A Nonlinear Predictive Function Control Method for Polyolefin Processes

Abstract

The present invention belongs to the field of industrial automation and discloses a non - linear predictive function control method for polyolefin processes. First, the time constant and lag time of the process model are identified according to the step - response data of the non - linear chemical process collected. Then, the gain is deduced based on the mechanism model formula of the non - linear process. After that, a model predictive controller for the non - linear chemical process is designed. Finally, the obtained precise optimal control law is implemented in the controlled non - linear chemical process. The technical solution of the present invention is to establish a non - linear model predictive control method for chemical processes based on mechanism models through means such as step - response data acquisition of non - linear chemical processes, partial model parameter identification, gain formula derivation, and non - linear model predictive controller design, avoiding the prediction errors caused by model linearization in traditional model predictive control, ultimately achieving precise control of non - linear chemical processes and further enhancing the stability of non - linear chemical process production.

Description

Technical Field

[0001] The present invention belongs to the field of industrial automation, and particularly relates to a non-linear predictive function control method for polyolefin processes. Background Art

[0002] For polyolefin processes in industry, they are divided into dynamic models and steady-state models. For dynamic models, their time constants and lag times can be simply identified through process data, and their steady-state models are generally represented by mechanism models. For these processes, the model gains between process variables calculated from the steady-state model are time-varying in most cases. Therefore, in the application process of predictive function control technology, inaccurate predictions will be caused by the time-varying gain parameters, ultimately affecting the overall control effect of the polyolefin process. If these time-varying gain parameters can be introduced into the predictive function control for accurate prediction derivation, the problem of prediction deviation existing in traditional predictive function control in the polyolefin control process will be fundamentally solved, ultimately promoting the application development of non-linear predictive function control technology in the polyolefin production process. Summary of the Invention

[0003] The purpose of the present invention is to provide a non-linear predictive function control method for polyolefin processes to solve the technical problem that traditional predictive function control cannot effectively solve the prediction deviation caused by time-varying gain parameters in the polyolefin production process.

[0004] To solve the above technical problem, the specific technical solution of a non-linear predictive function control method for polyolefin processes of the present invention is as follows:

[0005] A non-linear predictive function control method for polyolefin processes includes the following steps: Step 1: Collect the step response data of the polyolefin process and fit the dynamic model parameters of the process; Step 1.1: Give a step signal to the input end of the polyolefin process and start recording the corresponding step response data of the polyolefin process;

[0006] Step 1.2: Convert the obtained step response data y a (k) into a dimensionless form y a * (k);

[0007] Step 1.3: Select two points that satisfy y a * (k1) = 0.39 and y a * (k1) = 0.63, and calculate the time constant and lag time of the polyolefin process;

[0008] Step 1.4: List the corresponding mechanism model according to the process mechanism of the specific polyolefin process. This mechanism model is also called the steady-state model, and the real-time gain of the polyolefin process is obtained from this mechanism model; Step 1.5: Finally, obtain the transfer function model of the polyolefin process;

[0009] Step 2: Design a non-linear predictive function controller for the polyolefin process;

[0010] Step 2.1: At the sampling time T s and under the zero-order hold, the transfer function model of the polyolefin process is converted into a discrete equation;

[0011] Step 2.2: Introduce smith prediction to compensate for the time delay in the discrete equation and correct the model without time delay;

[0012] Step 2.3: Select the step function as the basis function of the predictive function control to obtain the process prediction output based on the model without time delay;

[0013] Step 2.4: Select the objective function for the design of the predictive function controller;

[0014] Step 2.5: Transform the prediction output formula;

[0015] Step 2.6: Implement the obtained optimal control law u(k) of the predictive function control on the polyolefin process, and sequentially solve the latest optimal control law in the next sampling period according to the steps in Steps 2.2 to 2.5.

[0016] Furthermore, in Step 1.2, the obtained step response data y a (k) is converted into a dimensionless form y a * (k):

[0017] y a * (k) = y a (k) / y s

[0018] where y s is the steady-state value of y a (k) in the step test.

[0019] Furthermore, in Step 1.3, calculate the time constant and lag time of the polyolefin process according to the following formula:

[0020] T = 2(k2 - k1)

[0021] τ = 2k1 - k2

[0022] where T and τ are the time constant and lag time of the polyolefin process model respectively.

