Temperature control method and system of plastic extruder

Abstract

The invention discloses a temperature control method and system of a plastic extruder, the temperature control system comprises a system identifier, a comparator, a multiplier, a controller, an adaptive module and a Smith predictor, the system identifier is used for identifying actual controlled system parameters; the comparator is used for comparing the output of the updated reference model with the output of the time-delay-free mathematical model and acquiring an error signal; the Smith predictor is used for eliminating a time delay link of a controlled object in a control process in controller design, and outputs of the Smith predictor are time-delay-free output and actual temperature output of the controlled object; the adaptive module enables the actual temperature output to track the temperature input. According to the invention, after the system parameters of the actual controlled object are identified based on the response sensitivity method, the influence of the time delay link on the temperature control in the plastic extruder is reduced through the Smith predictor, the overshoot of the control system is reduced, and the dynamic performance and robustness are improved.

Description

Technical Field

[0001] The invention relates to a temperature control method and system, and in particular to a temperature control method and system for a plastic extruder. Background Art

[0002] A plastic extruder is a device used for processing and molding plastic products. During the plastic extrusion process, temperature is one of the key factors affecting product quality. Common temperature control methods include PID control and fuzzy PID control. PID control often fails to achieve ideal control effects for systems with time lag and large inertia, and is prone to large overshoot. Fuzzy PID control introduces a fuzzy logic inference mechanism to dynamically adjust PID parameters based on system status, demonstrating greater adaptability in nonlinear system control. However, the construction of its fuzzy rule base relies on expert experience, and its ability to compensate for time lag is still insufficient. Plastic extruders have complex thermodynamic characteristics with large inertia, large time lag, and nonlinearity, making it difficult for traditional temperature control methods to meet their control requirements. Therefore, there is an urgent need for a temperature control method that can better eliminate the effects of time lag and improve system stability and dynamic performance. Summary of the Invention

[0003] Purpose of the invention: The first purpose of the present invention is to provide a temperature control method for a plastic extruder that can reduce overshoot and improve dynamic performance and robustness; the second purpose of the present invention is to provide a temperature control system for a plastic extruder.

[0004] Technical solution: A temperature control method for a plastic extruder of the present invention comprises:

[0005] (1) Identifying the time-delay system parameters of a mathematical model having a time-delay link by a response sensitivity method; the mathematical model having a time-delay link is a mathematical model of a barrel temperature control system;

[0006] (2) Using the identified time-delay system parameters, the time-delay system parameters in the reference model are updated. The reference model is initially a mathematical model with a time-delay link.

[0007] (3) Subtracting the time-delay-free output obtained by the Smith prediction method from the output of the updated reference model to obtain an error signal; the updated reference model uses the barrel temperature monitoring value as input;

[0008] (4) Using the barrel temperature monitoring value as the adjustable gain, multiplying it by the error signal to amplify the error signal;

[0009] (5) obtaining a first control signal through a PI control method based on the amplified error signal;

[0010] (6) Multiplying the first control signal by the barrel temperature setting value to obtain a second control signal;

[0011] (7) Based on the second control signal, a hysteresis compensation control is performed on the mathematical model with a time lag link by using the Smith prediction method to obtain an actual temperature output for controlling the barrel temperature;

[0012] (8) Loop through steps (2) to (7).

[0013] Furthermore, in step (1), a second-order link transfer function with delay is used to identify the mathematical model of the barrel temperature control system. The relationship of the second-order link transfer function with delay is:

[0014]

[0015] Where T(s) represents the barrel temperature; P(s) represents the electric heating power; τ represents the time lag parameter; a, b, and K are system parameters.

