Ethylene concentration control method for safety production

Abstract

The application provides a kind of safety production-oriented ethylene concentration control method, comprising: selecting ethylene feed rate as input variable, selecting the ethylene concentration after polymerization in CSTR as output variable, establishing the dynamic equation of ethylene concentration in CSTR;Define equality constraints so that the ethylene concentration after reaction tends to the desired concentration;Define inequality constraints so that the ethylene concentration remains in the safe range throughout the reaction process;State conversion is carried out on the ethylene concentration after reaction;State feedback control law considering equality constraints and inequality constraints is designed by using constraint following control method.The application controls the ethylene feed rate, controls the ethylene concentration of the whole process by using constraint following method, can handle equality constraints and inequality constraints at the same time, and designs the controller to solve the ethylene concentration safety control problem in CSTR polyethylene production process, to avoid fire, explosion and other dangers.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of chemical control, in particular but not exclusively to an ethylene concentration control method for safe production. BACKGROUND

[0002] Polyethylene (PE) is the largest variety of general-purpose synthetic resin, because of its cheap price, good performance, widely used in industry, agriculture, packaging and daily life, occupies a pivotal position in the plastics industry, so the market demand is huge.

[0003] Polyethylene is usually made by polymerization of ethylene in a continuous stirred tank reactor (CSTR). Because the operation of ethylene production is carried out under high temperature and high pressure conditions, and there is also a deep cold operation, most of the materials are in gaseous state during the production process, and the production is continuous. According to the characteristics of ethylene, the concentration of ethylene in CSTR is generally selected as 50.0% to 70.0%. When the concentration of ethylene exceeds 70.0%, the motor current of the stirrer is too high, causing overload trip and stop, which will cause the polymer in the tank to be blocked, and even cause temperature rise and explosion accident, which will cause significant economic loss. Therefore, it is particularly important to control the concentration of ethylene in the production process.

[0004] Therefore, it is necessary to provide a new structure or control method to solve at least part of the above problems. SUMMARY

[0005] In view of one or more problems in the prior art, the present application provides an ethylene concentration control method for safe production. By controlling the ethylene feed rate and using the constraint following method to control the ethylene concentration in the whole process, the equation constraints and inequality constraints can be processed at the same time, and the controller is designed to solve the ethylene concentration safety control problem in the CSTR polyethylene production process, avoiding fire, explosion and other dangers.

[0006] The technical solution for achieving the purpose of the present application is as follows:

[0007] An ethylene concentration control method for safe production, comprising:

[0008] S1, selecting the ethylene feed rate F0 as the input variable, selecting the ethylene concentration CA1 after the polymerization reaction in the CSTR as the output variable, and establishing the initial ethylene concentration dynamic equation;

[0009] S2, defining the equation constraint so that the ethylene concentration CA1 after the reaction in the CSTR tends to the desired concentration CA1 * , wherein L is a parameter; define the inequality constraint CA1∈[CA1* -w, CA1 * +w], so that the ethylene concentration in the CSTR is kept in a safe range throughout the reaction process, w is the controllable upper and lower limit tending to the desired concentration;

[0010] S3, state conversion is performed on the reacted ethylene concentration CA1 based on inequality constraints, to obtain an output variable after state conversion, and to obtain an ethylene concentration dynamic equation after state conversion;

[0011] S4, based on the ethylene concentration dynamic equation after state conversion, combined with equality constraints, a state feedback control law considering both equality constraints and inequality constraints is designed by using a constraint following control method.

[0012] Further, in the ethylene concentration control method for safe production of the application, the initial ethylene concentration dynamic equation is established in S1 as follows:

[0013]

[0014] In the formula, V1 is the volume of the CSTR, with the unit of L; CA0 is the initial ethylene concentration, with the unit of mol / L; CA1 is the reacted ethylene concentration, with the unit of mol / L; K is the polymerization reaction rate, with the unit of mol / (L·s); F0 is the ethylene feed rate, with the unit of L / s.

