Ethylene concentration robust control method for safety production

Abstract

The invention provides a safe production-oriented ethylene concentration robust control method, which comprises the following steps: selecting an ethylene feeding rate as an input variable, selecting an ethylene concentration after polymerization reaction in a CSTR as an output variable, and establishing an ethylene concentration dynamic equation in the CSTR; defining an equality constraint to enable the ethylene concentration after the reaction to tend to an expected concentration; an inequality constraint is defined, so that the ethylene concentration is kept in a safe range in the whole reaction process; performing state conversion on the ethylene concentration after the reaction; designing a state feedback control law considering equality constraints and inequality constraints at the same time by adopting a constraint following control method; and the uncertainty of the system is solved through a robust control method. The ethylene feeding rate is controlled, the ethylene concentration in the whole process is controlled, the uncertainty of the system is handled through a robust control method, and the controller is designed to solve the ethylene concentration safety control problem in the CSTR polyethylene production process, so that dangers such as fire disasters and explosions are avoided.

Description

Technical Field

[0001] This invention relates to the field of chemical control technology, specifically to a robust method for controlling ethylene concentration for safe production. Background Technology

[0002] Polyethylene (PE) is the most produced general-purpose synthetic resin. Due to its low price and good performance, it is widely used in industry, agriculture, packaging and daily life, and occupies a pivotal position in the plastics industry, resulting in huge market demand.

[0003] Polyethylene is typically produced by polymerizing ethylene in a continuous stirred tank reactor (CSTR). Because ethylene production is carried out under high temperature and pressure conditions, and also involves cryogenic processes, most of the material is in a gaseous state during the process. Production is highly continuous. Based on the characteristics of ethylene, the concentration of ethylene in the CSTR is generally selected between 50.0% and 70.0%. When the ethylene concentration exceeds 70.0%, it causes excessive current in the agitator motor, leading to overload tripping and shutdown. This can cause polymer agglomeration within the reactor, and even trigger runaway temperatures and explosive polymerization accidents, resulting in significant economic losses. Therefore, controlling the concentration of ethylene during the production process is crucial. Simultaneously, uncertainties exist in the system, such as the amount of ethylene retained; addressing these uncertainties is also essential.

[0004] In view of this, there is a need to provide a new structure or control method in order to solve at least some of the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a robust ethylene concentration control method for safe production. By controlling the ethylene feed rate, the ethylene concentration of the entire process is controlled using a constraint following method. This method can simultaneously handle equality constraints and inequality constraints, and a controller is designed. Through the robust control method, system uncertainties are addressed, and the controller design solves the problem of safe ethylene concentration control in the CSTR polyethylene production process, avoiding dangers such as fire and explosion.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is: a robust method for controlling ethylene concentration for safe production, comprising the following steps:

[0007] S1. Select the ethylene feed rate F0 as the input variable and the ethylene concentration CA1 after polymerization in CSTR as the output variable to establish the initial ethylene concentration dynamic equation.

[0008] S2, Define equality constraints The concentration of ethylene CA1 in the CSTR after the reaction should be brought closer to the desired concentration CA1. *Where L is a parameter; define the inequality constraint CA1∈[CA1 * -w, CA1 * +w], where w is the controllable upper and lower limits for approaching the desired concentration;

[0009] S3. Based on inequality constraints, the ethylene concentration CA1 after the reaction is transformed to obtain the output variable after the state transformation, and the dynamic equation of the ethylene concentration after the state transformation is obtained; combined with equality constraints, the constraint following control method is used to design a state feedback control law that considers both equality constraints and inequality constraints.

[0010] S4: By using robust control methods, a state feedback control law with uncertainties is designed to keep the ethylene concentration in CSTR within a safe range throughout the entire reaction process.

