Cracking furnace outlet temperature multi-step compensation prediction control method with time lag characteristic

Abstract

A cracking furnace outlet temperature multi-step compensation predictive control method with a time-lag characteristic belongs to the field of advanced control of an industrial process and comprises the following steps: step 1, modeling a cracking furnace outlet temperature control system, and establishing a state space model combining a linear model and an unmodeled dynamic state; 2, establishing an expanded incremental model; 3, designing a robust time-delay prediction controller according to the time-varying and time-delay characteristics of the system; and 4, designing an unmodeled dynamic multi-step compensation controller. A brand new scheme is provided for designing a controller of a cracking furnace outlet temperature control system with uncertainty, strong nonlinearity and time-varying and time-lag, and system tracking errors are eliminated as far as possible by combining data driving and a multi-step compensation principle, so that the system can better track a set value, and meanwhile, the long-term operation capability of the system is improved.

Description

Technical Field

[0001] The invention belongs to the field of advanced control of industrial processes and relates to a multi-step compensation prediction control method of cracking furnace outlet temperature with time lag characteristics. Background Art

[0002] With the development of the national economy and the improvement of people's living standards, the petrochemical industry has achieved unprecedented development. Cracking furnaces are an indispensable part of the petrochemical industry, mainly used in processes such as the production of ethylene by steam cracking hydrocarbons. The outlet temperature of the cracking furnace can directly reflect the efficiency and quality of the product. Keeping the outlet temperature within the required range is essential for optimal operation and product yield. Due to the complex dynamics and inherent time delays in the cracking furnace outlet system, traditional outlet temperature regulation control methods often face some challenges, such as: nonlinearity, interference with feedstock composition and flow rate, heat transfer dynamics, and changes in operating conditions. Therefore, for actual industrial objects with characteristics such as uncertainty, nonlinearity, and time-varying lag, how to design a controller with good control performance while ensuring system stability has always been a difficulty and focus of industrial control research.

[0003] This patent studies complex industrial control systems. Due to the large uncertainty and hysteresis characteristics of the system, it is difficult to establish an accurate control system model. Accurate dynamic models are essential for predictive control. When modeling complex systems with nonlinear characteristics, we usually use simple systems to approximate the characteristics of complex systems, which will cause some implicit dynamic and static information to be ignored during modeling. This patent calls this part of the ignored implicit dynamic and static information unmodeled dynamics. If it is directly ignored, modeling errors will occur during the modeling process. Therefore, we need to design an advanced control algorithm to offset the impact of unmodeled dynamics on system stability.

[0004] At present, people often use PID control methods for complex industrial control systems such as the ethylene cracking furnace outlet temperature control system. The classic PID method is a one-step optimal control method that achieves effective control of the output by adjusting the control input, which makes the input fluctuate greatly. With the development of industry, the requirements for control performance and other aspects are getting higher and higher. The existing methods can no longer meet the high-precision control of complex system processes. Therefore, it is necessary to conduct further research, combine modern robust predictive control theory, and derive appropriate strategies from existing methods, which is of great significance to the research of industrial process control systems. Summary of the invention

[0005] In order to solve the current technical problems, this patent proposes a multi-step compensation predictive control method for the cracking furnace outlet temperature with time-lag characteristics. This method is aimed at the ethylene cracking furnace outlet temperature control system, and adopts a method combining robust time-lag predictive control and multi-step compensation. In order to reduce the conservatism of the design, a multi-step compensation strategy is adopted to design the controller to reduce the impact of unmodeled dynamics on the system. While making the system have better robust performance and stability, it improves the long-term operation capability of the system and better controls the ethylene cracking furnace outlet temperature within the required range.

[0006] In order to make the controller better applied to the actual system, when designing the controller, it is necessary to give full consideration to the uncertainty, strong nonlinearity and time-varying delay of the system. This method studies this problem of the cracking furnace outlet temperature control system. First, the state space model of the ethylene cracking furnace is established, and the incremental model is further derived. Considering the possible adverse effects of uncertain parameters and time-varying delays in the linear part of the incremental model, a robust time-delay predictive controller is designed. Then, for the data information that was not modeled dynamically at the previous moment, a multi-step compensation adaptive controller is designed to eliminate its influence on the closed-loop system.

