# Decoupling Control Strategy of Alkali Recovery Furnace

^{1}; Xuanzi Chu

^{2}

^{, †}; Qingyu Dai

^{3}

1Shaanxi Agricultural Products Processing Technology Research Institute Xi’an, 710021, Researcher, China

2Department of Electrical & Control Engineering, Shaanxi University of Science & Technology, Xi’an, 710021, Student, China

3Department of Electrical & Control Engineering, Shaanxi University of Science & Technology, Weiyang District, Xi’an, 710021, Lecturer, China

^{†}E-mail: 951763567@qq.com (Adddress: Department of Electrical & Control Engineering, Shaanxi University of Science & Technology, Xi’an, 710021, China)

## Abstract

In order to analyze the correlation between the variables in the combustion process of the alkali recovery furnace, this paper uses the control variable method to design the combustion process experiment of the alkali recovery furnace in the actual field. Through the analysis of the experimental results, it is shown that the first two of the three key parameters of furnace temperature, flue gas oxygen content, and furnace negative pressure have a strong coupling relationship, while the interaction between furnace temperature, flue gas oxygen content and furnace negative pressure is relatively weak. For this reason, this paper introduces the linear active disturbance rejection control strategy into the control of the alkali recovery furnace, regards the mutual influence between variables as disturbances, designs disturbance observers for estimation, and designs error feedback control laws to compensate. The results of simulation and actual operation show that, compared with the traditional PID controller, the control strategy can effectively eliminate the mutual interference between variables, and obtain a better control effect, to ensure that the alkali recovery furnace can run more safely, stably, and efficiently.

## Keywords:

Alkali recovery furnace, linear active disturbance rejection control, decoupling control## 1. Introduction

Alkali recovery is a production technology measure accompanying the occurrence and development of the modern pulp and paper industry, and it has a history of more than 100 years. Chemical pulp cooking waste liquid is the main source of pollution in pulp and paper mills. The best technical means to solve the environmental pollution problem of paper mills is alkali recovery. Therefore, alkali recovery is the basis for achieving cleaner production in the entire industry. The operating condition of the alkali recovery furnace has a great influence on the alkali recovery efficiency, the emission of pollutants in the flue gas, and the heat utilization rate. At present, the conventional PID feedback control method is often used in the alkali recovery combustion section. However, due to the strong coupling of the alkali recovery combustion process, it is difficult to achieve satisfactory control effects with pure PID control. Given this situation, many scholars have turned to the direction of intelligent control on the control strategy of the alkali furnace. In reference to the problem of variable coupling of the combustion process, the literature [1,2] realized the decoupling control of various variables by summarizing the influence law of the dynamic characteristics of the process parameters and designing fuzzy control rules; But for objects with time-varying parameters and strong interference, it is often difficult to establish a complete fuzzy control rule, which reduces the control effect. Dong et al. [3] designed a multi-input combustion optimization control system based on Implicit Generalized Predictive Control decouping control in order to solve the strong coupling of the combustion process. The multi-input multi-output prediction model is decoupled through PID neural network, and the objective function can be optimized in real time through rolling optimization. In order to make the output of each control variable reach the set value, an error-based feedback correction algorithm is also introduced, Finally, the dynamic characteristics of the combustion system are significantly improved. Feng et al. [4] proposed an adaptive fuzzy controller for combustion process based on BP neural network decoupling. The control system can not only achieve variable decoupling but also has a certain adaptive ability, which can effectively reduce the adverse effects of fuel calorific value changes.

The above strategies have broken through the control bottleneck of the combustion process of the alkali recovery furnace to a certain extent, but they all use neural networks and fuzzy control methods for decoupling optimization. However, in actual engineering, the characteristic parameters of the controlled object generally fluctuate greatly, and the model is not accurate, which easily causes the failure of the compensator. [5] The neural network selected in the literature [3] needs to use a large amount of actual data for learning, and the calculation time and cost of the entire system are expensive, which greatly limits the application of neural networks. However, the fuzzy control in literature [4,6] needs to formulate complex control rules. All these have brought great difficulties to the practical application of the control device.

