An Industrial Control System for Cement Sulfates Content Using a Feedforward and Feedback Mechanism

: This study examines the design and long-term implementation of a feedforward and feedback (FF–FB) mechanism in a control system for cement sulfates applied to all types of cement produced in two mills at a production facility. We compared the results with those of a previous controller (SC) that operated in the same unit. The Shewhart charts of the annual SO 3 mean values and the nonparametric Mann–Whitney test demonstrate that, for the FF–FB controller, the mean values more effectively approach the SO 3 target than the older controller in two out of the three cement types. The s-charts for the annual standard deviation of all cement types and mills indicate that the ratio of the central lines of FF–FB to SC ranges from 0.39 to 0.59, representing a significant improvement. The application of the error propagation technique validates and explains these improvements. The effectiveness of the installed system is due to two main factors. The feedforward (FF) component tracks the set point of SO 3 when the mill begins grinding a different type of cement, while the feedback (FB) component effectively attenuates the fluctuations in the sulfates of the raw materials


Introduction
There is widespread agreement that the sulfate (SO 3 ) content of cement is a crucial quality parameter because it affects the compressive strength, setting time, and long-term performance of cement.For this reason, cement standards [1,2] stipulate that cement must contain clinker and calcium sulfate (Cs) and define a high SO 3 limit for each product type.Gypsum is the primary form of calcium sulfate and is accurately fed into the cement mill (CM) during the grinding process.
One of the essential mineral phases of clinker is the tricalcium aluminate (3CaO • Al 2 O 3 or C 3 A), which reacts very fast with water (H).Gypsum addition retards the fast hydration of C 3 A by generating ettringite (C 3 A.3Cs.32H) [3], according to Equation (1).
In concrete production, transfer, and placement, the formation of ettringite prevents flash setting caused by rapid C 3 A hydration.Conversely, an excess of gypsum leads to harmful expansion and a decrease in the strength of concrete and mortar [3][4][5].Therefore, there is an optimal value for the sulfates.To the best of the author's knowledge, numerous researchers have investigated the ideal SO 3 level over the past 80 years due to its significance, researching the effects of sulfates on several important cement properties.Lerch [6], a pioneer in cement research, conducted the first in-depth study on sulfate optimization.Several researchers [7][8][9][10][11][12][13] have investigated and identified the modifications in the hydration rate of clinker mineral phases after adding different amounts of sulfates.These modifications affect fundamental cement properties, such as water demand for normal consistency, setting times, compressive strength at various ages, heat of hydration, and hydration degree.
The cement industry has prioritized reducing its carbon footprint in recent years by decreasing CO 2 emissions in clinker production and clinker consumption per ton of product.The latter is achievable by incorporating supplementary cementitious materials (SCM) into the cement composition.Optimizing SO 3 can reduce the incorporation of clinker into cement while maintaining or improving product performance.The best sulfate content in systems containing clinker and one or more SCMs has been extensively investigated [4,[14][15][16][17][18][19][20].The optimal position depends on the property that needs optimization.Niemuth [4] studied the impact of incorporating fly ash into Portland cement on the optimum sulfate content.At various SO 3 levels, he presented experimental data on strength development and heat release during early hydration.Adu-Amankwah et al. [14] investigated the effects of sulfate additions on the hydration and performance of ternary slag-limestone composite cement through porosity and strength measurements.Han et al. (2015) examined the influence of gypsum on the characteristics of composite binders containing slag and iron tailing powder using a range of measurement techniques.Yamashita et al. [16] studied the not negligible impact of limestone powder on the optimal SO 3 for Portland cement with varying Al 2 O 3 content, using compressive strength as a criterion.Liu et al. [17] examined the effect of gypsum content on cementitious mixtures containing limestone, fly ash, and slag by studying various properties, including initial and final setting time, paste fluidity, water demand, and strength.Fiscan [18] studied the optimal sulfates in cement-slag blends using calorimetry and early strength results.Tsamatsoulis et al. [19] attempted to determine the SO 3 optimum of Portland, Portland composite, and pozzolanic cement types by implementing a unified approach and shallow artificial neural networks.Andrade Neto et al. [20] compiled laboratory techniques for estimating the optimal sulfate content and described the benefits and drawbacks of each method.
Simply knowing the optimal level of sulfates for each type of cement and setting it as a target in daily production is insufficient for cement manufacturing.The measured SO 3 levels should closely align with this target with minimal variance.Therefore, continuous regulation of gypsum, particularly with a controller, is essential to achieve this goal.To the best of the author's knowledge, it is hard to find a description of cement sulfate controllers installed in milling systems in the literature.In the author's experience, most cement plants use manual step-change rules for SO 3 regulation.In a previous study [21], we developed simulations to compare the results of manual regulation with those of a controller comprising both feedback (FB) and feedforward (FF) parts.The FB component attenuates process disturbances, whereas the FF tracks changes at the set point (SP).Combining these two independent regulators has several practical applications.Ko et al. [22] analyzed an FF-FB regulator for an electro-hydraulic valve system utilizing a proportional control valve.The FB component was a proportional-integral-derivative (PID) controller.Wang et al. [23] designed a composite control model containing FF and FB controllers for optical fiber alignment using a piezoelectric actuator.Araque et al. [24] implemented the same technique by combining the two control types for temperature uniformity control.The authors demonstrated that incorporating a model-based feedforward loop improves the tracking of reference signals.
This study analyzes the design and implementation of an FF-FB system to control the SO 3 content in the cement mill outlet by adjusting the percentage of gypsum in the CM inlet.We applied this control technique to two CMs of the Halyps plant for the cement types (CEM) produced.The simulation presented in [21] used the same cement mills.The main novelty of this study is the design and long-term implementation of such a system in cement manufacturing, as it is difficult to find a description of such controllers installed in milling systems in the literature.The structure of the paper is as follows.Section 2 provides a brief description of the grinding process, the types of CEM used, and raw materials analyses.Subsequently, we present the design of the FF-FB control system and its digital implementation in the quality control of sulfates during cement production.The author developed all the software in C# 9.0.Additionally, we briefly describe the rules previously applied to adjust SO 3 in the same milling facilities.We conclude Section 2 by comparing the two control techniques using a process simulator.Section 3 analyzes the long-term results of the controller by comparing them with the results of previous SO 3 adjustments applied to the same installations.We conducted the assessment based on industrial data from 19 consecutive years, covering the period from 2005 to 2023.Finally, Section 4 summarizes the primary findings of this industrially applied research.