[0015] Further, in the ethylene concentration control method for safe production of the application, in S3, the differential homeomorphism is used to perform state conversion on the reacted ethylene concentration CA1.

[0016] Further, in the ethylene concentration control method for safe production of the application, the specific steps of state conversion on the reacted ethylene concentration CA1 in S3 include:

[0017] S3-1, according to the differential homeomorphism transformation, the state conversion equation is selected as:

[0018] y=tan(aCA1+b)

[0019] Wherein, y is the expression of CA1 after state conversion, a and b are both state conversion parameters;

[0020] S3-2, according to the properties of the tangent function, combined with the inequality constraint CA1∈[CA1 * -w, CA1 * +w], so that the ethylene concentration in the CSTR is kept in a safe range throughout the reaction process, w is the controllable upper and lower limit tending to the desired concentration;

[0021] a(CA1 * +w)+b=π / 2

[0022] a(CA1 * -w)+b=-π / 2

[0023] Obtained:

[0024]

[0025]

[0026] Wherein, w is the controllable upper and lower limit of the desired concentration;

[0027] S3-3, the final state transition equation of the ethylene concentration CA1 after reaction is:

[0028]

[0029] Then the state transition of the ethylene concentration CA1 after reaction is completed.

[0030] Further, the specific steps of obtaining the state transition of the ethylene concentration dynamic equation in S3 of the ethylene concentration control method for safety production of the application include:

[0031] According to the final state transition equation of the ethylene concentration CA1 after reaction, using the definition of inverse function, we have:

[0032]

[0033] The dynamic equation of the ethylene concentration in CSTR is obtained as:

[0034]

[0035] Simplify and move terms to get:

[0036]

[0037] In the formula, V1 is the volume of CSTR, unit: L; CA0 is the initial ethylene concentration, unit: mol / L; K is the polymerization rate, unit: mol / (L·s); F0 is the feed rate, unit: L / s.

[0038] Further, the state feedback control law for designing the ethylene concentration control method for safety production of the application in S4 specifically includes:

[0039] Define the equality constraint Combined with the state transition of the ethylene concentration dynamic equation, the state feedback control law for making the ethylene concentration meet the constraint is obtained as:

[0040]

[0041] Wherein, F0 represents the ethylene feed rate, and is the controller of the ethylene concentration control system.

[0042] Compared with the prior art, the safety production-oriented ethylene concentration control method has the following technical effects:

[0043] 1、The safety production-oriented ethylene concentration control method does not need to linearize a nonlinear system, and can obtain an explicit differential equation of a system state feedback control law without any auxiliary variable or pseudo variable; meanwhile, the method can ensure that the ethylene concentration does not exceed a safety range in the whole production process, and ensures production safety.

[0044] 2、The safety production-oriented ethylene concentration control method ensures that whether the initial ethylene concentration exceeds the safety range or not, the final ethylene concentration will tend to the expected concentration value in a short time, and the system is actually stable.

[0045] 3、The safety production-oriented ethylene concentration control method can effectively solve the ethylene concentration safety control problem in the CSTR polyethylene production process, and avoid fire, explosion and other dangers. BRIEF DESCRIPTION OF DRAWINGS

[0046] The accompanying drawings are included to provide a further understanding of the present application, and are incorporated in and constitute a part of this specification, illustrate embodiments of the present application, and together with the description serve to explain the principles of the present application, and should not be taken as limiting the present application. In the drawings:

[0047] Figure 1 is a flow chart of the safety production-oriented ethylene concentration control method.

[0048] Figure 2 is a simulation diagram of the safety production-oriented ethylene concentration control method when the initial ethylene concentration exceeds the upper limit.

[0049] Figure 3 is a simulation diagram of the safety production-oriented ethylene concentration control method when the initial ethylene concentration does not exceed the upper limit.

[0050] Figure 4 is a simulation diagram of the safety production-oriented ethylene concentration control method when the initial ethylene concentration exceeds the lower limit.

