Large heat flow test control method for model prediction compensation

Abstract

The invention provides a large heat flow test control method for model prediction compensation, which takes a graphite heating finite element model as a prediction model for large heat flow test system control, and comprises the following steps of: firstly, expressing a radiation heating process of a test piece by using a graphite heating element according to a virtual work principle; establishing a transfer function between input electric power and output radiation heat of a controlled object, and substituting a temperature field, which is obtained by calculation of the prediction model and changes along with time, of graphite heating into closed-loop control of a test system; and finally, establishing a time sequence prediction model, comparing a test heating target temperature field, predicting an error generated by a test system, applying the error as an input to a controller of the system, and carrying out pre-adjustment compensation on controller parameters. According to the large heat flow test control method for model prediction compensation provided by the invention, the problems of large inertia, nonlinearity and time-varying control of a thermal test system formed by graphite heating elements are solved, and the construction accuracy of a ground aerodynamic thermal simulation test environment is ensured.

Description

Technical Field

[0001] The invention relates to the field of aerodynamic thermal simulation tests, and in particular to a large heat flux test control method with model prediction compensation. Background Art

[0002] With the development of high Mach number weapons, the thermal environment faced by aircraft has become increasingly harsh, and the temperature field distribution characteristics of the structure surface change rapidly over time, showing high transient characteristics. In ground tests, the use of graphite heating can conduct megawatt-level heat flow tests to assess the thermal protection performance of spacecraft and the structural mechanical response in high-temperature environments. However, the thermal test heating control system composed of graphite heating elements has the characteristics of large inertia, nonlinearity, and time-varying, and is prone to problems of "over-control" and "under-control". Summary of the invention

[0003] In order to solve the above problems, the purpose of the present invention is to provide a large heat flux test control method with model prediction compensation, using the graphite heating finite element model as the prediction model for the control of the large heat flux test system. First, the process of radiant heating of the test piece by the graphite heating element is expressed according to the principle of virtual work, and then the transfer function between the input electric power and the output radiant heat of the controlled object is established, and the temperature field of graphite heating that changes with time calculated by the prediction model is substituted into the closed-loop control of the test system. Finally, a time series prediction model is established to compare the test heating target temperature field, predict the error generated by the test system, and apply this error as input to the system controller to pre-adjust and compensate the controller parameters. The specific steps are as follows:

[0004] S1. Establishing the virtual work equation for heat conduction

[0005] During the working process of the graphite heating element, the test piece is heated by radiation heating, and the heat conduction virtual work equation expression is obtained according to the virtual work principle:

[0006]

[0007] Where T is the graphite temperature, R h is the chemical reaction heat source term, P h is the heat source term of phase change reaction, ρ is the resistivity of graphite, c is the electrothermal conversion coefficient, k is the thermal conductivity, x and y represent the coordinate position, Q is the heat source inside graphite, that is, the Joule heat generated by the current, and the boundary condition of graphite heating radiation is:

[0008]

[0009] Where q0 is the heat flux, Γ is the graphite boundary, T1 is the absolute temperature of the graphite outer wall, T0 is the absolute temperature of the surrounding environment, and ε is the total radiation coefficient.

[0010] S2. Establishing graphite heating finite element model

[0011] The spatial domain is discretized into finite element bodies, and the symbol e represents the finite element body. The temperature inside the element is represented by the node temperature T i Interpolation is obtained, N i Using the shape function of a two-dimensional rectangular element, the function expression of the node temperature over time is:

[0012]

[0013] Substituting the above formula into formula (1), T i The finite element solution equation is:

[0014] MV+ST=F (4)

[0015] Among them, M is the heat source matrix, V is the matrix of the derivatives of node temperature with respect to time, S is the heat conduction matrix, and F is the temperature load array.

[0016]

[0017] in,

[0018]

[0019] The heat source in graphite is the Joule heat generated by the electric current:

[0020] Q=ρ e J 2 (12)

[0021] In the formula, ρ e is the unit resistivity, J is the current density:

[0022]

[0023] S3. Solve the finite element model of dynamic heat transfer field

[0024] The solution is obtained by using the backward Euler method, and the expression is as follows:

[0025] MV+ST t+△t =F t+△t (14)

[0026] make Substituting into the above formula, we get the iterative solution form:

[0027] (M+△tS)T t+△t =F t+△t +MT t (15) The Newton iteration method is used to calculate the temperature field of graphite heating that varies with time.

