Ethylene cracking process robust prediction cascade control method based on time delay and unmodeled dynamic multi-step compensation

Abstract

An ethylene cracking process robust prediction cascade control method based on time lag and unmodeled dynamic multi-step compensation belongs to the field of industrial process advanced control, and comprises the following steps: step 1, establishing an incremental state space model considering unmodeled dynamics and uncertainty in an inner ring ethylene cracking process; 2, designing an inner loop robust prediction controller and an inner loop unmodeled dynamic one-step optimal compensator; 3, designing an inner ring unmodeled dynamic increment comprehensive compensation controller; 4, establishing an incremental state space model considering unmodeled dynamics, a time delay process and uncertainty in the outer ring ethylene cracking process; 5, designing an outer ring robust time-delay prediction controller and an outer ring unmodeled dynamic multi-step time-delay compensation controller; step 6, designing an outer ring unmodeled dynamic increment multi-step time delay compensation controller; the invention provides a brand new scheme for the design of an ethylene cracking process controller, so that the system has smaller output error and stronger anti-time-lag capability.

Description

Technical Field

[0001] The invention belongs to the field of advanced industrial process control and relates to a robust predictive cascade control method for an ethylene cracking process based on time lag and unmodeled dynamic multi-step compensation. Background Art

[0002] In the modern industrial field, the ethylene cracking process is the core link of the petrochemical industry. Its product ethylene is widely used in many key fields such as plastics, synthetic rubber, and synthetic fibers. The output and quality of ethylene are of far-reaching significance to the petrochemical industry and even the national economic development. However, the ethylene cracking process is affected by many factors, and the synergy between various links is complex and changeable, which brings many obstacles to the precise control of its outlet temperature.

[0003] On the one hand, there is a significant time lag in the ethylene cracking process. The material is transported in the huge and complex cracking unit pipeline with a time lag process, and there are inherent delays in the heat transfer and chemical reaction process, resulting in a time difference from the adjustment of the control variable to the outlet temperature response. For example, when adjusting the fuel gas flow to change the temperature in the furnace, the heat needs to be conducted, convected and chemically reacted before affecting the outlet temperature. There is a significant time lag in the process, and traditional control methods are difficult to compensate for this time lag in time, which can easily cause control lag and overshoot, and even affect product quality.

[0004] On the other hand, the ethylene cracking process is affected by many factors such as raw material quality fluctuations, equipment coking and fouling, and external temperature changes. There are a large number of parts that are difficult to accurately model, that is, unmodeled dynamics. When facing these complex situations, traditional control methods often find it difficult to simultaneously ensure good control performance and robustness. The cascade control structure has been widely used in industrial processes because it can effectively handle the main disturbances in the system and improve control accuracy. Cascade control sets up two control loops, the main and the auxiliary loop. The auxiliary loop can quickly suppress the secondary disturbances that affect the main variable and can respond to the disturbance in a shorter time. The main loop gives the control input to the auxiliary loop, and receives the control signal from the auxiliary loop to the main controlled object. The main loop can effectively suppress the main interference factors in the production process to ensure product quality and production safety. However, in the presence of time lag and unmodeled dynamics, the performance of the traditional cascade control method will be seriously affected. Time lag may cause the control action to fail to act on the controlled object in time, causing problems such as increased overshoot and longer adjustment time. Unmodeled dynamics may deteriorate the stability of the control system and even cause system instability.

[0005] Therefore, the design of a precise and efficient controller for the ethylene cracking process has become a key problem that the petrochemical industry needs to overcome urgently. It is urgent to develop advanced control methods that fit the characteristics of the process and resist time lag and unmodeled dynamic interference. This is of great significance to enhancing the competitiveness of the petrochemical industry and promoting industrial upgrading. Summary of the invention

[0006] In order to solve the above technical problems, this patent proposes a robust predictive cascade control method for the ethylene cracking process based on time lag and unmodeled dynamic multi-step compensation to reduce the output fluctuation of the outlet temperature of the ethylene cracking process and improve the control accuracy. This patent establishes the inner loop fuel gas flow and valve opening model and the outer loop outlet temperature and fuel gas flow model as a composite state space model of linear model plus unmodeled dynamics. In the inner loop, the robust model prediction method and the one-step optimal compensation strategy are combined to facilitate rapid compensation and reduce the output fluctuation of the inner loop. For the outer loop, the robust predictive controller considering time lag and the multi-step predictive compensation strategy considering time lag are combined to effectively reduce the fluctuation of the inner loop set value while improving the control accuracy of the outlet temperature of the ethylene cracking process.

[0007] In order to make the controller better applied in practice, when designing the controller, it is necessary to consider the different characteristics of the inner and outer loops of the cascade system and the uncertainty, strong nonlinearity and time-delay process in the system. This method studies these problems. According to the mathematical model of the inner loop fuel gas flow and valve opening, an inner loop incremental state space model considering unmodeled dynamics and uncertainties is established, and an inner loop robust predictive controller and an inner loop unmodeled dynamic one-step optimal compensator, as well as an inner loop unmodeled dynamic incremental comprehensive compensation controller are designed. According to the mathematical model of the outer loop outlet temperature and fuel gas flow, an outer loop incremental state space model considering unmodeled dynamics, time-delay processes and uncertainties is established, and an outer loop robust time-delay predictive controller and an outer loop unmodeled dynamic multi-step time-delay compensation controller, as well as an outer loop unmodeled dynamic incremental multi-step time-delay compensation controller are designed.

