A Temperature Model Predictive Control Method for Sulfuric Acid Production from Flue Gas Based on Equivalent Input Disturbance

Abstract

The present invention discloses a method for model predictive control of the temperature in sulfuric acid production from flue gas based on equivalent input disturbance. This method analyzes the desulfurization process of sulfuric acid production from flue gas. First, it is necessary to combine a large amount of production monitoring data to identify the parameters of the controlled system, so as to obtain the system model. Secondly, a system control structure block diagram based on model predictive control and equivalent input disturbance is designed. On this basis, a continuous-time model predictive controller is designed, which can reduce the computational amount and facilitate engineering applications. Then, a method combining model predictive control and equivalent input disturbance is adopted to effectively suppress the influence of system uncertainty and external disturbance on the system performance while achieving accurate tracking of the temperature value. Finally, the stability of the closed-loop system is verified according to the stability theorem. By realizing the rapidity, accuracy, and robustness of the temperature value tracking process, the conversion rate of SO2 and the sulfuric acid production are ultimately improved.

Description

Technical Field

[0001] The present invention belongs to the field of optimization control algorithms, and particularly relates to a flue gas sulfuric acid production temperature model predictive control method based on equivalent input disturbance. Background Art

[0002] In nature, most non-ferrous metal minerals exist in the form of sulfides. Therefore, a large amount of flue gas containing SO 2 is generated during the smelting process. If the flue gas containing SO 2 is directly discharged into the atmosphere, it will cause a series of environmental problems such as air pollution and soil acidification. At the same time, SO 2 , as a Group 3 carcinogen, will also pose a great threat to human health. Therefore, how to effectively reduce the emission of SO 2 during the smelting process is particularly crucial. Flue gas sulfuric acid production, as an extremely important sulfuric acid production method in industry, can effectively solve the above problems. The flue gas sulfuric acid production industry recovers SO 2 from flue gas to produce high-concentration sulfuric acid.

[0003] The flue gas sulfuric acid production process includes four sections: the purification section, the conversion section, the drying and absorption section, and the spent acid treatment section. Among them, in the conversion section, the catalytic reaction of the catalyst occurs to make SO 2 in the flue gas react with O 2 to generate SO 3 . And the conversion rate of SO 2 is an important index in the sulfuric acid production process. Therefore, the conversion section is the core section of the flue gas sulfuric acid production process, and the method of the present invention is also designed for the conversion section. The conversion reaction of SO 2 is a reversible reaction. For a reversible reaction, the factors affecting the reaction rate include temperature, reactant concentration, catalyst activity, air pressure, etc. For the conversion process of flue gas sulfuric acid production, the flue gas can only stay in the converter for a short time. Therefore, the conversion rate of SO 2 is closely related to the reaction rate. Considering the flue gas sulfuric acid production process, the air pressure in the converter is basically constant at about standard atmospheric pressure; the concentration of the reactants is related to the flue gas flow rate, the initial oxygen concentration, and the initial carbon dioxide concentration. These three factors are the operating conditions of the flue gas sulfuric acid production, which are determined by the production status and cannot be changed; the activity of the catalyst cannot be directly controlled; the only thing that can be controlled is the temperature of the flue gas. It can be seen that only by adjusting the inlet temperature of the converter can the temperature of the flue gas in the reaction be indirectly controlled. To sum up, that is, only by adjusting the inlet temperature of the converter can the conversion rate of SO 2 be adjusted.

[0004] At present, for the problem of controlling the inlet temperature in the flue gas to sulfuric acid process, a variety of control methods have been widely proposed, including PID control based on the LM algorithm, PID control based on the RBF neural network, and the method of combining model predictive control and PID, etc. However, due to the existence of external disturbances in the flue gas to sulfuric acid process, and advanced control algorithms including model predictive control still suppress the influence of disturbances through classical feedback control design, resulting in the closed-loop system having to sacrifice other control performances to improve the disturbance resistance performance.

