A predictive control method for stratified economic optimization of distillation columns

Abstract

This invention discloses a layered economic optimization predictive control method for distillation columns. The two-layer predictive control strategy of this invention includes an economically self-optimizing steady-state optimization layer and a setpoint tracking dynamic control layer, aiming to simultaneously satisfy economic and control performance objectives. The steady-state optimization layer solves for the optimal objective function of the distillation column's steady-state model under constraints of input and output values ​​such as the distillation column outlet concentration and reflux flow rate, determining the optimal steady-state input and output that maximize economic benefits. The dynamic control layer employs an improved dynamic matrix control algorithm, outputting the optimal manipulated variables to the valve opening or the setpoint of a traditional PID controller, achieving dynamic tracking control of the optimal setpoint, and ultimately completing the multi-objective layered predictive control of the distillation column.

Description

Technical Field

[0001] This invention belongs to the field of process industry optimization control, and specifically relates to a two-level predictive control method based on nonlinear model discretization. Background Technology

[0002] Distillation columns are highly nonlinear chemical production devices and are core equipment in chemical production processes. Their control performance directly impacts production efficiency and product quality. Therefore, many scholars have dedicated themselves to researching control methods for distillation columns. However, due to the complex nonlinearity of the model, a consistent control method has yet to be found.

[0003] While control methods that solely consider the control objective ensure product quality, they neglect economic benefits, which is detrimental to factory production in the long run. Two-level hierarchical control methods, which use a steady-state objective function as a weighted average for each optimization objective function, consider both control objectives and economic benefits, but the priority of each optimization objective function is difficult to guarantee, and there are no established criteria for weight selection. Two-level hierarchical control methods using model linearization suffer from linearization errors, the impact of which is particularly significant for highly nonlinear, real-time control systems like distillation columns. Therefore, this invention, based on the characteristics of distillation column models and addressing the shortcomings of existing distillation column control methods, proposes a hierarchical economic optimization predictive control method for distillation columns. Summary of the Invention

[0004] The purpose of this invention is to propose a layered economic optimization predictive control method for distillation columns, which addresses the characteristics of strong nonlinearity and the need to balance control performance and economic indicators during production. This method can handle the impact of disturbances on the control algorithm, avoid linearizing the model, and ensure the control optimization objective according to priority.

[0005] The objective of this invention is achieved through the following technical solution: a method for predictive control of economic optimization in stratified distillation columns, comprising the following steps:

[0006] (1) Establish a steady-state mathematical model of the distillation column controlled system: collect the initial values ​​of the distillation column outlet concentration, sensitive plate temperature, reflux flow rate, and reboiler heating amount to construct a steady-state mathematical model of the distillation column; (2) Under the constraints of the output and input values ​​such as the distillation column outlet concentration and reflux flow rate, solve the optimal objective function of the distillation column steady-state model to determine the predicted values ​​of the optimal values ​​of outlet concentration, sensitive plate temperature, reflux flow rate, and reboiler heating amount that maximize economic benefits; (3) Dynamic predictive control of the distillation column: finally, based on the control objectives provided by the steady-state optimization layer of the distillation column, determine the dynamic optimization proposition, and use the improved dynamic matrix control algorithm to output the optimal operating variable to the valve opening or the set value of the traditional PID controller to achieve dynamic tracking control of the optimal set point, and finally complete the multi-objective hierarchical predictive control of the distillation column.

[0007] Preferably, the steady-state mathematical model of the distillation column constructed in step 1 is as follows:

[0008] The initial values ​​of the state variables of the distillation column are collected: the distillation column outlet concentration and the temperature of the sensitive plate. The initial values ​​of the input variables are: the reflux flow rate and the reboiler heating amount. These are then substituted into the dynamic model of the distillation column.

[0009]

[0010] The above system satisfies the following constraints at any sampling time:

[0011]

[0012] In the formula, P is the prediction time domain. Let be the state vector of the system. Let be the input vector of the distillation column system. Let y(k) be the output vector of the distillation column system, and e(k) be the error between the measured value y(k) and the predicted value y(k|k-1). min ≤y max ,u min ≤u max These are n-dimensional and m-dimensional vectors, respectively.

[0013] The obtained dynamic model is then transformed into a steady-state mathematical model of the distillation column.

