Ethylene cracking furnace outlet temperature set value optimization control method with state delay compensation

Abstract

The invention discloses an ethylene cracking furnace outlet temperature set value optimization control method with state time lag compensation, belongs to the field of advanced control of an industrial process, and breaks through the limitation that a system is separated from an overall economic optimal state under the influence of time lag in a traditional method. The method specifically comprises the following steps of 1, establishing a control loop expansion state space model of the ethylene cracking furnace outlet temperature control system; 2, designing a loop controller with time delay compensation on the basis of the lower extension system; step 3, lifting a control loop to an operation optimization layer expansion state space model; 4, designing a set value optimizer for running optimization layer time-delay multi-step compensation; according to the method, the problem that the ethylene cracking furnace process outlet temperature control system is separated from the optimal state under state time lag, uncertainty, strong nonlinearity and unknown interference can be effectively solved, and it is ensured that the system can give the optimal set value in the current system state in real time.

Description

Technical Field

[0001] The invention belongs to the field of advanced control of industrial processes and relates to an ethylene cracking furnace outlet temperature setting value optimization control method with state time lag compensation. Background Art

[0002] In recent years, with the continuous advancement of industrialization, competition in the field of industrial processes has become increasingly fierce. As a very important position in the national economy, the production and application of ethylene is directly related to the production capacity and development level of multiple downstream industries. In order to maintain competitive advantage, ethylene production must be operated in the most economical way and be able to respond quickly to changes that affect its economic benefits and control performance. As a key factor in ethylene production, the outlet temperature of the ethylene cracking furnace directly reflects the production efficiency and quality of ethylene. The control of the outlet temperature of ethylene cracking is an important indicator in the industrial production process. However, such systems usually have large uncertainties and significant strong nonlinear characteristics. At the same time, the time-lag characteristics widely present in various industrial productions also increase the difficulty of temperature control. Therefore, how to quickly and accurately find the optimal set value suitable for the current situation in the economic optimal state of the entire ethylene production plant, and enable the system to be effectively controlled under various internal and external environmental conditions, has become one of the challenges to be solved in the control field.

[0003] This patent studies the optimization control of the outlet temperature set point of the ethylene cracking furnace with state time lag compensation. First of all, it is difficult to establish an accurate system model for the ethylene cracking temperature control system, and changes in external conditions will cause changes in the control system, so that the system may deviate from the set point given under ideal conditions, which may cause the overall system to be unable to operate in the economically optimal state, resulting in inestimable production losses. In addition, control systems usually have strong nonlinear and time-lag characteristics, and simplification is inevitable when modeling and designing controllers for such complex systems. However, these ignored dynamic characteristics may have a significant impact on the system. If these characteristics are simply ignored, modeling and controller design are performed under ideal conditions, and the actual control effect is often difficult to achieve expectations. Therefore, designing an advanced control set point optimization control method for the above-mentioned problems has become an inevitable requirement in actual industrial process control.

[0004] At present, the mainstream control method of the ethylene cracking furnace outlet temperature control system is real-time optimization control. However, with the increasing complexity of the production environment and the increasing requirements for economic performance such as output and efficiency, the traditional optimization control method has been difficult to effectively control the outlet temperature while ensuring ethylene production due to the state lag, uncertainty, strong nonlinearity and unknown interference problems that are prevalent in the production process. Therefore, in-depth research on equipment with characteristics of ethylene cracking process and combined with modern control theory are of great significance to the improvement of industrial process control systems. Summary of the invention

[0005] In order to solve the above technical problems, this patent proposes an optimization control method for the set value of the outlet temperature of an ethylene cracking furnace with state lag compensation. This method adopts a combination of robust multi-step predictive control, signal compensation and improvement technology for systems with state lag, uncertainty, strong nonlinearity and unknown interference in the control system. While ensuring the production efficiency of the ethylene production project, the optimal set value of the outlet temperature of the ethylene cracking furnace is calculated and effectively tracked and controlled.

