realize the new process targets. The application of automatic control on line lets to a mean energy saving of about 4% on total consumption and a stabilization of the plant response too. Stabilization brings also to an overall correct plant managing with the reduction of trip events and unwanted stops. Operators are supplied with a multi-purpose instrument capable to manage in automatic the process for any kind of quality charged, setting the optimal reducing gas composition and temperature, pointing both the process target and the minimum transformation cost.

(a)

(b)

(c)

7.

REFERENCES

Skogestad, S., Postlethwhite, I. (2001), Multivariable Feedback Control, John Wiley & Sons. 6LPRQ ' 2SWLPDO 6WDWH (VWLPDWLRQ .DOPDQ +’ and Nonlinear Approaches, John Wiley & Sons. Yang, X., Marjanovic, O. (2011), LQG Control with EKF for Power System with Unknown Time-Delays, Paper of the 18th IFAC World Congress, Milano. Di Giorgio, F.M., Martinis, A., and others (2011), Driving Process Optimization via the Energiron Advanced L2 Control, METEC InSteelCon 2011, Paper of 6th European Coke Iron Making Congress, Dusseldorf. Voros, J., Mikles, J., Cirka L. (2008), Parameter Estimation of Nonlinear Systems, Acta Chimica Slovaca, Vol. 1, No. 1, 2008,309-320.

(d) Fig. 7: (a) LQG result for a new working point with augmented metallization (+1[%]) with same carburation and productivity. New level 1 set points for Reducing (Bustle) and Reformed gas (b), and for Natural gas (c). (d) Whole plant Natural gas consumption response. The LQG produced directly the new working point sets (shaded lines on Fig 7b, 7c). The level 1 accepts the sets and controls directly the process flows (continuous lines on Fig 7b, 7c). The result of the control action is reported in figure 7a with the new quality set reached (EKF continuous line) vs. 345