Process Description and Materials Analysis
Cement plants typically grind cement in closed milling systems.Figure 1 shows a simplified flowchart of a grinding circuit, including all essential installations.We used the same configuration in [25] in a study of optimization of the process control of cement milling.The weight feeders feed the raw materials to either the ball mill or the separator (fly ash).The recycling elevator directs the output from the mill to the dynamic separator.The fine stream from the classifier constitutes the final product, whereas the coarse material returns to the CM for further grinding.The critical parameters related to quality include (i) cement fineness, (ii) separator speed, (iii) ratio of the coarse material-flow rate to the mill-feed rate, (iv) recycling elevator power, and (v) air-flow rate through the mill and pipes.developed all the software in C# 9.0.Additionally, we briefly describe the rules previously applied to adjust SO3 in the same milling facilities.We conclude Section 2 by comparing the two control techniques using a process simulator.Section 3 analyzes the long-term results of the controller by comparing them with the results of previous SO3 adjustments applied to the same installations.We conducted the assessment based on industrial data from 19 consecutive years, covering the period from 2005 to 2023.Finally, Section 4 summarizes the primary findings of this industrially applied research.

Process Description and Materials Analysis
Cement plants typically grind cement in closed milling systems.Figure 1 shows a simplified flowchart of a grinding circuit, including all essential installations.We used the same configuration in [25] in a study of optimization of the process control of cement milling.The weight feeders feed the raw materials to either the ball mill or the separator (fly ash).The recycling elevator directs the output from the mill to the dynamic separator.The fine stream from the classifier constitutes the final product, whereas the coarse material returns to the CM for further grinding.The critical parameters related to quality include (i) cement fineness, (ii) separator speed, (iii) ratio of the coarse material-flow rate to the mill-feed rate, (iv) recycling elevator power, and (v) air-flow rate through the mill and pipes.The plant quality department regulates the sulfates by sampling the cement in the mill outlet, measuring its SO3 content, and adjusting the gypsum proportion in the CM feed.The control was applied to five CEM types produced according to EN 197-1:2011 [1] and is shown in Table 1.We presented the same Table in [19], where we optimized the sulfate content of the same CEM types.The range of the products is broad, covering Portland (I, II) and pozzolanic (IV) types as well as all three strength classes (32.5, 42.5, and 52.5).Table 2 presents the long-term statistics of the SO3 content in the raw materials.The lab conducted analyses of Portland CEM types on Oxford Instruments (Oxfordshire, UK) LAB X 3000 (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) and Hitachi (Tokyo, Japan) X-Supreme 8000 (2016-2023) XRF analyzers, while Malvern-Panalytical (Almelo, Netherlands) Axios-Cement and Zetium carried out the analyses of the raw materials and pozzolanic CEM types.The plant quality department regulates the sulfates by sampling the cement in the mill outlet, measuring its SO 3 content, and adjusting the gypsum proportion in the CM feed.The control was applied to five CEM types produced according to EN 197-1:2011 [1] and is shown in Table 1.We presented the same Table in [19], where we optimized the sulfate content of the same CEM types.The range of the products is broad, covering Portland (I, II) and pozzolanic (IV) types as well as all three strength classes (32.5, 42.5, and 52.5).Table 2 presents the long-term statistics of the SO 3 content in the raw materials.The lab conducted analyses of Portland CEM types on Oxford Instruments (Oxfordshire, UK) LAB X 3000 (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) and Hitachi (Tokyo, Japan) X-Supreme 8000 (2016-2023) XRF analyzers, while Malvern-Panalytical (Almelo, The Netherlands) Axios-Cement and Zetium carried out the analyses of the raw materials and pozzolanic CEM types.
Both clinker and fly ash contain significant amounts of SO 3 , with noticeable variations.The coefficient of variation %CV (=Std.Dev./Aver.× 100) lies within the range of 35.5% to 44.8%.The above causes two types of disturbance.(a) When the CEM type changes, the running composition can lead to a low-frequency step disturbance in the flow rate of sulfates due to differing percentages of clinker and (or) fly ash.Therefore, it is likely necessary to adjust the gypsum to achieve the current target.(b) The variation in SO 3 content of the two mentioned materials causes disturbances during operation with the same CEM type, necessitating attenuation by adjusting the proportion of gypsum.

