Soft Constrained MPC Applied to an Industrial Cement Mill Grinding Circuit

Transcription

1 Soft Constrained MPC Applied to an Industrial Cement Mill Grinding Circuit Guru Prasath a,b,c, M. Chidambaram c, Bodil Recke b, John Bagterp Jørgensen a, a Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet, Building 33B, DK-28 Kgs Lyngby, Denmark b FLSmidth Automation A/S, Høffdingsvej 34, DK-25 Valby, Denmark c Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli-6215, TamilNadu, India Abstract Cement mill grinding circuits using ball mills are used for grinding cement clinker into cement powder. They use about 4% of the power consumed in a cement plant. In this paper, we introduce a new Model Predictive Controller (MPC) for cement mill grinding circuits that improves operation and therefore has the potential to decrease the specific energy consumption for production of cement. The MPC is based on linear models that are identified using step tests. The key novelty in the MPC is that it uses soft constraints to form a piecewise quadratic penalty function with a dead zone. The MPC with this penalty function mitigates the effect of large inevitable uncertainties in the identified models for cement mill grinding circuits. The new MPC accommodates plantmodel mismatch and provides better control than conventional MPC and fuzzy controllers. This is demonstrated by simulations using linear systems, simulations using a detailed cement grinding circuit simulator, and by tests in an industrial cement mill grinding circuit. Keywords: Model Predictive Control, Cement Mill Grinding Circuit, Ball Mill, Industrial Process Control, Uncertain Systems 1. Introduction The annual world consumption of cement is around 1.7 billion tonnes and is increasing at about 1% a year. The electrical energy consumed in the cement production is approximately 11 kwh/tonne. 3% of the electrical energy is used for raw material crushing and grinding while around 4% of this energy is consumed for grinding clinker to cement powder (Fujimoto, 1993; Jankovic et al., 24; Madlool et al., 211). Hence, global cement production uses 18.7 TWh which is approximately 2% of the worlds primary energy consumption and 5% of the total industrial energy consumption. Fig. 1 illustrates the cement manufacturing process. Cement manufacturing consists of raw meal grinding, blending, pre-calcining, clinker burning and cement grinding. In the crusher, mixing bed, and raw mill, limestone and other materials containing calcium, silicon, aluminium and iron oxides are crushed, blended and milled into a raw meal of a certain chemical composition and size distribution. This raw meal is blended and heated in the pre-heating system (cyclones) to start the dissociation of calcium carbonate into calcium oxide. In the kiln, the material is heated, kept at a temperature of C, and reacts to form calcium silicates and calcium aluminates. The reaction products leave the kiln as a nodular material called clinker. The clinker is cooled in the clinker coolers before being stored in the clinker silos. The clinker is ground with gypsum and other materials such as fly ash in a cement mill to form Portland cement. The final step in manufacture of cement consists of grinding cement clinker into cement powder in a cement mill grinding Corresponding Author. jbjo@dtu.dk Tel.: circuit. Typically, ball mills are used for grinding the cement clinkers because of their mechanical robustness. Fig. 2 illustrates a ball mill. The cement mill grinding circuit consists of a ball mill and a separator as illustrated in Fig. 3. Fresh cement clinker and other materials such as gypsum and fly ash are fed to the ball mill along with recycle material from the separator. The ball mill crushes these materials into cement powder. This crushed material is transported to a separator that separates the fine particles from the coarse particles. The fine particles constitute the final cement product, while the coarse particles are recycled to the ball mill. Ball mills for cement grinding consume approximately 4% of the electricity used in a cement plant. Loading the ball mill too little results in early wear of the steel balls and a very high specific energy consumption. Conversely, loading the ball mill too much results in inefficient grinding such that the product quality cannot be met. Loading the ball mill too much, may even result in a phenomena called plugging such that the plant must be stopped and plugged material must be removed from the mill. Consequently, optimization and control of the cement mill grinding circuit operation is very important for running the cement plant efficiently, i.e. minimizing the specific electricity consumption and delivering a consistent product that meets the specifications. In this paper, we present a new control technology based on Model Predictive Control with soft output constraints used in a novel way for robust operation of cement mill grinding circuits (Prasath and Jørgensen, 29b; Prasath et al., 21, 213). The MPC algorithm uses soft constraints to create a piecewise quadratic penalty function in such a way that the closed loop system is less sensitive to model uncertainties than MPC with a quadratic penalty function. Predictive models for cement Preprint submitted to Control Engineering Practice October 18, 214

2 Quary Crusher Transport Mixing bed Dust filter Raw Mill Preheater / calciner Kiln Clinker cooler Clinker silo Cement mill Cement silos / Packaging Figure 1: Cement plant. Discharge diaphragm Intermediate diaphragm Mill inlet Mill discharge Ball filling 2. compartment Ball filling 1. compartment Drive Figure 2: Ball mill. Figure 3: Cement mill grinding circuit. mill grinding circuits are very uncertain. Variations and heterogeneities of the cement clinker feed affects the gains, time constants, and time delays of the cement mill grinding circuit. To avoid the MPC being turned off shortly after commissioning due to bad closed-loop behavior, it is important that these unmeasurable uncertainties are accounted for. Accordingly, compared to traditional MPC algorithms, the MPC algorithm described in this paper gives robust performance to such uncertainties and provides easier tuning and maintenance. This in turns leads to longer life time of the control system and the improved operation resulting from these controllers can potentially lead to very large energy savings. Model predictive control technology is by far the most successful advanced control