[0014]

[0015] Where ss represents steady state, y ss ,u ss Let Δy represent the steady-state output and input of the distillation column system, respectively. ss (k+1)=y ss (k+1)-y ss (k) is the steady-state output increment of the system, Δu ss (k)=u ss (k)-u ss (k-1) is the steady-state input increment of the system. Since the increment of the disturbance cannot be measured, Δe is used. ss (k)=e ss (k)-e ss (k-1) is used to estimate the steady-state error correction Δe. ss (k). It is the steady-state gain matrix.

[0016] Preferably, the steady-state target calculation of the distillation column in step 2 is specifically as follows:

[0017] (2.1) Real-time optimization of the global nonlinear model of the distillation column is performed to solve for the optimal solution y. * ,u * MinJ = f(y,u)

[0018]

[0019] (2.2) Quadratic programming is used to achieve target tracking of the distillation column, and the solution y is obtained. ss (k+1) and u ss (k)

[0020]

[0021] y * ,u * These are the optimal output and input operation objectives calculated from the real-time optimization layer, respectively, where Q and V are positive definite penalty matrices, and u... min It is the lower bound of the input variable, u max It is the upper limit of the input variable, y min It is the lower bound of the output variable, y max It is the upper limit of the output variable.

[0022] (2.3) Economic optimization: Determine the input variable value u of the distillation column to maximize the economic benefits of the entire plant. ss (k) and output variable value y ss (k+1).

[0023]

[0024] Where J represents the economic optimization objective, c T =[c1,c2,…,c m ] are the parameters of each standardized control variable, and MP is the system's potential maximum economic benefit value.

[0025] Preferably, the input-output constraints in step 2 are as follows:

[0026] Feasibility analysis and soft constraint adjustment adopt a priority strategy, and the order of relaxing constraints is determined based on a weighted strategy.

[0027]

[0028] Where C is the user-defined relaxation weight coefficient corresponding to a soft constraint with priority of 1, and I 1 It is the corresponding identity matrix. By solving the optimization problem, the relaxation magnitude ε of the constraint with priority 1 can be obtained. 1 At the same time, update b to b update =b+ε 1 .

[0029] Preferably, the dynamic optimization proposition algorithm in step 3 specifically includes:

[0030]

[0031] Where P is the prediction time domain, M is the control time domain, and Q, R, S, and T are the weighting coefficients of the relevant terms. ε is a slack variable that ensures the existence of a feasible solution to the objective function. min u max [y] represents the constraints on the input variables. min y max ] represents the soft constraint value of the controlled variable in the system.

[0032] The dynamic matrix control algorithm used in step (3) is as follows:

[0033] Introduce a function similar to the exponential function into In the prediction vector of the feedback correction part shown, the variables of the new function can change with the sampling frequency and can converge in the discrete system. The new error correction matrix is ​​represented as H′=β. n H, where n = 0, 1, ..., N; β ∈ (0, 1), and the new prediction vector is represented as

[0034] In the formula Based on this, a compensation correction parameter s is introduced, and the shift matrix S0 is improved. Then the corrected prediction vector is... :

[0035]

[0036] In the shift matrix In the last row, the last two columns contain non-zero elements, while all other elements are zero; in the other rows, only one element is 1, and all other elements are 0.

[0037] The specific principle for determining the controller parameters of the distillation column using the dynamic matrix control algorithm in step (3) is as follows:

[0038] a. Determine the cutoff length N and sampling period T of the distillation column model;

[0039] b. Determine the control time domain M. For the temperature and liquid level of the sensitive plate, select M = 4 to 8. For the flow rate and pressure, select M = 2 to 4.

[0040] c. Initially determine the error weight matrix Q, control weight matrix R, and feedback correction coefficient H of the distillation column;

[0041] d. Preliminarily determine the prediction time domain P of the distillation column;

[0042] e. Is the performance of the closed-loop system of the distillation column satisfactory at this point?

[0043] f. If not satisfied, return to step c and reset the distillation column controller parameters until satisfied.

[0044] Repeat the above steps continuously to complete the control of multi-objective hierarchical prediction.