[0016] Furthermore, step (1) includes:

[0017] (101) The original time-delay differential equation is constructed based on the second-order link transfer function with delay;

[0018] (102) Define a sensitivity variable for each parameter to be identified in the original time-delay differential equation; obtain the dynamic equation of the sensitivity variable by differentiating the original time-delay differential equation, and transform each sensitivity variable S i (t) are substituted into the derived dynamic equations to obtain the sensitivity equations; the original delay differential equation and all the sensitivity equations are combined to form an extended neutral differential equation, and the adaptive step size algorithm is used to solve the extended neutral differential equation;

[0019] (103) Based on the response data T mea With the calculated data T cal Define the objective function J(θ);

[0020] (104) Use sensitivity variables to directly calculate the objective function gradient;

[0021] (105) The trust region reflective algorithm is used to iteratively update the time-delay system parameters.

[0022] Furthermore, step (101) includes:

[0023] The second-order link transfer function with delay is simplified by cross-multiplication and Laplace transformation according to the automatic control principle to obtain the original time-delay differential equation:

[0024]

[0025] Where T(t) is the temperature output, P(t-τ) is the power input, and the parameter set to be identified is θ = [a, b, K, τ], where a>0, b>0, K>0, τ>0.

[0026] Furthermore, step (102) includes:

[0027] For each parameter θ to be identified i ∈θ, define the sensitivity variable S i (t) is:

[0028]

[0029] The individual sensitivity equations are:

[0030]

[0031] The expanded neutral differential equation is:

[0032]

[0033] Furthermore, step (103) includes:

[0034]

[0035] Where N represents the number of data; t k represents the kth moment.

[0036] Furthermore, step (104) includes:

[0037]

[0038] Among them, S i (t k ) is the sensitivity variable at sampling time t k The value of .

[0039] Furthermore, step (105) includes:

[0040]

[0041] Among them, θ (n) is the system parameter of the nth iteration, is the objective function gradient H (n) is the Hessian matrix approximation, and α is the adaptive step size factor that controls the amplitude of parameter updates;

[0042] The Hessian matrix is ​​approximately updated by the BFGS quasi-Newton method;

[0043]

[0044] Where s = θ (n+1) -θ (n) ,

[0045] Furthermore, the temperature control method for the plastic extruder further comprises: performing singular value decomposition on the sensitivity matrix to avoid overfitting;

[0046]

[0047] Where U is the left singular vector, Σ is the singular value matrix, and V is the right singular vector;

[0048] Set the threshold ξ, clear the singular values ​​in Σ that are smaller than ξ, and get the modified matrix ∑ + ;

[0049] Therefore, the target gradient is corrected to:

[0050]

[0051] Among them, (∑ + ) + Yes + Take the reciprocal of the non-zero elements in .

[0052] A temperature control system for a plastic extruder of the present invention comprises:

[0053] A system identifier is used to identify time-delay system parameters of a mathematical model with a time-delay link by a response sensitivity method; the mathematical model with a time-delay link is a mathematical model of a barrel temperature control system; the identified time-delay system parameters are used to update the time-delay system parameters in a reference model; the reference model is initially a mathematical model with a time-delay link;

[0054] a comparator for subtracting the time-delayed output of the Smith predictor from the output of the updated reference model to obtain an error signal; the updated reference model uses the barrel temperature monitoring value as input;

[0055] A multiplier is used to use the barrel temperature monitoring value as an adjustable gain, multiply it by the error signal, and amplify the error signal;

[0056] a controller for obtaining a first control signal by a PI control method based on the amplified error signal;

[0057] An adaptive module, configured to multiply the first control signal by a barrel temperature monitoring value to obtain a second control signal;

[0058] The Smith predictor is used to perform hysteresis compensation control on a mathematical model with a time lag link through the Smith predictor method based on the second control signal to obtain an actual temperature output for controlling the barrel temperature.