[0051] Figure 5 is a simulation diagram of the safety production-oriented ethylene concentration control method when the initial ethylene concentration does not exceed the lower limit. DETAILED DESCRIPTION

[0052] In order to further understand the present application, the preferred embodiments of the present application are described below in conjunction with the embodiments, but it should be understood that these descriptions are only for further illustrating the features and advantages of the present application, and are not limiting the claims of the present application.

[0053] The description of this part is only for the typical embodiments, and the application is not limited to the scope described in the embodiments. The combination of different embodiments, the mutual replacement of some technical features in different embodiments, and the mutual replacement of some technical features in the same or similar prior art means are also within the scope of the description and protection of the application.

[0054] Embodiment 1

[0055] The safety production-oriented ethylene concentration control method of the embodiment includes the following steps:

[0056] S1, the feed rate F0 of ethylene is selected as the input variable, and the concentration CA1 of ethylene after the polymerization reaction in the CSTR is selected as the output variable, and the dynamic equation of the system is formula (1):

[0057]

[0058] In the formula, V1 is the volume of the CSTR, unit: L,

[0059] CA0 is the initial ethylene concentration, unit: mol / L,

[0060] CA1 is the ethylene concentration after the reaction, unit: mol / L,

[0061] K is the polymerization rate, unit: mol / (L·s),

[0062] F0 is the feed rate, unit: L / s.

[0063] S2, the concentration of ethylene in the CSTR is generally selected as 50.0% to 70.0%, Figures 2-5 The simulation diagram when the initial concentration of ethylene exceeds / does not exceed the upper and lower limits, when the ethylene concentration exceeds 70.0%, the current of the agitator motor is too high, causing overload trip, stop rotation, which will cause the polymer in the kettle to be blocked, and even cause the temperature to rise and the polymerization to explode, which will cause significant economic losses. In order to keep the ethylene concentration in the safe range of 50.0% to 70.0%, additional constraints need to be applied to ensure that the ethylene concentration CA1 after the reaction is within the boundary line, which is an inequality constraint problem. Through differential homeomorphism transformation, the inequality constraint is integrated into the equality constraint to form a new equality constraint, based on the new equality constraint and the constraint following control method, the state feedback control law required by the system is derived, so that the ethylene concentration can meet the equality constraint and the inequality constraint in the whole running process, and the safety operation goal is achieved.

[0064] S3. Using the constraint following control method, considering the inequality constraints that the system needs to satisfy, the output variable CA1 of the control system is first transformed into a state, and the inequality constraints are integrated into the equality constraints to obtain new equality constraints. Then, based on the new equality constraints and the constraint following control method, the state feedback control law required by the system is derived.

[0065] In order to make the target concentration CA1 approach the desired concentration CA1 * Apply the following constraints to the variable y after the state transition. By constraining By combining the dynamic equations of the system, an expression for the input F0 that makes the ethylene concentration satisfy the constraint can be derived, so that the control system changes according to the given reference input, ensuring that the inequality constraint is satisfied at every time step (including the process of converging to the desired concentration), where L is the setting parameter.

[0066] The specific steps include:

[0067] The first step is to relax the inequality constraints in order to transform the state equation from a bounded space to an unbounded space. According to the definition of differential homeomorphism, the equation for the state transition is obtained as equation (2).

[0068] y=tan(aCA1+b) (2)

[0069] The second step, based on the properties of the tangent function, is to derive equation (3).

[0070]

[0071] Then, this system of equations is solved to obtain... w represents the controllable upper and lower limits for approaching the desired concentration. CA1 in the equation system... * This represents the desired concentration of ethylene after the reaction, which is the value that the system needs to control.

[0072] Third, based on equation (3), the final state transition equation can be derived as equation (4).

[0073]

[0074] Equation (4) has completed the state transition of CA1.

[0075] Fourth step: Based on equation (4), using the definition of an inverse function, derive the expression of equation (5) CA1 with respect to y.

[0076]

[0077] Fifth, based on the relationship between CA1 and y in equation (5), substitute it into the dynamic change equation (1) for ethylene concentration to obtain equation (6).