technology applied by the process industries (Qin and Badgwell, 23; Bauer and Craig, 28). Model predictive control technologies are increasingly being adopted in the cement industry for control of raw mills, kilns, and cement mill grinding circuits (Sahasrabudhe et al., 26; Stadler et al., 211; Samad and Annaswamy, 211). In the following, we review the approaches to control cement mill grind- 2 ing circuits. van Breusegem et al. (1994, 1996); Van Breusegem et al. (1996) and de Haas et al. (1995) developed an LQG controller for the cement mill circuit. This controller was based on a first order 2 2 transfer function model identified from step response experiments. Magni and Wertz (1997), Magni et al. (1999), Wertz et al. (2), and Grognard et al. (21) developed a Nonlinear Model Predictive Control algorithm based on a lumped nonlinear model of the cement mill circuit. All these controllers controlled the product and recycle flow rate by manipulating the fresh feed flow rate and the separator speed. The same lumped nonlinear model was used by Efe and Kaynak (22) for nonlinear model reference control and by Topalov and Kaynak (24) for neural network based adaptive control. Lepore et al. (22, 23, 24, 27) as well as Boulvin et al. (1998, 1999, 23) applied a distributed reduced order model for Nonlinear Model Predictive Control of a cement mill circuit. They controlled the particle size distribution of the cement product by manipulating the fresh feed flow rate and the separator speed. Martin and McGarel (21) used a neural network model for Nonlinear Model Predictive Control of the cement

3 mill circuit. Sanchez and Rodellar (1996) control the cement mill circuit using adaptive predictive control. The cement mill grinding circuit resembles to some extent grinding circuits used in the mineral industry. Model based control technologies for such grinding circuits in the mineral processing industries have been surveyed by Pomerleau et al. (2), Hodouin et al. (21), and Wei and Craig (29). Rajamani and Herbst (1991a,b) and Herbst et al. (1992) developed nonlinear dynamic models for SAG mills and applied optimal control technology using these models. Craig and MacLeod (1995, 1996) developed robust controllers based on µ-synthesis, while Coetzee et al. (21) used robust nonlinear model predictive control in their control systems design. Najim et al. (1995) handled systems with varying parameters using adaptive control. Chen et al. (27, 28, 29a,b) applied constrained DMC based on a second order time delay models identified from step response experiments to ball mill grinding. Lestage et al. (22) discussed the combination of real-time optimization and model predictive control for an ore grinding circuit. This paper is organized as follows. Section 2 reviews the soft MPC algorithm with a simple estimator. Section 3 illustrates the robustness properties of soft MPC by simulating the performance of the soft MPC for uncertain linear systems. Section 4 provides an overview of the cement manufacturing process, while Section 5 discusses the cement mill grinding circuit operating strategy. Section 6 compares the soft MPC to the normal MPC using a commercial rigorous cement mill grinding circuit simulator. Section 7 describes the implementation of the soft MPC for an industrial cement mill grinding circuit and compares the performance of the soft MPC to the existing fuzzy logic controller. Conclusions are provided in Section Soft MPC Algorithm In this section, we describe the Soft MPC algorithm used to control the cement mill grinding circuit (Prasath and Jørgensen, 29b). The controller consists of an estimator and a regulator as illustrated in Fig. 4. The input to the controller is the set points, r, and the measurements, y. The output from the controller is the manipulated variables, u. The set points, r, are the target values for the controlled variables, z Regulator Stable processes can be represented by the finite impulse response (FIR) model z k = b k + n H i u k i (1) in which {H i } n i=1 are the impulse response coefficients (Markov parameters). b k is a bias term generated by the estimator. b k accounts for discrepancies between the predicted output and the actual output. In this paper, the output predictions used by the regulator are based on the FIR model (1). Using the FIR model (1), the regularized l 2 output tracking problem with hard input i=1 3 r MPC ˆb Regulator Estimator u y Plant Sensors, Lab analysis Figure 4: Generic model predictive control system. constraints and soft l 2 /l 1 output constraints may be formulated as (Maciejowski, 22; Prasath and Jørgensen, 28) min φ = 1 N 1 z k+1 r k+1 2 Q {z,u,η} 2 z + k= subject to the constraints z k = b k + N k=1 + u k 2 S 1 2 η k 2 S η + s ηη k (2a) n H i u k i k = 1,... N (2b) i=1 u min u k u max k =,... N 1 (2c) u min u k u max k =,... N 1 (2d) z k r max,k + η k k = 1,... N (2e) z k r min,k η k k = 1,... N (2f) η k k = 1,... N (2g) in which u k = u k u k 1. Equation (2) can be converted to a dense convex quadratic program and solved efficiently (Prasath and Jørgensen, 28, 29b). Model predictive control is based on the moving horizon implementation of open-loop optimal control solutions. At each sample when new measurements arrive, the bias term is computed and the corresponding open-loop optimal control sequence, {u k } N 1 k=, is computed by solution of (2). Only the first element, u, of this sequence is implemented on the process. The entire procedure is repeated at the next sample with a new measurement. Fig. 5 illustrates the moving horizon implementation principle Soft Constraints and Penalty Functions with a Dead Zone The key feature of the convex quadratic program representing the regulator is its use of soft constraints. Soft constraints in MPC are not new and has previously been discussed by e.g. Scokaert and Rawlings (1999), Havlena and Lu (25) and Havlena and Findejs (25). In this paper, we do not use the soft constraints to guarantee feasibility of output constraints but z