[0011] Furthermore, in step S1, the initial dynamic equation for ethylene concentration is established as follows:

[0012]

[0013] In the formula, V1 is the ethylene retention of CSTR in L; CA0 is the initial ethylene concentration in mol / L; CA1 is the ethylene concentration after the reaction in mol / L; K is the polymerization rate in mol / (L·s); and F0 is the ethylene feed rate in L / s.

[0014] Furthermore, in step S3, differential isomorphism is used to perform state transformation on the ethylene concentration CA1 after the reaction.

[0015] Furthermore, in step S3, the specific steps for state transformation of the ethylene concentration CA1 after the reaction include:

[0016] S3-1. Based on the differential homeomorphism transformation, the state transition equation is selected as follows:

[0017] y = tan(aCA1 + b)

[0018] Where y is the expression after state transition of CA1, and a and b are both state transition parameters;

[0019] S3-2. Based on the properties of the tangent function, and combined with the inequality constraint CA1∈[CA1], * -w, CA1 * +w], let:

[0020] a(CA1 * +w)+b=π / 2

[0021] a(CA1 * -w)+b=-π / 2

[0022] get:

[0023]

[0024]

[0025] Where w is a controllable upper and lower limit for approaching the desired concentration;

[0026] S3-3, The final state transition equation for the ethylene concentration CA1 after the reaction is:

[0027]

[0028] This completes the state transition of the ethylene concentration CA1 after the reaction;

[0029] S3-4, The dynamic equation for ethylene concentration in CSTR is obtained as follows:

[0030]

[0031] S3-5, Define Equality Constraints Combining the dynamic equation of ethylene concentration after the state transition, the state feedback control law that satisfies the constraints on ethylene concentration is obtained as follows:

[0032]

[0033] Wherein, F0 is a controller in the ethylene concentration control system that does not contain uncertainties.

[0034] Furthermore, in step S4, the robust control method is as follows:

[0035] X(t)=f(x,t)+h(x,t)+[B(x,t)+ΔB(x,t)]u(t)

[0036] Based on the dynamic equation of ethylene concentration obtained in S3-4, and corresponding one-to-one with the robust control method, we can conclude that:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] u(t)=p k (a2,t)

[0043] pk (a2,t) represents the controller with uncertainties, and h(x,t) represents the uncertainty of ethylene retention.

[0044]

[0045] S4-1. Using the Lyapunov function, a2 can be calculated:

[0046] Lyapunov functions:

[0047]

[0048]

[0049]

[0050] S4-2, according to p k (a2,t) and The relationship between them allows us to determine p. k (a2,t):

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] p k (κ k ,t)=ε k

[0057] p can be calculated from the above formula. k (a2,t):

[0058]

[0059] Therefore, the controller with uncertainty is p. k (a2,t)+F0.

[0060] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0061] 1. The ethylene concentration control method for safe production of the present invention does not require linearization of the nonlinear system, and can obtain the explicit differential equation of the system state feedback control law without the appearance of any auxiliary variables or pseudo-variables; at the same time, the method can ensure that the ethylene concentration will not exceed the safe range throughout the entire production process, thus ensuring production safety.

[0062] 2. The ethylene concentration control method of the present invention for safe production ensures that, regardless of whether the initial ethylene concentration exceeds the safe range, the final ethylene concentration will tend to the desired concentration value within a short period of time, thus achieving actual system stability.

[0063] 3. The ethylene concentration control method of the present invention, aimed at safe production, can effectively solve the problem of ethylene concentration safety control in the CSTR polyethylene production process, avoiding dangers such as fire and explosion. Robust control methods can effectively address system uncertainties. Attached Figure Description

[0064] Figure 1 This is a flowchart of the robust ethylene concentration control method for safe production according to the present invention.

[0065] Figure 2 This is a simulation diagram of an embodiment of the present invention when the initial concentration of ethylene exceeds the upper limit.

[0066] Figure 3 This is a simulation diagram of another embodiment of the present invention when the initial concentration of ethylene does not exceed the upper limit.