[0078]

[0079] Then, by equation (6), equation (7) can be obtained

[0080]

[0081] In the sixth step, according to equation (7), it is simplified and moved to obtain In this form, equation (8) can be obtained

[0082]

[0083] In the last step, the constraint is changed to In combination with equation (8), the expression (9) of the control input F0 that makes the ethylene concentration meet the constraint can be obtained

[0084]

[0085] F0 is the controller of the system, which can make CA1 tend to the desired concentration CA1 * , and make CA1 in a controllable range that will not explode, that is, CA1 * -w < CA1 < CA1 * +w.

[0086] Example 2

[0087] The ethylene concentration control method in the CSTR of the present embodiment comprises the following steps:

[0088] As shown in Figure 1 , the whole process of the ethylene concentration in the CSTR is modeled first, and the constraint following method is used to control the ethylene concentration in the CSTR, the ethylene feed rate is selected as the input variable, and the concentration of ethylene after the polymerization reaction in the CSTR is selected as the output variable, and there is the following relationship:

[0089]

[0090] In the formula, V1 = 100 L is the volume of the CSTR; CA0 = 0.725 mol / L is the initial concentration of ethylene; K = 7 × 10 -5 mol / (L·s) is the polymerization rate.

[0091] Because of the unpredictable initial condition, the equality constraint cannot guarantee the concentration within the safe range during the convergence process, which may lead to serious explosion accidents. Therefore, it is necessary to impose another constraint on the ethylene concentration, i.e. the concentration is bounded. By using the method of differential homeomorphism, the state equation is converted from one coordinate space to another coordinate space, which is converted from bounded space to unbounded space, so that the inequality constraint can be relaxed. In order to handle the equality and inequality constraints at the same time, the state conversion is carried out.

[0092] The appropriate differential homeomorphism is selected to convert the inequality constraint into the equality constraint, and formula (2) can meet a series of requirements.

[0093] y=tan(aCA1+b) (2)

[0094] According to the properties of tangent function, the equation (3) is obtained from the selected differential homeomorphism as formula (2)

[0095]

[0096] The upper and lower addition and subtraction cancellation of formula (3) is solved to obtain CA1 * The expected value of ethylene concentration after reaction is equal to 0.6 mol / L; w is the controllable upper and lower limit of the expected concentration, which is equal to 0.1.

[0097] The parameters of a and b obtained are brought into formula (2) to obtain the final state conversion equation (4)

[0098]

[0099] According to the definition of inverse function, the expression (5) of CA1 and y is obtained through formula (4)

[0100]

[0101] According to the relationship between CA1 and y in formula (5), formula (5) is brought into the dynamic change formula (1) of ethylene concentration to obtain the equation (6) after state conversion

[0102]

[0103] Through formula (6), formula (7) is obtained

[0104]

[0105] According to formula (7), it is simplified and moved to obtain This form is obtained from formula (8)

[0106]

[0107] To derive the expression of the controller F0, by combining and the dynamic equation of the system, the expression of the control input F0 that makes the ethylene concentration meet the constraints can be derived. This is a negative feedback control system, also known as a closed-loop control system, and the system output is stable, so that the control system changes according to the given reference input.

[0108] The expression of F0 is as formula (9)

[0109]

[0110] Compared with the prior art, the embodiment has the following beneficial effects: the method controls the initial concentration of ethylene flowing into the CSTR, controls the ethylene concentration in the whole process by using the constraint following method, can process the equality constraints and inequality constraints at the same time, and then designs the controller to solve the safety problem of the ethylene concentration in the CSTR. Compared with other control methods, the method does not need to linearize the nonlinear system, and can obtain the explicit differential equation of the system state feedback control law without any auxiliary variable or pseudo variable, in addition, the obtained control force satisfies the Lagrange form of the Gauss minimum principle and the d'Alembert principle, and can provide moderate control in the actual process. The equality constraints cannot guarantee that the concentration does not exceed the safe range during the convergence process, which may cause the problem of serious explosion accident. The method ensures that the final ethylene concentration tends to the expected concentration value regardless of whether the initial ethylene concentration exceeds the safe range, and ensures that it does not exceed the upper and lower limits of safety during the whole running process, thereby ensuring safe operation.