In order to analyze the coupling relationship between the variables, this paper took the 130 tds/d alkali recovery furnace of a papermaking enterprise in Henan as the research object, collected field data, analyzed and verified the correlation between the variables in the combustion process of the alkali recovery furnace, and analyzed. The results provided a certain theoretical basis for the design of the alkali recovery furnace control scheme. A linear auto-disturbance rejection control scheme is proposed for the coupling problem existing in the alkali furnace. At the same time, it is compared and analyzed with the controller designed by the traditional PID feed-forward decoupling control method, which shows that the linear auto-disturbance rejection controller can effectively eliminate the mutual interference between variables and reduce the change range of variables in the actual operation process.

## 2. Materials and Methods

### 2.1 Materials

This experiment was conducted in a paper-making company in Henan. The process flow of the alkali recovery combustion section of the company is shown in Fig. 1. First, the thick black liquor is pumped into the thick black liquor tank during the black liquor burning process and is further concentrated by the disc evaporator, mixed with soda ash and Glauber’s salt, and sprayed into the furnace by the black liquor spray gun at high pressure in the thick black liquor heater carry out suspension drying and burning. Among them, the black liquor flow is mainly adjusted by changing the speed of the black liquor pump. The black liquor droplets entering the alkali recovery furnace are heated by high-temperature radiant heat and rising high-temperature flue gas in the furnace and are further dried into black ash with a water content of only 10-15%. Part of the black ash is cracked at high temperature, releasing combustible organic gases such as methanol, acetone, phenol, hydrogen sulfide, and falling on the cushion of the alkali recovery furnace. The remaining black ash continues to burn, generating a lot of heat. Inorganic substances continue to melt, and some organic substances undergo carbonization to generate elemental carbon, which continues to burn in the cushion layer and also releases a large amount of heat, which provides conditions for the melting of inorganic salts and the reduction of Glauber’s salt. After the reaction is completed, Glauber’s salt is reduced to sodium sulfide, and the resulting melt flows out of the chute. The air required for the combustion of black liquor is fed in by the air supply system of the alkali recovery furnace. Generally speaking, the air blower adopts three air supply, and the air volume is mainly adjusted by changing the frequency of the frequency converter to change the speed of the blower. Among them, the primary air is located 450-1000 mm from the bottom of the furnace, and its main function is to supply the oxygen required for the combustion of free carbon in the cushion. The position of the secondary air is at the upper and lower points of the nozzle of the black liquor spraying gun, which has the function of accelerating the vaporization of the black liquor moisture drying of the solids, and maintaining the height of the cushion to make it complete. The position of the tertiary air is above the black liquor spray gun. It is mainly used for the further combustion of combustible volatile gases and a small amount of incomplete combustion products to increase the heat content of the flue gas. At the same time, it can also close the furnace mouth and collect the alkali dust in the flue gas. The air volume of the primary, secondary and tertiary air is controlled by the inverter, and the proportion of the three is 45%, 40%, and 15%. The high-temperature flue gas produced by the burning of black liquor first passes through the economizer, disc evaporator, and other equipment to absorb the waste heat, then passes through the electrostatic precipitator to remove dust, and is drawn and discharged by the induced draft fan. The adjustment of the induced air volume is mainly realized by finely adjusting the frequency of the frequency converter. The melt produced by the burning of black liquor is discharged to the dissolution tank through the melt chute and sent to the causticizing section after the green liquor filter for causticizing, thereby recovering industrial alkali.

### 2.2 Experimental program design

In order to study the specific relationship between the various variables under actual working conditions, the research team designed and completed the combustion process experiment of the alkali recovery furnace. [7] This test is carried out under the condition that the alkali recovery furnace is operating normally and the output is stable. The time interval for collecting data from the production line is 1 minute, and the change data of each output variable within 70 minutes is obtained. Using the pauta criterion (also known as the 3*δ* criterion), it is assumed that a set of test data contains only random errors. Through the calculation and processing of the data, the standard deviation is obtained, and then a certain interval is determined according to a certain probability. Finally, it is considered that any error beyond this interval is not a random error and should be eliminated. While ensuring that the other two quantities remain unchanged, the research team used the controlled variable method to impose a short-term small disturbance with a stable value of 5% on one of the black liquor flow into the furnace, the supply air flow, and the induced air flow. Collect three output data of furnace temperature, furnace pressure, and flue gas oxygen content to analyze the relationship between the three outputs.