[0006] This method is aimed at studying this problem. First, a simulation model is established for the outlet temperature control system of the ethylene cracking furnace. The lower-level control loop model is constructed based on the underlying controlled object and a robust time-delay compensation predictive controller is designed. The lower-level control loop model is upgraded and the upper-level operation control layer model is constructed, and the set value optimizer is designed. The state time lag, uncertainty, strong nonlinearity and external interference in the upper and lower control loops are considered at the beginning of the design. In addition, the unmodeled dynamics and time-delay compensation methods are used to obtain the compensation controller and optimizer of the unmodeled dynamic data information of the operation control model, eliminating the influence of the unmodeled dynamics on the closed-loop system, so that the system can still show the expected control performance even when facing changing conditions in actual operation.

[0007] The method is implemented through the following technical solutions:

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

[0009] The discrete underlying state space model with state lags, parameter uncertainties, and unmodeled dynamics is established as follows:

[0010]

[0011] Where x(k+1) represents the underlying system state at discrete time k+1, u(k) represents the underlying control input at discrete time k, v(k) represents the unmodeled dynamics between the discretized underlying model and the original model at discrete time k, and A(k) = A+Δ a(k) is the underlying state matrix of the system at discrete time k, B(k) = B + Δ b (k) is the underlying input matrix of the discrete k-time system, A d is the underlying state delay matrix of the system, d(k) is the delay step size of the state delay matrix (where d m ≤d(k)≤d M , d m and d M are the upper and lower constraints of the time-delay step length respectively), A is the underlying state matrix to be identified, B is the underlying input matrix to be identified, C is the underlying output matrix, y(k) represents the underlying system output at discrete time k, Δ a (k) is the uncertain perturbation of the underlying state matrix at discrete time k, Δ b (k) is the uncertainty perturbation of the underlying input matrix at discrete time k, satisfying:

[0012] [Δ a (k) Δ b (k)] = NΔ(k)[H a H b ] (2) Where N is the unified matrix of the underlying system uncertainty, H a is the state matrix of the underlying system uncertainty, H b is the input matrix of the underlying system uncertainty, is the uncertain perturbation that depends on the discrete time k, where Δ1, Δ2 are random numbers between [-1, 1];

[0013] The output error, error integral term and unmodeled dynamics are introduced into the new state space variables to obtain the new extended control loop state space vector X d (k)=[x(k),v(k-1),E(k),e(k-1)] T , where X d (k) is the state space vector of the loop control layer at time k, e(k-1) is the relationship between the bottom system output y(k-1) and the set value y at time k-11 * (k-1), v(k-1) is the unmodeled dynamics of the underlying system at time k-11, E(k) is the cumulative error of the output error e(k) of the underlying system from time k=0 to time k; the state space equation of the new extended loop control layer established at the same time is as follows:

[0014]

[0015] In the formula, is the system state at discrete time k in the loop control layer, is the extended matrix 1 of the loop control layer at discrete k moments about the underlying state, is the extended matrix 2 of the loop control layer with respect to the underlying state, is the expansion matrix 3 of the loop control layer controller with respect to the underlying control law gain, K d1 is the control law gain of the controller at discrete time k in the loop control layer, is the system state delay matrix at discrete time k in the loop control layer, is the system state input matrix of the loop control layer at discrete time k, C d =[C 0 0 0] is the system state output matrix of the loop control layer, is the unmodeled dynamics of the loop control layer at discrete time k, and I is the identity matrix of appropriate dimension;

[0016] Step 2: Based on the lower-level extended system, design a loop controller with time-delay compensation;

[0017] The signal compensation robust predictive controller u(k) in the loop control layer is expressed as:

[0018]

[0019] In the formula is the control law gain K of the traditional robust predictive controller for time delay compensation at discrete time k d1 The expanded matrix can be obtained by solving the linear matrix inequality;

[0020] Step 3: Elevate the control loop to the upper operation optimization layer to expand the state space model;