[0005] Therefore, applying the method of combining model predictive control and equivalent input disturbance to the flue gas to sulfuric acid process can effectively solve the problem of the decline in the performance of the control system caused by system uncertainty and external disturbances. This method first converts the system uncertainty and external disturbances into an equivalent input disturbance applied to the control input end, the observer estimates the equivalent input disturbance, and feeds forward compensation is performed on the estimated value to obtain the final composite control rate, so as to achieve the rapidity, accuracy and robustness of the temperature value tracking process, and ultimately improve the conversion rate of SO 2 and the sulfuric acid production. Summary of the Invention

[0006] The present invention proposes a flue gas to sulfuric acid temperature model predictive control method based on equivalent input disturbance. This method uses the actual data of the flue gas to sulfuric acid production process of a certain copper plant as input to establish a system model of the controlled object. By using the method of combining model predictive control and equivalent input disturbance, it effectively suppresses the influence of system uncertainty and external disturbances on the system performance and realizes the precise control of the inlet temperature. At the same time, different from the existing model predictive control methods, the optimal predictive controller proposed by the method of the present invention is given in the form of an explicit analysis formula, which can reduce the calculation amount and is convenient for engineering application. The flow chart of the present invention is as Figure 1 shown.

[0007] A flue gas to sulfuric acid temperature model predictive control method based on equivalent input disturbance, characterized by comprising the following steps:

[0008] Step 1: Identify the parameters of the controlled object according to the collected data to obtain the system model.

[0009] Step 2: Design a system control structure block diagram based on model predictive control and equivalent input disturbance.

[0010] Step 3: Improve the existing model predictive controller and design a continuous-time model predictive controller.

[0011] Step 4: For the nominal system, design a state feedback controller, a state observer and an estimator.

[0012] Step 5: Verify the stability of the closed-loop system through the Hurwitz stability condition and adjust relevant parameters to achieve the stable tracking performance of the system.

[0013] In Step 1, parameter identification is performed on the controlled system, and the mathematical model of the controlled object is obtained based on the actually collected data. The state-space equation form can be expressed as:

[0014]

[0015] where x(t) is the state variable, u(t) is the control input, y(t) is the control output, d(t) is the external disturbance, and A, B, B d , C are coefficient matrices. This is the standard for the design of control systems.

[0016] In Step 2, the system control structure block diagram based on model predictive control and equivalent input disturbance is designed as Figure 2 shown. This method first converts the system uncertainty and external disturbance into an equivalent input disturbance applied at the input end, and then uses an equivalent input disturbance observer to estimate the state variables of the system and the equivalent input disturbance, and performs feedforward compensation on the estimated values to obtain the final composite control rate.

[0017] In Step 3, the existing model predictive controller is improved. The main steps for designing a continuous-time model predictive controller are as follows:

[0018]

[0019] where T p is the prediction time domain, and are the predicted output and the predicted reference trajectory respectively. This performance index can ensure that the predicted output value approaches the given reference input as soon as possible. The relative order σ of the output quantity with respect to the input quantity is defined as the nth derivative of the output quantity with respect to time (n = 0, 1, 2...), until the output quantity is included. Expand the predicted output at time t according to the Taylor series as:

[0020]

[0021] where η is the control order. Since it is inclined to select a lower control order to obtain a smaller control force to facilitate the implementation of this work. Without considering the influence of the disturbance in (1), the higher derivative of the nominal system output y(t) with respect to time is:

[0022]

[0023] Define the control sequence as follows:

[0024]

[0025] Among them, u c (t) is the desired control input, then the control sequence under the action of predicts the output is expressed in the following form:

[0026]

[0027] Among them, Moreover, Similarly, the predicted reference trajectory can be expressed as:

[0028]

[0029] Among them Combining equations (6) and (7), the performance index J can be expressed as:

[0030]

[0031] Among them,[[]] Taking the partial derivative of J with respect to and setting Then the control quantity can be obtained, and thus the continuous-time predictive control law

[0032] In step 4, the idea of equivalent input disturbance is introduced on the basis of model predictive control, thus effectively solving the problem of the degradation of the control system performance caused by system uncertainty and external disturbance. The equivalent input disturbance control system consists of a controlled object, an internal model, a state observer, a state estimator and state feedback.

[0033] Considering a system with uncertainty: G a (s) = [I + W Δ (s)]G(s), where G(s) and W Δ (s) represent the nominal system and multiplicative uncertainty respectively. The uncertainty may be caused by parameter perturbations (due to fuel combustion, payload changes, etc.), neglected dynamics, modeling errors or other unspecified effects. Assume that W Δ (s) can be written as: W Δ (s) = Δ(s)W(s), where Δ(s) is a stable, normalized uncertainty satisfying ||Δ(s)|| ∞ ≤ 1, and W(s) represents a low-order, stable transfer function matrix for capturing frequency characteristics.

[0034] The internal model is a design principle that implants the dynamic model of an external signal into a controller to form a high-precision feedback control system, which can suppress interference signals and gradually track them. The internal model can be expressed as:

[0035]

[0036] where, x r (t) is the state variable, is the control input, and A r , B r are coefficient matrices.