[0028] S4. Establish the transfer function of the controlled object

[0029] Establish the transfer function between the input electric power and the output radiant heat of the controlled object. During the working process of the graphite heating element, the energy conservation law can be obtained:

[0030]

[0031] Where P is the input power of the graphite heating element, c is the electrothermal conversion coefficient, C p is the specific heat capacity of graphite material, m is the mass of the heating element, q is the heat radiated outward by the heating element, and the expression is as follows:

[0032] q=ε·σ·T 4 ·A (17)

[0033] Where ε is the blackness of the heating element surface, σ is the blackbody radiation constant, and A is the radiation surface area of ​​the heating element.

[0034] Convert equation (16) and equation (17) into incremental form:

[0035]

[0036] Substituting formula (18) into formula (19), we can obtain:

[0037]

[0038] In the formula,

[0039]

[0040] The transfer function between the input electric power and the output radiant heat of the controlled object is obtained by Laplace transforming equation (20), where s is the Laplace operator and τ is the time constant of the heating element:

[0041]

[0042] S5. Establishment of large heat flux test control system with model prediction compensation

[0043] The graphite heating finite element model is used as the prediction model for the experimental system control, and the prediction model is substituted into the closed-loop control algorithm;

[0044] S6. Calculate the time domain prediction value and pre-adjust the controller output for compensation

[0045] Relying on the prediction model analysis, the predicted value of the heating temperature at each moment is obtained. By comparing the target temperature field of the test heating, the error generated by the test system is predicted, and this error is applied as input to the controller of the system. The controller pre-adjusts and compensates the output control quantity U to improve the control accuracy of the graphite heating system.

[0046] The autoregressive moving average method is used for time domain prediction. The process is as follows:

[0047] S6.1: Assume that the predicted data forms a data sequence O according to the change of time t Data sequence O t With each stimulus I at the previous l moments t-1 , I t-2 , I t-3 , L, I t-l It can be expressed as:

[0048] O t =β1I t-1 +β2I t-2 +β3I t-3 +L+β l I t-l +Z I (twenty three)

[0049] Z in formula (23) I Represents error, β1, β2, β3, L, β l For each influencing factor I t-1 ,I t-2 ,I t-3 LI t-l The coefficient of .

[0050] Data sequence O t At the same time, it will be affected by its own changing rules, and each value O of the previous n steps t-1 , O t-2 , O t- 3L t-n The law is expressed by the following formula:

[0051] O t =α1O t-1 +α2O t-2 +α3O t-3 +L+α n O t-n +Z O (twenty four)

[0052] Z in formula (24) O Represents the error, α1, α2, α3, L, α n , is the value O of the data sequence in the first n steps t-1 , O t-2 , O t-3 LO t-n The coefficient of .

[0053] S6.2: Based on the relationship between variables in the multiple linear regression analysis, we get the expression:

[0054]

[0055] After finishing, we get:

[0056]

[0057] S6.3: For the graphite heating system, the transfer function of the heating system is discretized according to the temperature change data predicted by the model, and the Z function form of the heating system is obtained by the transformation equation:

[0058] Z[O(jT-nT)]=Z -n O(Z) (27)

[0059] Transforming the system Z function, we get the difference equation of the heating system:

[0060]

[0061] S6.4: Establish a time series prediction model for the heating system, and use the input variables I(ji) and output variables O(ji) of the system in the past to predict the change state of the system temperature O(j) in the short future time, and obtain the predicted value of the heating temperature at the corresponding time. Compare the heating target temperature field of the test, predict the error generated by the test system, and apply this error as input to the controller of the system, and pre-adjust the controller parameters to improve the control accuracy of the graphite heating system.

[0062] The beneficial effects achieved by the present invention are as follows: the model prediction compensation control method provided by the present invention is innovative in that a prediction model as a feedforward link is introduced into the original control system, which is an improvement on the original system, has simple development, convenient operation in the test process, precise control, and repeatable application, and solves the large inertia, nonlinearity, and time-varying control problems of the thermal test system composed of graphite heating elements, and ensures the accuracy of the construction of the ground aerodynamic thermal simulation test environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Flow chart of the large heat flux test control method with model prediction compensation provided by the present invention;

[0064] Figure 2 Schematic diagram of the graphite heating finite element model provided by the present invention.