4 handling / ;;Data computations Horizon index k-2 Estimation Penalty Function k-1 u k Estimation Estimation Regulation Regulation Regulation injected u Process time Figure 5: The principle of moving horizon estimation and control Normal MPC Soft MPC Error, e = z r Figure 6: The principle of soft MPC and normal MPC. The normal MPC uses a quadratic penalty function, while the soft MPC uses a piecewise quadratic penalty function that is designed to have a dead zone. 4 to shape the objective function such that the resulting control becomes more robust against stochastic noise and model-plant mismatch (Prasath and Jørgensen, 29b; Huusom et al., 211). We use the soft constraints to create a dead zone where the penalty function is almost zero (Boyd and Vandenberghe, 24). The penalty function within the dead zone is strictly convex and small but not exactly zero. This requirement ensures that the quadratic program (2) has a unique minimizer. The requirement is fulfilled by selecting a small but positive definite penalty matrix, Q z, in (2a). Outside the dead zone, the penalty function is designed such that it rapidly becomes much larger than the penalty function within the dead zone. This is achieved by selecting the soft constraint weights, S η and s η in (2a), such that the associated terms, η k 2 S η and s ηη k, becomes significantly larger than the error term, z k r k 2 Q z. The size of the dead zone is specified by r min,k and r max,k which are bounds around the set point, r k. Within these bounds, the penalty function should be small; outside these bounds, the penalty function should be large. The size of the bounds may be determined based on a covariance analysis of the nominal system. The red curve in Fig. 6 illustrates a piecewise quadratic penalty function that has been designed according to these principles. For short this penalty function is called soft MPC as this is the penalty function in MPC with soft constraints. For comparison, we have also shown a quadratic penalty function that is used in a classic MPC. For short we call the penalty function normal MPC. The effect of the penalty function in the soft MPC is that little control action is taken as long as the process is within the dead zone. This implies that the controller does not amplify small errors by reacting and introducing a real perturbation due to the significant plant-model mismatch existing in uncertain systems. Using simulation examples, Prasath and Jørgensen (29b) and Huusom et al. (211) illustrate how penalty functions with dead zones may be used to create controllers that are robust (in a practical sense) despite significant plant-model mismatch Estimator To have offset free steady state control when unknown step disturbances occur, we use a simple estimator with integrators as described in Prasath and Jørgensen (29b). Integrators in the feedback loop are necessary to have offset free control despite unknown step disturbances. Integrators in the feedback loop for the FIR based MPC may be obtained using a FIR model in difference variables. Assume that the relation between the inputs and outputs may be represented as y k = z k = e k + n H i u k i (3) in which is the backward difference operator, i.e. y k = y k y k 1, z k = z k z k 1, and u k = u k u k 1. This representation is identical with the FIR model (1) if ˆb k is computed by y k = z k = ˆb k + e k = y k i=1 n H i u k i (4) i=1 n H i u k i i=1 ˆb k = ˆb k 1 + e k (5a) (5b) Note that in the regulator optimization problem b 1 = b 2 =... = b N = ˆb k at each time instant. This is based on the assumption that the disturbances enter the process as constant output disturbances. Of course this may not be how the disturbances enter the process in practice, and significant performance deterioration may result as a consequence of this representation. The performance of the controller can be improved by using more sophisticated estimators that use a filter to avoid the dead-beat estimate of the simple estimator used in this paper (Jørgensen et al., 211; Huusom et al., 212). Alternatively, a moving horizon estimation approach can be adopted. Prasath and Jørgensen

5 (29a) illustrates by simulation the performance of the moving horizon estimator in a closed loop system with an MPC. However, in the trade-off between sophisticated estimators with many tuning parameters and better estimates versus simple estimators with few tuning parameters but slightly worse estimates, we have chosen the latter for the industrial implementation. 3. Soft MPC Simulation for Uncertain Linear Systems In this section, we demonstrate the performance of the soft MPC by simulation of linear systems. Even with significant model-plant mismatch, the soft MPC provides good performance. The performance of the soft MPC is evaluated for both SISO and MIMO systems with delays and it is compared to the performance of a normal MPC Linear System Description The system is simulated by the discrete-time stochastic linear state space model x k+1 = Ax k + Bu k + B d d k + Gw k z k = Cx k (6a) (6b) x is the state vector, u is the vector of manipulated variables (MVs), d is the vector of unmeasured disturbances, and w is stochastic process noise. z denotes the controlled variables (CVs). The measured outputs, y, are the controlled outputs, z, corrupted by measurement noise, v. Consequently y k = z k + v k (7) The initial state, the process noise, and the measurement noise are assumed to be normally distributed stochastic vectors: x N( x, P ), w k N iid (, R ww ), and v k N(, R vv ). While (6) is useful for simulation, the more compact continuous-time transfer function representation Z(s) = G(s)U(s) + G d (D(s) + W(s)) y(t k ) = z(t k ) + v(t k ) (8a) (8b) is used for the system description. In (8) we assume that the input signals of (8a) are piecewise constant and that the measurements are obtained at discrete times. Using these assumptions, (8) may be realized as the discrete-time state space system (6)- (7). Consequently, we specify our system as a continuous-time transfer function model (8) but realize and simulate it using the discrete-time state space model (6)-(7) SISO System Consider a SISO system represented by (8) and the transfer functions K(βs + 1) G(s) = (τ 1 s + 1)(τ 2 s + 1) e τs (9a) K d (β d s + 1) G d (s) = (τ d1 s + 1)(τ d2 s + 1) e τ d s (9b) The parameters for the nominal system are: K d = K = 1, τ d1 = τ d2 = τ 1 = τ 2 = 5, β d = β = 2, and τ d = τ = 5. The system is converted to the discrete time state space model (6)-(7) using a sample time of T s = 1 and a zero-order-hold assumption on the inputs. The initial state used for all simulation is x = x =. The variances of the stochastic process noise and measurement noise are: R ww =.1 and R vv =.1. Both the normal MPC and the soft MPC have been designed based on the nominal transfer function G(s) and using n = 4 impulse response coefficients and a prediction and control horizon of N = 3n = 12. In the normal