Controller Design
The presence of two distinct types of disturbances in the process variable provides the benefit of employing two controllers, acting separately on the control variable.Our earlier study introduced a dual regulator [21], comprising feedforward and feedback modules (FF-FB).Figure 2     Both clinker and fly ash contain significant amounts of SO3, with noticeable variations.The coefficient of variation %CV (=Std.Dev./Aver.× 100) lies within the range of 35.5% to 44.8%.The above causes two types of disturbance.(a) When the CEM type changes, the running composition can lead to a low-frequency step disturbance in the flow rate of sulfates due to differing percentages of clinker and (or) fly ash.Therefore, it is likely necessary to adjust the gypsum to achieve the current target.(b) The variation in SO3 content of the two mentioned materials causes disturbances during operation with the same CEM type, necessitating attenuation by adjusting the proportion of gypsum.

Controller Design
The presence of two distinct types of disturbances in the process variable provides the benefit of employing two controllers, acting separately on the control variable.Our earlier study introduced a dual regulator [21], comprising feedforward and feedback modules (FF-FB).Figure 2    The signal SP represents the SO 3 target of the current CEM, and D SP is the signal for the SO 3 target in case the mill starts to grind another CEM type.D SP is a low-frequency disturbance in the control loop that takes nonzero values only when there is a change in the cement type.X FB and X FF are signals expressing gypsum percentages derived from the FB and FF controllers.D p is the SO 3 disturbance inserted into the process through the ingredient feeders (clinker, gypsum, and fly ash) due to the variance in the rawmaterials composition.Signal Y represents the sulfate content of the product exiting the closed grinding circuit.S i expresses the SO 3 percentage of the cement after sampling and measurement.Figure 2 shows the following transfer functions.G P refers to the gypsum mixing within the milling system.G M is a time delay function for sampling and sulfate measurement.G FB and G FF indicate the FB and FF controllers, respectively.If D SP = 0, then A FB = 1 and A FF = 0. On the contrary, if D SP ̸ = 0, then A FB = 0 and A FF = 1.
Equations ( 2) and (3) provide, in the Laplace domain, the open loop transfer function G OL and the transfer function from SP and disturbances to the output Y. G OL represents the function of the system where the SO 3 output is not fed back to control the gypsum percentage.
Equation ( 4) expresses the G M function.The average sampling and measuring time, T M , which is a pure delay, is 0.25 h.As shown in reference [21], the transfer function G P between the gypsum percentage in the CM feed and the %SO 3 in the final product can be modeled using first-order dynamics with time delay (FOTD).Equation ( 5) describes the model, where T D is the delay time, T 0 is the time constant, and K V is the gain.
According to [21], the milling circuit's dynamic parameters are K V = 0.4, T D = 0.133 h, and T 0 = 0.233 h.The gain meaning is the increase in %SO 3 for a 1% increase in gypsum dosage.We conclude that the gain value is near the respective value computed from Table 2 (43.67/100 = 0.44).The meaning of T D and T 0 is that after T D , a step increase in gypsum will affect SO 3 in the CM outlet.After T 0 , the SO 3 change is 63% of the total increase.Equation ( 6) provides the G P transient response in the time domain after a ∆G step change in %gypsum. SO SO 3 (0) and SO 3 (t) are the %SO 3 values at the beginning of the step increase and at time t, respectively.In the steady state, the maximum %SO 3 increase is ∆SO 3 = K V •∆G.Equation ( 7) computes the fraction a(t) of ∆SO 3 at time t.
Assuming that the system is near the steady state when the fraction α(t) reaches the value of 0.98, the required time calculated from Equation ( 7) is T TP = 1.04 h.After this transient period, the system is in equilibrium with respect to step changes in gypsum feeding.For spot sampling, the delay time between the next and previous feedback controller outlets is the sum of T TP and T M , which is equal to T s,Min = 1.29 h.T s,Min is the minimum sampling period to avoid transient phenomena.
A simple integral controller (I) appropriately regulates the feedback control loop [21] with gain ki.Similarly, a proportional controller of gain K FF attenuates the low-frequency disturbances of the feedforward loop.Equation (8) provides the respective transfer functions.