[0007] The specific steps include:

[0008] Step 1: Establish the state space model of the ethylene cracking furnace outlet temperature control system;

[0009] The ethylene cracking furnace outlet temperature control system is established as the following state space model:

[0010]

[0011] Where x(l) represents the system state at discrete time l, x(l+1) represents the system state at discrete time l+1, d(l) represents the time lag step at discrete time l, and x(ld(l)) represents the system state under the consideration of step d(l) at discrete time l. u(l) represents the system control input at discrete time l, y(l) represents the system state output at discrete time l, and ν(l) is a high-order nonlinear function, which represents the unmodeled dynamics that are ignored when the model is linearized at discrete time l. A(l) = A + Δ a (l) is the state matrix of the system at discrete time l, A, B and C are parameter matrices of appropriate dimensions, A d is the time delay matrix, Δ a (l) is the parameter uncertainty disturbance at discrete time l. From the system description of uncertainty, we know that Δ a (l)Satisfy Δ a (l) = NΔ(l)H, N is a known constant matrix of appropriate dimension, H is a known state matrix of appropriate dimension, is the parameter uncertainty disturbance at discrete time l.

[0012] Since the data ν(l) of the unmodeled dynamics at time l cannot be obtained, considering that the data ν(l-1) of the previous moment of the unmodeled dynamics can be obtained by calculation, the unmodeled dynamics can be expressed as ν(l)=ν(l-1)+Δν(l), where Δν(l) is the unmodeled dynamic increment of the system at discrete time l.

[0013] Step 2: Build an expanded incremental model;

[0014] In order to reduce the amount of subsequent control law calculations, the incremental model is designed according to the discrete state equation as follows:

[0015]

[0016] In the formula, Δx(l+1) is the state increment of the system at discrete time l-1, Δx(l)=x(l)-x(l-1) is the state increment of the system at discrete time l, Δu(l)=u(l)-u(l-1) is the control input increment of the system at discrete time l, and Δy(l)=y(l)-y(l-1) is the system output increment of the system at discrete time l. From (1), we can see that ν(l)=x(l+1)-A(l)x(l)-B(l)u(l), so the lumped unmodeled dynamics of the system at discrete time l is Where x(l-1) is the system state at discrete time l-1, u(l-1) is the control input at discrete time l-1, y(l-1) is the system output at discrete time l-1, Δ a (l-1) is the uncertain disturbance of the state matrix at discrete time l-1.

[0017] Therefore, the relationship between the incremental state of the system at time l-1 in equation (2) is used to infer the lumped unmodeled dynamics at time l, and based on this, the increment of the lumped unmodeled dynamics at time l is given as:

[0018]

[0019] In the formula, is the lumped unmodeled dynamic increment of the system at discrete time l, is the lumped unmodeled dynamics of the system at discrete time l-1.

[0020] This method deeply integrates the advantages of feedback, feedforward, data-driven and robust multi-step predictive control. The proposed multi-step compensation robust predictive controller can be expressed as:

[0021]

[0022] Among them, Δu 1 (l) is the robust time-delay compensation predictive controller, Δu2 (l) is a multi-step compensation adaptive controller.

[0023] Step 3: Design a robust time-delay predictive controller based on the time-varying delay characteristics of the system;

[0024] Design of robust time-delay compensation predictive controller Δu 1 (l) are as follows:

[0025] Δu 1 (l) = K 1 (l)Δx(l) (5)

[0026] In the formula, K 1 (l) is the control law gain of the traditional robust time-delay compensation predictive controller at discrete time l, which can be obtained by solving the linear matrix inequality.

[0027] Step 4: Design an unmodeled dynamic multi-step compensation adaptive controller

[0028] Design a multi-step compensation adaptive controller Δu based on the virtual unmodeled dynamic data information of the previous moment 2 (l), namely:

[0029]

[0030] Where K 2 (l) is the control law gain of the compensator at discrete time l.

[0031] In order to ensure the compensator Δu 2 (l) Yes The control performance of the multi-step prediction performance index function is introduced:

[0032] In the formula, Δx(l+i+1)=x(l+i+1)-x(l+i), Δu(l+i)=u(l+i)-u(l+i-1), P(q -1 )=1-q -1 AHr -1 K 1 (l), D(q -1 )=-q -1 A d , N is the prediction step length, q -1 is the backshift operator, P(q -1 ) is Δx(l+i+1) about q -1 The weighted polynomial of -1 ) is Δx(l+i+1-d(l)) about q -1 The weighted polynomial of is Δu(l+i) with respect to q -1The weighted polynomial of for About q -1 The weighted polynomial of -1 )=1-q -1 for q -1 The backshift compensation parameters.