MPC, the tuning parameters used are Q z = 1, S = 1 3, while the soft MPC uses Q z =.1, S = 1 3, S η = 1, and s η =. The inputs are constrained such that u k 1 and u k.2. The soft constraint limits for specification of the dead zone used are r min,k =.2 and r max,k =.2. These values for the soft constraints are obtained based on the noise of the outputs for the closed loop system. Both the normal MPC and the soft MPC provide good control performance for the nominal system (Prasath and Jørgensen, 29b). Fig. 7 illustrates the performance of the soft MPC compared to the normal MPC for a situation with a model-plant mismatch. The controller uses the nominal gain, K = 1., while the plant has a gain of K = 2.. Fig. 7(a) illustrates the external signals used for the simulation. These signals are unknown to the controller. The soft MPC has been designed such that controller hardly reacts to signals due to measurement noise and stochastic process noise, when the output is within the soft limits. However, when the output is outside the soft limits, the soft MPC is penalized in almost the same way as the normal MPC is penalized. Fig. 7(b) is a closed-loop simulation for the deterministic case (w k = and v k = ). It is evident by inspection that the soft MPC handles the disturbance and the plant-model mismatch in an acceptable manner. In contrast, the normal MPC is very oscillatory, unable to stabilize the system, and useless from a practical point of view. Fig. 7(c) illustrates the closed-loop performance with stochastic process noise and measurements corrupted by stochastic noise. The closed-loop simulation for the stochastic system confirms that soft MPC is able to stabilize the system in an acceptable manner, while the normal MPC with the chosen tuning is useless for this situation with unknown disturbances and a large model-plant mismatch. Prasath and Jørgensen (29b) provide similar closed-loop simulations for model-plant mismatches in the gain, time delay, zero, and time-constant. The soft MPC is able to handle these uncertainties while the normal MPC with the chosen tuning is not MIMO System Consider a MIMO (2 2) system represented by (8) and the transfer functions.62 (45s+1)(8s+1) G(s) = e 5s.29(8s+1) (2s+1)(38s+1) e 1.5s (1a) G d (s) = 15 (6s+1) e 5s 5 (14s+1)(s+1) e.1s [ 1 ] (32s+1)(21s+1) e 3s 6 (3s+1)(2s+1) (1b) 5

6 D v w Y U time (a) External signals Soft MPC Normal MPC time 2 1 (b) Deterministic simulation with gain mismatch. These transfer functions are identified for a simulated cement mill grinding circuit using ECS/CEMulator (FLSmidth A/S, 214). ECS/CEMulator is a simulator for complete cement plants including the cement mill grinding circuit. Typically, ECS/CEMulator is used for operator training. The model in ECS/CEMulator is a detailed nonlinear partial differential equation model for the cement grinding circuit. The controlled variables (CVs) are the elevator load, Y 1 (s), and the fineness, Y 2 (s). The manipulated variables (MVs) are the feed rate, U 1 (s), and the separator speed, U 2 (s). The unmeasured disturbance, D(s), to the system is the hardness of the feed material, in particular the hardness of the clinker. This linear system is simulated to investigate the resilience of the normal MPC and the soft MPC to model-plant mismatch for a system resembling the cement mill grinding circuit. The MPCs for the linear system (8) and (1) are designed using the nominal transfer function (1a) as well as the constraints u min = [ 5; 3], u max = [5; 3], u min = [ 1.5;.3], and u max = [1.5;.3]. The horizon of the impulse response model is n = 75. The control and prediction horizon is N = 3n = 225. The normal MPC is based on the weights Q z = diag([8; 1]) and S = diag([.1;.1]), while the soft MPC is designed with the weights Q z = diag([.5;.1]), S = diag[.1;.1]), S η = diag([8; 1]), and s η = [; ]. The soft output constraints are r min,k = [.8; 3.5] and r max,k = [.8; 3.5]. Fig. 8 illustrates the closed-loop controlled variables (CVs) and manipulated variables (MVs) for the normal MPC and the soft MPC in the case with a gain mismatch. The controllers are designed for the nominal gain K = [.62,.29; 15., 5.], while the plant gain is K = [1.69, 1.42; 14.98, 5.2]. As for the SISO system, this case illustrates that the soft MPC is more resilient to model-plant mismatch than the normal MPC. Using simulations, we observed the same resilience properties of soft MPC for mismatches in the zeros, the time constants, and the time delays (Prasath and Jørgensen, 29b). 4. The Cement Manufacturing Process U Y time (c) Stochastic simulation with gain mismatch. Figure 7: Closed-loop simulation with the soft MPC and the normal MPC for the SISO system (9) when the controllers have been designed based on the nominal gain, K = 1, and the actual plant gain is K = 2. 6 As illustrated in Fig. 1, the preparation of cement involves mining, crushing and grinding of raw materials (principally limestone and clay), calcining and sintering the materials in a rotary kiln to form clinker, cooling the resulting clinker, mixing the clinker with gypsum, grinding the clinker-gypsum mixture to cement powder, and storing and bagging the finished cement powder. The three main steps are 1) preparation of the raw mixtures, 2) production of the clinker, and 3) grinding the clinker into cement powder. The raw materials used in cement production are limestone, sand, shale and iron ore. The main material, limestone, is normally mined on site while other materials may either be mined on site or in nearby quarries. These materials are crushed and screened to a size less than 1 mm. The crushed material is transported to the cement plant at which they are roughly blended in a pre-homogenization pile (mixing bed). The next step in the cement production depends on whether the wet or the dry process is used. In the wet process each material is proportioned to meet a desired chemical composition and fed to a