Digital Implementation
The feedback element of the controller calculates the gypsum setting of the CM feeder after each SO 3 measurement of an instantaneous (spot) sample, which is performed at regular time intervals.In contrast, the feedforward element acts only when the CM starts producing a different CEM type.Consequently, the controller operates in discrete time intervals characterized by the sampling period T s .Equation (9) computes the error e i between the SO 3 set point, S SP , and the SO 3 of the sample taken at time i, S i .
The discrete implementation of the feedback integral controller utilizes the backward form [26] to calculate the gypsum percentage Gi at time i by adding the control action to the gypsum content Gi−1 of time i − 1. Equation ( 10) expresses this function.The sampling period is T s = 2 h, and the optimal gain ki is 0.8, as found in an earlier simulation study [21].The controller is unconstrained.The set of Equations ( 11)-( 15) implements the feedforward proportional controller.
S P is the SO 3 measured at time i, G Prev is the feedback controller output at time i, d SP is the disturbance due to the CEM type change, and S N is the SO 3 content considering the disturbance.Cl CEM,P , Cl CEM,N , Ash CEM,P , and Ash CEM,N are the average clinker and fly-ash contents of the previous and current CEM types, respectively.S Cl , S Ash , and S G are the mean SO 3 contents of clinker, fly ash, and gypsum, as shown in Table 2. Equation (13) calculates the unconstrained output of the controller, DG.However, the optimal feedforward controller is constrained, as proven in [21].The conditions in (14) implement the constraints for the maximum absolute change of the DG.Equation ( 16) calculates the value of the margin Marg, which depends on the previous and current CEM types.
S SP,P and S SP,N are the SO 3 targets of the previous and current CEM, respectively, and M 0 is an additional margin of gypsum.In our application, M 0 = 0.5.

Comparisons Using a Process Simulator
For the past eleven years, the FF-FB controller designed in Section 2.2 has been operating in CM5 and CM6 of the Halyps plant to regulate the sulfates for all the CEM types produced.Before using this regulator, the plant employed the step rules (SC) controller, as mentioned in [21] and shown in Equation (17).This regulator consists of a dead band of 0.4 for SO 3 and provides step changes in the gypsum feed with a gain of 0.5 or a multiple thereof.The description of Equations ( 11)- (15) provides the physical meaning of the parameters of Equation ( 17).
Process simulators allow comparisons between SC and FF-FB controllers.The simulator runs the CM for 600 h.The cement type changes every 20 h between CEM II B-M (P-L) 32.5 and CEM II A-L 42.5.A disturbance occurs in clinker SO 3 every 10 h, i.e., two disturbances appear every 20 h.Clinker SO 3 never changes when the CEM type changes.The simulator creates the magnitude of each disturbance using a predefined mean and standard deviation of clinker SO 3 , a randomly generated probability, and the inverse normal distribution.The simulator also calculates a low variation in gypsum sulfate every 2 h.Table 3 lists the parameters of the developed simulation.Figure 3 shows the SO 3 results for the SC and FF-FB controllers for the CEM II B-M (P-L) 32.5.The simulator used the same disturbances for both control techniques.Compared to SC, the FF-FB results have less dispersion around the target.
Process simulators allow comparisons between SC and FF-FB controllers.The simulator runs the CM for 600 h.The cement type changes every 20 h between CEM II B-M (P-L) 32.5 and CEM II A-L 42.5.A disturbance occurs in clinker SO3 every 10 h, i.e., two disturbances appear every 20 h.Clinker SO3 never changes when the CEM type changes.The simulator creates the magnitude of each disturbance using a predefined mean and standard deviation of clinker SO3, a randomly generated probability, and the inverse normal distribution.The simulator also calculates a low variation in gypsum sulfate every 2 h.Table 3 lists the parameters of the developed simulation.Figure 3 shows the SO3 results for the SC and FF-FB controllers for the CEM II B-M (P-L) 32.5.The simulator used the same disturbances for both control techniques.Compared to SC, the FF-FB results have less dispersion around the target.A quantitative comparison of the two controllers' performances is feasible by implementing the simulator multiple times.The simulator used the same disturbances for each run.Table 4 presents the average statistical results after 100 implementations.We used three criteria to evaluate the closeness to S SP : (a) the average standard deviation, (b) the percentage of the population out of the interval [0.95•S SP , 1.05•S SP ], and (c) the same statistic as (b) but for the first SO 3 values when the CEM type changes.Criterion (c) assesses the efficiency in set-point tracking, whereas criteria (a) and (b) evaluate the degree of disturbance rejection.The three statistics' ratios are consistently smaller than one, indicating that the FF-FB system outperforms the SC in disturbance attenuation and set-point tracking.