[0008] The specific steps include:

[0009] Step 1: Establish an incremental state-space model of the endocyclic ethylene cracking process considering unmodeled dynamics and uncertainties;

[0010] The output and tracking errors are introduced into the state space model, and the incremental state space model of the inner ring fuel gas flow and valve opening is established:

[0011]

[0012] In the formula, x 21 (k) = y 2 (k), x 22 (k) = e 2 (k), e 2 (k) = y r2 -y 2 (k) represents the tracking error of the inner loop at time k, y 2 (k) is the output variable, which represents the system output at time k in the inner loop, x21 (k+1)=y 2 (k+1), x 22 (k+1)=e 2 (k+1), e 2 (k+1)=y r2 -y 2 (k+1), represents the tracking error of the outer loop at time k+1, y 2 (k+1) is the output variable, which represents the system output at time k+1 of the outer loop, y r2 is a constant, representing the setting value of the inner loop system, Δx 2 (k+1)=x 2 (k+1)-x 2 (k) is the state variable, which represents the system state increment at time k+1 in the inner loop, x 2 (k), x 2 (k+1) is the system state at time k and time k+1 of the inner loop, Δx 2 (k) = x 2 (k)-x 2 (k-1) is the state variable, which represents the system state increment at time k in the inner loop, x 2 (k-1) is the system state at time k-1 of the inner loop, Δu 2 (k) = u 2 (k)-u 2 (k-1) is the input variable, which represents the system input increment at time k in the inner loop, u 2 (k) and u 2 (k-1) is the system input at time k and time k-1 of the inner loop, Δy 2 (k) = y 2 (k)-y 2 (k-1) is the output variable, which represents the system output increment at time k in the inner loop, y 2 (k), y 2 (k-1) is the system output at time k and time k-1 of the inner loop, is a high-order nonlinear function, representing the unmodeled dynamic increment of the inner loop at time k, Δv 2 (k) = v 2 (k)-v 2 (k-1), v 2 (k), v 2 (k-1) is the unmodeled dynamics of the inner loop at time k and time k-1, A 2 (k) = A 2 +Δ a2 (k), represents the state matrix of the inner loop at time k. From the system description of uncertainty, we know that Δ a2 (k) satisfies Δ a2 (k) = N2 Δ(k)H 2 , N 2 , H 2 is the inner loop system model constant matrix of appropriate dimension, is the parameter uncertainty disturbance of the inner loop system at time k, where Δ 1 , Δ 2 is a random number between [-1,1], A 2 , B 2 , C 2 is the inner loop system model constant matrix of appropriate dimension;

[0013] Step 2: Design the inner loop robust predictive controller and the inner loop unmodeled dynamic one-step optimal compensator;

[0014] The inner loop of this design integrates the advantages of feedback, feedforward, data-driven control and robust predictive control into the design of the inner loop controller. The proposed inner loop controller can be expressed as:

[0015]

[0016] In the formula, Δu 21 (k) is a conventional incremental robust predictive controller, Δu 22 (k) is a conventional incremental unmodeled dynamic one-step optimal compensation controller, Δu 23 (k) is an incremental unmodeled dynamic incremental comprehensive compensation controller;

[0017] Inner loop conventional incremental robust predictive controller Δu 21 (k), the design method is as follows:

[0018] Δu 21 (k) = K 21 (k)Δx 2 (k) (3)

[0019] In the formula, K 21 (k) = Y 2 L 2 -1 is the control law gain of the conventional incremental robust predictive controller at time k in the inner loop, is the unknown positive definite matrix that needs to be solved by linear matrix inequality, which can be obtained by solving linear matrix inequality;

[0020] Using the data information of the virtual unmodeled dynamics of the inner loop at the previous moment, a conventional incremental unmodeled dynamic one-step optimal compensation controller for the inner loop is designed:

[0021]

[0022] In the formula, K 22(k) is the control law gain of the conventional incremental one-step optimal compensation controller at time k in the inner loop, is a high-order nonlinear function, representing the unmodeled dynamic increment of the inner loop at time k-1, v 2 (k-1), v 2 (k-2) is the unmodeled dynamics of the inner loop at time k-1 and time k-2;

[0023] Step 3: Design the inner loop unmodeled dynamic incremental comprehensive compensation controller;

[0024] In order to reduce the inner loop input fluctuation and speed up the convergence speed, the following comprehensive compensation performance indicators are designed:

[0025] J 1 =||e 2 (k+1)|| 2 +||λ 1 Δu 23 (k)|| 2 +||λ 2 Δx 2 (k+1)|| 2 (5)