7 Y1 Y2 U1 U (a) Controlled variables (CVs) time (b) Manipulated variables (MVs). Figure 8: Deterministic closed-loop simulation of the linear cement grinding model (8) and (1). The plots illustrates the CVs and MVs using the normal MPC (blue) and the soft MPC (red) for the case with a gain mismatch between the plant and the controller model. An unknown disturbance of size 2.5 enters at time 2. 7 rotating ball mill with water. The raw material is ground to a size where the majority of the material is less than 75 micron. The slurry is pumped to the blending tanks and homogenized to ensure that the chemical composition is correct. In the dry process, each raw material is proportioned to meet a desired chemical composition and fed to either a rotating ball mill or a vertical roller mill. The raw materials are dried with waste process gases and ground to a size where the majority of the material is less than 75 micron. The material from either type of mill is blended to ensure that the chemical composition is well homogenized. This so-called raw mix is stored in silos until required. This raw mix is a mixture of calcium carbonate, silicon-, alumina- and iron-oxides. Calcium and silicon are present to form strength producing calcium silicates. Aluminium and iron are present to produce liquid in the kiln burning zone. The liquid act as a solvent for the silicate forming reactions. In the wet process, the slurry is fed to a rotary kiln. In the dry process the raw mix is fed to the preheater/calciner tower. The same basic physical and chemical process takes place in the kiln for the wet and the dry process. The raw mix is gradually heated by contact with the hot gases generated by combustion of the kiln feed. A number of chemical reactions take place as the temperature rises. At 7-11 C the water is evaporated. At 4-6 C clay like materials decompose into principally SiO 2 and Al 2 O 3. Dolomite, CaMg(CO 3 ) 2, decomposes to CaCO 3, MgO and CO 2. At 65-9 C CaCO 3 reacts with SiO 2 to form belite, 2CaO SiO 2. At 9-15 C the remaining CaCO 3 decomposes to CaO and CO 2. At C the material partial melts (2-3%), and belite reacts with CaO to form alite, 3CaO SiO 2. Alite is the characteristic constituent of Portland cement. A peak temperature of C is required to complete the reaction. The partial melting causes the material to aggregate into lumps or nodules with a typical diameter of 1-1 mm. This is called clinker. As the hot clinker leaves the kiln, they fall into a cooler that recovers most of the heat and cools the clinker to around 1 C. The clinker is stored in clinker silos. In the final stage in the manufacture of cement, clinker is mixed with approximately 5% gypsum (calcium sulphate) and possible other materials such as fly ash and grinned to cement powder. Either a rotating ball mill or a vertical mill is used for grinding. In this paper we consider a rotating ball mill (Fig. 2). As the mill rotates, the steel balls inside the mill collide with clinker and raw material to form a fine gray powder. Typically, by mass 15% of the particles in this cement powder have a diameter less than 5 µm and 5% of the particles have a diameter larger than 45 µm. Fineness is a measure of the specific surface area of the cement powder and it is directly related to the properties of cement. General purpose cement has a specific surface area of cm 2 /g (32-38 m 2 /kg), while rapid hardening cement has a specific surface area of cm 2 /g (45-65 m 2 /kg). The various cement qualities are stored in cement silos before being packed in bags or shipped by truck, rail or boat The Cement Mill Grinding Circuit To obtain a cement powder with the desired specific surface area, the ball mill is operated in conjunction with a separator that returns coarse material to the ball mill for further grinding. This system is called a cement mill grinding circuit and is illustrated in Fig. 3. As illustrated in Fig. 2, the ball mills used for grinding have two chambers separated by a metallic diaphragm. The first chamber is filled with large steel balls and is supposed to do the coarse grinding. The second chamber is the fine grinding chamber and is equipped with small steel balls. Both chambers are equipped with classifying liners to ensure that the ball charge segregate with large balls accumulating at the inlet of the chamber and small balls accumulating at the outlet of the chamber. The fine ground particles leaving the ball mill are lifted by a bucket elevator and sent to an air classifier. As the particles from the bucket elevator enter the classifier, they are suspended

8 in an air stream. The air is sucked from the bottom of the classifier and transports the particles into the rotating equipment. In this rotational gravity field, large and heavy particles impact the wall and are collected in cyclones as they drop down. Small and fine particles are transported away towards the center of the classifier. The coarse particles are recycled to the mill for further grinding. The fine particles are collected in cement silos and constitute the final cement. Consequently, the overall function of the classifier is to separate coarse particles from fine particles. 5. Control Strategy for the Cement Mill Grinding Circuit The objective in controlling the cement mill grinding circuit is to produce cement powder with a desired specific surface area while minimizing the energy consumption (cost) in doing so. The energy consumption is largely connected to rotating the ball mill and its steel balls. It depends only weakly on the cement material loading in the mill. Therefore, the most profitable mode of operation consists of maximizing the production rate while meeting the specific surface area. In this way, least energy is used for cement grinding per produced tonnes of cement. The specific surface area of the material in the product stream is the primary controlled variable in cement mill grinding circuits. In many cement plants, the specific surface area can only be measured by sampling the product stream and analyzing the sample in the lab. In such plants, the specific surface area of the product is only measured infrequently and the result is available to the process control systems with a variable delay of about 3 min (the approximate duration of the laboratory procedure). Modern plants are equipped with an on-line particle size analyzer and the specific surface area is directly available to the process control system. The particle size distribution and thus the specific surface area of the product stream depends on the rotational speed of the classifier, the air speed, the feed rate to the classifier, and the particle size distribution of the classifier feed stream. The air speed is often kept constant and the rotational speed of the classifier is manipulated to control the specific surface area of the product stream. The grinding efficiency in the ball mill depends on its filling. Too little cement material in the mill causes steel balls to hit steel balls without using this