Shewhart Control Charts and Nonparametric Analysis
The Shewhart control charts [27] (pp.8-9) are suitable for comparing the results of the two control techniques in the long term.These charts require data in rational subgroups taken at approximately regular intervals during the process.In this study, each subgroup contains all the SO 3 results of samples taken during one year per CM and CEM type.We performed the comparison by generating mean (X) and standard deviation (s) charts.We separated the results into two groups: (a) the period of SO 3 adjustment using Equation ( 16) (2005-2012) and (b) the period of FF-FB controller application (2013-2023).The central line (CL) of the X-chart is a prespecified process parameter equal to the SO 3 target per CEM type.Because the number of samples n i varies annually, we used the pooled standard deviation s Pk [28] (p.93) to determine the central line of the s-chart and the control limits, as shown in Equation (18).
where M k is the number of years in the selected period and s ik is the SO 3 standard deviation of year i and period k.The annual number of samples is sufficient to calculate statistics when n ik ≥ 20.
There is a maximum size of 25 samples in each subgroup in Table 2 of ISO 7870-2 [27] (p.9), which includes the factors to compute the lower and upper control limits, L CL and U CL .This table is not suitable because all n ik exceed this value.Reference [29] provides the general formulae to determine the control limits L CL and U CL , applicable to any number N of samples and given by Equations ( 19)- (21).
where the coefficient c 4 uses the noninteger factorial, determined by the Gamma function and its properties: Γ(x + 1) = x•Γ(x) and Γ(½) = π 1/2 .Figures 4-8 illustrate the two kinds of control charts for the CEM types produced in both periods under examination.For each period, the number N needed for determining the upper and lower control limits is the average of the populations of yearly samples.
ChemEngineering 2024, 8, x FOR PEER REVIEW 9 of 17 where the coefficient c4 uses the noninteger factorial, determined by the Gamma function and its properties: Figures 4a,b-8a,b illustrate the two kinds of control charts for the CEM types produced in both periods under examination.For each period, the number N needed for determining the upper and lower control limits is the average of the populations of yearly samples.The mean charts depict the closeness of the annual mean SO 3 to the target.In all CEM types and both CMs, applying the FF-FB controller leads these two variables into proximity.In the case of the SC regulator, the average sulfates and their target are close for the Portland types but not for the pozzolanic cement.The comparison of the differences between the target, ST ik , and the realized SO 3 , Sav ik , requires a statistical test.Equation (22) computes the absolute value d ik of this difference, and Figure 9a The mean charts depict the closeness of the annual mean SO3 to the target.In all CEM types and both CMs, applying the FF-FB controller leads these two variables into proximity.In the case of the SC regulator, the average sulfates and their target are close for the Portland types but not for the pozzolanic cement.The comparison of the differences between the target, STik, and the realized SO3, Savik, requires a statistical test.Equation ( 22) The mean charts depict the closeness of the annual mean SO3 to the target.In all CEM types and both CMs, applying the FF-FB controller leads these two variables into proximity.In the case of the SC regulator, the average sulfates and their target are close for the Portland types but not for the pozzolanic cement.The comparison of the differences between the target, STik, and the realized SO3, Savik, requires a statistical test.Equation ( 22) The mean charts depict the closeness of the annual mean SO3 to the target.In all CEM types and both CMs, applying the FF-FB controller leads these two variables into proximity.In the case of the SC regulator, the average sulfates and their target are close for the Portland types but not for the pozzolanic cement.The comparison of the differences between the target, STik, and the realized SO3, Savik, requires a statistical test.Equation ( 22)  Due to the asymmetry of all distributions, statistical tests based on the normal distribution are not applicable.Therefore, estimating the difference of means ( [30], pp.18-19) is inapplicable, and the test shall be nonparametric.Mann and Whitney [31] developed such a statistic, which the relative literature [32][33][34] continuously refers to, finding implementation in several research fields [35][36][37][38].This test concerns the sets D1 and D2 with populations M1 and M2 described in (23).
The method considers the set D = D1∪D2 and finds the rank of each element within the union D after sorting them in increasing order.R1 and R2 are the sum of the ranks for observations one and two.Equation (24) provides the test statistic , which shall be compared with the critical values  .
The null hypothesis H0 is that there is no tendency for the ranks of D1 to be significantly higher than that of D2 occurring when  >  .The alternative hypothesis HA is that the ranks of D1 are systematically higher than that of D2 occurring when  ≤  .The hypotheses show that the test is one tail, and reference [39] provides the critical values for probabilities a = 0.01 and a = 0.05.Table 5 presents the results of the Mann-Whitney test for sets D1 and D2, leading to the following conclusions.The two controllers have equivalent performance concerning the CEM II B-M (P-L) 32.5.On the contrary, in CEM II A-L 42.5, the annual mean values better approximate the target using the FF-FB controller than applying the SC, with a probability of 95%.This improvement is most noticeable at CEM B (P-W) 32.5, where the values of the D1 set are higher than those of D2 with a probability of 99%.Due to the asymmetry of all distributions, statistical tests based on the normal distribution are not applicable.Therefore, estimating the difference of means ( [30], pp.18-19) is inapplicable, and the test shall be nonparametric.Mann and Whitney [31] developed such a statistic, which the relative literature [32][33][34] continuously refers to, finding implementation in several research fields [35][36][37][38].This test concerns the sets D 1 and D 2 with populations M 1 and M 2 described in (23).
The method considers the set D = D 1 ∪D 2 and finds the rank of each element within the union D after sorting them in increasing order.R 1 and R 2 are the sum of the ranks for observations one and two.Equation (24) provides the test statistic U, which shall be compared with the critical values U cr .
The null hypothesis H 0 is that there is no tendency for the ranks of D 1 to be significantly higher than that of D 2 occurring when U > U cr .The alternative hypothesis H A is that the ranks of D 1 are systematically higher than that of D 2 occurring when U ≤ U cr .The hypotheses show that the test is one tail, and reference [39] provides the critical values for probabilities a = 0.01 and a = 0.05.Table 5 presents the results of the Mann-Whitney test for sets D 1 and D 2 , leading to the following conclusions.The two controllers have equivalent performance concerning the CEM II B-M (P-L) 32.5.On the contrary, in CEM II A-L 42.5, the annual mean values better approximate the target using the FF-FB controller than applying the SC, with a probability of 95%.This improvement is most noticeable at CEM B (P-W) 32.5, where the values of the D 1 set are higher than those of D 2 with a probability of 99%.The s-charts shown in Figures 4b-8b illustrate a pronounced decrease in the annual standard deviation after the FF-FB controller started operating.The U CL of FF-FB is always lower than the L CL of SC, indicating that the former controller attenuates disturbances caused by sulfate variability in the raw materials better than the latter.Table 6 shows the pooled standard deviations for the five CEM types produced and their ratios when a CEM covers both periods (SC and FF-FB).The severe and systematic improvement of SO 3 stability using the FF-FB controller is apparent in this table.The ratio of s P2 -s P1 ranges from 0.51 to 0.59 for Portland CEM types, where the regulating action is the attenuation of clinker variability in SO 3 .The improvement is better in pozzolanic cement CEM IV B (P-W) 32.5, where SO 3 disturbances originate from fly ash and clinker.The two pozzolanic types show similar standard deviations.Despite its high clinker content, CEM I 52.5 shows a lower pooled standard deviation during FF-FB operation than the respective values of all CEM types during SC operation.