[0033] Expanding formula (7) yields:

[0034] J=||DΔU+SV+G D X D || 2 (8)

[0035] In the formula

[0036] Assume that at time l+1, in order to model the dynamics of the previous moment Perform dynamic and static compensation:

[0037]

[0038] Easy to know

[0039] V l+1 =k v V (10)

[0040] X D(l+1) =k x X D (11)

[0041] Among them, k u =[1 0 0 0 … 0 0], k v =[1 1 1 1 … 1 1] Τ , k x =[1 1 0 0 ... 0 0] Τ , so we have:

[0042]

[0043] From formula (1) and (12), we can know that:

[0044]

[0045] Eliminate the influence of ν(l) on the system, let

[0046] The unmodeled dynamics at the previous moment can be obtained The optimal feedforward control law gain for compensation is:

[0047]

[0048] Compared with the prior art, the method has the following beneficial effects: for the ethylene cracking furnace outlet temperature control system, the proposed robust time-delay predictive control method based on multi-step compensation, on the basis of the traditional robust predictive control method, expresses the dynamic and static information implicit in the controlled object model as unmodeled dynamics, and designs a feedforward signal compensator based on the unmodeled dynamics to eliminate the impact of the implicit dynamic and static information on the system. On the other hand, unlike the one-step optimal control method, the multi-step compensation adaptive controller is designed in combination with the multi-step prediction idea, thereby reducing the tracking error of the system and making the system have better performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a random noise signal;

[0051] Figure 2 The input response simulation comparison diagram of the method proposed by the present invention and the traditional robust predictive control method;

[0052] Figure 3 This is a comparison diagram of the output response simulation between the method proposed by the present invention and the traditional robust predictive control method;

[0053] Figure 4 This is a control performance simulation comparison chart between the method proposed in the present invention and the traditional robust predictive control method. DETAILED DESCRIPTION

[0054] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0055] Implementation Cases:

[0056] The present invention studies the time-varying time lag and uncertainty of complex industrial control systems. Taking the ethylene cracking furnace system as the research object, the recursive least squares method is used to identify the model to obtain: x(l) = [Δy(l)Δu(l-1)Δu(l-2)Δu(l-3)y(l)], and through repeated experiments, the state space model parameters of the ethylene cracking furnace outlet temperature control system are: A(l) = A+Δ a (l),

[0057] The random noise signal noise(l) superimposed on the simulation model of the controlled object is as follows: Figure 1 shown.

[0058] The control objective can be expressed as:

[0059] e(l)|=|y r (l)-y(l)|<1, 0<l<∞ (15)

[0060] The set value y r (l) = 855°C.

[0061] Since the controller parameters designed by this method will be optimized in a rolling manner as the system runs, and the controller parameters will only fluctuate within a small range, only the controller parameters when l = 1500 are given here for reference. When l = 1500, the multi-step compensation robust predictive controller u(1500) = 3199.

[0062] The performance evaluation indicators introduced are:

[0063]

[0064] Where E(l) is the tracking performance evaluation index at discrete time l.

[0065] The present invention simulates the outlet temperature control system of the ethylene cracking furnace. The simulation adopts the traditional robust predictive control method and the method proposed in this paper. The input response, output response and control performance of the two methods are shown in the figure Figure 2 , 3 and 4.

[0066] Depend on Figure 2 It can be seen that under the condition of superimposing the same external noise, the control input fluctuation of the traditional robust predictive control method is large, which greatly reduces the controller accuracy of the outlet temperature of the ethylene cracking furnace. On the contrary, the fluctuation of the proposed method is small, indicating that the unmodeled dynamics are effectively compensated and the control accuracy is improved.

[0067] Depend on Figure 3 It can be seen that the proposed method can effectively control the outlet temperature within the target range, while the traditional robust predictive control method leads to an increase in overshoot and cannot effectively control the outlet temperature, which further verifies the effectiveness of the proposed method.

[0068] Depend on Figure 4 It can be seen that the tracking performance of the traditional robust predictive control method is poor, while the proposed method controls the outlet temperature of the ethylene cracking furnace within the control requirement range, thereby improving the tracking performance of the system.

[0069] In summary, the signal compensation robust predictive control method can be effectively applied to the ethylene cracking furnace outlet temperature control system. The simulation results show that this method can effectively control the cracking furnace outlet temperature within the target range, verifying the effectiveness of the proposed method. Therefore, the robust time-delay predictive control method based on multi-step compensation can better meet the actual control needs and propose a new solution for the controller design of industrial control systems with time-varying time delays and uncertainties. This method has the importance and potential of practical application and plays a key role in promoting China's industry to become a global technology leader.