## 3. Results and Discussion

### 3.2 Discussion

It can be seen from Fig. 2 that while keeping the air supply and induced air volume constant, when the black liquor flow rate increases, the furnace temperature rises, the flue gas oxygen content decreases, and the furnace pressure slightly increased. It can be seen from Fig. 3 that while keeping the black liquor flow rate and the induced air volume constant, when the air supply volume increases, the furnace temperature decreases, the flue gas oxygen content increases, and the furnace pressure also slightly increases. Fig. 4 shows that while keeping the black liquor flow rate and air supply constant, when the induced air volume increases, the furnace temperature decreases to a certain extent, the oxygen content of the furnace flue gas increases slightly, and the furnace pressure decreases. This phenomenon is consistent with the situation indicated by the mathematical model [7] shown in the expression (1) established by the research group through mechanism analysis.

$$$\begin{array}{c}\left[\begin{array}{c}{t}_{g}\left(S\right)\hfill \\ {\omega}_{{O}_{2}}\left(S\right)\hfill \\ {P}_{g}\left(S\right)\hfill \end{array}\right]=\left[\begin{array}{ccc}{G}_{11}& {G}_{12}& {G}_{13}\\ {G}_{21}& {G}_{22}& {G}_{23}\\ {G}_{31}& {G}_{32}& {G}_{33}\end{array}\right]\left[\begin{array}{c}{W}_{f}\left(S\right)\\ {W}_{a}\left(S\right)\\ {W}_{g}\left(S\right)\end{array}\right]\hfill \\ =\left[\begin{array}{ccc}\frac{66.9}{4617.4s+1}& \frac{-17.61}{4617.4s+1}& \frac{-0.23}{4617.4s+1}\\ \frac{-0.02}{91.5s+1}& \frac{0.071}{91.5s+1}& 0\\ \frac{20.28\left(460.35s+1\right)}{\left(4617.4s+1\right)s}& \frac{5.07\left(523.69s+1\right)}{\left(4617.4s+1\right)s}& \frac{-47.6\left(455.7s+1\right)}{\left(4617.4s+1\right)s}\end{array}\right]\hfill \\ \times \left[\begin{array}{c}{W}_{f}\left(S\right)\\ {W}_{a}\left(S\right)\\ {W}_{g}\left(S\right)\end{array}\right]\hfill \end{array}$$$ | [1] |

In the formula, *t*_{g} is the furnace temperature, *ω*_{0} is the flue gas oxygen content, *P*_{g} is the furnace negative pressure, *W _{f}* is the black liquor flow,

*W*is the air supply volume, and

_{a}*W*

_{g}is the induced air volume.

Therefore, the experimental results and theoretical analysis results show that there is a strong coupling relationship between the furnace temperature and the flue gas oxygen content, while the interaction between the furnace temperature, the flue gas oxygen content, and the negative pressure of furnace is small.

Based on the above conclusions, this paper introduces the linear active disturbance rejection control (LADRC) strategy with natural decoupling characteristics into the control of the alkali recovery furnace, and the actual operating results are shown in the figure:

It can be seen from the Fig. 5 that the three key parameters of the alkali recovery furnace (furnace temperature, furnace pressure, and flue gas oxygen content) run smoothly, with small fluctuations, and good control results have been achieved.

## 4. Introduction and Simulation

### 4.1 Introduction

Linear Active Disturbance Rejection Control is obtained by Professor Zhiqiang Gao [8] after linear processing of the extended state observer and error feedback control in the Active Disturbance Rejection Control (ADRC) proposed by Mr. Jingqing Han. It is mainly composed of tracking differentiator (TD), linear extended state observer (LESO), and linear state error feedback control law (LSEF). TD is mainly used for the acquisition of differential signals and the configuration of the transition process. LESO uses the input and output of the system to estimate the total disturbance of the system, and LSEF is used for the generation of control variables, and at the same time, to compensate for the disturbance.