[0065] Markings in the figure: R is the test heating target temperature field; T is the graphite heating temperature; E is the system error; U is the control quantity output by the controller, that is, the voltage intensity; I is the control system input variable, O is the output variable; T i (t) is the unit node temperature at time t, where i = 1, 2, …, 8; q0 is the heat flux density; Ω represents the unit volume domain; Γ is the graphite boundary. DETAILED DESCRIPTION

[0066] The following is a further detailed description of the adaptive adjustment control method for aerodynamic thermal simulation test proposed by the present invention in conjunction with the accompanying drawings and specific embodiments. The advantages and features of the present invention will become more apparent from the following description and claims. It should be noted that the accompanying drawings are in a very simplified form and use non-precise ratios, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention.

[0067] S1. Establishing the virtual work equation for heat conduction

[0068] like Figure 2 As shown, the graphite heating element heats the test piece by radiation heating during operation, and the heat conduction virtual work equation expression is obtained according to the virtual work principle:

[0069]

[0070] Where T is the graphite temperature, R h is the chemical reaction heat source term, P h is the heat source term of phase change reaction, ρ is the resistivity of graphite, c is the electrothermal conversion coefficient, k is the thermal conductivity, x and y represent the coordinate position, Q is the heat source inside graphite, that is, the Joule heat generated by the current, and the boundary condition of graphite heating radiation is:

[0071]

[0072] Where q0 is the heat flux, Γ is the graphite boundary, T1 is the absolute temperature of the graphite outer wall, T0 is the absolute temperature of the surrounding environment, and ε is the total radiation coefficient.

[0073] S2. Establishing graphite heating finite element model

[0074] The spatial domain is discretized into finite element bodies, and the symbol e represents the finite element body. The temperature inside the element is represented by the node temperature T i Interpolation is obtained, N i Using the shape function of a two-dimensional rectangular element, the function expression of the node temperature over time is:

[0075]

[0076] Substituting the above formula into formula (1), T i The finite element solution equation is:

[0077] MV+ST=F (4)

[0078] Among them, M is the heat source matrix, V is the matrix of the derivatives of node temperature with respect to time, S is the heat conduction matrix, and F is the temperature load array.

[0079]

[0080] in,

[0081]

[0082] The heat source in graphite is the Joule heat generated by the electric current:

[0083] Q=ρ e J 2 (12)

[0084] In the formula, ρ e is the unit resistivity, J is the current density:

[0085]

[0086] S3. Solve the finite element model of dynamic heat transfer field

[0087] The solution is obtained by using the backward Euler method, and the expression is as follows:

[0088] MV+ST t+△t =F t+△t (14)

[0089] make Substituting into the above formula, we get the iterative solution form:

[0090] (M+△tS)T t+△t =F t+△t +MT t (15) The Newton iteration method is used to calculate the temperature field of graphite heating that varies with time.

[0091] S4. Establish the transfer function of the controlled object

[0092] Establish the transfer function between the input electric power and the output radiant heat of the controlled object. During the working process of the graphite heating element, the energy conservation law can be obtained:

[0093]

[0094] Where P is the input power of the graphite heating element, c is the electrothermal conversion coefficient, C p is the specific heat capacity of graphite material, m is the mass of the heating element, q is the heat radiated outward by the heating element, and the expression is as follows:

[0095] q=ε·σ·T 4 ·A (17)

[0096] Where ε is the blackness of the heating element surface, σ is the blackbody radiation constant, and A is the radiation surface area of ​​the heating element.

[0097] Convert equation (16) and equation (17) into incremental form:

[0098]

[0099] Substituting formula (18) into formula (19), we can obtain:

[0100]

[0101] In the formula,

[0102]

[0103] The transfer function between the input electric power and the output radiant heat of the controlled object is obtained by Laplace transforming equation (20), where s is the Laplace operator and τ is the time constant of the heating element:

[0104]

[0105] S5. Establishment of large heat flux test control system with model prediction compensation

[0106] The graphite heating finite element model is used as the prediction model for the experimental system control, and the prediction model is substituted into the closed-loop control algorithm, such as Figure 1 As shown, the large heat flux test system is a closed-loop control system, the graphite heating element is the controlled object, R represents the given variable, that is, the test heating target temperature field; T represents the controlled variable, that is, the graphite heating temperature; E represents the system error; U represents the control quantity output by the controller, that is, the voltage intensity.