[0026] In the formula, Δu 23 (k) is the inner loop incremental unmodeled dynamic incremental comprehensive compensation controller, λ 1 , 2 are constants, representing the input weight coefficient and the state weight coefficient respectively;

[0027] Assume that J in formula (5) 1 For Δu 23 The partial derivative of (k) is zero, that is:

[0028]

[0029] In the formula, For J 1 For Δu 23 The partial derivative of (k), Indicates e 2 (k+1) for Δu 23 The partial derivative of (k), express For Δu 23 Partial derivatives of (k);

[0030] It can be obtained that the inner loop unmodeled dynamic incremental comprehensive compensation controller is:

[0031]

[0032] In the formula, Δe 2 (k) = e 2 (k)-e2 (k-1) is the tracking error increment at time k in the inner loop, e 2 (k), e 2 (k-1) is the tracking error at time k and time k-1 of the inner loop, is the lumped unmodeled dynamics of the inner loop at time k, is the unmodeled dynamic increment at time k and time k-1 of the inner loop;

[0033] Step 4: Establish an incremental state-space model of the exocyclic ethylene cracking process considering unmodeled dynamics, time-delay processes, and uncertainties;

[0034] The output and tracking errors are introduced into the state space model to obtain the incremental state space model of the outer ring outlet temperature and fuel gas flow rate:

[0035]

[0036] In the formula, x 11 (T) = y 1 (T), x 12 (T) = e 1 (T), e 1 (T) = y r1 -y 1 (T) is the tracking error of the outer loop at time T, y 1 (T) is the output variable, which represents the system output x at time T of the outer loop 11 (T+1)=y 1 (T+1), x 12 (T+1)=e 1 (T+1), e 1 (T+1)=y r1 -y 1 (T+1), represents the tracking error of the outer loop at time T+1, y 1 (T+1) is the output variable, which represents the system output of the outer loop at time T+1, y r1 is a constant, representing the setting value of the outer loop system, Δx 1 (T+1)=x 1 (T+1)-x 1 (T) is the state variable, which represents the system state increment at time T+1 of the outer loop, x 1 (T), x 1 (T+1) is the system state of the outer loop at time T and time T+1, Δx 1 (T) = x 1 (T)-x 1 (T-1) is the state variable, which represents the system state increment at time T in the outer loop, x 1 (T), x 1(T-1) is the system state at time T and time T-1 of the outer loop, Δx 1 (Td 1 (T)) = x 1 (Td 1 (T))-x 1 (Td 1 (T-1)-1) represents the time-delay state increment of the outer loop at time T, x 1 (Td 1 (T))、x 1 (Td 1 (T-1)-1) is the system lag state at time T and time T-1 of the outer loop, d 1 (T) is an appropriate constant representing the time-varying delay step size, Δu 1 (T) = u 1 (T)-u 1 (T-1) is the input variable, which represents the system input increment at time T of the outer loop, u 1 (T),u 1 (T-1) is the system input at time T and time T-1 of the outer loop, Δy 1 (T) = y 1 (T)-y 1 (T-1) is the output variable, which represents the output increment of the system at time T of the outer loop, y 1 (T), y 1 (T-1) is the system output of the outer loop at time T and time T-1, is a high-order nonlinear function, representing the unmodeled dynamic increment of the outer loop at time T, Δv 1 (T) = v 1 (T)-v 1 (T-1), v 1 (T), v 1 (T-1) is the unmodeled dynamics of the outer loop at time T and time T+1, A 1 (T) = A 1 +Δ a1 (T), represents the state matrix of the outer loop at time T. From the system description of uncertainty, we know that Δ a1 (T) satisfies Δ a1 (T) = N 1 Δ(T)H 1 , N 1 , H 1 is the outer loop system model constant matrix of appropriate dimension, is the parameter uncertainty disturbance of the outer loop system at time T, where Δ 1 , Δ 2 is a random number between [-1,1], A 1 , B 1 , C1 is the constant matrix of the outer loop system model with appropriate dimension, A d1 is a constant matrix of appropriate dimension representing the time delay size of the outer loop system;

[0037] Step 5: Design the outer loop robust time-delay predictive controller and the outer loop unmodeled dynamic multi-step time-delay compensation controller;

[0038]

[0039] In the formula, Δu 11 (T) is the conventional incremental robust time-delay predictive controller, Δu 12 (T) is the incremental unmodeled dynamic multi-step time-delay compensation controller, Δu 13 (T) is an incremental unmodeled dynamic incremental multi-step time-delay compensation controller;

[0040] The design method of the outer loop conventional incremental robust time-delay predictive controller is as follows:

[0041] Δu 11 (T) = K 11 (T)Δx 1 (T) (10)

[0042] In the formula, K 11 (T) is the control law gain of the conventional incremental robust time-delay predictive controller of the outer loop at time T, which can be obtained by solving the linear matrix inequality;