Assessing Controllers' Quality by Combining Standard Uncertainties
Cement SO 3 is the sum of the sulfates in the clinker, fly ash, and gypsum.Consequently, accounting for error propagation, the variance and covariance of input variables affect cement SO 3 variability.We assume that between an output y and input variables, there is a functional relationship y = f (x 1 , x 2 , . . .x N ).Then, Equation (25) provides the square of the combined standard uncertainty u 2 c (y) as a function of the uncertainties u(x i ) [28]  (pp.[18][19][20][21][22][23]. where r(i, j) is the correlation coefficient between x i and x j .r(i, j) = 0 for uncorrelated variables, and it is positive or negative for positively or negatively correlated variables.Equation (26) illustrates the sulfate mass balance of cement, where CL, G, and FA denote the fractions of clinker, gypsum, and fly ash in the cement composition, S CL , S G , and S FA are the sulfates coming from the raw materials, and SO 3,CEM , SO 3,CL , SO 3,G , and SO 3,FA are the SO 3 percentages in cement and in the three materials.
The pairs of variables (CL, SO 3,CL ), (G, SO 3,G ), and (FA, SO 3,FA ) are uncorrelated.Therefore, Equations ( 27)-(29) give the uncertainties u S,CL , u S,G , and u S,FA of SO 3 of each component within the CEM composition.
where u CL , u G , u FA are the uncertainties of the fractions CL, G, and FA in the CM feeders, SO 3,CL , SO 3,G , SO 3,FA are the sulfates of CL, G, and FA, and u SO3,CL , u SO3,G , u SO3,FA are the respective uncertainties.If a controller regulates cement SO 3 by changing the gypsum, Equations ( 31) and ( 32) provide these two variables.This figure clearly explains the significant increase in R 2 in the FF-FB case compared with the R 2 of SC.