[0037] The suppression of equivalent input disturbance for interference is defined according to the influence of the interference on the system input as an input disturbance equivalent to the external interference. The interference information is obtained through a full-order state observer and mapped to the input channel of the system for external interference analysis. The interference at the input end is estimated and compensated in the reverse direction, thereby improving the interference suppression performance of the entire control system. The total interference received by the original control system is converted into an equivalent interference d e (t) acting on the control input channel. The control system uses the following Luenberger state observer:

[0038]

[0039] where, u f (t), are the observer state, observer input, and observer output respectively, and L ∈ n is the observer gain to be determined. The estimator of the equivalent input disturbance can be expressed as:

[0040]

[0041] where, x e (t), d e (t) are the estimator state and estimator output respectively, and A e , B e , C e are coefficient matrices. Combining the interference estimate value d e (t) and the original state feedback control law u f (t) gives a new control law:

[0042]

[0043] where, K P and K r are the state feedback control gains to be determined. Let the state estimation error be:

[0044]

[0045] Then we can obtain: Combining equations (1), (12) and (13), we have: Meanwhile, we can also obtain:

[0046] In summary, the enhanced system obtained can be expressed in the following form:

[0047]

[0048] where

[0049]

[0050]

[0051] In step 5, the stability of the closed-loop system is analyzed. Define the tracking error as: e(t) = y(t) - r(t). This method adopts model predictive control in the continuous time domain. According to Figure 2 , the control law of the continuous-time model predictive control can be obtained as: By calculation, the expression forms of e and its derivatives of each order are obtained, that is:

[0052]

[0053] where:

[0054] δ = (A 2 + BK r B r CA 3 CA 2 B -1 ), γ = (ABK r + BK P BK r ), σ = (ABK P + BK P A + BK P BK P )

[0055] Λ = (ABC e + BC e A e ), η = (BK P LC - BC e B e C), ζ = (I - CγB r CA 2 B -1 k 3 ) -1 C, ρ = B r CA 2 B -1

[0056] ψ = (I - k 3 BK r B r CA 2 B -1 ) -1 C

[0057] The description of the resulting closed-loop system is as follows:

[0058]

[0059] where

[0060]

[0061] and

[0062]

[0063] Actually, when the reference input r(t) and the disturbance d e (t) are bounded, we can rewrite as:

[0064]

[0065] where

[0066]

[0067] According to the above matrix, by appropriately selecting the prediction horizon T p , the observer gain, the low-pass filter, the internal model controller, and the state observer can ensure that Ξ 11 and Ξ 22 are Hurwitz stable.

[0068] According to the lemma, if is Hurwitz stable, that is is Hurwitz stable, is Hurwitz stable, then the closed-loop system is globally uniformly bounded. It can be obtained that the closed-loop system (16) is globally uniformly stable.

[0069] The present invention is a method for predicting and controlling the temperature of sulfuric acid production from flue gas based on equivalent input disturbance. Compared with the existing methods, the beneficial effects of the present invention are as follows: The difference from the existing model predictive control methods lies in that the optimal predictive controller proposed by the method of the present invention is given in the form of an explicit analysis formula, which greatly reduces the computational amount and is more suitable for engineering applications. The method of combining model predictive control and equivalent input disturbance effectively improves the tracking performance of the system and can better suppress the influence of system uncertainty and external disturbance on the system performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. In the accompanying drawings:

[0071] Figure 1 is the flowchart of the method for controlling the inlet temperature of sulfuric acid production from flue gas based on model predictive control and equivalent input disturbance of the present invention

[0072] Figure 2 is the block diagram of the system control structure based on model predictive control and equivalent input disturbance

[0073] Figure 3 is the output response result diagram in the embodiment of the present invention Specific embodiments

[0074] The embodiments of the present invention will be described in detail below. These embodiments are implemented on the premise of the technical solution of the present invention, and detailed implementation manners and specific operation processes are given. However, the protection scope of the present invention is not limited to the following embodiments.

[0075] In view of the uncertainty of the system and external disturbances, the existing optimal control methods suppress the influence of disturbances through classical feedback control design, resulting in that the closed-loop system has to sacrifice other control performances to improve the disturbance rejection performance. To solve such problems, the present invention gives the following ideas:

[0076] Step 1: Identify the parameters of the controlled system according to the collected data to obtain the system model.

[0077] Step 2: Design the block diagram of the system control structure based on model predictive control and equivalent input disturbance.

[0078] Step 3: Improve the existing model predictive controller and design a continuous-time model predictive controller.