[0045] The beneficial effects of this invention are as follows: This invention proposes a stratified economic optimization predictive control method for distillation columns. Compared with traditional methods, this method is more accurate in processing models, has a better suppression effect on disturbances, and can guarantee the optimization objectives according to priorities in steady-state optimization, thus providing a better method for the control and optimization of distillation columns. Attached Figure Description

[0046] Figure 1 Structural diagram of advanced control scheme for C1 in dealcoholization tower

[0047] Figure 2 Schematic diagram of a two-level model predictive control algorithm

[0048] Figure 3 Schematic diagram of the dual-layer optimized control structure of the dealcoholization tower

[0049] Figure 4 A schematic diagram of the dual-layer optimized control structure of the dealcoholization tower ((a) temperature response curve; (b) concentration response curve). Detailed Implementation

[0050] The dealcoholization tower system has two controlled variables and two control variables. The state-space model of the process is as follows:

[0051] δx(k+1)=Aδx(k)+Bδu(k)

[0052] δy(k)=Cδx(k)

[0053] Where, δy=[y1 y2] T Let δu = [u1u2] be the temperature of the sensitive plate in the distillation column and the concentration of methanol in the bottom product, respectively. T To measure the reflux flow rate and reboiler heating amount, a sampling period of 36 seconds was used. Considering system constraints on input and output variables, dynamic matrix control and two-layer predictive control were used to simulate the distillation process of the dealcoholization column, and the control effects under the two control strategies were compared. The upper and lower limit constraints of the controlled variables were set as follows: the sensitive plate temperature range of the dealcoholization column was 75-80℃, and the soft constraint range was 75.5-79.5℃; the methanol composition range of the bottom product of the dealcoholization column was 4%-10%, and the soft constraint range was 4.2%-9.5%.

[0054] Therefore, based on the effectiveness of the traditional control loop, an advanced control scheme is designed. The traditional control scheme for the dealcoholization tower C1 is as follows: upstream material enters the dealcoholization tower C1 through the feed valve; the condenser pressure is controlled by adjusting the condenser load within the dealcoholization tower C1; the condenser level is controlled by the flow rate of the liquid distillate at the top of the tower; the reboiler level is controlled by adjusting the flow rate of the product at the bottom of the tower; and the temperature of the sensitive plate (19th plate) is controlled by adjusting the heat input to the reboiler. The advanced control strategy, however, controls the key control variables of the system, namely the methanol concentration at the bottom of tower C1 and the temperature of the 19th sensitive plate of the distillation tower, as the controlled variables, and uses the reflux flow rate at the top of the tower and the heating amount of the reboiler as manipulated variables. The advanced control scheme diagram for the dealcoholization tower C1 is shown below. Figure 1 As shown.

[0055] In the design of the dynamic matrix control loop for the C1 column in the ethylene glycol distillation process, the initial setpoint for the methanol concentration at the C1 outlet was 0.0583, and the initial setpoint for the temperature of the nineteenth sensitive plate was 77.65℃.

[0056] After tuning, the main parameters of the dynamic matrix controller are selected as follows: sampling period T is 36s, model cutoff length N is 2000, prediction time domain P is 14, control time domain M is 3, error weight matrix Q is 1.5×E, control weight matrix R is E, β=0.6, s=0.57.

[0057] Multivariable dynamic matrix control can ensure product quality and process stability, but in actual production, the energy consumption of distillation columns is extremely demanding. To reduce energy consumption while ensuring that the distillation column reboiler temperature (temperature of the nineteenth sensitive plate) and the concentration of the product components meet the set requirements, a proposed multivariable two-layer predictive model predictive control strategy is used to achieve these requirements. The reboiler temperature is a crucial indicator for verifying the quality of the product, and it is closely related to the circulating water flow rate and the reboiler heating load. The controller prioritizes controlling the reboiler temperature and product component concentration, with minimizing energy consumption as the second priority control objective, focusing primarily on controlling these two parameters. The two-layer predictive control strategy includes an economically self-optimizing steady-state optimization layer and a setpoint-tracking dynamic control layer, aiming to simultaneously meet both economic and performance control objectives.