[0021] The upper operation control layer uses a larger sampling period T in one cycle. u Sampling, the lower loop control layer uses a smaller sampling period T in one cycle d To sample, where T u =αT d The sampling rate α is a positive integer. At the same time, the system state equation of the upper operation control layer considering the sampling period is established based on the expansion of the lower control loop as follows:

[0022]

[0023] In the formula, is the system state matrix of the operation control layer, The system state input matrix for the operation control layer, is the system state matrix of the operation control layer, A u (αk) is the base system state matrix of the operation control layer, B u The base system state input matrix for the operation control layer, is the system status of the operation control layer (where e u (αk) = r* -r(αk) is the performance error of the ethylene revenue performance index, r* is the ideal performance index of the ethylene revenue of the operating layer, and r(αk) is the actual performance index of the ethylene revenue performance index of the operating layer). is the virtual unmodeled dynamics of the operational control layer, D(αk) (where d m -T d <D(αk)<d M -(α-1)T d ) is the extended state lag of the operation control layer, is the benefit coefficient matrix of the positive benefit of the ethylene benefit performance index after the operation control layer is expanded, where M e is the benefit coefficient matrix of the positive benefit of the base ethylene benefit performance index of the operating control layer, N e The benefit coefficient matrix of negative consumption of the basic ethylene benefit performance indicator of the operation control layer;

[0024] Step 4: Design and run the set-point optimizer for multi-step compensation of optimization layer delay;

[0025] The setpoint optimizer with state lag compensation at the operational control level can be expressed as:

[0026] y * (αk)=u u1 (αk)+u u2 (αk) (6)

[0027] Among them, y * (αk) is the controller output of the running control layer at discrete time αk and is also the set value input of the lower loop control layer. u1 (αk) is the traditional robust predictive controller at discrete time αk of the operating control layer, u u2 (αk) is the unmodeled dynamic multi-step compensation controller at the previous discrete time αk of the operating control layer;

[0028] First, a traditional robust predictive controller u is designed to operate the control layer. u1 (αk) is as follows:

[0029] u u1 (αk)=K u1 (αk)X u (αk) (7)

[0030] Where K u1 (αk) is the control law gain of the traditional robust predictive controller at the discrete αk moment of the operating control layer, which can be obtained by solving the linear matrix inequality;

[0031] Secondly, according to the virtual unmodeled dynamic data information of the operation control layer at the previous moment, the unmodeled dynamic multi-step compensator u of the operation control layer is designed. u2 (αk), that is:

[0032]

[0033] Among them, K u2 (αk) is the control law gain of the compensation controller at the discrete time αk of the operation control layer, To run the control layer discrete αk-α time unmodeled dynamics, is the unmodeled dynamic increment of the system at the discrete time αk-α of the operational control layer, e u (αk+α)e=r * -r(αk+α) is the performance error of the ethylene revenue performance index at the discrete time αk+α of the operation control layer, z -1 is the backshift operator, E(z -1 ) is e u (αk) about z -1 The weighted polynomial of ξ(z -1 ) is X u (αk) about z -1 The weighted polynomial of ρ(z -1 )for About z- 1 The weighted polynomial of θ(z -1 )for About z- 1 A weighted polynomial of ;

[0034] In order to perform dynamic and static multi-step compensation for the unmodeled dynamics of the control layer running at the previous moment, ensure that the controller u u2 (ak) control performance, the following performance indicators are introduced:

[0035]

[0036] Where N is the prediction step length, P u (z -1 ) is X u (αk+α) about z -1 The weighted polynomial, Q u (z -1 ) is y * (αk+i) about z- 1 The weighted polynomial of for About z- 1 The weighted polynomial of -1 )=1-z -1 For about z -1 The backshift compensation parameter, u u2'(αk+i) is the output of the unmodeled dynamic incremental compensation controller at the discrete αk+i moment of the operating control layer;

[0037] Expanding the above formula, we can get:

[0038]

[0039] In the formula

[0040]

[0041]

[0042] Solving the optimization problem of equation (9) and performing dynamic and static compensation for the unmodeled dynamics at the previous moment, the following multi-step predictive compensation control law can be obtained:

