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In limestone-gypsum wet flue gas desulfurization process, the change process of pH value of slurry in absorption tower is a typical nonlinear system with time delay and various uncertainties, so it is difficult to establish an accurate mathematical model of slurry pH control process. According to the pH control process of the slurry of wet flue gas desulfurization process, a model-free adaptive control algorithm based on compact form dynamic linearization (CFDL-MFAC) is designed to realize the tracking control of the pH value of the slurry. Due to various interference factors in the pH control process of slurry in absorption tower, it is easy to cause jump change of control system parameters and even structure. Therefore, a model-free adaptive control algorithm based on switching strategy is proposed in this paper. According to different working conditions, several model-free adaptive controllers are established. The stability of the algorithm is analyzed for the two cases of fixed system parameters and jumping system parameters. It was found that the model-free adaptive controller based on the switching strategy can switch multiple controllers under the condition of system parameter jump, so as to realize the fast tracking control of the slurry pH value of the system absorption tower under different working conditions. Through this method, the overshoot can be reduced and the control quality can be improved.

Sulfur dioxide is one of the main air pollutants. The pollution caused by sulfur dioxide not only has a great impact on the economy, but also has a great threat to human health. In recent years, the emission of sulfur dioxide in China has been high. More than 55% of sulfur dioxide comes from coal combustion in coal-fired power plants. China’s growing demand for electricity leads to the continuous growth of coal consumption, which leads to the increase of sulfur dioxide emissions from coal combustion. Therefore, the reduction of sulfur dioxide emission from coal-fired power plants will improve the atmospheric environment quality. At present, limestone-gypsum wet flue gas desulfurization (WFGD) process [

At present, the commonly used methods for controlling the slurry pH in coal-fired power plants are manual control and PID control. The manual control requires the power plant staff to have good working experience, and the control requirements of the slurry valve opening are high, so large pH fluctuation is easy to be caused in the control process. Although PID control has improved the automation level of slurry pH control to a certain extent, for the complex control object such as the slurry pH of absorption tower, when PID control is used, the controller parameters are difficult to adjust, and the adaptive ability is poor. In recent years, many experts and scholars use advanced control methods to study the pH control of absorption tower slurry in WFGD process. In [

Although some achievements have been made in the study of pH value control of absorption tower slurry in WFGD process, the change process of slurry pH value in absorption tower has the characteristics of nonlinear, time-varying, and large lag, so it is impossible to establish its accurate mathematical model. In the process of pH control of absorber slurry, a lot of process data will be generated every moment. For such a system, model-free adaptive control (MFAC) [

The paper is organized as follows. In Section

As the most widely used desulfurization technology, WFGD process flow is shown in Figure

WFGD process flow.

The pH value of the slurry in the absorption tower is a key factor affecting not only the desulfurization efficiency, but also the limestone utilization rate and the purity of gypsum. The pH value of the slurry is usually maintained between 5.0 and 6.0. In the desulfurization process, the control of the pH value is realized by controlling the flow of the limestone slurry, and the size of limestone slurry flow is controlled by the opening of the slurry valve, so the control of the pH value of the slurry can be regarded as the control of limestone slurry valve opening. In this paper, the slurry pH value control process takes limestone slurry valve opening as control input and slurry pH value as system output.

Hammerstein model [

It is assumed that the discrete nonlinear input-output system of the slurry pH control process is as follows:

In system (

System (

From the practical point of view, the above assumption of control object is reasonable and acceptable. Assumption

For the nonlinear system (

According to Theorem

If the control increment of two adjacent moments is too large, the input of the system will jump change sharply, and the burden of the actuator will be increased. Therefore, the following control input criterion functions are considered:

Substituting model (

It can be known from the controller (

Calculating the extremum of (

The slurry pH control is a time-varying system. In order to make the estimation algorithm (

If

Equations (

For a given bounded expected output signal

For any time

For the nonlinear system (

The output tracking error of the system converges monotonically, and

The closed-loop system is bounded-input bounded-output (BIBO) stable; that is, the output sequence

If the condition

In other cases, we define

Taking absolute values on both sides of (

It is noted that the function

According to the conclusion

Equation (

The system tracking error is defined as

Substituting the CFDL data model (

From Assumption

Taking

According to (

Combining (

Formula (

Since

Using inequalities

Using (

Therefore, conclusion (

The pH control process of the absorption tower slurry is a complex object with nonlinear, time-varying parameters and many uncertainties. In this paper, we mainly consider how to improve the control effect of slurry pH value control system when the parameters of absorption tower slurry pH control system change under different working conditions. In view of the characteristics of the time-varying parameters of the slurry pH control system, we consider the jump change of parameters which is a special case of time-varying parameters. Multiple model-free adaptive controllers are designed to cover all jump parameters according to different working conditions to improve the control accuracy of slurry pH control system in the case of parameters’ jump change.

According to the system input and output data under different working conditions, the mathematical models of absorption tower slurry pH control system are established. The model of slurry pH control system under different working conditions is as follows:

The corresponding model-free adaptive controllers are established according to the different working conditions of the slurry pH control process of the absorption tower:

If

Index switching function is established:

The switching steps of the CFDL-MAFC controller based on the switching strategy are as follows:

According to different working conditions, the corresponding model and corresponding model-free adaptive controller are established, and the index switching function is established.

Before each sampling time, the best model describing the current working condition is selected according to the system switching index function; i.e., model

At the next sampling time, the system controller is switched to the optimal CFDL-MAFC controller

(see [

For an arbitrary positive

Due to

From the functional analysis, compatible norm satisfies

Hence

This completes the proof.

For the nonlinear system (

The output tracking error of the system converges monotonically, and

The closed-loop system is bounded-input bounded-output (BIBO) stable; that is, the output sequence

System parameters jump change among a limited number of values.

The proof of Theorem

Assuming that, during the process of pH control of the absorption tower slurry, the system parameters change among a limited number of values, we can write (

From Lemma

Substituting (

According to Lemma

The parameters of the Hammerstein model of the pH control system of the absorption tower slurry are as follows:

The desired output of the system is as follows:

Using CFDL-MFAC algorithm for MATLAB simulation, we set the simulation parameters to

The simulation results are shown in Figures

pH tracking curve.

pH tracking error curve.

The simulation results in Section

In modeling process, the model parameters we get are often inaccurate. We randomly take several estimations of

When the system parameters jump during the pH control of the slurry, the simulation results using the CFDL-MFAC algorithm are shown in Figures

pH tracking curve.

pH tracking error curve.

For the jumping parameter system, the simulation results of CFDL-MFAC algorithm based on switching strategy are shown in Figures

pH tracking curve.

pH tracking error curve.

Switching sequence of controller.

Aiming at the pH control of the absorption tower slurry in limestone-gypsum wet flue gas desulfurization, a model-free adaptive control algorithm is proposed in this paper, and a CFDL-MFAC controller is designed according to the slurry pH control process. The slurry pH value is a complex controlled object with characteristics of nonlinearity, large inertia, hysteresis, time-varying, etc., and the system parameters jump easily due to external interference in the process of pH control, so a model-free adaptive control algorithm based on switching strategy is proposed. The convergence of the algorithm is proved theoretically. The simulation results show that the model-free adaptive control algorithm based on switching strategy can deal with the jumping system parameters in the process of slurry pH control. Compared with CFDL-MFAC algorithm, it can effectively reduce the overshoot and improve the effect of pH control.

The experimental data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by National Natural Science Foundation of China (61873006 and 61673053) and National Key Research and Development Project (2018YFC1602704 and 2018YFB1702704).