It can be seen from the transfer function that the furnace pressure system is a second-order object, and the furnace temperature and flue gas oxygen content are both first-order objects. The design of the linear auto disturbance rejection controller for the first-order object is simpler than that of the second-order object. Therefore, this article takes the furnace pressure object as an example to introduce the design process of the linear active disturbance rejection controller. Fig. 6 shows the block diagram of the second-order linear active disturbance rejection control.

Transforming the transfer function of the furnace pressure into a differential equation, we can get:

$$$\begin{array}{c}{\ddot{p}}_{g}=\left[-{\dot{p}}_{g}+20.28\left(460.35{\dot{W}}_{f}+{W}_{f}\right)+5.07\left(523.69{\dot{W}}_{a}+{W}_{a}\right)\right.\hfill \\ \left.-47.6\left(455.7{\dot{W}}_{g}+{W}_{g}\right)\right]/4617.4\hfill \end{array}$$$ | [2] |

The items in the dashed line representing coupling, all uncertainties and disturbances are marked as *f* (•), u is the control input, that is *W*_{g}, the amount of induced air, and b is the input gain of the system. Formula (2) can be simplified as:

$$${\ddot{p}}_{g}=f\left(\u2022\mathrm{}\right)+{b}_{0}u$$$ | [3] |

In this paper, the tracking differentiator shown in formula (4) is used to realize the acquisition of differential signals and the configuration of the transition process.

$$$\left\{\begin{array}{c}{\nu}_{1}\left(k+1\right)={\nu}_{1}\left(k\right)+h{\nu}_{2}\left(k\right)\hfill \\ {\nu}_{2}\left(k+1\right)={\nu}_{2}\left(k\right)+h{f}_{han}\hfill \end{array}\right.$$$ | [4] |

*f _{han}* it can be expressed as

$$$\left\{\begin{array}{c}{d}_{0}=rh\hfill \\ {d}_{1}={d}_{0}h\hfill \\ \delta \left(k\right)={\nu}_{1}-{\delta}_{d}\left(k\right)+{h}_{\nu 2}\left(k\right)\hfill \\ {a}_{0}=\left\{\begin{array}{c}{\nu}_{2}\left(k\right)+\frac{{a}_{0}-{d}_{0}}{2}\text{sgn}\delta \left(k\right),\left|\delta \left(k\right)\right|{d}_{1}\hfill \\ {\nu}_{2}\left(k\right)+\frac{\delta \left(k\right)}{h},\left|\delta \left(k\right)\right|\le {d}_{1}\hfill \end{array}\right.\hfill \\ {f}_{han}=-\left\{\begin{array}{c}{r}_{sign}\left(a\right),\left|a\right|{d}_{0}\hfill \\ ra/{d}_{0},\left|a\right|\le {d}_{0}\hfill \end{array}\right.\hfill \end{array}\right.$$$ | [5] |

Among them: *δ _{d}*(

*k*) is the set value of the furnace negative pressure; r and h are the speed factor and filter factor respectively;

*v*

_{1}(

*k*) and

*v*

_{2}(

*k*) are the output of the tracking differentiator respectively.

Define the state of the system *x*_{1}=*p*_{g}, *x*_{2}=$$ {\dot{p}}_{g}$$, and define f as an expanded state of the system, so that *x*_{3}=f. Assuming that f is differentiable, define *h*=$$ {\dot{x}}_{3}$$, transform equation (3) into space state equation and expand:

$$$\left\{\begin{array}{c}{\dot{x}}_{1}={x}_{2}\hfill \\ {\dot{x}}_{2}={x}_{3}+{b}_{0}u\hfill \\ {\dot{x}}_{3}=h\hfill \\ y={x}_{1}\hfill \end{array}\right.$$$ | [6] |

The state space form of the original system is

$$$\left\{\begin{array}{c}\dot{x}=Ax+Bu+Eh\hfill \\ y=cx\hfill \end{array}\right.$$$ | [7] |