[0043]

[0044] Where K I0 =[1 0 0 … 0], K II =[1 1 1 … 1] T ;

[0045] Substituting formula (11) into formula (5), we can obtain:

[0046]

[0047] In order to eliminate the influence of unmodeled dynamics on the system, it can be obtained:

[0048]

[0049] Compared with the prior art, this method has the following advantages: for the ethylene cracking furnace outlet temperature control system, a set value optimization control method with state time lag compensation is proposed. On the one hand, this method analyzes and combines the operating data of the cracking furnace outlet temperature control system, regards the implicit dynamic and static information ignored in the controlled object model as unmodeled dynamics, and designs a compensator with state compensation based on the dynamics to increase the control accuracy of the controller, thereby reducing the conservatism in the application of traditional methods. On the other hand, unlike traditional real-time optimization methods, this method uses a robust multi-step predictive compensation control method with time lag compensation when optimizing the set value at the upper level to simultaneously deal with the state time lag and unmodeled dynamic influences, and fully utilizes the system dynamic error information to design the compensator, and finally realizes a nonlinear controller with few restrictions, wide applicability, and low conservatism. While ensuring the overall ethylene benefits, it can give the optimal set value in the current state in real time and enable the controller to effectively track and control.

[0050] Instruction Manual

[0051] Figure 1 This is a simulation diagram of a random noise signal;

[0052] Figure 2 The simulation comparison diagram of the setpoint output tracking response between the proposed method and the traditional real-time optimization method is shown;

[0053] Figure 3 This is a simulation comparison chart of ethylene revenue between the proposed method and the traditional real-time optimization method;

[0054] Figure 4 The simulation comparison diagram of the lower-level loop input response between the proposed method and the traditional real-time optimization method. DETAILED DESCRIPTION

[0055] For further explanation, a detailed description is given below in conjunction with the accompanying drawings and simulation examples.

[0056] Implementation Cases:

[0057] The present invention takes the ethylene cracking furnace outlet temperature control system as the research object to solve this problem. Through repeated tests, the state space model parameters of the ethylene cracking furnace outlet temperature control system are: A(k) = A + Δ a (k), B(k)=B+Δ b (k), C = [0 00 01], [Δ a (k)Δ b (k)] = NΔ(k)[H a H b ],

[0058] Where Δ1, Δ2, Δ3, Δ4, Δ5 are random numbers between [-1 1].

[0059] The estimated values ​​of the model parameters in equation (1) obtained by alternating recursive least squares and neural network identification are:

[0060]

[0061] The benefit coefficient matrix M of the base ethylene benefit performance index of the operation control layer and the positive benefit e =100, the benefit coefficient matrix N of the negative consumption of the base ethylene benefit performance index of the operation control layer e =-0.1, initial test setting value y of lower loop control layer * =850, ethylene benefit performance index ideal performance index r * =1790, the lower loop sampling period T d =1, upper loop sampling period T u =40.

[0062] 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 k = 100s are given here for reference, and the values ​​are as follows:

[0063]

[0064] The present invention simulates the ethylene cracking furnace outlet temperature control system. The simulation adopts the traditional real-time optimization control method and the proposed robust multi-step prediction compensation set value optimization control method with state lag. The set value output tracking response, ethylene revenue simulation control effect and lower loop input response of the proposed method are shown in the figure. Figure 2 , 3 , as shown in Figure 4.

[0065] Depend on Figure 2 and Figure 3 It is known that under the influence of the same external noise, the proposed method can optimize the outlet temperature control set value near its economic optimal state while ensuring the ethylene production revenue. At the same time, the control loop controller ensures the tracking of the controlled object. The traditional real-time optimization control method has several large fluctuations in the process of tracking the set value generated by the upper layer. The occurrence of these situations greatly reduces the controller accuracy of the ethylene cracking furnace outlet temperature.