[0107] S6. Calculate the time domain prediction value and pre-adjust the controller output for compensation

[0108] Relying on the prediction model analysis, the predicted value of the heating temperature at each moment is obtained. By comparing the target temperature field of the test heating, the error generated by the test system is predicted, and this error is applied as input to the controller of the system. The controller pre-adjusts and compensates the output control quantity U to improve the control accuracy of the graphite heating system.

[0109] The autoregressive moving average method is used for time domain prediction. The process is as follows:

[0110] S6.1: Assume that the predicted data forms a data sequence O according to the change of time t Data sequence O t With each stimulus I at the previous l moments t-1 , I t-2 , I t-3 , L, I t-l It can be expressed as:

[0111] O t =β1I t-1 +β2It-2 +β3I t-3 +L+β l I t-l +Z I (twenty three)

[0112] Z in formula (23) I Represents error, β1, β2, β3, L, β l For each influencing factor I t-1 ,I t-2 ,I t-3 LI t-l The coefficient of .

[0113] Data sequence O t At the same time, it will be affected by its own changing rules, and each value O of the previous n steps t-1 , O t-2 , O t- 3L t-n The law is expressed by the following formula:

[0114] O t =α1O t-1 +α2O t-2 +α3O t-3 +L+α n O t-n +Z O (twenty four)

[0115] Z in formula (24) O Represents the error, α1, α2, α3, L, α n , is the value O of the data sequence in the first n steps t-1 , O t-2 , O t-3 LO t-n The coefficient of .

[0116] S6.2: Based on the relationship between variables in the multiple linear regression analysis, we get the expression:

[0117]

[0118] After finishing, we get:

[0119]

[0120] S6.3: For the graphite heating system, the transfer function of the heating system is discretized according to the temperature change data predicted by the model, and the Z function form of the heating system is obtained by the transformation equation:

[0121] Z[O(jT-nT)]=Z -n O(Z) (27)

[0122] Transforming the system Z function, we get the difference equation of the heating system:

[0123]

[0124] S6.4: Establish a time series prediction model for the heating system, and use the input variables I(ji) and output variables O(ji) of the system in the past to predict the change state of the system temperature O(j) in the short future time, and obtain the predicted value of the heating temperature at the corresponding time. Compare the heating target temperature field of the test, predict the error generated by the test system, and apply this error as input to the controller of the system, and pre-adjust the controller parameters to improve the control accuracy of the graphite heating system.

[0125] The contents not described in detail in this specification belong to the prior art known to those skilled in the art. It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention.

Claims

1. A large heat flux test control method with model prediction compensation, characterized in that: The method firstly expresses the process of radiation heating of the test piece by using a graphite heating element according to the principle of virtual work, then establishes a transfer function between the input electric power and the output radiation heat of the controlled object, and substitutes the temperature field of graphite heating that changes with time calculated by the prediction model into the closed-loop control of the test system, and finally establishes a time series prediction model, compares the test heating target temperature field, predicts the error generated by the test system, and applies this error as input to the controller of the system to pre-adjust and compensate the controller parameters.