[0079] Step 4: For the nominal system, design a state feedback controller, a state observer and an estimator.

[0080] Step 5: Verify the stability of the closed-loop system through the Hurwitz stability condition, and adjust the relevant parameters to achieve the stable tracking performance of the system.

[0081] The following is a numerical example simulation: For the method proposed by the present invention, an example is given below for illustration.

[0082] Consider the control process of sulfuric acid production from flue gas in a copper smelter. After system identification based on the actual production data of flue gas provided by the copper smelter, the state space parameters of the nominal system model are as follows:

[0083]

[0084] The weighting function of the uncertainty of the controlled object is as follows:

[0085]

[0086] The input and desired output of the control system are:

[0087]

[0088] The disturbance to which the system is subjected is:

[0089]

[0090] According to the internal model principle, we have: A r = -0.001, B r = 83. Then, by using the linear quadratic (LQR) method to determine the control gains (K p , K r ), we select Q 1 = diag{1, 1, 1, 10}, R 1 = 0.01. The calculation results are:

[0091] K p = [-29.2 -1435.6 -2890.6], K r = -31.6165 (22)

[0092] Subsequently, we select Q L = diag{1, 1, 1}, R L = 1. The calculation results are:

[0093] L = [-0.4365 0.7515 0.7741] T (23)

[0094] Finally, it is verified that the designed parameters meet the stability conditions. Figure 3 The output response of the designed control system is shown, indicating that the sulfuric acid production control system from flue gas is stable and has good disturbance rejection performance.

[0095] The present invention has been described in the form of examples. Those skilled in the art should understand that the present disclosure is not limited to the above-described embodiments, and various changes, alterations, and substitutions can be made without departing from the scope of the present invention.

Claims

1. A method for model predictive control of the temperature in sulfuric acid production from flue gas based on equivalent input disturbance, comprising the following steps: Step 1: Identify the parameters of the controlled system to obtain the system model; Step 2: Design a system control block diagram based on model predictive control and equivalent input disturbance; Step 3: Improve the existing model predictive controller and design a continuous-time model predictive controller; Step 4: For the nominal system, design a state feedback controller, a state observer and an estimator; Step 5: Verify the stability of the closed-loop system through the Hurwitz stability condition and adjust relevant parameters to achieve the stable tracking performance of the system; In Step 1, identify the parameters of the controlled system. According to the actually collected data of the mathematical model of the controlled object, the obtained state space equation can be expressed as: where \(x(t)\) is the state variable, \(u(t)\) is the control input, \(y(t)\) is the control output, \(d(t)\) is the external disturbance, and \(A\), \(B\), \(B\ d , \(C\) are coefficient matrices; In Step 2, design a system control block diagram based on model predictive control and equivalent input disturbance. Convert the system uncertainty and external disturbance into an equivalent input disturbance applied at the input end, and then use an equivalent input disturbance observer to estimate the state variables of the system and the equivalent input disturbance, and perform feedforward compensation on the estimated values to obtain the final composite control rate; In Step 3, improve the existing model predictive controller. First, design the cost function J of the continuous-time model predictive controller as follows: where T p is the prediction horizon, and are the predicted output and the predicted reference trajectory respectively. This cost function can ensure that the predicted output value approaches the given reference input as soon as possible; In Step 4, introduce the idea of equivalent input disturbance on the basis of model predictive control, so as to effectively solve the problem of the degradation of the control system performance caused by system uncertainty and external disturbance; The equivalent input disturbance control system consists of a controlled object, an internal model, a state observer, a state estimator and a state feedback; Step 5 is to analyze the stability of the closed-loop system.

2. A method for model predictive control of the temperature in sulfuric acid production from flue gas based on equivalent input disturbance according to Claim 1, characterized in that: Convert the system uncertainty and external disturbance into an equivalent input disturbance applied at the input end, and then use an equivalent input disturbance observer to estimate the state variables of the system and the equivalent input disturbance, and perform feedforward compensation on the estimated values, so that the system has better robustness and stability.

3. A method for model predictive control of the temperature in sulfuric acid production from flue gas based on equivalent input disturbance according to Claim 1, characterized in that: Improve the existing model predictive controller and design a continuous-time model predictive controller.

4. A method for model predictive control of the temperature in sulfuric acid production from flue gas based on equivalent input disturbance according to Claim 1, characterized in that: Verify the stability of the control system based on the state space method and the Hurwitz stability theorem by making full use of the frequency domain information of the dynamic uncertainty of the controlled object.

Images