[0058] In optimizing energy consumption during the distillation process of a dealcoholization column, ensuring that the column temperature and the methanol content in the top and bottom feeds are within the soft constraint range is the primary objective. Under this premise, the reflux flow rate and reboiler heating amount are optimized. To achieve this goal, a two-layer control strategy can be adopted. The upper steady-state optimization layer optimizes economic indicators, while the lower control layer implements dynamic performance control. In the upper steady-state optimization layer, a quadratic programming function is used to solve for the constrained economic indicator optimization function. By solving the economic optimization problem, the steady-state objectives of the controlled variable and the manipulated variable are obtained as setpoints. In the lower control layer, a dynamic matrix control algorithm is used to achieve dynamic performance control. Figure 2 and Figure 3 The diagrams show a two-layer model predictive control algorithm and a two-layer optimized control structure for the dehydrogenation tower. The setpoints of the sensitive plate temperature and reflux flow rate in the real-time optimization layer are updated to the dynamic matrix control algorithm in the lower layer to achieve dynamic control of the reflux flow rate and reboiler heating.

[0059] In summary, the two-tiered predictive control method for DMC based on LP economic indicators can be expressed as follows:

[0060]

[0061] Where k is the system sampling time, P is the prediction time domain, M is the control time domain, and Q, R, S, T, V, W are the weighting coefficients of the relevant terms. min u max ,[Δu min Δu max []] represents the input variables and their constraints, [y min y max ] represents the soft constraint value of the controlled variable of the system, [y MIN ,y MAX ] represents the hard constraint value of the controlled variable in the system, ε is the soft constraint slack variable of the output variable, and A ss It is the steady-state gain model of the system.

[0062] The dual-layer predictive control operates at the same frequency, avoiding steady-state errors. This dual-layer control strategy balances economic efficiency and dynamic performance, achieving energy consumption optimization of the dealcoholization column within a safe and stable range. Random feed disturbances were added to test the system's control performance in the face of unknown disturbances. Figure 4 (a) shows the temperature response curve under random feed disturbance. It can be seen that when the system faces random feed disturbance, the temperature change of the sensitive plate in the dealcoholization tower is small under both control strategies and is controlled within an acceptable range. Figure 4(b) shows the control response of methanol concentration in the product of the dealcoholization tower. It can be seen that under both control strategies, the change in methanol concentration in the product of the tower bottom is small and is controlled within a certain range.

Claims

1. A distillation column layered economic optimization predictive control method, characterized by the following steps: (1) Establishing a distillation column steady-state optimization layer: collecting initial values of distillation column outlet concentration, sensitive plate temperature, reflux flow, and reboiler heating capacity to construct a distillation column steady-state mathematical model; (2) Steady-state target solving: solving the optimal objective function of the distillation column steady-state mathematical model under the constraints of output and input values including distillation column outlet concentration and reflux flow to determine the predicted values of the optimal values of outlet concentration, sensitive plate temperature, reflux flow, and reboiler heating capacity that maximize economic benefits; the specific process of distillation column steady-state target solving in step (2) is: (2.1) Real-time optimization of the global object nonlinear model of the distillation column, solving the optimal solution y * * ​ Min J = f(y, u) The optimal solution to the above problem is: y = y * u = u * , J real-time optimization target, g1 stability constraint, g2 feasibility constraint; (2.2) Target tracking for the distillation column is achieved by using quadratic programming to solve y ss (k+1) and u ss (k) determining an input variable u ss and an output variable y ss a prediction of the input variable u ss (k) and the output variable y ss (k+1) at time instant k+1 from the input variable u y * ,u * are the optimal output and input operation targets calculated from the real-time optimization layer, respectively, Q, V are positive definite penalty matrices, u min is the lower bound of the input variable, u max is the upper bound of the input variable, y min is the lower bound of the output variable, y max is the upper bound of the output variable; (2.3) Economic optimization, determining the optimal input variable values u of the rectifying column for maximizing the economic benefit of the whole plant ss (k) and optimal output variable values y ss (k+1): wherein J represents an economic optimization goal, c T = [c1, c2, …, c m ] is a parameter of each control variable after standardization, and MP is a potential maximum economic benefit value of the system. The soft constraint strategy in the constraints of input and output in step (2) is: Using a priority strategy, the order of relaxing the constraints is determined based on the weighting strategy: where C is a relaxation weight coefficient of the soft constraint user with priority 1, I 1 is a corresponding identity matrix, and the relaxation amplitude ε of the constraint with priority 1 can be obtained by solving the optimization problem 1 , and b is updated as b update = b + ε 1 ; (3) Dynamic predictive control of the distillation column dynamic control layer: finally determining the dynamic optimization proposition based on the control target provided by the distillation column steady-state optimization layer, using a control algorithm to output the optimal operating variable to the opening of the valve or the set value of the traditional PID controller, realizing dynamic tracking control of the optimal set point, and finally completing the multi-objective layered prediction control of the distillation column.

