Ethylene cracking process outlet temperature robust predictive control method based on adaptive interference compensation

Abstract

An ethylene cracking process outlet temperature robust predictive control method based on adaptive interference compensation belongs to the field of advanced control of industrial processes, and comprises the following steps: step 1, establishing a dynamic model of ethylene cracking process outlet temperature and fuel gas flow; 2, establishing a discrete state space model with parameter uncertainty and external interference; 3, establishing an incremental robust time-delay model to predict a main controller; 4, designing a historical moment interference multi-step prediction feed-forward compensator of adaptive interference; 5, designing a current-moment unknown interference multi-step prediction feed-forward compensator of adaptive interference; a brand new design scheme is provided for the design of a controller of an outlet temperature control system in the ethylene cracking process with uncertainty, nonlinearity and complex external interference, the fuel gas flow fluctuation can be effectively reduced, the control precision of the outlet temperature is improved, and the burden of an actuator is reduced.

Description

Technical Field

[0001] The invention belongs to the field of advanced control of industrial processes and relates to a robust predictive control method for outlet temperature of an ethylene cracking process based on adaptive interference compensation. Background Art

[0002] In today's industrial production landscape, with the continued advancement of industrialization, companies are placing increasingly stringent demands on their processes. Temperature control systems, a key area of ​​industrial process control, are widely used in various production scenarios. However, in the case of ethylene cracking process outlet temperature control systems, the inherent uncertainties, nonlinearities, and complex external interferences inherent in these systems make effective outlet temperature control, energy loss reduction, and maintenance cost reduction a persistent and challenging challenge.

[0003] The ethylene cracking process occupies a central position in the petrochemical industry. As the core equipment in ethylene production, precise control of the outlet temperature of the ethylene cracking furnace is crucial for ensuring product quality, improving production efficiency, and reducing energy consumption. However, in practice, this process faces numerous challenges. Complex external environmental interference is a key factor influencing precise outlet temperature control. Fluctuations in feedstock quality are the most common source of interference. Different batches of cracking feedstock exhibit significant variations in composition, hydrogen-to-carbon ratio, and impurity content. These variations directly alter the heat release and reaction rate of the cracking reaction, leading to significant fluctuations in outlet temperature. Furthermore, as external conditions dynamically change during the control process, control system characteristics also vary, introducing significant system uncertainty. Furthermore, seasonal variations in ambient temperature and pressure, as well as deviations in equipment operating parameters caused by grid voltage fluctuations, also pose significant challenges to the ethylene cracking process. These interdependent and dynamic external interference factors pose challenges to stable outlet temperature control.

[0004] Currently, PID control is the mainstream method for controlling the outlet temperature of ethylene cracking processes. However, with the increasing complexity of industrial process control objects and the increasing demands for control indicators, traditional PID control is increasingly unable to meet practical needs and achieve ideal control results. Therefore, in-depth research on such complex industrial equipment and the integration of advanced control algorithms into the equations are of great practical significance and urgent need to promote the development of industrial process control systems and enhance the intelligent and refined level of industrial production. Summary of the Invention

[0005] In order to solve the current technical problems, this patent proposes a robust predictive control method for the outlet temperature of the ethylene cracking process based on adaptive interference compensation. This method is aimed at the outlet temperature control system of the ethylene cracking process and adopts a design mode that combines the robust predictive control method and the multi-step predictive feedforward compensation method. The robust predictive controller serves as the main controller and provides a guarantee of asymptotic stability for the closed-loop system. The design of the multi-step predictive feedforward compensator can effectively reduce the fluctuation of the fuel gas flow without affecting the closed-loop performance of the system, reduce the impact of external interference on the system, and reduce the burden on the actuator. This makes the system have better robust performance and stability, better controls the outlet temperature of the ethylene cracking furnace within the required range, and achieves the goal of energy saving, consumption reduction, and equipment maintenance cost reduction.