[0043] Here, we propose to use the linear matrix inequality (LMI) method to obtain the control law gain K of the robust time-delay predictive controller at time T in the outer loop. 11 (T): If there are known parameters θ 1 >0,0≤d m1 ≤d M1 , the unknown matrix L 1 , S 1 , S 2 、M 3 、M 4 , X 1 , and the unknown parameter ε 1 >0, assuming the following linear matrix inequality holds, the stability of the control system can be guaranteed and the control law gain is given by gives:

[0044]

[0045] In the formula,

[0046]

[0047]

[0048] φ 1 =-L 1 +M 3 +D 1 S 2 +S 2 -X 2 , D 1 =(d M1 -d m1 +1)I,D 2 =(d M1 ) 2 I, I is the identity matrix of appropriate dimension, * represents the transposed element in the symmetric position, Q 1 , R 1 is the parameter matrix Δu of the time-delay robust predictor of appropriate dimension M , Δy M The state increments for the input and output of the outer loop controller;

[0049] Using the data information of the virtual unmodeled dynamics of the outer loop at the previous moment, a multi-step compensation controller of the unmodeled dynamics of the outer loop at the previous moment is designed:

[0050] In order to ensure that the compensator has the ability to evaluate long-term performance, the following multi-step compensation performance indicators are designed:

[0051]

[0052] In the formula, Δx 1 (T+i+1)=x 1 (T+i+1)-x 1 (T+i), is the system state increment at time T+i+1 of the outer loop, x 1 (T+i+1), x 1 (T+i) is the system state at the outer loop time T+i+1 and T+i, Δu 1 (T+i)=u 1 (T+i)-u 1 (T+i-1) is the system input increment at time T+i of the outer loop, u 1 (T+i),u 1 (T+i-1) is the system state of the outer loop at time T+i and time T+i-1, i represents the i-th step length, G is the total predicted step length, z -1 is the backshift operator, P 1 (z -1 ) is Δx 1 (T+i+1) about z -1 The weighted polynomial, Q 1 (z -1 ) is Δu 1 (T+i) about z-1 The weighted polynomial of for About z -1 The weighted polynomial, H 1 (z -1 )=1-z -1 For about z -1 The backshift compensation parameters, is the unmodeled dynamic increment of the outer loop at time T+i-1, u 13 (T+i) is the output of the unmodeled dynamic incremental compensation controller of the outer loop at time T+i;

[0053] Considering the time lag process, the performance index formula (12) is expanded from the first step prediction to the Gth step:

[0054] J 2 =||FΔU+WV+MX 1 +HU 3 +LΔX d || (13)

[0055] In the formula,

[0056]

[0057] K u =[1 0 0 … 0], is the response time control matrix, K v =[1 1 1 … 1] T , is the response compensation matrix, pinv(B 1 ) is B 1 The pseudo-inverse matrix, pinv(K v ) is K v The pseudo-inverse matrix, Δx d (Td(T)) to Δx d (T+Gd(T)) is the time-delay state increment from the outer loop Td(T) to T+Gd(T), d(T) is the time-delay step number, Δu 1 (T) to Δu 1 (T+G) is the system input increment from time T to time T+G of the outer loop. to is the unmodeled dynamics of the outer loop from time T to time T+G, u 13 (T) to u 13 (T+G) is the output of the unmodeled dynamic incremental compensation controller from time T to time T+G of the outer loop, x 1 (T) to x 1 (T+G) is the system status from time T to time T+G of the outer loop;

[0058] Therefore, the control law gain of the outer loop multi-step compensation controller at time T is:

[0059] K 12 (T) = pinv(B 1 )pinv(K v )FK u T (14)

[0060] It is obtained that the outer loop has not modeled the dynamic multi-step time-delay compensation controller at the previous moment:

[0061]

[0062] In the formula, is the unmodeled dynamic increment of the outer loop at time T-1, v 1 (T-1), v 1 (T-2) is the unmodeled dynamics of the outer loop at time T-1 and time T-2,

[0063] Step 6: Design an outer loop unmodeled dynamic incremental multi-step time-delay compensation controller;

[0064] Finally, the outer loop unmodeled dynamic increment multi-step compensation controller is designed by using the outer loop virtual unmodeled dynamic increment information:

[0065] To design the outer loop unmodeled dynamic incremental multi-step compensation controller Δu 13 (T), introduce the following performance indicators:

[0066] J 3 =||e 1 (T+i+1)|| 2 (16)

[0067] Performance indicators are expanded from the first step prediction to the G step:

[0068]

[0069] In the formula,

[0070]

[0071]

[0072] e(T) to e(T+G) is the system output error from time T to time T+G of the outer loop, Δu 13 (T) to Δu 13 (T+G-1) is the output increment of the unmodeled dynamic incremental compensation controller from time T to time T+G-1 of the outer loop, to is the unmodeled dynamic increment of the outer loop from time T to time T+G-1, z -1 is the backshift operator, to is the unmodeled dynamics of the outer loop from time T-1 to time T+G, A 1 (T) to A 1 (T+G-1) is the outer loop state matrix from time T to time (T+G-1);

[0073] It can be obtained that the outer loop is not modeled dynamic incremental multi-step time-delay compensation controller:

[0074]

[0075] In the formula, is the lumped unmodeled dynamics of the outer loop at time T-1, are the unmodeled dynamic increments of the outer loop at time T-1 and time T-2.