[0023] Furthermore, the specific calculation formula in Step 1.4 is as follows:

[0024] y(k) = f(u(k))

[0025] K(k) = f′(u(k))

[0026] where y(k) is the model output of the polyolefin process, u(k) is the input of the polyolefin process, K(k) is the real-time gain of the polyolefin process, and f and f′ are the mechanism model of the polyolefin process and its corresponding first derivative respectively.

[0027] Furthermore, the transfer function model of the polyolefin process finally obtained in Step 1.5 is

[0028]

[0029] where G(k) and s are the real-time transfer function of the polyolefin process and the Laplace operator respectively.

[0030] Furthermore, the transfer function model of the polyolefin process in Step 2.1 is converted into the following discrete equation:

[0031] y(k) = αy(k - 1) + K(k - 1)(1 - α)u(k - 1 - d)

[0032] where Furthermore, the corrected model without time delay in Step 2.2 is as follows:

[0033] y c (k) = αy c (k - 1) + K(k - 1)(1 - α)u(k - 1)

[0034] where y c (k) is the output of the corrected model without time delay;

[0035] The actual output after correction is

[0036] y ac (k) = y a (k) + y c (k) - y c (k - d)

[0037] where y ac (k) is the corrected actual output.

[0038] Furthermore, the process prediction output based on the model without time delay obtained in Step 2.3 is as follows:

[0039] y c (k + P) = α Py c (k)+K(k)Bu(k)

[0040] where P is the prediction horizon,

[0041]

[0042] Furthermore, the design of the predictive functional controller in step 2.4 selects the following objective function:

[0043]

[0044] where y r (k) is the corresponding reference trajectory point, Q is the weighting matrix of the tracking error, e(k) is the compensated prediction error, and e(k) = y ac (k) - y c (k);

[0045] The reference trajectory generally takes the following formula:

[0046] y r (k + i) = β i y a (k) + (1 - β i )c(k)

[0047] where β is the reference trajectory softening coefficient and c(k) is the corresponding set value.

[0048] Furthermore, in step 2.5, the predictive output formula is transformed to obtain the following form:

[0049] y c (k + P) = α P y c (k) + Bθ(k)

[0050] where θ(k) = K(k)u(k);

[0051] Taking the derivative of the above objective function, the optimal solution is

[0052] θ(k) = ((β i - 1)y a (k) + (1 - β i )c(k) - α P y c (k) + y c (k - d)) / B

[0053] The optimal control law u(k) is obtained by solving the following non-linear univariate equation:

[0054] f′(u(k))u(k) = θ(k).

[0055] A non - linear predictive function control method for a polyolefin process of the present invention has the following advantages:

[0056] Through means such as non - linear chemical process step - response data acquisition, partial model parameter identification, gain formula derivation, and non - linear model predictive controller design, the present invention establishes a non - linear model predictive control method for chemical processes based on mechanism models, avoiding the prediction errors caused by model linearization in traditional model predictive control, and finally achieving precise control of non - linear chemical processes and further improving the stability of non - linear chemical process production. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] None. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] To better understand the purpose, structure, and function of the present invention, a non - linear predictive function control method for a polyolefin process of the present invention will be further described in detail below.

[0059] A non - linear predictive function control method for a polyolefin process of the present invention includes the following specific steps:

[0060] Step 1: Collect the step - response data of the polyolefin process and fit the dynamic model parameters of the process, specifically as follows:

[0061] a. Give a step signal to the input end of the polyolefin process and start recording the corresponding step - response data of the polyolefin process.

[0062] b. Convert the obtained step - response data y a (k) into a dimensionless form y a * (k), and the conversion formula is as follows:

[0063] y a * (k) = y a (k) / y s

[0064] where y s is the steady - state value of y a (k) in the step test.

[0065] c. Select two points that satisfy y a * (k1)=0.39 and y a * (k1)=0.63, and calculate the time constant and lag time of the polyolefin process according to the following formula.

[0066] T = 2(k2 - k1)

[0067] τ = 2k1 - k2

[0068] Among them, T and τ are the time constant and the lag time of the polyolefin process model, respectively.