[0006] To better adapt the controller to practical systems, the design of the controller must account for system uncertainty, nonlinearity, and complex external disturbances. This approach addresses this issue in a cracking furnace outlet temperature control system. First, a dynamic model of the outlet temperature and fuel gas flow rate of the ethylene cracking process is established. Second, based on this dynamic model, a discrete state-space model is constructed with parameter uncertainty and external disturbances. Considering the potential adverse effects of uncertainty in the linear portion of the model, an incremental robust time-delay model predictive master controller is established. Finally, to mitigate the impact of external disturbances on the system, an adaptive historical-time-interval multi-step predictive feedforward compensator and an adaptive current-time-interval multi-step predictive feedforward compensator are designed.

[0007] The specific steps include the following:

[0008] Step 1: Establish a dynamic model of the outlet temperature and fuel gas flow rate of the ethylene cracking process;

[0009]

[0010] Where t is a continuous time variable, T u is the outlet temperature, κ a is the absorption rate, q l is the calorific value of fuel gas, F l is the raw material flow rate, Θ r is the heat transfer coefficient of the radiation section, A r is the heat transfer area of ​​the radiation section, Θ c is the heat transfer coefficient of the convection section, A c is the heat transfer area of ​​the convection section, T c is the outlet temperature of the convection section, T i is the inlet temperature of the convection section, Θ k is the heat transfer parameter of the radiation section, κ r is the emissivity, E ctis the radiation heat rate of the radiation section, Λ1 is the moisture content in the flue gas, Ψ1 is the ash content in the flue gas, q j is the calorific value of each component in the fuel gas, m j is the mass of each component in the fuel gas, F yl is the fuel gas flow rate, T c is the outlet temperature of the convection section;

[0011] Step 2: Establish a discrete state space model with parameter uncertainty and external disturbances;

[0012] Based on (1), the outlet temperature control system of the ethylene cracking process is established as the following state space model:

[0013]

[0014] where Γ is a discrete time variable, ΔX(Γ+1)=X(Γ+1)-X(Γ) is the system state increment at discrete time Γ+1, ΔX(Γ)=X(Γ)-X(Γ-1) is the system state increment at discrete time Γ, ΔX(Γ-d(Γ))=X(Γ-d(Γ))-X(Γ-1-d(Γ)) is the time-delayed state increment at discrete time Γ, d(Γ) is the time-varying delay, and X(Γ)=[y(Γ)e(Γ)] T , y(Γ) is the system output at discrete Γ, e(Γ) is the system output error at discrete Γ, Δu(Γ)=u(Γ)-u(Γ-1) is the control input increment at discrete Γ, Δy(Γ)=y(Γ)-y(Γ-1) is the system output increment at discrete Γ, is the external interference matrix of the system at discrete time Γ, is the external disturbance of the system at discrete time Γ, A1(Γ)=A1+Δ a (Γ) is the system state matrix at discrete time Γ, Δ a (Γ)=N a Δ(Γ)H a , A1, N a 、H a is the system constant matrix of appropriate dimension, Δ(Γ)∈[-1,1], A d (Γ) is the system delay matrix of the system at discrete Γ time, B1 is the system input matrix of the system at discrete Γ time, and C1 is the system output matrix of the system at discrete Γ time;

[0015] Step 3: Establish an incremental robust time-delay model to predict the main controller;

[0016] First, the design method of the conventional incremental robust time-delay model predictive controller Δu1(Γ) is as follows:

[0017] Δu1(Γ)=K1(Γ)ΔX(Γ) (3)

[0018] Where K1(Γ) is the control law gain of the conventional incremental robust time-delay predictive controller at discrete time Γ;

[0019] Step 4: Design a multi-step predictive feedforward compensator for adaptive disturbance history;

[0020] Since the interference to the cracking furnace includes various instantaneous or non-instantaneous influences such as equipment wear, coke accumulation, communication delay, sensor noise, external ambient temperature changes, etc., the composite interference is not completely known at the current moment. Therefore, the composite interference at the current moment is Can be decomposed into historical moment interference and unknown interference at the current moment That is, it satisfies:

[0021]

[0022] The current system state will be affected by historical moments Influence of the problem, the design of historical moment interference multi-step prediction feedforward compensator Δu2(Γ);

[0023]

[0024] In order to better compensate for historical disturbances and optimize the control performance of the compensator Δu2(Γ), a multi-step prediction performance index function J2 is introduced:

[0025]