[0076] Compared with the prior art, the beneficial effects of this method are as follows: a robust predictive cascade control method for ethylene cracking process based on time lag and unmodeled dynamic multi-step compensation. On the basis of the traditional cascade control method, this method regards the part of the controlled object model that is difficult to accurately model as unmodeled dynamic. In the inner loop, an inner loop robust predictive controller and an inner loop unmodeled dynamic one-step optimal compensator, as well as an inner loop unmodeled dynamic incremental comprehensive compensation controller are designed. Considering the characteristics of the inner loop that require rapid compensation, the inner loop output fluctuation is reduced. For the outer loop, an outer loop robust time lag predictive controller and an outer loop unmodeled dynamic multi-step time lag compensation controller, as well as an outer loop unmodeled dynamic incremental multi-step time lag compensation controller are designed. Considering the time lag characteristics of the outer loop, the designed controller reduces the fluctuation of the outer loop set value after effective time lag compensation, and effectively improves the control accuracy of the outlet temperature of the ethylene cracking process, so that the system has better control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 This is a simulation comparison diagram of the outer loop output response of the method proposed by the present invention and the traditional robust predictive cascade control method;

[0078] Figure 2 This is a simulation comparison diagram of the outer loop input response between the method proposed in the present invention and the traditional robust predictive cascade control method;

[0079] Figure 3 This is a simulation comparison diagram of the outer loop tracking performance between the method proposed in the present invention and the traditional robust predictive cascade control method;

[0080] Figure 4 This is a simulation comparison diagram of the inner loop output response of the method proposed by the present invention and the traditional robust predictive cascade control method;

[0081] Figure 5This is a simulation comparison diagram of the inner loop input response of the method proposed by the present invention and the traditional robust predictive cascade control method;

[0082] Figure 6 This is a simulation comparison diagram of the inner loop tracking performance of the method proposed by the present invention and the traditional robust predictive cascade control method;

[0083] Figure 7 It is a flow chart of the steps of the present invention. DETAILED DESCRIPTION

[0084] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0085] Example:

[0086] Ethylene production is a complex industrial process, which usually has significant nonlinearity, large time lag and model uncertainty, which places extremely high demands on the design of equipment materials and control systems. In addition to the application of advanced hardware equipment, a more important part is to optimize the design of the control system in the ethylene cracking process to improve the control accuracy of the outlet temperature, further increase the output of ethylene and reduce the generation of by-products, so as to maximize the company's profits.

[0087] The present invention conducts research on time-varying time delay and unmodeled dynamic problems of complex industrial control systems. Taking ethylene cracking process as the research object, the traditional robust predictive cascade control method and the robust predictive cascade control method for ethylene cracking process based on time delay and unmodeled dynamic multi-step compensation proposed by the present invention are used for simulation comparison. The comparison images of the outer loop output response, control input, output error, inner loop output response, control input, output error of the two methods are shown in the figure below. Figures 1 to 6 shown.

[0088] According to the mathematical model of fuel gas flow rate and outlet temperature, an outer loop extended state space model with uncertainty, time-varying delay and unmodeled dynamics of the cascade control system of ethylene cracking process is established, and the model parameters are as follows:

[0089]

[0090] In the formula, Δy 1 (T) = y r1 -y 1 (T), y r1 =850 is the outer loop setting value, A(T)=A 1 +Δ a1 (T), Δ a1 (T) = N 1 Δ(T)H 1 , Δ 1, Δ 2 is a random number between [-11], 1<d 1 (T)<5, is a random number between [-1.5 1.5], C 1 =[1 0], the parameters of the incremental robust time-delay predictive controller are: R 1 =0.1;

[0091] The input and output constraints of the system are:

[0092]

[0093] Depend on Figure 1 It can be seen that the outer loop output fluctuation range of the proposed method is smaller. Under the influence of the same noise disturbance signal, the proposed method takes into account the outer loop time lag process and reduces the adverse effects of outer loop time lag and unmodeled dynamics on the system output by designing a multi-step prediction compensator for the unmodeled dynamics.

[0094] Depend on Figure 2 It can be seen that the outer loop control input of the proposed method has smaller fluctuations. The outer loop control input is the inner loop set value. The smaller inner loop set value fluctuation greatly reduces the difficulty of the inner loop system to track the set value, facilitates rapid compensation, and improves the inner loop control accuracy.

[0095] Depend on Figure 3 It can be seen that the outer loop output error of the proposed method is smaller. Under the same conditions, the outer loop tracking error of the comparison method is about 3°C, and the outer loop tracking error of the proposed method can be controlled within 1.5°C. At the same time, through multiple simulation analyses, it is found that if the outer loop time lag has a large range within a small range, the control performance of the comparison method will be greatly reduced. The proposed method designs a controller that takes time lag into account and a multi-step prediction compensator to predict and adjust the system, which can effectively reduce the output fluctuation of the system.