[0069] d. List the corresponding mechanism model according to the process mechanism of the specific polyolefin process. This mechanism model is also called the steady-state model. The real-time gain of the polyolefin process needs to be obtained from this mechanism model. The specific calculation formula is as follows:

[0070] y(k) = f(u(k))

[0071] K(k) = f′(u(k))

[0072] Among them, y(k) is the model output of the polyolefin process, u(k) is the input of the polyolefin process, K(k) is the real-time gain of the polyolefin process, and f and f′ are the mechanism model of the polyolefin process and the corresponding first derivative, respectively.

[0073] e. The finally obtained transfer function model of the polyolefin process is

[0074]

[0075] Among them, G(k) and s are the real-time transfer function of the polyolefin process and the Laplace operator, respectively.

[0076] Step (2). Design a non-linear predictive function controller for the polyolefin process. The specific steps are as follows:

[0077] a. At the sampling time T s and under the zero-order hold, the transfer function model of the polyolefin process can be converted into the following discrete equation:

[0078] y(k) = αy(k - 1) + K(k - 1)(1 - α)u(k - 1 - d)

[0079] Among them,

[0080] b. Introduce the smith predictor to compensate for the time delay in the discrete equation. The corrected model without time delay is as follows:

[0081] y c (k) = αy c (k - 1) + K(k - 1)(1 - α)u(k - 1)

[0082] Among them, y c (k) is the output of the corrected model without time delay.

[0083] Furthermore, the actual output after correction is

[0084] y ac (k) = ya (k) + y c (k) - y c (k - d)

[0085] where y ac (k) is the corrected actual output.

[0086] c. Here, the basis function of the predictive function control is selected as the step function, and the process prediction output based on the non-delay model can be obtained as follows:

[0087] y c (k + P) = α P y c (k) + K(k)Bu(k)

[0088] where P is the prediction horizon,

[0089]

[0090] d. The design of the predictive function controller selects the following objective function

[0091]

[0092] where y r (k) is the corresponding reference trajectory point, Q is the weighting matrix of the tracking error, e(k) is the compensated prediction error, and e(k) = y ac (k) - y c (k).

[0093] The reference trajectory generally takes the following formula:

[0094] y r (k + i) = β i y a (k) + (1 - β i )c(k)

[0095] where β is the reference trajectory softening coefficient and c(k) is the corresponding set value.

[0096] e. Transforming the prediction output formula, the following form can be obtained:

[0097] y c (k + P) = α P y c (k) + Bθ(k)

[0098] where θ(k) = K(k)u(k).

[0099] Taking the derivative of the above objective function, the optimal solution is

[0100] θ(k) = ((β i - 1)ya (k)+(1-β i )c(k)-α P y c (k)+y c (k - d)) / B

[0101] Furthermore, the optimal control law u(k) can be obtained by solving the following non - linear univariate equation.

[0102] f′(u(k))u(k) = θ(k)

[0103] f. Implement the obtained optimal control law u(k) of predictive functional control in the polyolefin process, and solve the latest optimal control law in sequence according to the steps in (b) - (e) in the next sampling period.

[0104] The present invention proposes a non - linear predictive functional control method for polyolefin processes. In this method, precise derivation is carried out by combining time - varying gain parameters, avoiding the prediction errors caused by linearization in traditional methods, ultimately improving the control accuracy of polyolefin processes, and also making further preparations for the application and development of non - linear predictive functional control.

[0105] Example:

[0106] Taking the ethylene content control in the ethylene - propylene copolymerization production process as an example, where the controlled variable is the ethylene content and the adjustment means is the ethylene concentration.

[0107] Step 2: Collect the step - response data of the ethylene content control loop and fit the dynamic model parameters of the ethylene content control process, specifically as follows:

[0108] (a) Add a step signal to the ethylene concentration in the ethylene content control loop and start recording the step - response data corresponding to the ethylene content.

[0109] (b) Convert the obtained step - response data y a (k) of the ethylene content into the corresponding dimensionless form y a * (k), and the conversion formula is as follows:

[0110] y a * (k) = y a (k) / y s

[0111] where y s is the steady - state value of the ethylene content y a (k) in the step test.