[0026] Where ΔX(Γ+κ+1)=X(Γ+κ+1)-X(Γ+κ) is the state increment of the system at the discrete moment Γ+κ+1, ΔX d (Γ+κ-d(Γ)+1)=X d (Γ+κ-d(Γ)+1)-X d (Γ+κ-d(Γ)) is the time-delay state increment of the system at the discrete moment Γ+κ-d(Γ)+1, Δu(Γ+κ)=u(Γ+κ)-u(Γ+κ-1) is the control input increment of the system at the discrete moment Γ+κ, is the external interference matrix of the system at discrete Γ+κ-1 moment, u3(Γ+κ) is the output of the multi-step prediction feedforward compensator of the current interference of the system at discrete Γ+κ moment. γ represents the prediction step size, κ represents the κth step size, ζ -1 is the backshift operator, P1(ζ -1 ) is ΔX(Γ+κ+1) with respect to ζ -1 The weighted polynomial, L1(ζ -1 ) is ΔXd (Γ+κ+1) about ζ -1 The weighted polynomial, Q1(ζ -1 ) is Δu(Γ+κ) with respect to ζ -1 The weighted polynomial of Λ1(ζ -1 )for About -1 The weighted polynomial of H1(ζ -1 )=1-ζ -1 About -1 The backward step length parameter of

[0027] Since P(ζ -1 )=1-ζ -1 A1(Γ)-ζ -1 K1(Γ)-ζ -1 A d (Γ), so we can get:

[0028]

[0029] Substituting (7) into (6), we can get the expanded multi-step prediction performance index function J2:

[0030]

[0031] Where,

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] In order to ensure that the multi-step prediction performance index J2 is minimized and J2=0, the control rate gain of the historical interference multi-step prediction feedforward compensator satisfies:

[0039]

[0040] Where, κ u =[1 0 … 0 0], κ v =[1 1 … 1 1] T ;

[0041] From (9), we can see that in order to achieve dynamic compensation for historical interference, I-B1κ must be satisfied. uF1 -1 W1κ v =0, therefore, W1 = F1κ u * B1 * κ v * , then the historical disturbance multi-step prediction feedforward compensator controller is:

[0042]

[0043] Where, B1 * =B1 T (B1B1 T ) -1 , κ u * =κ u T (κ u κ u T ) -1 , κ v * =κ v T (κ v κ v T ) -1 ;

[0044] Step 5: Design a multi-step predictive feedforward compensator for the current unknown disturbance of the adaptive disturbance;

[0045] The current system state will be affected by unknown interference at the current moment To solve the problem of the influence of the unknown interference, a multi-step prediction feedforward compensator Δu3(Γ) is designed for the current moment:

[0046] Based on (3), (10) and (2), the relationship between the output error and the unknown disturbance multi-step predictive feedforward compensator Δu3(Γ) at the current moment can be established:

[0047]

[0048] In the formula, e1(Γ+κ+1)=y1(Γ+κ+1)-y r is the system error of the system at the discrete Γ+κ+1 moment, y1(Γ+κ+1) is the system output of the system at the discrete Γ+κ+1 moment, and y r is the system output setting value, N1(Γ+κ)=1-ζ -1 A1(Γ+κ)-ζ -1-d(Γ) A d (Γ+κ);

[0049] In order to reduce as much as possible To reduce the impact caused by the interference, while reducing the fluctuation of Δu3(Γ) and reducing the burden on the actuator, we propose a multi-step prediction feedforward compensation performance index for the current moment interference:

[0050]

[0051] Introducing the Diophantine equation: H1(ζ -1 )N1(Γ+κ)-ζ -1 B1K1+ζ -2 B1K1+ζ -1 G(ζ -1 )=1, we can get:

[0052]

[0053] In the formula, g1(κ)=1+A1(Γ+κ)+B1K1+ζ -d(Γ) A1(Γ+κ), g2(κ)=A1(Γ+κ)+B1K1+ζ -d(Γ) A1(Γ+κ);

[0054] Therefore, the expanded multi-step prediction performance index function J3 is:

[0055]

[0056] Where,

[0057]

[0058]

[0059]

[0060] Due to the use of the multi-step predictive compensation control method, a total of γ control rates will be calculated at time Γ. However, at time Γ, only the control rate of the response time is required. Therefore, the compensation signal Δu3(Γ) that can minimize the performance index J3 can be obtained as:

[0061]

[0062] Where, is the external disturbance increment of the system at discrete Γ-1 moment.