[0059] Beneficial Effects: Compared with existing technologies, this invention offers the following significant advantages: It proposes a temperature control system that uses a Smith predictor to reduce the impact of time lag on temperature control in a plastic extruder after identifying the system parameters of the actual controlled object based on the response sensitivity method. The comparator, Smith predictor, and adaptive module work together to regulate the barrel temperature of the plastic extruder, reducing system control overshoot and improving system dynamic performance and robustness. The response sensitivity method offers advantages such as accurate identification results and strong anti-interference capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a block diagram of a temperature control system for a plastic extruder provided by an embodiment of the present invention;

[0061] Figure 2 is the recognition effect of the system identifier in the embodiment of the present invention under 1% Gaussian noise;

[0062] Figure 3 is the tracking curve in the embodiment of the present invention when there is no temperature requirement change, where Figure 3 (a) is a comparison chart of actual temperature output and ideal temperature output. Figure 3 (b) is the temperature error diagram;

[0063] Figure 4 is a tracking curve in the embodiment of the present invention when the temperature requirement changes, wherein Figure 4 (a) is a comparison chart of actual temperature output and ideal temperature output. Figure 4 (b) is the temperature error diagram. DETAILED DESCRIPTION

[0064] The present invention will be further described below with reference to the accompanying drawings.

[0065] Example 1

[0066] Example 1 provides a temperature control method for a plastic extruder, comprising the following steps:

[0067] (1) Identifying the time-delay system parameters of a mathematical model with a time-delay link by a response sensitivity method; the mathematical model with a time-delay link is a mathematical model of a barrel temperature control system.

[0068] The principle of identifying time-delay system parameters using the response sensitivity method is as follows:

[0069] The general time-delay system can be represented by the following time-delay differential equation:

[0070]

[0071] Where x=[x1,x2,…,xn ] T represents the n-dimensional system response; τ represents the time delay parameter; θ i is a general system parameter, i=1,2,…,m, m represents the number of parameters; t0 represents the initial time, t f Represents the final moment.

[0072] Assume measurement data The relationship with the observed variable x is Where L is the preset linear operator. Then the measurement data set is All general system parameters and time-delay parameters in formula (1) form a parameter column vector Then the calculated data corresponding to the measured data can be recorded as R(θ)=(d(t1),d(t2),…,d(t n )) T .

[0073] Then the time-delay parameter identification problem can be transformed into a least squares optimization problem:

[0074]

[0075] Among them, θ * is the parameter finally identified; J(θ) is the least squares objective function; For the vector λ=[λ1,λ2,…,λ n ] T The second norm of .

[0076] For the minimum value problem of formula (2), the iterative optimization method is used to solve it. (k) Perform a first-order Taylor expansion of R(θ):

[0077] R(θ)≈R(θ (k) )+S(θ (k) )Δθ (3)

[0078] Among them, θ (k) is the value of the system parameters in the kth iteration, S(θ (k) ) is the sensitivity matrix, Δθ is θ-θ (k) Substituting formula (3) into the minimum value problem in formula (2), formula (2) can be approximately transformed into a linear least squares objective function

[0079]

[0080] in, It is called the response residual; the sensitivity matrix S(θ (k) ) is:

[0081]

[0082] The system response x(t) is related to the general system parameter θ i The sensitivity of follows the following differential equation:

[0083]

[0084] in, is the first-order derivative of x with respect to t, F is F in formula (1), x τ =x(t-τ).

[0085] The sensitivity of the system response x(t) to the time delay parameter τ satisfies:

[0086]

[0087] in, is x τ The first derivative with respect to t.

[0088] For the linear least squares objective function obtained by formula (4), gradient calculation and trust region reflection algorithm are used to iteratively update the time-delay system parameters.

[0089] Combine Figure 1 The mathematical model with a time-delay link includes a system model 11 and a time-delay link 12. The system model 11 is a time-delay-free model of the actual controlled system, and the time-delay link 12 is a lag link of the actual controlled system.

[0090] The starting temperature of the barrel is the initial temperature of the circulating water, that is, the temperature of the circulating water in the indoor environment. As the electric heating system heats the circulating water, the water temperature gradually rises. Because it takes a certain amount of time for the water temperature to be transferred to the barrel, the barrel temperature will not change for a period of time, showing a certain hysteresis, which can be expressed as a hysteresis link. When the electric heating power is changed to adjust the circulating water temperature, the circulating water temperature will not rise to the set value immediately, but requires a certain amount of time to change, so this process can be expressed as an inertia link. The rate of increase of the circulating water temperature is related to the electric heating power and can be expressed as a proportional link. Therefore, a second-order link transfer function with delay is used to identify the mathematical model of the barrel temperature control system. The relationship between the second-order link transfer function with delay is:

[0091]

[0092] Where T(s) represents the barrel temperature; P(s) represents the electric heating power; τ represents the time lag parameter; a, b, and K are system parameters.