[0067] Figure 4 This is a simulation diagram of an embodiment of the present invention when the initial concentration of ethylene exceeds the lower limit.

[0068] Figure 5 This is a simulation diagram of another embodiment of the present invention when the initial concentration of ethylene does not exceed the lower limit. Detailed Implementation

[0069] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0070] Example 1

[0071] This embodiment of a robust ethylene concentration control method for safe production includes the following steps:

[0072] S1, with the ethylene feed rate F0 selected as the input variable and the ethylene concentration CA1 after polymerization in the CSTR selected as the output variable, the dynamic equation of the system is equation (1):

[0073]

[0074] In the formula, V1 represents the volume percentage of ethylene in the tank, in liters (L).

[0075] CA0 represents the initial ethylene concentration, in mol / L.

[0076] CA1 represents the concentration of ethylene after the reaction, in mol / L.

[0077] K is the polymerization rate, expressed in mol / (L·s).

[0078] F0 is the feed rate, in L / s.

[0079] In S2, the concentration of ethylene in the CSTR is typically chosen to be between 50.0% and 70.0%. When the ethylene concentration exceeds 70.0%, the current of the agitator motor becomes excessive, causing overload tripping and shutdown. This can lead to polymer agglomeration inside the reactor, and even cause runaway temperatures and explosive polymerization accidents, resulting in significant economic losses. To maintain the ethylene concentration within the safe range of 50.0% to 70.0%, additional constraints need to be applied to ensure that the post-reaction ethylene concentration CA1 fluctuates within the boundary line. This is an inequality constraint problem. Through differential homeomorphism, the inequality constraints are integrated into the equality constraints to form new equality constraints. Based on the new equality constraints and constraint-following control method, the required state feedback control law for the system is derived, thereby enabling the ethylene concentration to satisfy both equality and inequality constraints throughout the entire operation, achieving the goal of safe operation.

[0080] 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.

[0081] S4, through robust control methods based on Lyapunov functions, can effectively address the uncertainties present in the system.

[0082] 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 target 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.

[0083] The specific steps include:

[0084] First, in order to transform the state equation from a bounded space to an unbounded space, the inequality constraints can be relaxed. According to the definition of differential homeomorphism, the equation for the state transition is obtained as equation (2):

[0085] y=tan(aCA1+b) (2)

[0086] The second step, based on the properties of the tangent function, is to derive equation (3):

[0087]

[0088] 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.

[0089] Third, based on equation (3), the final state transition equation can be derived as equation (4):

[0090]

[0091] Equation (4) has completed the state transition of CA1.

[0092] Fourth step, according to equation (4), using the definition of an inverse function, derive the expression of equation (5) CA1 with respect to y:

[0093]

[0094] Fifth step, based on the relationship between CA1 and y in equation (5), substituting it into the dynamic change equation (1) for ethylene concentration, we can obtain equation (6):

[0095]

[0096] Then constraints Change to writing Combining the form and equation (8), we can derive the expression (7) for the control input F0 that makes the ethylene concentration satisfy the constraint:

[0097]

[0098] F0 is a controller in the system without uncertainty, capable of making CA1 approach the desired concentration CA1. * And ensure that CA1 is within a controllable range that will not explode, i.e., CA1 * -w<CA1<CA1 * +w.

[0099] Step 6: Based on the dynamic equation of ethylene concentration (6) and the robust control method, equation (8) can be derived:

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] Based on equation (8), we can derive (9):

[0106] u(t)=p k (a2,t)

[0107]

[0108] Based on the Lyapunov function (10), we can derive a2 (11).

[0109] Lyapunov functions:

[0110]

[0111]

[0112]

[0113] According to p k (a2,t) and The relation (12) allows us to determine p. k (a2,t):

[0114]

[0115]

[0116]

[0117]

[0118]

[0119] p k (κ k ,t)=ε k

[0120] p can be calculated from the above formula. k Equation (13) (a2,t):

[0121]

[0122] Therefore, the controller with uncertainty is p. k (a2,t)+F0 is Equation (7)+Equation (13).