[0112] (c) Select those that satisfy y a *(k1) = 0.39 and y a * For two points where (k1) = 0.39 and (k1) = 0.63, calculate the time constant and dead time of the ethylene content control loop according to the following formula.

[0113] T = 2(k2 - k1)

[0114] τ = 2k1 - k2

[0115] Where T and τ are the time constant and dead time of the ethylene content control loop respectively.

[0116] (d) List the mechanism model for ethylene content control based on the process mechanism of the specific ethylene - propylene copolymerization production process. This mechanism model is also called the steady - state model. The real - time gain of the ethylene content control process needs to be obtained from this mechanism model. The specific calculation formula is as follows:

[0117] y(k) = f(u(k))

[0118] K(k) = f′(u(k))

[0119] Where y(k) is the model output of ethylene content, u(k) is the ethylene concentration, K(k) is the real - time gain of the ethylene content control process, and f, f′ are the mechanism model of the ethylene content control process and its corresponding first - order derivative respectively.

[0120] (e) The transfer function model of the finally obtained ethylene content control process is

[0121]

[0122] Where G(k) and s are the real - time transfer function of the ethylene content control process and the Laplace operator respectively.

[0123] Step (2). Design a non - linear predictive function controller for the ethylene content control process. The specific steps are as follows:

[0124] (a) At the sampling time T s And under the zero - order hold, the transfer function model of the ethylene content control process can be converted into the following discrete equation:

[0125] y(k) = αy(k - 1)+K(k - 1)(1 - α)u(k - 1 - d)

[0126] Where,

[0127] (b) Introduce smith prediction to compensate for the time delay in the discrete equation of the ethylene content control process. The corrected model without time delay is as follows:

[0128] y c(k) = αy c (k - 1) + K(k - 1)(1 - α)u(k - 1)

[0129] where y c (k) is the output of the corrected ethylene content model without time delay.

[0130] Furthermore, the actual ethylene content after correction is

[0131] y ac (k) = y a (k) + y c (k) - y c (k - d)

[0132] where y ac (k) is the actual output of the corrected ethylene content.

[0133] (c) Here, the basis function of predictive functional control is selected as the step function, and the predicted output of the ethylene content process based on the model without time delay is as follows:

[0134] y c (k + P) = α P y c (k) + K(k)Bu(k)

[0135] where P is the prediction horizon,

[0136]

[0137] (d) The design of the predictive functional controller for the ethylene content control process selects the following objective function

[0138]

[0139] where y r (k) is the reference trajectory point corresponding to the ethylene content, Q is the weighted matrix of the ethylene content tracking error, e(k) is the compensated ethylene content prediction error, and e(k) = y ac (k) - y c (k).

[0140] The ethylene content reference trajectory generally takes the following formula:

[0141] y r (k + i) = β i y a (k) + (1 - β i )c(k)

[0142] where β is the reference trajectory softening coefficient of the ethylene content, and c(k) is the set value of the ethylene content.

[0143] (e) By transforming the predicted output formula of the ethylene content, the following form can be obtained:

[0144] y c (k + P) = α P y c (k) + Bθ(k)

[0145] where θ(k) = K(k)u(k).

[0146] Taking the derivative of the objective function of the above ethylene content prediction function control, the corresponding optimal solution can be obtained as

[0147] θ(k) = ((β i -1)y a (k) + (1 - β i )c(k) - α P y c (k) + y c (k - d)) / B

[0148] Furthermore, by solving the following non - linear unary equation, the optimal ethylene concentration u(k) in the ethylene content control process can be obtained.

[0149] f′(u(k))u(k) = θ(k)

[0150] Implement the obtained optimal ethylene concentration u(k) in the ethylene content control process, and sequentially solve the latest optimal ethylene concentration in the next sampling period according to the steps in (b) - (e) in a loop.

[0151] It can be understood that the present invention is described through some embodiments. Those skilled in the art know that without departing from the spirit and scope of the present invention, various changes or equivalent replacements can be made to these features and embodiments. Additionally, under the teaching of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application belong to the scope protected by the present invention.