[0063] Compared with the existing technology, the beneficial effects of this method are as follows: for the outlet temperature control system of the ethylene cracking process, the proposed robust predictive control method for the outlet temperature of the ethylene cracking process based on adaptive interference compensation can effectively overcome the shortcomings of the traditional PID control strategy in its insufficient ability to handle complex interference, model uncertainty and nonlinearity. By introducing the multi-step predictive feedforward compensation method, the system can dynamically compensate for the impact of complex interference factors such as feed flow fluctuations and changes in fuel calorific value in real time. At the same time, combined with the robust predictive control algorithm, it can ensure the stability of the system while enhancing the system's dynamic response capability to sudden changes in operating conditions. It effectively reduces the fluctuation of the fuel gas flow rate, improves the control accuracy of the outlet temperature, and reduces the fluctuation of product quality caused by temperature deviation. In addition, this method can maintain stable control performance under different cracking raw materials and operating conditions, significantly reducing the system's dependence on manual experience, improving the safety and economy of the operation of the ethylene cracking unit, and providing core technical support for the intelligent upgrade of the petrochemical industry.

[0064] Figures in the specification

[0065] Figure 1 This is a comparison chart of the output response simulation of the control method proposed by the present invention and the robust one-step optimal predictive control method;

[0066] Figure 2 This is a control input simulation comparison diagram of the control method proposed by the present invention and the robust one-step optimal predictive control method;

[0067] Figure 3 This is a comparison chart of the output error simulation between the control method proposed by the present invention and the robust one-step optimal predictive control method;

[0068] Figure 4 A comparison diagram of the output response simulation root mean square error between the control method proposed in the present invention and the robust one-step optimal predictive control method;

[0069] Figure 5 A comparison chart of control input simulation standard deviations between the control method proposed by the present invention and the robust one-step optimal predictive control method;

[0070] Figure 6 A comparison chart of the output error simulation mean absolute error between the control method proposed in the present invention and the robust one-step optimal predictive control method;

[0071] Figure 7 It is a flow chart of the steps of the present invention. DETAILED DESCRIPTION

[0072] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0073] Implementation Cases:

[0074] This paper studies the complex interference and uncertainty issues of complex industrial control systems. Taking the ethylene cracking furnace outlet temperature control system as the research object, using the cracking furnace input and output data, and applying the least squares and neural network alternating identification method, the discrete state space model parameters with parameter uncertainty and external interference can be obtained as follows: C1=[1 0], y r =850, γ=5,1<d(Γ)<5。

[0075] Since the controller parameters designed by this method will be rolling optimized to adapt to system changes as the system runs, only the simulation process image of 300 steps is given here, which already includes a complete operation cycle and can fully reflect the control performance of the control method proposed in this invention and the one-step optimal predictive control method.

[0076] Depend on Figure 1 As can be seen, under the same disturbance, the proposed control method can control outlet temperature fluctuations to within ±1.5°C, a significantly smaller fluctuation range than the ±2°C observed in the comparative control method. This improvement is attributed to the design of an adaptive multi-step predictive feedforward compensator for historical disturbances and an adaptive multi-step predictive feedforward compensator for current unknown disturbances, which better compensate for the effects of disturbances.

[0077] Depend on Figure 2 As can be seen, the curve of the comparative control method occasionally exhibits peaks and valleys. Compared to the comparative control method, the control method proposed in this invention improves input smoothness and reduces fuel flow fluctuations. The combination of the robust model predictive control method and the multi-step predictive compensation method predicts the system state, enabling the controller to adjust the fuel flow input in a timely manner based on the predicted state, effectively reducing fuel flow oscillations. This demonstrates that the proposed control method can better improve the system's control performance.

[0078] Depend on Figure 3 As can be seen, the tracking error distribution presented by the proposed control method quantifies the superior performance of the proposed method. Compared with the control method, the proposed method achieves a lower tracking error, indicating that the proposed method has greater outlet temperature stability.