[0111] The description and application of the present application herein are illustrative, and are not intended to limit the scope of the present application to the above-mentioned embodiments. The related descriptions of effects or advantages in the specification may not be embodied in actual experimental examples due to the uncertainty of specific condition parameters or other factors, and the related descriptions of effects or advantages are not used to limit the scope of the application. Variations and changes of the disclosed embodiments are possible, and the alternatives and equivalent components of the embodiments are known to those skilled in the art. It should be clear to those skilled in the art that the present application can be realized in other forms, structures, arrangements, proportions, and with other components, materials and parts without departing from the spirit or essential characteristics of the present application. Other variations and changes of the disclosed embodiments can be made without departing from the scope and spirit of the present application.

Claims

1. A method for controlling ethylene concentration for safe production, characterized in that, include: S1. Select the ethylene feed rate The ethylene concentration after polymerization in the CSTR was selected as the input variable. As the output variable, establish the dynamic equation for the initial ethylene concentration; S2, Define equality constraints This reduces the concentration of ethylene in the CSTR after the reaction. tending towards the desired concentration ,in Define parameters; define inequality constraints This ensures that the ethylene concentration in the CSTR remains within a safe range throughout the entire reaction process. These are controllable upper and lower limits that tend towards the desired concentration; S3. Using the differential isomorphism to determine the ethylene concentration after the reaction. Perform a state transition to obtain the output variables after the state transition, and obtain the dynamic equation for the ethylene concentration after the state transition; S4. Based on the dynamic equation of ethylene concentration after state transition, and combined with equality constraints, a state feedback control law considering both equality and inequality constraints is designed using the constraint-following control method: Define equality constraints. Combining the dynamic equation of ethylene concentration after the state transition, the state feedback control law that makes the ethylene concentration satisfy the constraint is obtained as follows: ， in, This represents the ethylene feed rate and is the controller for the ethylene concentration control system. The polymerization rate, Let y be the volume of the CSTR. The expression after state transition. This represents the initial ethylene concentration.

2. The ethylene concentration control method for safe production according to claim 1, characterized in that, The initial dynamic equation for ethylene concentration in S1 is as follows: ， In the formula, The volume of the CSTR is expressed in liters (L). This represents the initial ethylene concentration, in mol / L. The concentration of ethylene after the reaction is expressed in mol / L. The value represents the polymerization rate, expressed in mol / (L·s). This represents the ethylene feed rate, expressed in L / s.

3. The ethylene concentration control method for safe production according to claim 1, characterized in that, S3 represents the concentration of ethylene after the reaction. The specific steps for performing a state transition include: S3-1. Based on the differential homeomorphism transformation, the state transition equation is selected as follows: ， Where y is The expression after state transition, where a and b are both state transition parameters; S3-2. Based on the properties of the tangent function, combined with inequality constraints... ,make: ， get: ， ， in, These are controllable upper and lower limits that tend towards the desired concentration; S3-3, Ethylene concentration after the reaction The final state transition equation is: ， Then complete the determination of the ethylene concentration after the reaction. Perform a state transition.

4. The ethylene concentration control method for safe production according to claim 3, characterized in that, The specific steps to obtain the dynamic equation for the ethylene concentration after the state transition in S3 include: Based on the ethylene concentration after the reaction The final state transition equation, using the definition of an inverse function, is: ， The dynamic equation for ethylene concentration in CSTR is obtained as follows: ， Simplifying and rearranging, we get: ， In the formula, The volume of the CSTR is expressed in liters (L). This represents the initial ethylene concentration, in mol / L. The value represents the polymerization rate, expressed in mol / (L·s). This represents the feed rate, expressed in L / s.

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