2. The method of claim 1, wherein In step (1), the distillation column steady-state mathematical model is constructed, specifically: (1.1) Collecting initial values of distillation column state variables: distillation column outlet concentration, sensitive plate temperature, and input variable initial values: reflux flow, reboiler heating capacity, and substituting them into the distillation column dynamic model: The above system satisfies the following constraints at any sampling time: where A represents a state matrix of the distillation column system, B represents a control matrix of the distillation column system, C represents an output matrix of the distillation column system, P is a prediction horizon, is a state vector of the system, is an input vector of the distillation column system, is an output vector of the distillation column system, respectively represent real number vectors of p dimensions, m dimensions, and n dimensions, y(k|k-1) represents an output prediction value at time K for time K-1, e(k) is an error between a measured value y(k) and a predicted value y(k|k-1), y min ≤y max ,u min ≤u max are n-dimensional and m-dimensional vectors, respectively; (1.2) The obtained dynamic model is converted into a steady-state mathematical model of the distillation column: where ss represents the steady state, y ss , ss represent the steady state output and input of the distillation column system, respectively, Δy ss (k+1) = y ss (k+1) - y ss (k) is the steady state output increment of the system, Δu ss (k) = u ss (k) - u ss (k-1) is the steady state input increment of the system, since the increment of the disturbance cannot be measured, the estimated steady state error correction Δe ss (k) = e ss (k) - e ss (k-1) is used to estimate the steady state error correction Δe ss (k); is the steady state gain matrix.

3. The method of claim 1, wherein The dynamic optimization proposition in step (3) is: where Δu M(k) J(k) denotes a dynamic optimization proposition, P is a prediction horizon, M is a control horizon, Q, R, S, T are weight coefficients of related terms respectively; ε is a relaxation variable to ensure the existence of feasible solutions of the optimization objective function; [u min u max ] is a constraint condition of the input variable, [y min y max ] represents a soft constraint value of the controlled variable of the system, w(k) is a set value vector, represents a prediction value of the output under the action of M-step control input at P future time points, is an initial prediction value vector, A is a step response test coefficient matrix, Δu M (k), Δu M (k+i) represent the increments of the input variable at k and k+i time points respectively, represents the output variable at k+j time point, u set represents the set value of the input variable, u M (k) represents the prediction value of the input under the action of M-step control output.

4. The method of claim 1, wherein The dynamic matrix control algorithm in step (3) is: A function similar to the exponential function is introduced into the prediction vector of the feedback correction part shown in ; the variable of the new function can vary with the sampling frequency and convergence can be achieved in a discrete system, and the new error correction matrix is represented as H' = β n H, where n = 0, 1, …, N; β ∈ (0, 1), and the new prediction vector is represented as On the basis of the formula a compensation correction parameter s is introduced to improve the shift matrix S0, and the corrected prediction vector In shift array In the last row, the last two columns have non-zero elements, and all other elements are zero; in the other rows, only one element is 1, and all other elements are 0.

5. The method of claim 4, wherein The controller parameter determination principle of the distillation column using the dynamic matrix control algorithm in step (3) is: a. Determine the distillation column model truncation length N and the sampling period T; b. Determine the control time domain M, the sensitive plate temperature, and the control time domain of the liquid level, select M = 4-8, and the control time domain of the flow and pressure, select M = 2-4; c. Preliminarily determine the distillation column error weight matrix Q, the control weight matrix R, and the feedback correction coefficient H; d. Preliminarily determine the distillation column prediction time domain P; e. Is the performance of the distillation column closed-loop system satisfactory at this time? f. If not, return to step c to re-determine the distillation column controller parameters until satisfactory.

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