[0096] According to the mathematical model of valve opening and fuel gas flow, the inner loop extended state space model with uncertainty and unmodeled dynamics of the cascade control system of ethylene cracking process is established, and the model parameters are as follows:

[0097]

[0098] In the formula, Δ a2 (k) = N 2 Δ(k)H 2 , Δ 1 , Δ 2 is a random number between [-1 1], is a random number between [-1 1], C 2 =[1 0], the parameters of the incremental robust time-delay predictive controller are: R 2 =0.05,Δy 2 (k) = y r2 -y 2 (k), y r2 It is the inner loop set value, and in the cascade control system it is the control input of the outer loop system;

[0099] The input and output constraints of the system are:

[0100]

[0101] Depend on Figure 4 It can be seen that the inner loop output of the proposed method has a smaller fluctuation range. The proposed method performs multi-time domain compensation for the unmodeled dynamics of the outer loop and takes into account the time lag process of the outer loop. While ensuring a better control effect of the outer loop output, the fluctuation of the outer loop control input is smaller. The outer loop input is used as the set value of the inner loop system. Smaller fluctuations can reduce the tracking difficulty and improve the control accuracy of the inner loop system.

[0102] Depend on Figure 5 It can be seen that the inner loop control input fluctuation of the proposed method is smaller. Under the same interference conditions, the numerical fluctuation and range of the proposed method are smaller, which can effectively reduce the regulating pressure of the inner loop input valve opening and achieve a more stable control effect for the inner loop.

[0103] Depend on Figure 6 It can be seen that the inner loop output error of the proposed method is smaller, the overall error fluctuation of the proposed method is smaller and is all below 5kg / h. When the disturbance is large, the comparison method has exceeded 5kg / h many times. This means that the control effect of the proposed method is better, and the use of fuel gas flow can be reduced on the basis of ensuring the control effect, thereby reducing production costs.

[0104] at last, Figure 1 and Figure 4 It was found that under the outer loop time T and the inner loop time k, the output fluctuation of the proposed method (robust predictive cascade control method for ethylene cracking process based on time lag and unmodeled dynamic multi-step compensation) was significantly smaller than that of the comparison method (traditional robust predictive cascade control method), and the control effect was better.

[0105] In summary, the present invention takes the control of the outlet temperature of the ethylene cracking process as an example to verify the stability and effectiveness of the designed controller. According to the mathematical model of fuel gas flow and outlet temperature, an outer loop extended state space model of the ethylene cracking process cascade control system with uncertainty, time-varying time lag and unmodeled dynamics is established. According to the mathematical model of valve opening and fuel gas flow, an inner loop extended state space model of the ethylene cracking process cascade control system with uncertainty and unmodeled dynamics is established, and the corresponding model parameters and the input and output constraints of the system are determined. According to the characteristics of the inner and outer loops, a robust predictive cascade control method for the ethylene cracking process based on time lag and unmodeled dynamic multi-step compensation is designed. Finally, a comparative simulation is performed using the traditional robust predictive cascade control method and the robust predictive cascade control method for the ethylene cracking process based on time lag and unmodeled dynamic multi-step compensation proposed by the present invention. The results show that the method proposed in the present invention has significant advantages in reducing output fluctuations, reducing output errors, and improving anti-disturbance and anti-time-delay capabilities. It effectively verifies the stability and effectiveness of the designed controller in the ethylene cracking process, and proposes a feasible and efficient control scheme for the controller design of industrial control systems with time lag, uncertainty and strong nonlinearity. It has important reference value and practical application significance in the field of industrial process control.