[0079] Depend on Figure 4 It can be seen that the root mean square error of the output response of the comparative control method is 1.2518°C, while that of the control method proposed in the present invention is 0.5493°C, which is 56.12% lower than that of the comparative method.

[0080] Depend on Figure 5It can be seen that the standard deviation of the control input of the comparative control method is 3.2629 kg / h, while that of the control method proposed in the present invention is 1.4831 kg / h, which is 49.04% lower than that of the comparative method.

[0081] Depend on Figure 6 It can be seen that the standard deviation of the output error of the comparative control method is 1.0014°C, while that of the control method proposed in the present invention is 0.4302°C, which is 57.04% lower than that of the comparative method.

[0082] Figure 7 It is a flow chart of the steps of the present invention.

[0083] In summary, the robust predictive control method for the outlet temperature of the ethylene cracking process based on adaptive interference compensation proposed in the present invention can be effectively applied to the ethylene cracking process to achieve a better outlet temperature control effect. It provides a new design scheme for the ethylene cracking process control system with uncertainty, nonlinear characteristics and complex external interference, and has good industrial application value. At the same time, the control method proposed in the present invention can also be extended to temperature control systems with complex characteristics in other related fields such as oil refining, chemical industry, metallurgy, etc., providing a reusable technical solution for the intelligent upgrade of industrial control. Through continuous optimization and innovation, the present invention is expected to provide strong technical support for energy conservation, emission reduction and high-quality development in the global industrial field.