[0123] Example 2

[0124] The method for controlling ethylene concentration in CSTR in this embodiment includes the following steps:

[0125] like Figure 1 As shown, a model is first established for the entire process of ethylene concentration in the CSTR. The constrained 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 polymerization in the CSTR is selected as the output variable. The following relationship exists:

[0126]

[0127] In the formula, V1 = 100L is the volume of the CSTR; CA0 = 0.725mol / L is the initial concentration of ethylene; K = 7 × 10 -5 mol / (L·s) represents the polymerization rate.

[0128] Because initial conditions are unpredictable, equality constraints cannot guarantee that the concentration will not exceed a safe range during convergence, potentially leading to a serious explosion. Therefore, it is necessary to impose another constraint on the ethylene concentration: that the concentration be bounded. Using the homeomorphism method, the state equation is transformed from one coordinate space to another, converting it from a bounded space to an unbounded space, thus relaxing the inequality constraints. To handle both equality and inequality constraints simultaneously, a state transformation is performed.

[0129] Choosing a suitable differential homeomorphism to convert inequality constraints into equality constraints, equation (2) can satisfy a series of requirements.

[0130] y=tan(aCA1+b) (2)

[0131] The chosen differential homeomorphism is given by equation (2). Based on the properties of the tangent function, equation (3) is derived:

[0132]

[0133] Solving equation (3) by adding and subtracting the upper and lower parts to cancel each other out, we get the following result. CA1 * is the expected concentration of ethylene after the reaction, which is equal to 0.6 mol / L; w is the controllable upper and lower limits for approaching the expected concentration, which is equal to 0.1.

[0134] Substituting the calculated parameters of a and b into equation (2), we obtain the final state transition equation (4):

[0135]

[0136] According to the definition of an inverse function, through equation (4), we obtain the expression (5) for finding CA1 and y:

[0137]

[0138] Based on the relationship between CA1 and y in equation (5), substituting it into equation (1) for the dynamic change of ethylene concentration, we can obtain equation (6):

[0139]

[0140] Then constraints Change to writing Combining the form and equation (8), we can derive the expression (7) for the control input F0 that makes the ethylene concentration satisfy the constraint:

[0141]

[0142] F0 is a controller in the system without uncertainty, capable of making CA1 approach the desired concentration CA1. * And ensure that CA1 is within a controllable range that will not explode, i.e., CA1 * -w<CA1<CA1 * +w.

[0143] Based on the dynamic equation of ethylene concentration (6), and corresponding one-to-one with the robust control method, equation (8) can be derived:

[0144]

[0145]

[0146]

[0147]

[0148]

[0149] Based on equation (8), we can derive (9):

[0150] u(t)=p k (a2,t)

[0151]

[0152] Based on the Lyapunov function (10), we can derive equation (11) for a2:

[0153] Lyapunov functions:

[0154]

[0155]

[0156]

[0157] According to p k (a2,t) and The relation (12) allows us to determine p. k (a2,t):

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] p k (κ k ,t)=ε k

[0164] p can be calculated from the above formula. k Equation (13) (a2,t):

[0165]

[0166] Therefore, the controller with uncertainty is p. k (a2,t)+F0 is Equation (7)+Equation (13).

[0167] In summary, this method controls the initial concentration of ethylene flowing into the CSTR, utilizes a constrained following method to control the ethylene concentration throughout the process, and can simultaneously handle both equality and inequality constraints. A controller is then designed to address the safety issues related to ethylene concentration within the CSTR, and robust control methods are employed to address system uncertainties. Equality constraints cannot guarantee that the concentration will not exceed the safe range during convergence, potentially leading to serious explosions. This method ensures that regardless of whether the initial ethylene concentration exceeds the safe range, the final ethylene concentration will tend towards the desired value, and guarantees that it will not exceed the upper or lower safety limits throughout the entire operation, thus ensuring safe operation.