[0093] The response sensitivity method for identifying time-delay system parameters specifically includes the following steps:

[0094] (101) The original time-delay differential equation is constructed based on the second-order link transfer function with delay;

[0095] The second-order link transfer function with delay is simplified by cross-multiplication and Laplace transformation according to the automatic control principle to obtain the original time-delay differential equation:

[0096]

[0097] Where T(t) is the temperature output, P(t-τ) is the power input, and the parameter set to be identified is θ = [a, b, K, τ], where a>0, b>0, K>0, τ>0.

[0098] (102) Define a sensitivity variable for each parameter to be identified in the original delay differential equation;

[0099] For each parameter θ to be identified i ∈θ, define the sensitivity variable S i (t) is:

[0100]

[0101] The dynamic equation of the sensitivity variable is obtained by differentiating the original time-delay differential equation, and each sensitivity variable S i (t) are substituted into the derived kinetic equations to obtain the sensitivity equations;

[0102]

[0103] The individual sensitivity equations are:

[0104]

[0105] The original delay differential equation and all sensitivity equations are combined to form an extended neutral differential equation, and the adaptive step-size algorithm is used to solve the extended neutral differential equation.

[0106]

[0107] (103) Based on the response data T mea (The actual output of the controlled system is the measured value) and the calculated data T cal (The output of the controlled system is identified and is a calculated value) Define the objective function J(θ);

[0108]

[0109] Where N represents the number of data; t k represents the kth moment;

[0110] (104) Use sensitivity variables to directly calculate the objective function gradient;

[0111]

[0112] Among them, S i (t k ) is the sensitivity variable at sampling time t k The value of .

[0113] (105) The trust region reflective algorithm is used to iteratively update the time-delay system parameters.

[0114]

[0115] Among them, θ (n) is the system parameter of the nth iteration, is the objective function gradient H (n) is the Hessian matrix approximation, and α is the adaptive step size factor that controls the amplitude of parameter updates.

[0116] The Hessian matrix is ​​approximately updated by the BFGS quasi-Newton method;

[0117]

[0118] Where s = θ (n+1) -θ (n) ,

[0119] In the process of identifying the time-delay system parameters using the response sensitivity method of this embodiment, the following operations are also performed:

[0120] Perform singular value decomposition on the sensitivity matrix to avoid overfitting;

[0121]

[0122] Among them, U is the left singular vector (orthogonal matrix), Σ is the singular value matrix (diagonal matrix), and V is the right singular vector (orthogonal matrix).

[0123] Set the threshold ξ, clear the singular values ​​in Σ that are smaller than ξ, and get the modified matrix ∑ + ;

[0124] Therefore, the target gradient is corrected to:

[0125]

[0126] Among them, (∑ + ) + Yes + Take the reciprocal of the non-zero elements in .

[0127] (2) Using the identified time-delay system parameters, the time-delay system parameters in the reference model are updated. The reference model is initially a mathematical model with a time-delay link.

[0128] (3) Subtracting the time-delay-free output obtained by the Smith prediction method from the output of the updated reference model to obtain an error signal; the updated reference model uses the barrel temperature monitoring value as input;

[0129] (4) Using the barrel temperature monitoring value as the adjustable gain, multiplying it by the error signal to amplify the error signal;

[0130] (5) obtaining a first control signal through a PI control method based on the amplified error signal;

[0131] (6) Multiply the first control signal by the barrel temperature setting value to obtain the second control signal (the multiplication is to control to the expected temperature faster, make the overshoot smaller, and stabilize faster);

[0132] (7) Based on the second control signal, a hysteresis compensation control is performed on the mathematical model with a time lag link by using the Smith prediction method to obtain an actual temperature output for controlling the barrel temperature;

[0133] (8) Loop through steps (2) to (7).