Claims

1. A multi-step compensation predictive control method for cracking furnace outlet temperature with time lag characteristics, characterized in that: The specific steps are as follows: Step 1: Establish the state space model of the ethylene cracking furnace outlet temperature control system; The ethylene cracking furnace outlet temperature control system is established as the following state space model: Where x(l) represents the system state at discrete time l, x(l+1) represents the system state at discrete time l+1, d(l) represents the time lag step at discrete time l, x(ld(l)) represents the system state under the consideration of step d(l) at discrete time l, u(l) represents the system control input at discrete time l, y(l) represents the system state output at discrete time l, ν(l) is a high-order nonlinear function, which represents the unmodeled dynamics that are ignored when the model is linearized at discrete time l, and A(l) = A+Δ a (l) is the state matrix of the system at discrete time l, A, B and C are parameter matrices of appropriate dimensions, A d is the time delay matrix, Δ a (l) is the parameter uncertainty disturbance at discrete time l. From the system description of uncertainty, we know that Δ a (l)Satisfy Δ a (l) = NΔ(l)H, N is a known constant matrix of appropriate dimension, H is a known state matrix of appropriate dimension, is the parameter uncertainty disturbance at discrete time l; Since the data v(l) of the unmodeled dynamics at time l cannot be obtained, considering that the data ν(l-1) before the unmodeled dynamics can be obtained by calculation, the unmodeled dynamics can be expressed as ν(l)=ν(l-1)+Δν(l), where Δν(l) is the unmodeled dynamic increment of the system at discrete time l; Step 2: Build an extended incremental model; In order to reduce the amount of subsequent control law calculations, the incremental model is designed according to the discrete state equation as follows: In the formula, Δx(l+1) is the state increment of the system at discrete time l-1, Δx(l)=x(l)-x(l-1) is the state increment of the system at discrete time l, Δu(l)=u(l)-u(l-1) is the control input increment of the system at discrete time l, Δy(l)=y(l)-y(l-1) is the system output increment of the system at discrete time l. From (1), we can see that ν(l)=x(l+1)-A(l)x(l)-B(l)u(l), so the lumped unmodeled dynamics of the system at discrete time l is Where x(l-1) is the system state at discrete time l-1, u(l-1) is the control input at discrete time l-1, y(l-1) is the system output at discrete time l-1, Δ a (l-1) is the uncertain perturbation of the state matrix at discrete time l-1; This method deeply integrates the advantages of feedback, feedforward, data-driven and robust multi-step predictive control. The proposed multi-step compensation robust predictive controller can be expressed as: Among them, Δu1(l) is a robust time-delay compensation predictive controller, and Δu2(l) is a multi-step compensation adaptive controller; Step 3: Design a robust time-delay predictive controller based on the time-varying delay characteristics of the system; The robust time-delay compensation predictive controller Δu1(l) is designed as follows: Δu1(l)=K1(l)Δx(l) (4) Where K1(l) is the control law gain of the traditional robust time-delay compensation predictive controller at discrete time l; Step 4: Design an unmodeled dynamic multi-step compensation adaptive controller According to the virtual unmodeled dynamic data information of the previous moment, a multi-step compensation adaptive controller Δu2(l) is designed, that is: Where K2(l) is the control law gain of the compensator at discrete time l; In order to ensure that the compensator Δu2(l) The control performance of the multi-step prediction performance index function is introduced: In the formula, Δx(l+i+1)=x(l+i+1)-x(l+i), Δu(l+i)=u(l+i)-u(l+i-1), P(q -1 )=1-q -1 AHr -1 K1(l), D(q -1 )=-q -1 A d , N is the prediction step length, q -1 is the backshift operator, P(q -1 ) is Δx(l+i+1) about q -1 The weighted polynomial of -1 ) is Δx(l+i+1-d(l)) about q -1 The weighted polynomial of is Δu(l+i) with respect to q -1 The weighted polynomial of for About q -1 The weighted polynomial of -1 )=1-q -1 for q -1 The backshift compensation parameters of Expanding formula (6) yields: J=||DΔU+SV+G D X D || 2 (7) In the formula Assume that at time l+1, in order to model the dynamics of the previous moment Perform dynamic and static compensation: Easy to know V l+1 =k v V (9) X D(l+1) =k x X D (10) Among them, k u =[1 0 0 0 … 0 0], k v =[1 1 1 1 … 1 1] Τ , k x =[1 1 0 0 … 0 0] Τ , so we have: From formula (1) and (11), we can know that: Eliminate the influence of ν(l) on the system, let The unmodeled dynamics at the previous moment can be obtained The optimal feedforward control law gain for compensation is: By designing robust time-delay predictive control and multi-step compensation adaptive controller, a multi-step compensation robust predictive controller is finally constructed.

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