Where: $$ A=\left[\begin{array}{ccc}0\hfill & 1\hfill & 0\hfill \\ 0\hfill & 0\hfill & 1\hfill \\ 0\hfill & 0\hfill & 0\hfill & \hfill \end{array}\right];B=\left[\begin{array}{c}0\hfill \\ {b}_{0}\hfill \\ 0\hfill \end{array}\right];E=\left[\begin{array}{c}0\hfill \\ 0\hfill \\ 1\hfill \end{array}\right];C=\left[\begin{array}{ccc}0\hfill & 0\hfill & 0\hfill \end{array}\right]\circ $$

According to equation (7), the established third-order LESO is as follows:

$$$\left\{\begin{array}{c}\dot{z}=Az+Bu+L\left(y-\widehat{y}\right)\hfill \\ \widehat{y}=cz\hfill \end{array}\right.$$$ | [8] |

Where L is the gain of the state observer *L=*[*β*_{1} *β*_{2} *β*_{3}]^{T}

For the expanded system shown in equation (6), the observer model corresponding to this state space model is:

$$$\left\{\begin{array}{c}{\dot{z}}_{1}={z}_{2}+{\beta}_{1}\left({x}_{1}-{z}_{1}\right)\hfill \\ {\dot{z}}_{2}={z}_{2}+{b}_{0}u+{\beta}_{2}\left({x}_{1}-{z}_{1}\right)\hfill \\ {\dot{z}}_{3}={\beta}_{3}\left({x}_{1}-{z}_{1}\right)\hfill \end{array}\right.$$$ | [9] |

Where, *β*_{1}·*β*_{2} and *β*_{3} are the gains of the extended state observer, *z*_{1}·*z*_{2} and *z*_{3} are the estimated values of *x*_{1}·*x*_{2} and *x*_{3} respectively.

In order to simplify the adjustable parameters of LESO, a hypothetical observer bandwidth *ω*_{0} is introduced to LESO, and the relationship between *ω*_{0} and the observer gain *β* is *β*_{1}＝3*ω*_{0}, *β*_{2}＝3*ω*_{0}^{2}，*β*_{3}＝3*ω*_{0}^{3}. So the gain matrix of the observer is:

$$$L={\left[3{\omega}_{0}3{{\omega}_{0}}^{2}3{{\omega}_{0}}^{3}\right]}^{T}$$$ | [10] |

Make:

$$$\lambda \left(s\right)=\left|sI-\left(A-LC\right)\right|={\left(s+{\omega}_{0}\right)}^{3}$$$ | [11] |

Observer gain matrix [3*ω*_{0} 3*ω*_{0}^{2} 3*ω*_{0}^{3}] controls the accuracy of the observer, A is the system matrix of LESO. It can be seen from the above formula that the gain matrix of the observer is uniquely related to the bandwidth of the observer.

Use the control rate as (10) to compensate the estimated total system disturbance f:

$$$u=\frac{{u}_{0}-{z}_{3}}{{b}_{0}}$$$ | [12] |

The design linear error feedback law is

$$${u}_{0}={k}_{p}\left(\nu -{z}_{1}\right)+{k}_{d}\left(\dot{\nu}-{z}_{2}\right)$$$ | [13] |

Among them, *k _{p}* and

*k*are the gains of the controller, v is the set value of the furnace pressure loop. According to the pole configuration method, the closed-loop feedback poles are configured at

_{d}*ω*places, and we can get:

_{c}$$$\left\{\begin{array}{c}{k}_{p}={\omega}_{c}^{2}\hfill \\ {k}_{d}={2\omega}_{c}\hfill \end{array}\right.$$$ | [14] |

Among them, *ω _{c}* is the controller bandwidth, so that the PD controller parameters can be uniquely related to the controller bandwidth, which further simplifies the design of the controller.