[0066] Depend on Figure 4 It is known that the input response of the traditional real-time optimization control method fluctuates more than that of the proposed method, and there are several cases where the constraint range is exceeded.

[0067] In summary, the set value optimization control method of the outlet temperature of the ethylene cracking furnace with state lag compensation can be effectively applied to the ethylene production process. Through the analysis of simulation results, this method has a good control effect compared with the traditional real-time optimization control method. Therefore, the set value optimization control method with state lag compensation can better meet the actual control needs, and proposes a new solution for the controller design of industrial control systems with state lag, uncertainty, strong nonlinearity and external interference. It has good application value and application prospects, and is of great significance.

Claims

1. An ethylene cracking furnace outlet temperature setting value optimization control method with state lag compensation, characterized in that: The specific steps are as follows: Step 1: Establish the control loop extended state space model of the ethylene cracking furnace outlet temperature control system; The discrete underlying state space model with state lags, parameter uncertainties, and unmodeled dynamics is established as follows: Where x(k+1) represents the underlying system state at discrete time k+1, u(k) represents the underlying control input at discrete time k, v(k) represents the unmodeled dynamics between the discretized underlying model and the original model at discrete time k, and A(k) = A+Δ a (k) is the underlying state matrix of the system at discrete time k, B(k) = B + Δ b (k) is the underlying input matrix of the discrete k-time system, A d is the underlying state delay matrix of the system, d(k) is the delay step size of the state delay matrix (where d m ≤d(k)≤d M , d m and d M are the upper and lower constraints of the time-delay step length respectively), A is the underlying state matrix to be identified, B is the underlying input matrix to be identified, C is the underlying output matrix, y(k) represents the underlying system output at discrete time k, Δ a (k) is the uncertain perturbation of the underlying state matrix at discrete time k, Δ b (k) is the uncertainty perturbation of the underlying input matrix at discrete time k, satisfying: [Δ a (k) Δ b (k)] = NΔ(k)[H a H b ] (2) where N is the unified matrix of the underlying system uncertainty, H a is the state matrix of the underlying system uncertainty, H b is the input matrix of the underlying system uncertainty, is the uncertain perturbation that depends on the discrete time k, where Δ1, Δ2 are random numbers between [-1, 1]; The output error, error integral term and unmodeled dynamics are introduced into the new state space variables to obtain the new extended control loop state space vector X d (k)=[x(k),v(k-1),E(k),e(k-1)] T , where X d (k) is the state space vector of the loop control layer at time k, e(k-1) is the relationship between the bottom system output y(k-1) and the set value y at time k-11 * (k-1), v(k-1) is the unmodeled dynamics of the underlying system at time k-11, E(k) is the cumulative error of the output error e(k) of the underlying system from time k=0 to time k; the state space equation of the new extended loop control layer established at the same time is as follows: In the formula, is the system state at discrete time k in the loop control layer, is the extended matrix 1 of the loop control layer at discrete k moments about the underlying state, is the extended matrix 2 of the loop control layer with respect to the underlying state, is the expansion matrix 3 of the loop control layer controller with respect to the underlying control law gain, K d1 is the control law gain of the controller at discrete time k in the loop control layer, is the system state delay matrix at discrete time k in the loop control layer, is the system state input matrix of the loop control layer at discrete time k, C d =[C 0 0 0] is the system state output matrix of the loop control layer, is the unmodeled dynamics of the loop control layer at discrete time k, and I is the identity matrix of appropriate dimension; Step 2: Based on the lower-level extended system, design a loop controller with time-delay compensation; The signal compensation robust predictive controller u(k) in the loop control layer is expressed as: In the formula is the control law gain K of the traditional robust predictive controller for time delay compensation at discrete time k d1 The expansion matrix of Step 3: Elevate the control loop to the upper operation optimization layer to expand the state space model; The upper operation control layer uses a larger sampling period T in one cycle. u Sampling, the lower loop