Conclusions
This study analyzes the design of a feedforward and feedback mechanism and its implementation in an industrial control system for cement sulfates.The controller considers all the fundamental aspects and particularities of the grinding process and quality requirements.(a) Variability of the raw materials SO3; (b) CM dynamics; (c) sampling period and measuring delays; (d) cement composition and feeders' accuracy; and (e) grinding of various CEM types with different sulfate targets.The results of the FF-FB controller, longterm applied in two CMs of the Halyps plant for all CEM types, have been compared with those of the previously applied controller, which used step rules to adjust gypsum.The main conclusions of this study are as follows.
(1) The Shewhart  -charts of the annual SO3 mean values and the nonparametric Mann-Whitney statistical test prove that using the FF-FB controller, the mean values approach better the SO3 target than the SC controller in two out of the three CEM types produced continuously for eighteen years; (2) FF-FB is better than SC in target approximation with a probability of 95% (a = 0.05) in CEM II A-L 42.5.The two controllers do not show distinguishable performance for the same test level a in CEM II B-M 32.5.This resulted from the second CEM type reduced clinker content and the consequent milder variance of clinker SO3 within the cement composition.In contrast, the ability of FF-FB to regulate gypsum is better than SC so the SO3 values are closer to the target and appear in CEM II A-L 42.5.
Compared with CEM II B-M 32.5, this cement has a higher clinker content, which causes a higher variation in SO3 within the composition.The enhanced performance of FF-FB is more distinct in the pozzolanic cement, where clinker and fly ash are the two independent sources of sulfate disturbances because the test rejects the null hypothesis of equivalence with a probability of 99%; (3) The Shewhart s-charts of the annual standard deviation per CEM type and CM show that the FF-FB controller performs substantially better than the SC.The  of the former is always lower than the LCL of the latter.The ratio of the central lines of FF-FB to SC ranges from 0.51 to 0.59 for the Portland CEM types.This ratio is further reduced to 0.39 in pozzolanic cement CEM IV B (P-W) 32.5, where SO3 disturbances originate from fly ash and clinker;