energy for crushing material. In addition, the temperature in the mill becomes easily too high in this case. Conversely, as the mill gets loaded with too much cement material, the particles leaving the ball mill are too coarse. They are rejected in the separator and recycled back to the ball mill. The consequence is a very low production rate and too high specific energy consumption. In the extreme case, material builds up in the ball mill such that the diaphragm separating the first and second chambers plugs and material stops flowing. This situation should be avoided. Consequently, one objective in most cement mill grinding circuit control strategies is to control the mass of cement material in the ball mill. The mill should be filled as much as possible without plugging as this leads to the largest production rate. However, the cement mass hold up 8 cannot be measured directly. A so-called pholaphone (microphone) situated outside the cement mill can be used to infer the filling as an empty mill with steel balls hitting steel balls makes more noise than a mill filled with cement material. Although very nonlinearly, the material flowing out of the mill is related to the filling of the mill. This implies that the power used by the bucket elevator is related to the filling of the mill as the power is related to the flow. This elevator power is often used in direct control of the mill filling while the pholaphone is used for override control to avoid plugging. Consequently, one may control the cement mill grinding circuit by controlling the specific surface area of the cement product stream and the elevator load. This is done by manipulation of the fresh feed flow rate and the rotational speed of the classifier. The main disturbances affecting the cement mill circuit are the hardness of the clinker as well as their size distribution. These disturbances are unmeasurable and affect the gains and the time constants of the cement mill circuit. They also affect the relationship between the output flow rate and the ball mill cement hold up. This implies that the elevator load set point may be adjusted as consequence of large variations in the hardness Predictive Control of Cement Mill Grinding Circuits In the cement industry, control of the cement mill grinding circuit is considered to be a very difficult control problem. The main reason for this is the presence of significant non-linearities and uncertainties. These nonlinearities and uncertainties arise due to variations in material properties that cannot be measured online. Consequently, the gains, the time constants, the zeros, and the time delays in predictive models (1a) for the cement mill grinding circuit are very uncertain and they are dependent on operating conditions. As is evident for linear systems, the normal MPC is not as resilient to plant-model mismatch as the soft MPC. Therefore, the soft MPC is expected to be more appropriate than the normal MPC for controlling the cement mill grinding circuit. To demonstrate that the soft MPC can be used to successfully control cement mill grinding circuits in the face of inevitable model-plant mismatch, we test the soft MPC for a simulated cement mill grinding circuit using the ECS/CEMulator software and in an industrial cement mill grinding circuit. For the simulated case study, we compare the soft MPC to a normal MPC. In the industrial cement mill grinding circuit, we were only allowed to compare the soft MPC to the existing fuzzy based control system. For both the simulated and the industrial cement mill grinding circuit, the procedure for designing the soft MPC (and the normal MPC) is to obtain a process model, Y(s) = G(s)U(s), using step tests. As discussed by Prasath et al. (213), the step responses contain large variations and give rise to models with uncertain parameters. We obtain parsimonious well regularized models by fitting low order transfer functions of the type (9a) to each input-output pair. (1a) is an example of such a model for a cement grinding circuit. This identified model is then used to design and tune the soft MPC by simulation, i.e. by using the linear model, G(s), as well as perturbations of this model to

9 simulate the resulting performance of a specifically tuned soft MPC. When an acceptable controller is obtained, it is uploaded to the ECS/SCADA system and used to control the cement mill grinding circuit. The same ECS/SCADA system is used for both the simulated and the industrial cement mill grinding circuit. Fig. 9 illustrates this ECS/SCADA system. 6. MPC for a Simulated Cement Mill Grinding Circuit normal MPC and the soft MPC are able to bring the system to the target steady state and stabilize it there. However, the inputs for the soft MPC are much more stable than the inputs for the normal MPC. This indicates that the soft MPC is more plant friendly and robust towards disturbances and plant-model mismatch. The plant friendliness and small variations of the manipulated variables of the soft MPC can be translated into less plant wear and longer equipment life-time. The performance of the soft MPC is tested and compared to the performance of the normal MPC by simulation using the rigorous cement mill grinding circuit simulator, ECS/CEMulator (FLSmidth A/S, 214). ECS/CEMulator is based on a nonlinear distributed model and is normally used for operator training. In this paper, we use it as a realistic surrogate for an industrial cement mill grinding circuit to test our controllers. Using step response tests, the transfer function in (1a) has been identified. Both the soft MPC and the normal MPC are designed based on this model. The normal MPC and the soft MPC use the tuning described in Section 3.3. The sampling rate is T s = 1 min. The hard input constraints are u min = [11; 65], u max = [15; 85], u min = [ 1.5;.3], and u max = [1.5;.3]. The set points are r = [3; 31] and the soft output limits are r min = [28; 3] and r max = [31; 32]. Asymmetric soft output limits for the elevator power, y 1, have been chosen as it is more important that the controller lowers the mill filling quickly, if the mill is near the plugging limit, than the controller fills the mill quickly, if its filling is below the target. It should be noted that these limits and variables are listed as physical variables here, but they are converted to deviation variables in the MPC software. Both the normal MPC and the soft MPC performs well close to the nominal conditions. To illustrate the