[0134] Example 2

[0135] like Figure 1 As shown, embodiment 2 provides a temperature control system for a plastic extruder, comprising:

[0136] The system identifier 25 is used to identify the time-delay system parameters of the mathematical model with a time-delay link by using a response sensitivity method; the mathematical model with a time-delay link is the mathematical model of the barrel temperature control system; the identified time-delay system parameters are used to update the time-delay system parameters in the reference model 24 to ensure stable control; the reference model 24 is initially a mathematical model with a time-delay link;

[0137] The comparator 23 is used to subtract the time-delay-free output obtained by the Smith predictor 10 (i.e., the output of the mathematical model without the time-delay link, that is, the output of the aforementioned system model 11) from the output of the updated reference model 24 to obtain an error signal (representing the temperature error); the updated reference model 24 uses the barrel temperature monitoring value as input;

[0138] The multiplier 26 is used to use the barrel temperature monitoring value as an adjustable gain, multiply it by the error signal, amplify the error signal, and improve the tracking accuracy of the temperature output;

[0139] The controller 22 is a PI controller, configured to obtain a first control signal by a PI control method based on the amplified error signal;

[0140] Adaptive module 21, used to multiply the first control signal by the barrel temperature monitoring value to obtain a second control signal so that the actual temperature output can track the temperature input;

[0141] Smith Predictor 10 is used to perform hysteresis compensation control on a mathematical model with a time lag using the Smith Prediction method based on the second control signal, thereby obtaining an actual temperature output for controlling the barrel temperature. Smith Predictor 10 is actually the controlled object. To simplify the system structure, this embodiment combines the Smith Predictor and the actual controlled object into a single Smith Predictor. Smith Predictor 10 is used to eliminate time lag in the system's mathematical model during controller design.

[0142] Figure 2 This is the identification performance of the system identifier in the presence of 1% Gaussian noise. The true system model parameters are a = 300, b = 50, K = 0.9, and τ = 10. The identified system model parameters are a = 312.71, b = 50.4, K = 0.9, and τ = 9.56. High accuracy is maintained in the presence of 1% Gaussian noise.

[0143] Figure 3 This is the tracking curve for the present invention when no temperature change is required. The temperature is set at 80°C. The tracking curve and error curve show that the tracking effect is almost zero overshoot. At 300 seconds, temperature tracking is complete, and the temperature change is smooth and oscillatory.

[0144] Figure 4 This is the tracking curve for the present invention under varying temperature requirements. The temperature is initially set at 80°C, and at 1000 seconds the required temperature changes to 100°C. The tracking curve and error curve show that tracking of the required temperatures of 80°C and 100°C is completed at 300 seconds and 750 seconds, respectively, with virtually no overshoot or oscillation.

Claims

1. A temperature control method for a plastic extruder, characterized in that: include: (1) Identify the time-delay system parameters of the mathematical model with time-delay links through the response sensitivity method; The mathematical model with the time lag link is a mathematical model of the barrel temperature control system; (2) Using the identified time-delay system parameters, the time-delay system parameters in the reference model are updated. The reference model is initially a mathematical model with a time-delay link. (3) Subtracting the time-delay-free output obtained by the Smith prediction method from the output of the updated reference model to obtain an error signal; the updated reference model uses the barrel temperature monitoring value as input; (4) Using the barrel temperature monitoring value as the adjustable gain, multiplying it by the error signal to amplify the error signal; (5) obtaining a first control signal through a PI control method based on the amplified error signal; (6) Multiplying the first control signal by the barrel temperature setting value to obtain a second control signal; (7) Based on the second control signal, a hysteresis compensation control is performed on the mathematical model with a time lag link by using the Smith prediction method to obtain an actual temperature output for controlling the barrel temperature; (8) Loop through steps (2) to (7).