control layer uses a smaller sampling period T in one cycle d To sample, where T u =αT d The sampling rate α is a positive integer. At the same time, the system state equation of the upper operation control layer considering the sampling period is established based on the expansion of the lower control loop as follows: In the formula, is the system state matrix of the operation control layer, The system state input matrix for the operation control layer, is the system state matrix of the operation control layer, A u (αk) is the base system state matrix of the operation control layer, B u The base system state input matrix for the operation control layer, is the system status of the operation control layer (where e u (αk) = r * -r(αk) is the performance error of the ethylene revenue performance index, r* is the ideal performance index of the ethylene revenue of the operating layer, and r(αk) is the actual performance index of the ethylene revenue performance index of the operating layer). is the virtual unmodeled dynamics of the operational control layer, D(αk) (where d m -T d <D(αk)<d M -(α-1)T d ) is the extended state lag of the operation control layer, is the benefit coefficient matrix of the positive benefit of the ethylene benefit performance index after the operation control layer is expanded, where M e is the benefit coefficient matrix of the positive benefit of the base ethylene benefit performance index of the operating control layer, N e The benefit coefficient matrix of negative consumption of the basic ethylene benefit performance indicator of the operation control layer; Step 4: Design and run the set-point optimizer for multi-step compensation of optimization layer delay; The setpoint optimizer with state lag compensation at the operational control level can be expressed as: y * (αk)=u u1 (αk)+u u2 (αk) (6) Among them, y * (αk) is the controller output of the running control layer at discrete time αk and is also the set value input of the lower loop control layer. u1 (αk) is the traditional robust predictive controller at discrete time αk of the operating control layer, u u2 (αk) is the unmodeled dynamic multi-step compensation controller at the previous discrete time αk of the operating control layer; First, a traditional robust predictive controller u is designed to operate the control layer. u1 (αk) is as follows: u u1 (αk)=K u1 (αk)X u (αk) (7) In the formula, K u1 (αk) is the control law gain of the traditional robust predictive controller at the discrete time αk of the operating control layer; Secondly, according to the virtual unmodeled dynamic data information of the operation control layer at the previous moment, the unmodeled dynamic multi-step compensator u of the operation control layer is designed. u2 (αk), that is: Among them, K u2 (αk) is the control law gain of the compensation controller at the discrete time αk of the operation control layer, To run the control layer at discrete αk-α moments, the unmodeled dynamics are is the unmodeled dynamic increment of the system at the discrete time αk-α of the operational control layer, e u (αk+α)e=r * -r(αk+α) is the performance error of the ethylene revenue performance index at the discrete time αk+α of the operation control layer, z -1 is the backshift operator, E(z -1 ) is e u (αk) about z -1 The weighted polynomial of ξ(z -1 ) is X u (αk) about z -1 The weighted polynomial of ρ(z -1 )for About z- 1 The weighted polynomial of θ(z -1 )for About z- 1 A weighted polynomial of ; In order to perform dynamic and static multi-step compensation for the unmodeled dynamics of the control layer running at the previous moment, ensure that the controller u u2 (ak) control performance, the following performance indicators are introduced: Where N is the prediction step length, P u (z -1 ) is X u (αk+α) about z -1 The weighted polynomial, Q u (z -1 ) is y * (αk+i) about z- 1 The weighted polynomial of for About z- 1 The weighted polynomial of -1 )=1-z -1 For about z -1 The backshift compensation parameter, u u2' (αk+i) is the output of the unmodeled dynamic incremental compensation controller at the discrete αk+i moment of the operating control layer; Expanding the above formula, we can get: In the formula Solving the optimization problem of equation (10) and performing dynamic and static compensation for the unmodeled dynamics at the previous moment, the following multi-step predictive compensation control law can be obtained: Among them, K I0 =[1 0 0 … 0], K II =[1 1 1 … 1] T ; Substituting formula (11) into formula (5), we can obtain: In order to eliminate the influence of unmodeled dynamics on the system, it can be obtained: By combining the designed robust predictive controller with time-delay compensation and the set value optimizer of the operation control layer, a set value optimization control method with state time-delay compensation is finally formed.

Images