Claims

1. A robust predictive cascade control method for ethylene cracking process based on time lag and unmodeled dynamic multi-step compensation, characterized in that: The following steps are involved: Step 1: Establish an incremental state-space model of the endocyclic ethylene cracking process considering unmodeled dynamics and uncertainties; The output and tracking errors are introduced into the state space model, and the incremental state space model of the inner ring fuel gas flow and valve opening is established: In the formula, x 21 (k) = y2(k), x 22 (k) = e2(k), e2(k) = y r2 -y2(k) represents the tracking error at time k in the inner loop, y2(k) is the output variable, representing the system output at time k in the inner loop, and x 21 (k+1)=y2(k+1),x 22 (k+1)=e2(k+1), e2(k+1)=y r2 -y2(k+1) represents the tracking error of the outer loop at time k+1, y2(k+1) is the output variable, representing the system output of the outer loop at time k+1, y r2 is a constant, representing the setting value of the inner loop system, Δx2(k+1)=x2(k+1)-x2(k) is a state variable, representing the system state increment at the inner loop k+1 moment, x2(k) and x2(k+1) are the system states of the inner loop at the k and k+1 moments, Δx2(k)=x2(k)-x2(k-1) is a state variable, representing the system state increment at the inner loop k moment, x2(k-1) is the system state of the inner loop at the k-1 moment, Δu2(k)=u2(k)-u2(k-1) is an input variable, representing the system input increment at the inner loop k moment, u2(k) and u2(k-1) are the system inputs at the inner loop k and k-1 moments, Δy2(k)=y2(k)-y2(k-1) is an output variable, representing the system output increment at the inner loop k moment, y2(k) and y2(k-1) are the system outputs at the inner loop k and k-1 moments, is a high-order nonlinear function, representing the unmodeled dynamic increment at the inner loop at time k, Δv2(k)=v2(k)-v2(k-1), v2(k) and v2(k-1) are the unmodeled dynamics at the inner loop at time k and k-1, A2(k)=A2+Δ a2 (k), represents the state matrix of the inner loop at time k. From the system description of uncertainty, we know that Δ a2 (k) satisfies Δ a2 (k) = N2Δ(k)H2, N2, H2 are the inner loop system model constant matrices of appropriate dimensions, is the parameter uncertainty disturbance of the inner loop system at time k, where Δ1 and Δ2 are random numbers between [-1,1], and A2, B2, and C2 are the inner loop system model constant matrices of appropriate dimensions; Step 2: Design the inner loop robust predictive controller and the inner loop unmodeled dynamic one-step optimal compensator; The inner loop of this design integrates the advantages of feedback, feedforward, data-driven control and robust predictive control into the design of the inner loop controller. The proposed inner loop controller can be expressed as: In the formula, Δu 21 (k) is a conventional incremental robust predictive controller, Δu 22 (k) is a conventional incremental unmodeled dynamic one-step optimal compensation controller, Δu 23 (k) is an incremental unmodeled dynamic incremental comprehensive compensation controller; Inner loop conventional incremental robust predictive controller Δu 21 (k), the design method is as follows: Δu 21 (k)=K 21 (k)Δx2(k) (3) In the formula, K 21 (k) is the control law gain of the conventional incremental robust predictive controller at time k in the inner loop, which can be obtained by solving the linear matrix inequality; Using the data information of the virtual unmodeled dynamics of the inner loop at the previous moment, a conventional incremental unmodeled dynamic one-step optimal compensation controller for the inner loop is designed: In the formula, K 22 (k) is the control law gain of the conventional incremental one-step optimal compensation controller at time k in the inner loop, is a high-order nonlinear function, representing the unmodeled dynamic increment at the inner loop k-1, v2(k-1) and v2(k-2) are the unmodeled dynamics at the inner loop k-1 and k-2; Step 3: Design the inner loop unmodeled dynamic incremental comprehensive compensation controller; In order to reduce the inner loop input fluctuation and speed up the convergence speed, the following comprehensive compensation performance indicators are designed: J1=||e2(k+1)|| 2 +||λ1Δu 23 (k)|| 2 +||λ2Δx2(k+1)|| 2 (5) In the formula, Δu 23 (k) is the inner loop incremental unmodeled dynamic incremental comprehensive compensation controller, λ1 and λ2 are constants, representing the input weight coefficient and the state weight coefficient respectively; Assume that J1 in equation (5) is 23 The partial derivative of (k) is zero, that is: In the formula, J1 is the ratio of Δu 23 The partial derivative of (k), Represents the effect of e2(k+1) on Δu 23 The partial derivative of (k), express For Δu 23 Partial derivatives of (k); It can be obtained that the inner loop unmodeled dynamic incremental comprehensive compensation controller is: Where, Δe2(k)=e2(k)-e2(k-1) is the tracking error increment of the inner loop at time k, e2(k) and e2(k-1) are the tracking errors of the inner loop at time k and time k-1. is the lumped unmodeled dynamics of the inner loop at time k, is the unmodeled dynamic increment at time k and time k-1 of the inner loop; Step 4: Establish an incremental state-space model of the exocyclic ethylene cracking process considering unmodeled dynamics, time-delay processes, and uncertainties; The output and tracking errors are introduced into the state space model to obtain the incremental state space model of the outer ring outlet temperature and fuel gas flow rate: In the formula, x 11 (T) = y1(T), x 12 (T) = e1(T), e1(T) = y r1 -y1(T) is the tracking error of the outer loop at time T, y1(T) is the output variable, which represents the system output of the outer loop at time T, and x 11 (T+1)=y1(T+1),x 12 (T+1)=e1(T+1), e1(T+1)=y r1 -y1(T+1) represents the tracking error of the outer loop at time T+1. y1(T+1) is the output variable, which