2. The temperature control method for a plastic extruder according to claim 1, wherein: In step (1), the mathematical model of the barrel temperature control system is identified using the delayed second-order link transfer function. The relationship of the delayed second-order link transfer function is: Where T(s) represents the barrel temperature; P(s) represents the electric heating power; τ represents the time lag parameter; a, b, and K are system parameters.

3. The temperature control method for a plastic extruder according to claim 2, wherein: Step (1) includes: (101) The original time-delay differential equation is constructed based on the second-order link transfer function with delay; (102) Define a sensitivity variable for each parameter to be identified in the original time-delay differential equation; obtain the dynamic equation of the sensitivity variable by differentiating the original time-delay differential equation, and transform each sensitivity variable S i (t) are substituted into the derived dynamic equations to obtain the sensitivity equations; the original delay differential equation and all the sensitivity equations are combined to form an extended neutral differential equation, and the adaptive step size algorithm is used to solve the extended neutral differential equation; (103) Based on the response data T mea With the calculated data T cal Define the objective function J(θ); (104) Use sensitivity variables to directly calculate the objective function gradient; (105) The trust region reflective algorithm is used to iteratively update the time-delay system parameters.

4. The temperature control method for a plastic extruder according to claim 3, wherein: Step (101) comprises: The second-order link transfer function with delay is simplified by cross-multiplication and Laplace transformation according to the automatic control principle to obtain the original time-delay differential equation: Where T(t) is the temperature output, P(t-τ) is the power input, and the parameter set to be identified is θ = [a, b, K, τ], where a>0, b>0, K>0, τ>0.

5. The temperature control method for a plastic extruder according to claim 4, characterized in that: Step (102) includes: For each parameter θ to be identified i ∈θ, define the sensitivity variable S i (t) is: The individual sensitivity equations are: The expanded neutral differential equation is:

6. The temperature control method for a plastic extruder according to claim 5, characterized in that: Step (103) includes: Where N represents the number of data; t k represents the kth moment.

7. The temperature control method for a plastic extruder according to claim 6, wherein: Step (104) includes: Among them, S i (t k ) is the sensitivity variable at sampling time t k The value of .

8. The temperature control method for a plastic extruder according to claim 7, characterized in that: Step (105) includes: Among them, θ (n) is the system parameter of the nth iteration, is the objective function gradient H (n) is the Hessian matrix approximation, and α is the adaptive step size factor that controls the amplitude of parameter updates; The Hessian matrix is ​​approximately updated by the BFGS quasi-Newton method; where s = θ (n+1) -θ (n) , 9. The temperature control method for a plastic extruder according to any one of claims 1 to 8, characterized in that: It also includes: performing singular value decomposition on the sensitivity matrix to avoid overfitting; Where U is the left singular vector, Σ is the singular value matrix, and V is the right singular vector; Set the threshold ξ, clear the singular values ​​in Σ that are smaller than ξ, and get the modified matrix ∑ + ; Therefore, the target gradient is corrected to: Among them, (∑ + ) + Yes + Take the reciprocal of the non-zero elements in .

10. A temperature control system for a plastic extruder, characterized in that: include: A system identifier for identifying time-delay system parameters of a mathematical model with a time-delay link by using a response sensitivity method; The mathematical model with a time-delay link is a mathematical model of a barrel temperature control system; the identified time-delay system parameters are used to update the time-delay system parameters in the reference model; the reference model is initially a mathematical model with a time-delay link; a comparator for subtracting the time-delayed output of the Smith predictor from the output of the updated reference model to obtain an error signal; the updated reference model uses the barrel temperature monitoring value as input; A multiplier is used to use the barrel temperature monitoring value as an adjustable gain, multiply it by the error signal, and amplify the error signal; a controller for obtaining a first control signal by a PI control method based on the amplified error signal; An adaptive module, configured to multiply the first control signal by a barrel temperature monitoring value to obtain a second control signal; The Smith predictor is used to perform hysteresis compensation control on a mathematical model with a time lag link through the Smith predictor method based on the second control signal to obtain an actual temperature output for controlling the barrel temperature.

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