In summary, the adjustable parameters of linear active disturbance rejection are *ω*_{0} and *b*_{0}. Use the bandwidth method to set the above parameters, usually for most engineering objects *ω*_{0}=(3~5) *ω _{c}*. Therefore, only

*ω*needs to be selected. According to the trial and error method,

_{c}*ω*

_{0}=3

*ω*, the dynamic performance of the controlled system is the best.

_{c}Using a similar method, the second-order observer model of the furnace temperature loop and the flue gas oxygen content loop can be designed as:

$$$\left\{\begin{array}{c}{\dot{z}}_{1}={z}_{2}+{b}_{0}u+{\beta}_{1}\left({x}_{1}-{z}_{1}\right)\hfill \\ {\dot{z}}_{2}={\beta}_{2}\left({x}_{1}-{z}_{1}\right)\hfill \end{array}\right.$$$ | [15] |

The design linear error feedback law is:

$$${u}_{0}={k}_{p}\left(\nu -{z}_{1}\right)$$$ | [16] |

The setting parameters of LADRC are shown in Table 1.

### 4.2 Simulation

In order to compare with the control performance of LADRC, the most commonly used PID controller for the alkali recovery furnace control system was also designed. The integral of time-weighted absolute error (ITAE) indicator of the error signal was used to compare the PID controller after optimizing the parameters, make it compare with LADRC in control performance.

The step response is a severe working condition for the system and can be used to compare the performance of the controller. Fig. 7 shows the comparison curves of LADRC and PID step response curves of black liquor flow-furnace temperature, supply air flow-flue gas oxygen content, induced air volume-furnace pressure.

The adjustment time is calculated with an error band of 5%. From the simulation results, it can be seen that under the control of LADRC, the overshoot of the system is the smallest, and the response is the fastest. At the same time, under the use of disturbance, the disturbance amplitude is the smallest and returns to a stable the time is the shortest. Therefore, compared with the traditional PID control strategy, LADRC has better tracking and anti-disturbance capabilities in the control process of the alkali recovery furnace.

Aiming at the coupling system of black liquor flow-furnace temperature and supply air flow-flue gas oxygen content, the LADRC controller was used for control, and the control effect of conventional PID feed-forward decoupling was compared.

In order to test the decoupling effect, at t=0s, a step input of amplitude *r*_{1}=2 is added to the furnace temperature control loop, and the set value of the flue gas oxygen content control loop is *r*_{2}=0 at t=500s, the flue gas The oxygen content control loop adds a step input with a set value of *r*_{2}=1, and *r*_{1} remains unchanged. Take PID control based on feed-forward decoupling and LADRC without compensator as a comparison. At the same time, considering the difference between the actual object and the built model, while keeping the simulation conditions and control parameters unchanged, a 20% parameter perturbation was added to the main channel transfer function to simulate the model mismatch. The simulation curves under the nominal model and the non-nominal model are shown in Figs. 8 and 9.

It can be seen in Figs. 8 and 9 that under the nominal model, PID control based on feed-forward decoupling can almost completely remove the influence of coupling, but when the model is mismatched, its decoupling effect becomes worse. LADRC treats the coupling term as a disturbance, and eliminates the coupling through the anti-disturbance effect, so complete decoupling cannot be achieved, but from the perspective of the coupling effect and recovery time, the decoupling effect of the linear active disturbance rejection controller can fully meet the control requirements and when the model is mismatched, it has little influence on the control effect. In summary, compared to PID feed-forward decoupling control strategies, LADRC can not only achieve better decoupling effects but also has better robustness.

## 5. Conclusions

This paper analyzed the coupling of the main operating variables of the alkali recovery furnace by designing the combustion process experiment of the alkali recovery furnace. On the basis of the experimental results, the control system of the alkali recovery furnace was designed by using linear auto-disturbance rejection technology. The simulation experiment and the final field commissioning results show that:

- 1) There is a strong coupling relationship between furnace temperature and flue gas oxygen content.
- 2) LADRC has great advantages in dynamic performance, decoupling effect, and robustness, which proves that the decoupling control scheme has a better control effect on the alkali recovery furnace.

## Acknowledgments

This work was supported by the Key R&D Projects in Xianyang City （2020k02-16）. We sincerely thank for the funding of the project.

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