Conclusions
This study analyzes the design of a feedforward and feedback mechanism and its implementation in an industrial control system for cement sulfates.The controller considers all the fundamental aspects and particularities of the grinding process and quality requirements.(a) Variability of the raw materials SO 3 ; (b) CM dynamics; (c) sampling period and measuring delays; (d) cement composition and feeders' accuracy; and (e) grinding of various CEM types with different sulfate targets.The results of the FF-FB controller, long-term applied in two CMs of the Halyps plant for all CEM types, have been compared with those of the previously applied controller, which used step rules to adjust gypsum.The main conclusions of this study are as follows.
(1) The Shewhart X-charts of the annual SO 3 mean values and the nonparametric Mann-Whitney statistical test prove that using the FF-FB controller, the mean values approach better the SO 3 target than the SC controller in two out of the three CEM types produced continuously for eighteen years; (2) FF-FB is better than SC in target approximation with a probability of 95% (a = 0.05) in CEM II A-L 42.5.The two controllers do not show distinguishable performance for the same test level a in CEM II B-M 32.5.This resulted from the second CEM type reduced clinker content and the consequent milder variance of clinker SO 3 within the cement composition.In contrast, the ability of FF-FB to regulate gypsum is better than SC so the SO 3 values are closer to the target and appear in CEM II A-L 42.5.
Compared with CEM II B-M 32.5, this cement has a higher clinker content, which causes a higher variation in SO 3 within the composition.The enhanced performance of FF-FB is more distinct in the pozzolanic cement, where clinker and fly ash are the two independent sources of sulfate disturbances because the test rejects the null hypothesis of equivalence with a probability of 99%; (3) The Shewhart s-charts of the annual standard deviation per CEM type and CM show that the FF-FB controller performs substantially better than the SC.The U CL of the former is always lower than the L CL of the latter.The ratio of the central lines of FF-FB to SC ranges from 0.51 to 0.59 for the Portland CEM types.This ratio is further reduced to 0.39 in pozzolanic cement CEM IV B (P-W) 32.5, where SO 3 disturbances originate from fly ash and clinker; (4) Our analysis illustrates that the error propagation method is appropriate for comparing controller performance.If a controller regulates the cement sulfates by changing the gypsum, the SO 3 contained in the gypsum and clinker are negatively correlated.
The same occurs for SO 3 in gypsum and fly ash.The larger the absolute value of correlation coefficients, the more robustly the controller regulates the gypsum content to compensate for clinker or fly-ash sulfate disturbances or changes in cement composition.The coefficients r(CL, G) and r(FA, G) are 0.876 and 0.006, respectively, using the SC controller.In the FF-FB case, the values are essentially higher, 0.962 and 0.647, respectively.The above clearly explains the higher performance of the feedforward-feedback system compared with SC.
To the best of the author's knowledge, it is hard to find a description of cement sulfate controllers installed in milling systems in the literature.The technical novelty of this research is the design and long-term industrial implementation of such a system comprising a feedforward and feedback component.The FF component tracks the set-point changes of SO 3 when the cement mill starts to grind another CEM type, and the FB controller effectively attenuates the variations of the raw materials' sulfates.
Cement factories today use various alternative fuels to reduce their carbon footprint per clinker ton.Their highly changeable mix composition and sulfur level increase the SO 3 variance of clinker, making it indispensable to implement an optimized controller to regulate sulfates around the target.An optimal SO 3 target provides the maximum compressive strength [19] and permits clinker reduction in cement composition, further contributing to the decrease in CO 2 per ton of product.Consequently, the actions to optimize and regulate SO 3 are interconnected, resulting in a positive environmental impact.
We selected spot cement sampling and a sampling period such that transient dynamic phenomena are negligible.Further development of the research on optimal controllers regulating SO 3 in the CM outlet involves designing a control system where the sampling is continuous, providing an average sample for each T s period.This type of controller must account for the transient phenomena that occur during the mean sample preparation.

Figure 1 .
Figure 1.Flowchart of a closed grinding circuit.

Figure 1 .
Figure 1.Flowchart of a closed grinding circuit.
depicts the block diagram of the transfer functions and signals related to the sulfate control.
depicts the block diagram of the transfer functions and signals related to the sulfate control.

Figure 2 .
Figure 2. Block diagram of sulfates control.Figure 2. Block diagram of sulfates control.

Figure 2 .
Figure 2. Block diagram of sulfates control.Figure 2. Block diagram of sulfates control.

Figure 3 .
Figure 3.Comparison of SC and FF-FB systems for CEM II B-M (P-L) 32.5.

Figure 5 .
Figure 5.Control charts of CEM II A-L 42.5 produced in CM6: (a) X-chart and (b) s-chart.

Figure 9 .
Figure 9. Frequency distributions of the yearly SO3 mean values for (a) CEM II B-M (P-L) 32.5 and (b) CEM II A-L 42.5.

Figure 9 .
Figure 9. Frequency distributions of the yearly SO 3 mean values for (a) CEM II B-M (P-L) 32.5 and (b) CEM II A-L 42.5.

Figure 10 .
Figure 10.y act and y calc values for (a) SC and (b) FF-FB implementation.

Table 2 .
SO 3 of raw materials.
Figure 3.Comparison of SC and FF-FB systems for CEM II B-M (P-L) 32.5.

Table 4 .
Statistical results of simulator application.

Table 5 .
Mann-Whitney test for the sets D1 and D2.

Table 5 .
Mann-Whitney test for the sets D 1 and D 2 .