[0168] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the scope of protection of the present invention in any way, and all technical solutions obtained by equivalent substitution or other means fall within the scope of protection of the present invention. Parts not covered in this invention are the same as or can be implemented using existing technology.

Claims

1. A robust method for controlling ethylene concentration in safe production, characterized in that, Includes the following steps: S1. Select the ethylene feed rate F0 as the input variable and the ethylene concentration CA1 after polymerization in CSTR as the output variable to establish the initial ethylene concentration dynamic equation. S2, Define equality constraints The concentration of ethylene CA1 in the CSTR after the reaction should be brought closer to the desired concentration CA1. * Where L is a parameter; define the inequality constraint CA1∈[CA1 * -w, CA1 * +w], where w is the controllable upper and lower limits for approaching the desired concentration; S3. Based on inequality constraints, the ethylene concentration CA1 after the reaction is transformed to obtain the output variable after the state transformation, and the dynamic equation of the ethylene concentration after the state transformation is obtained; combined with equality constraints, the constraint following control method is used to design a state feedback control law that considers both equality constraints and inequality constraints. S4: By using robust control methods, a state feedback control law with uncertainties is designed to keep the ethylene concentration in CSTR within a safe range throughout the entire reaction process.

2. The robust ethylene concentration control method for safe production according to claim 1, characterized in that, In step S1, the initial dynamic equation for ethylene concentration is established as follows: In the formula, V1 is the ethylene retention of CSTR in L; CA0 is the initial ethylene concentration in mol / L; CA1 is the ethylene concentration after the reaction in mol / L; K is the polymerization rate in mol / (L·s); and F0 is the ethylene feed rate in L / s.

3. The robust ethylene concentration control method for safe production according to claim 1, characterized in that, In step S3, differential isomorphism is used to perform state transformation on the ethylene concentration CA1 after the reaction.

4. The robust ethylene concentration control method for safe production according to claim 3, characterized in that, In step S3, the specific steps for state transformation of the ethylene concentration CA1 after the reaction include: S3-1. Based on the differential homeomorphism transformation, the state transition equation is selected as follows: y = tan(aCA1 + b) Where y is the expression after state transition of CA1, and a and b are both state transition parameters; S3-2. Based on the properties of the tangent function, and combined with the inequality constraint CA1∈[CA1], * -w, CA1 * +w], let: a(CA1 * +w)+b6π / 2 a(CA1 * -w)+b6-π / 2 get: Where w is a controllable upper and lower limit for approaching the desired concentration; S3-3, The final state transition equation for the ethylene concentration CA1 after the reaction is: This completes the state transition of the ethylene concentration CA1 after the reaction; S3-4, The dynamic equation for ethylene concentration in CSTR is obtained as follows: S3-5, Define Equality Constraints Combining the dynamic equation of ethylene concentration after the state transition, the state feedback control law that ensures the ethylene concentration satisfies the constraints is obtained as follows: Wherein, F0 is a controller in the ethylene concentration control system that does not contain uncertainties.

5. The robust ethylene concentration control method for safe production according to claim 4, characterized in that, In step S4, the robust control method is as follows: X(t)=f(x,t)+h(x,t)+[B(x,t)+ΔB(x,t)]u(t) Based on the dynamic equation of ethylene concentration obtained in S3-4, and corresponding one-to-one with the robust control method, we can conclude that: u(t)=p k (a2,t) p k (a2,t) represents the controller with uncertainties, and h(x,t) represents the uncertainty of ethylene retention. S4-1. Using the Lyapunov function, a2 can be calculated: Lyapunov functions: S4-2, according to p k (a2,t) and The relationship between them allows us to determine p. k (a2,t): p k (k k ,t)=e k p can be calculated from the above formula. k (a2,t): Therefore, the controller with uncertainty is p. k (a2,t)+F0.

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