represents the system output of the outer loop at time T+1. r1 is a constant, representing the setting value of the outer loop system, Δx1(T+1)=x1(T+1)-x1(T) is a state variable, representing the system state increment of the outer loop at time T+1, x1(T) and x1(T+1) are the system states of the outer loop at time T and time T+1, Δx1(T)=x1(T)-x1(T-1) is a state variable, representing the system state increment of the outer loop at time T, x1(T) and x1(T-1) are the system states of the outer loop at time T and time T-1, Δx1(T-d1(T))=x1(T-d1(T))-x1(T-d1(T-1)-1) represents the system lag state of the outer loop at time T state increment, x1(T-d1(T)) and x1(T-d1(T-1)-1) are the system lag states at the outer loop at time T and time T-1, d1(T) is an appropriate constant, representing the time-varying lag step size, Δu1(T)=u1(T)-u1(T-1) is the input variable, representing the system input increment at the outer loop at time T, u1(T) and u1(T-1) are the system inputs at the outer loop at time T and time T-1, Δy1(T)=y1(T)-y1(T-1) is the output variable, representing the system output increment at the outer loop at time T, y1(T) and y1(T-1) are the system outputs at the outer loop at time T and time T-1, is a high-order nonlinear function, representing the unmodeled dynamic increment of the outer loop at time T, Δv1(T) = v1(T) - v1(T-1), v1(T) and v1(T-1) are the unmodeled dynamics of the outer loop at time T and time T+1, A1(T) = A1+Δ a1 (T), represents the state matrix of the outer loop at time T. From the system description of uncertainty, we know that Δ a1 (T) satisfies Δ a1 (T) = N1Δ(T)H1, N1, H1 are the constant matrices of the outer loop system model of appropriate dimensions, is the parameter uncertainty disturbance of the outer loop system at time T, where Δ1 and Δ2 are random numbers between [-1, 1], A1, B1, and C1 are the outer loop system model constant matrices of appropriate dimensions, and A d1 is a constant matrix of appropriate dimension representing the time delay size of the outer loop system; Step 5: Design the outer loop robust time-delay predictive controller and the outer loop unmodeled dynamic multi-step time-delay compensation controller; In the formula, Δu 11 (T) is the conventional incremental robust time-delay predictive controller, Δu 12 (T) is the incremental unmodeled dynamic multi-step time-delay compensation controller, Δu 13 (T) is an incremental unmodeled dynamic incremental multi-step time-delay compensation controller; The design method of the outer loop conventional incremental robust time-delay predictive controller is as follows: Δu 11 (T)=K 11 (T)Δx1(T) (10) In the formula, K 11 (T) is the control law gain of the conventional incremental robust time-delay predictive controller of the outer loop at time T, which can be obtained by solving the linear matrix inequality; Using the data information of the virtual unmodeled dynamics of the outer loop at the previous moment, the unmodeled dynamic multi-step compensation controller of the outer loop is designed: In order to ensure that the compensator has the ability to evaluate long-term performance, the following multi-step compensation performance indicators are designed: Wherein, Δx1(T+i+1)=x1(T+i+1)-x1(T+i), is the system state increment at the outer loop T+i+1, x1(T+i+1) and x1(T+i) are the system states at the outer loop T+i+1 and T+i, Δu1(T+i)=u1(T+i)-u1(T+i-1) is the system input increment at the outer loop T+i, u1(T+i) and u1(T+i-1) are the system states at the outer loop T+i and T+i+1, i represents the i-th step length, G is the total prediction step length, z -1 is the backshift operator, P1(z -1 ) is Δx1(T+i+1) about z -1 The weighted polynomial, Q1(z -1 ) is Δu1(T+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 parameters, is the unmodeled dynamic increment of the outer loop at time T+i+1, u 13 (T+i) is the output of the unmodeled dynamic incremental compensation controller of the outer loop at time T+i; The control law gain of the outer loop multi-step compensation controller at time T is: K 12 (T)=pinv(B1)pinv(K v )FK u T (12) In the formula, K u =[1 0 0 … 0], is the response time control matrix, K v =[1 1 1 … 1] T , is the response compensation matrix, pinv(B1) is the pseudo-inverse matrix of B1, pinv(K v ) is K v The pseudo-inverse matrix of The outer loop incremental unmodeled dynamic multi-step time-delay compensation controller is obtained: In the formula, is the unmodeled dynamic increment of the outer loop at time T-1, v1(T-1) and v1(T-2) are the unmodeled dynamics of the outer loop at time T-1 and time T-2; Step 6: Design an outer loop unmodeled dynamic incremental multi-step time-delay compensation controller; Finally, the outer loop incremental unmodeled dynamic incremental multi-step compensation controller is designed by using the outer loop virtual unmodeled dynamic incremental information: In order to design the outer loop incremental unmodeled dynamic incremental multi-step compensation controller, the following performance indicators are introduced: J3=||e1(T+i+1)|| 2 (14) Performance indicators are expanded from the first step prediction to the G step: In the formula, e(T) to e(T+G) is the system output error from time T to time T+G of the outer loop, Δu 13 (T) to Δu 13 (T+G-1) is the output increment of the unmodeled dynamic incremental compensation controller from time T to time T+G-1 of the outer loop, to is the unmodeled dynamic increment of the outer loop from time T to time T+G-1, z -1 is the backshift operator, to is the unmodeled dynamics of the outer loop from time T-1 to time T+G, A1(T) to A1(T+G-1) are the outer loop state matrices from time T to time T+G-1; The outer loop incremental unmodeled dynamic incremental multi-step time-delay compensation controller can be obtained: In the formula, is the lumped unmodeled dynamics of the outer loop at time T-1, are the unmodeled dynamic increments of the outer loop at time T-1 and time T-2.

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