Claims

1. A non-linear predictive function control method for a polyolefin process, characterized in that, It includes the following steps: Step 1: Collect the step response data of the polyolefin process and fit the dynamic model parameters of the process; Step 1.1: Give a step signal to the input end of the polyolefin process and start recording the corresponding step response data of the polyolefin process; Step 1.2: Convert the obtained step response data y a (k) into a dimensionless form y a * (k); Step 1.3: Select two points that satisfy y a * (k1) = 0.39 and y a * (k1) = 0.63, and calculate the time constant T and the lag time τ of the polyolefin process; Step 1.4: List the corresponding mechanism model according to the process mechanism of the specific polyolefin process. This mechanism model is also called the steady-state model, and the real-time gain of the polyolefin process is obtained from this mechanism model; The specific calculation formula of Step 1.4 is as follows: y(k) = f(u(k)) K(k) = f′(u(k)) where y(k) is the model output of the polyolefin process at time k, u(k) is the input of the polyolefin process at time k, K(k) is the real-time gain of the polyolefin process at time k, and f and f′ are the mechanism model of the polyolefin process and the corresponding first derivative respectively; Step 1.5: The finally obtained transfer function model of the polyolefin process; The transfer function model of the polyolefin process finally obtained in Step 1.5 is where τ is the lag time, T is the time constant, G(k) and l are the real-time transfer function of the polyolefin process and the Laplace operator respectively; Step 2: Design a non-linear predictive function controller for the polyolefin process; Step 2.1: At the sampling time T s and under the zero-order hold, the transfer function model of the polyolefin process is converted into a discrete equation; The transfer function model of the polyolefin process in Step 2.1 is converted into the following discrete equation: y(k) = αy(k - 1) + K(k - 1)(1 - α)u(k - 1 - d) Among them, τ is the lag time; Step 2.2: Introduce Smith prediction to compensate for the time delay in the discrete equation to obtain a modified model without time delay; The modified model without time delay in Step 2.2 is as follows: y c y(k) = αy c (k - 1)+K(k - 1)(1 - α)u(k - 1) Among them, y c (k) is the output of the corrected model without time delay; The actual output after correction is y ac y(k) = y a y(k) + y c y(k) - y c y(k - d) where y ac (k) is the corrected actual output; Step 2.3: Select the step function as the basis function of the predictive function control to obtain the process prediction output based on the model without time delay; The process prediction output based on the model without time delay obtained in Step 2.3 is as follows: y c (k + P) = α P y c (k) + K(k)Bu(k) where P is the prediction time domain, Step 2.4: Select the objective function for the design of the predictive function controller; The objective function selected for the design of the predictive function controller in Step 2.4 is as follows: where y r (k) is the corresponding reference trajectory point, Q is the weighting matrix of the tracking error, e(k) is the compensated prediction error, and e(k) = y ac (k) - y c (k); The reference trajectory takes the following formula: y r (k + i) = β i y a (k) + (1 - β i )c(k) where β is the reference trajectory softening coefficient and c(k) is the corresponding set value; Step 2.5: Transform the prediction output formula; The prediction output formula in Step 2.5 is transformed to obtain the following form: y c (k + P) = α P y c (k) + Bθ(k) where θ(k) = K(k)u(k); Taking the derivative of the above objective function, the optimal solution can be obtained as θ(k) = ((β i - 1)y a (k)+(1 - β i )c(k)-α P y c (k)+y c (k - d)) / B The optimal control input u(k) of the polyolefin process at the current time k is obtained by solving the following non-linear unary equation: f′(u(k))u(k) = θ(k); Step 2.6: Implement the obtained optimal control input u(k) of the predictive function control on the polyolefin process, and solve the latest optimal control law in sequence according to the steps in Steps 2.2 - 2.5 in the next sampling period.

2. The nonlinear predictive function control method for the polyolefin process according to claim 1, characterized in that The step 1.2 converts the obtained step response data y a (k) into a dimensionless form y a * (k): y a * r(k) = y a r(k) / y s where y s is the steady-state value of y a (k) in the step test.

3. The nonlinear predictive function control method for the polyolefin process according to claim 1, wherein Step 1.3 calculates the time constant and lag time of the polyolefin process according to the following formula: T = 2(k2 - k1) τ = 2k1 - k2 where T and τ are the time constant and lag time of the polyolefin process model respectively.

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