performance of the soft MPC in the realistic case with significant uncertainty, we simulated a change of material properties by changing the grindability of the feed. While the MPCs are designed for the nominal transfer function (1a), this change of grindability corresponds to changing the dynamics to something that can be approximated by the transfer function G(s) =.2 (45s+1)(8s+1) e 5s.12(8s+1) (2s+1)(38s+1) e 1.5s 8 (6s+1) e 5s 2 (14s+1)(s+1) e.1s (11) Comparison of (1a) and (12) demonstrates that this material property change, changes the gain of the linear approximation significantly. The time constants, the zeros, and the time delays are unchanged. Fig. 1 illustrates a simulation of this situation for the normal MPC and the soft MPC. The uncontrolled ECS/CEMulator is started at a steady state different from the target steady state. At time 1.35 hr, a significant change in hardness of the material is introduced and the controller is switched on at time 2. hr at which the cement mill grinding circuit is in a transient phase. We perform the simulation this way to mimic that the controller in an industrial cement mill grinding circuit is often in such transient conditions due to frequent starts and stops. Both the 9 7. MPC for an Industrial Cement Mill Grinding Circuit In this section, we describe the implementation and test of the soft MPC in an industrial cement grinding circuit. At the plant we were not allowed to implement a normal MPC with the purpose of comparing it to the soft MPC and expectedly demonstrate that the normal MPC would not perform as well as the soft MPC. Instead we compare the performance of the soft MPC to the existing fuzzy logic based control system at that plant An Independent Finish Grinding Plant The implementation of the soft MPC controller was tested in an industrial cement grinding unit in southern India. Cement grinding units are independent finish product grinding plants where the raw materials are obtained from different locations and ground to the final cement product. Cement grinding units consist of silos for storage of cement clinker and other raw materials, the cement mill grinding circuit (a ball mill and a separator), and equipment for cement packing and dispatch (see Fig. 1). The cement mill grinding circuit, where we tested the soft MPC, consists of a two-chamber ball mill (see Fig. 2) and a Sepax separator in a closed circuit (see Fig. 3). This cement mill grinding circuit has a design capacity of 15 tonnes/hour. Due to the large demand for cement, the cement mill grinding circuit is operated at maximum design capacity and beyond. The recirculation ratio of the circuit is 1.5%. The power frequency varies continuously depending on the electricity demand in the municipality where the cement mill grinding circuit is located. At periods with low frequency, the rotation speed as well as the air flows are reduced. This adversely affects the production rate and the product quality. The cement mill grinding circuit control system must be able to reject the effect of such disturbances. Furthermore, the cement mill grinding circuit runs only at night time and is shut-down in day time where the electricity price is high. This implies that the control system must be able to handle the effect of transients due to frequent start-ups and shut-downs. Since the plant, where we implement the controller, is an independent grinding unit, the clinker produced from multiple plants are transported to the cement grinding unit by railway wagons. Due to the multiple sources of clinker, the hardness and quality variations in the clinker are very large. This results in continuous and significant variations in the operating conditions for the cement mill grinding circuit. The final product recipes are Ordinary Portland Cement (OPC) and Puzzalona Portland Cement (PPC). The production of both

10 Figure 9: The ECS/SCADA system for high level control of a cement mill grinding circuit. OPC and PPC in the cement grinding unit introduces frequent product shifts. The control system must be able to facilitate frequent set-point changes as the result of product demand and dispatch requirements. All the signals coming from the sensors of the grinding process are collected in an ECS/SCADA system (see Fig. 9). ECS/SCADA is the Supervisory Control And Data Acquisition of FLSmidth. The measurement data is obtained from the PLC system and logged every 1 seconds in the ECS/SCADA. The fineness measurement of the product is obtained using an autosampling system that collects samples every hour. The time to analyze a sample is 2-3 min. This introduces a measurement delay that must be accommodated by the control system. FLSmidth has developed a high level control system tool called PXP that can be used to configure advanced controllers. PXP is used to configure the soft MPC. The MPC toolbox from 2-control ApS is used to solve the convex quadratic program associated with the constrained optimal control problem (2). This system is then interfaced to the ECS/SCADA. The execution interval of the soft MPC is 1 min and the data update interval in the expert tool is 3 seconds. The measurement data obtained from the PLC systems are filtered, scaled and validated using the expert system tool before entering the controller. The output from the controller is also scaled and configured for bumpless transfer. The bumpless transfer is important to obtain smooth transitions of manipulated variables when the controller is shifted from manual to automatic. Interlocks are also included to accommodate emergency shut down during abnormal conditions, e.g. power failure Model Identification The model used by the soft MPC is obtained from step response experiments in a single operating point (Prasath et al., 213). The step responses are obtained by stabilizing the plant at the operating point and individually perturbing the feed flow rate and the separator speed. The elevator power is measured continuously. The fineness measurement for modeling is obtained by sampling the product every 15 min and subsequent laboratory analysis of these samples. Conducting these step response experiments is the most time consuming part in the commissioning of the soft MPC. The resulting identified model is G(s) =.47(2s+1) (17s+1)(15s+1) e 4s 1 12s+1 e 3s (1s+1)(12s+1) e 5s 4s+1 (12) with Y(s) = G(s)U(s), Y(s) = [Elevator Load; Fineness], and U(s) = [Feed; Separator Speed]. Internally in the MPC, this model is converted to a FIR model. Due to the inherent variations in the cement grinding circuit process, the predictions of this models are uncertain (Prasath et al., 213). This is the motivation for the development and use of the soft MPC described in this paper Controller Performance Comparison Since the source of raw material for grinding is obtained from different regions, the physical and chemical properties of the clinker are different for each batch of the clinker used. This varies the grinding pattern for each of the clinker types and impacts the grinding efficiency of the cement mill. Therefore, the parameters characterizing mill operation vary significantly and