Claims

1. A robust predictive control method for outlet temperature of ethylene cracking process based on adaptive disturbance compensation, characterized in that: The following steps are involved: Step 1: Establish a dynamic model of the outlet temperature and fuel gas flow rate of the ethylene cracking process; Where t is a continuous time variable, T u is the outlet temperature, κ a is the absorption rate, q l is the calorific value of fuel gas, F l is the raw material flow rate, Θ r is the heat transfer coefficient of the radiation section, A r is the heat transfer area of ​​the radiation section, Θ c is the heat transfer coefficient of the convection section, A c is the heat transfer area of ​​the convection section, T c is the outlet temperature of the convection section, T i is the inlet temperature of the convection section, Θ k is the heat transfer parameter of the radiation section, κ r is the emissivity, E ct is the radiation heat rate of the radiation section, Λ1 is the moisture content in the flue gas, Ψ1 is the ash content in the flue gas, q j is the calorific value of each component in the fuel gas, m j is the mass of each component in the fuel gas, F yl is the fuel gas flow rate, T c is the outlet temperature of the convection section; Step 2: Establish a discrete state space model with parameter uncertainty and external disturbances; where Γ is a discrete time variable, ΔX(Γ+1)=X(Γ+1)-X(Γ) is the system state increment at discrete time Γ+1, ΔX(Γ)=X(Γ)-X(Γ-1) is the system state increment at discrete time Γ, ΔX(Γ-d(Γ))=X(Γ-d(Γ))-X(Γ-1-d(Γ)) is the time-delayed state increment at discrete time Γ, d(Γ) is the time-varying delay, and X(Γ)=[y(Γ)e(Γ)] T , y(Γ) is the system output at discrete Γ, e(Γ) is the system output error at discrete Γ, Δu(Γ)=u(Γ)-u(Γ-1) is the control input increment at discrete Γ, Δy(Γ)=y(Γ)-y(Γ-1) is the system output increment at discrete Γ, is the external interference matrix of the system at discrete time Γ, is the external disturbance of the system at discrete time Γ, A1(Γ)=A1+Δ a (Γ) is the system state matrix at discrete time Γ, Δ a (Γ)=N a Δ(Γ)H a , A1, N a 、H a is the system constant matrix of appropriate dimension, Δ(Γ)∈[-1,1], A d (Γ) is the system delay matrix of the system at discrete Γ time, B1 is the system input matrix of the system at discrete Γ time, and C1 is the system output matrix of the system at discrete Γ time; Step 3: Establish an incremental robust time-delay model to predict the main controller; First, the design method of the conventional incremental robust time-delay model predictive controller Δu1(Γ) is as follows: Δu1(Γ)=K1(Γ)ΔX(Γ) (3) Where K1(Γ) is the control law gain of the conventional incremental robust time-delay predictive controller at discrete time Γ; Step 4: Design a multi-step predictive feedforward compensator for adaptive disturbance history; Since the interference to the cracking furnace includes various instantaneous or non-instantaneous influences such as equipment wear, coke accumulation, communication delay, sensor noise, external ambient temperature changes, etc., the composite interference is not completely known at the current moment. Therefore, the composite interference at the current moment is Can be decomposed into historical moment interference and unknown interference at the current moment The current system state will be affected by historical moments Influence of the problem, the design of historical moment interference multi-step prediction feedforward compensator Δu2(Γ); In order to better compensate for the historical disturbance and optimize the control performance of the compensator Δu2(Γ), the expanded multi-step prediction performance index function J2 is introduced: Where, ΔX(Γ+κ)=X(Γ+κ)-X(Γ+κ-1) is the state increment of the system at the discrete Γ+κ moment, ΔX d (Γ+κ-d(Γ))=X d (Γ+κ-d(Γ))-X d (Γ+κ-d(Γ)-1) is the time-delay state increment of the system at the discrete Γ+κ moment, Δu(Γ+κ)=u(Γ+κ)-u(Γ+κ-1) is the control input increment of the system at the discrete Γ+κ moment, is the external interference matrix of the system at discrete Γ+κ moment, u3(Γ+κ) is the output of the multi-step prediction feedforward compensator of the current interference of the system at discrete Γ+κ moment, γ represents the prediction step size, κ represents the κth step size, ζ -1 is the backshift operator, Q1(ζ -1 ) is Δu(Γ+κ) with respect to ζ -1 The weighted polynomial of Λ1(ζ -1 )for About -1 A weighted polynomial of ; In order to ensure that the multi-step prediction performance index J2 is minimized and J2=0, the control rate gain of the historical interference multi-step prediction feedforward compensator satisfies: where κ u = [1 0 … 0 0], κ v = [1 1 … 1 1] T ; From (5), we can see that in order to achieve dynamic compensation for historical interference, I-B1κ must be satisfied. u F1 -1 W1κ v =0, therefore, W1 = F1κ u * B1 * κ v * , then the historical disturbance multi-step prediction feedforward compensator controller Δu2(Γ) is: Where, Step 5: Design a multi-step predictive feedforward compensator for the current unknown disturbance of the adaptive disturbance; The current system state will be affected by unknown interference at the current moment To solve the problem of the influence of the unknown interference, a multi-step prediction feedforward compensator Δu3(Γ) is designed for the current moment: Based on (3), (6) and (2), the relationship between the output error and the unknown disturbance multi-step predictive feedforward compensator Δu3(Γ) at the current moment can be established: In the formula, e1(Γ+κ+1)=y1(Γ+κ+1)-y r is the system error of the system at the discrete Γ+κ+1 moment, y1(Γ+κ+1) is the system output of the system at the discrete Γ+κ+1 moment, and y r is the system output setting value, N1(Γ+κ)=1-ζ -1 A1(Γ+κ)-ζ -1-d(Γ) A d (Γ+κ), H1(ζ -1 )=1-ζ -1 About -1 The backward step length parameter of Introducing the Diophantine equation: H1(ζ -1 )N1(Γ+κ)-ζ -1 B1K1+ζ -2 B1K1+ζ -1 G(ζ -1 )=1, we can get: In the formula, g1(κ)=1+A1(Γ+κ)+B1K1+ζ -d(Γ) A1(Γ+κ),g2(κ)=A1(Γ+κ)+B1K1+ζ -d(Γ) A1(C+k); In order to reduce as much as possible In order to reduce the impact caused by the interference, and at the same time reduce the fluctuation of Δu3(Γ), and reduce the burden on the actuator, we propose a multi-step prediction feedforward compensation performance index function J3 for the current moment interference: Where, Due to the use of the multi-step predictive compensation control method, a total of γ control rates will be calculated at time Γ. However, at time Γ, only the control rate of the response time is required. Therefore, the compensation signal Δu3(Γ) that can minimize the performance index J3 can be obtained as: Where, is the external disturbance increment of the system at discrete Γ-1 moment.

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