11 35 35 Elevator load 3 Elevator load 3 Fineness (a) Normal MPC. Controlled variables (CVs). Fineness (b) Soft MPC. Controlled Variables (CVs). Feed(TPH) Feed(TPH) Separator Speed(%) (c) Normal MPC. Manipulated variables (MVs). Separator Speed(%) (d) Soft MPC. Manipulated variables (MVs). Figure 1: Normal MPC (left) and Soft MPC (right) applied to a rigorous nonlinear cement mill simulator, ECS/CEMulator. The disturbances (change in hardness of the cement clinker) are introduced at time 1.35 hour (green line) and the controllers are switched on at time 2 hour (purple line). The soft constraints are indicated by the dashed lines. continuously. To compensate for the quality variations in the feed material, we include target adaptation using a real time optimizer in the control hierarchy level above the soft MPC and the fuzzy logic controller. This helps in deciding the optimum operating range of the mill and improves the grinding efficiency. The elevator load is the controlled variable indirectly measuring the filling of mill. Since the filling is dependent on the raw material properties, the target of the elevator load must be changed periodically. This periodic adjustment of the elevator target helps to maximize the production while still obtaining the desired fineness. The controller varies the feed and separator speed to maintain the elevator load and the fineness at the targets. The frequent power restrictions limit the operation of the cement mill to maximum 16 hours in a day. Normally, the plant 11 runs during the night, when the external electricity demand is low, and is stopped during the day. Most of the time, the cement mill produces PPC. Based on the demand, the cement plant may produce the OPC product for 3 4 hours. Consequently, we normally get only hours of continuous mill run to test our controllers. These frequent starts and stops are typical for cement mill grinding circuits all over the world and not only in regions with power limitations. To have a fair comparison between the fuzzy logic controller and the soft MPC, both controllers are tested under similar operating conditions. We do this by running the controllers for the same source of clinker. This implies that the controllers are tested for similar feed material properties and the resulting performance is an indication of their ability to suppress disturbances and process variations. Target adaptation and optimiza-

12 35 Soft MPC 35 Fuzzy Controller Elevator Fineness Feed (t/h) Sep Speed (%) Figure 11: Comparison of the soft MPC with the fuzzy logic controller for operation of an industrial cement mill grinding circuit. The controlled variables (CVs) are elevator (denotes the elevator load in kw) and fineness (m 2 /kg). The manipulated variables (MVs) are the feed rate (tph) and the separator speed (%). The red line indicates the targets for the controlled variables and the blue lines indicate the measured values. The dotted lines are used to denote soft constraint limits for the CVs and hard constraint limits for the MVs. tion to maximize the production are employed for both controllers. In the first test day, the fuzzy logic controller is switched on and controls the cement grinding circuit for 15 hours. In the second test day, the soft MPC is switched on and controls the cement grinding circuit for 12 hours. Both controllers are tested with the cement mill running continuously in a single recipe producing PPC. It is verified that the fuzzy logic controller is well tuned such that the soft MPC is tested against the best controller available in the plant. As an indication that the fuzzy logic controller can be considered well-tuned, we mention that before the tests with the soft MPC, the plant ran the fuzzy logic controller continuously whenever the mill was started and the plant personnel were quite satisfied with the performance of the fuzzy logic controller. The following configuration are used for the soft MPC applied to the industrial cement mill grinding circuit: Predictionand control horizon N = 3; number of impulse response parameters n = 1; the tuning weights on the errors are Q z = [5 1 2 ; ]; the tuning weights on the manipulated variables are S = [5 1 2 ; ]; and the quadratic soft constraint tuning weights are S η = [9 1 3 ; ]; the sampling time is T s = 1 min; the linear soft constraint tuning weight is set to zero; the constraint limits used by the soft MPC 12 are u min = [135; 64], u max = [152; 74], u min = [.5;.1], u max = [.5;.1], r min,k = r k [1; 1], and r max,k = r k + [1; 1]. The tuning weight for the fineness is chosen small compared to the tuning weight for the elevator load. The reason for this choice is that the fineness is an hourly sampled measurement and less accurate in comparison to the elevator load. The weight for the separator speed is set to a large value to smooth separator speed movements and avoid that it moves aggressively. These choices of the tuning weights ensure relatively stable operation of the cement mill grinding circuit. Fig. 11 indicates the performance of the soft MPC and the existing fuzzy logic control system in the industrial cement mill grinding circuit producing PPC. Fig. 12 reports the performance of the soft MPC for production of OPC in the cement mill grinding circuit. Fig. 11 illustrates that the soft MPC is able to control and stabilize the cement mill grinding circuit. The manipulated variable trajectories are smooth and the controlled variables are well controlled. However, the controller runs at its upper limits and hence the actuator movements are to a large extent restricted by these limits. This observation indicates that the MPC s ability to handle input constraints is important as the cement mill grinding circuit often operates at constraints. Compared to the fuzzy logic controller, the soft MPC yields smaller