2. A large heat flux test control method with model prediction compensation according to claim 1, characterized in that: The specific steps of the method are as follows: S1. Establishing the virtual work equation for heat conduction During the working process of the graphite heating element, the test piece is heated by radiation heating, and the heat conduction virtual work equation expression is obtained according to the virtual work principle: Where T is the graphite temperature, R h is the chemical reaction heat source term, P h is the heat source term of phase change reaction, ρ is the resistivity of graphite, c is the electrothermal conversion coefficient, k is the thermal conductivity, x and y represent the coordinate position, Q is the heat source inside graphite, that is, the Joule heat generated by the current, and the boundary condition of graphite heating radiation is: Where q0 is the heat flux, Γ is the graphite boundary, T1 is the absolute temperature of the graphite outer wall, T0 is the absolute temperature of the surrounding environment, and ε is the total radiation coefficient; S2. Establishing graphite heating finite element model Discretize the space domain into finite element bodies, symbol e represents the finite element body, and the element node temperature T i Interpolation is obtained, N i Using the shape function of a two-dimensional rectangular element, the function expression of the node temperature over time is: Substituting the above formula into formula (1), T i The finite element solution equation is: MV+ST=F (4) Where M is the heat source matrix, V is the derivative matrix of node temperature with respect to time, S is the heat conduction matrix, and F is the temperature load matrix; in, The heat source in graphite is the Joule heat generated by the electric current: Q=ρ e J 2 (12) In the formula, ρ e is the unit resistivity, J is the current density: S3. Solve the finite element model of dynamic heat transfer field The solution is obtained by using the backward Euler method, and the expression is as follows: MV+ST t+△t =F t+△t (14) make Substituting into the above formula, we get the iterative solution form: (M+△tS)T t+△t =F t+△t +MT t (15) The Newton iteration method is used to calculate the temperature field of graphite heating over time. S4. Establish the transfer function of the controlled object Establish the transfer function between the input electric power and the output radiant heat of the controlled object. During the working process of the graphite heating element, the energy conservation law can be obtained: Where P is the input power of the graphite heating element, c is the electric heat conversion coefficient, C p is the specific heat capacity of graphite material, m is the mass of the heating element, q is the heat radiated outward by the heating element, and the expression is as follows: q=e·s·T 4 ·A (17) In the formula, ε is the blackness of the heating element surface, σ is the blackbody radiation constant, A is the radiation surface area of ​​the heating element, Convert equation (16) and equation (17) into incremental form: Substituting formula (18) into formula (19), we can obtain: In the formula, The transfer function between the input electric power and the output radiant heat of the controlled object is obtained by Laplace transforming equation (20): Where s is the Laplace operator and τ is the time constant of the heating element; S5. Establishment of large heat flux test control system with model prediction compensation The graphite heating finite element model is used as the prediction model for the experimental system control, and the prediction model is substituted into the closed-loop control algorithm; S6. Calculate the time domain prediction value and pre-adjust the controller output for compensation Relying on the prediction model analysis to obtain the predicted value of the heating temperature at each moment, the error generated by the test system is predicted by comparing the test heating target temperature field, and this error is applied as input to the system controller. The output control quantity U is pre-adjusted and compensated by the controller to improve the control accuracy of the graphite heating system. S7. Compare the test heating target temperature field, predict the error generated by the test system, and apply this error as input to the system controller to pre-adjust the controller parameters to improve the control accuracy of the graphite heating system.

3. A large heat flux test control method with model prediction compensation according to claim 2, characterized in that: The time domain prediction value is calculated by using an autoregressive sliding average method for time domain prediction.

4. A large heat flux test control method with model prediction compensation according to claim 1, characterized in that: The specific process of calculating the time domain prediction value in S6 using the autoregressive moving average method to perform time domain prediction is as follows: S6.1: Assume that the predicted data forms a data sequence O according to the change of time t , data sequence O t With each stimulus I at the previous l moments t-1 , I t-2 , I t-3 , L, I t-l It can be expressed as: The t =β1I t-1 +β2I t-2 +β3I t-3 +L+β l I t-l +Z I (23) Z in formula (23) I Represents error, β1, β2, β3, L, β l For each influencing factor I t-1 ,I t-2 ,I t-3 LI t-l The coefficient of Data sequence O t At the same time, it will be affected by its own changing rules, and each value O of the previous n steps t-1 , O t-2 , O t-3 LO t-n The law is expressed by the following formula: The t =α1O t-1 +α2O t-2 +α3O t-3 +L+a n The t-n +Z O (24) Z in formula (24) O Represents the error, α1, α2, α3, L, α n , is the value O of the data sequence in the first n steps t-1 , O t-2 , O t-3 LO t-n The coefficient of S6.2: Based on the relationship between variables in the multiple linear regression analysis, we get the expression: After finishing, we get: S6.3: For the graphite heating system, the transfer function of the heating system is discretized according to the temperature change data predicted by the model, and the Z function form of the heating system is obtained by the transformation equation: Z[O(jT-nT)]=Z -n O(Z) (27) Transforming the system Z function, we get the difference equation of the heating system: S6.4: Establish a time series prediction model for the heating system, and use the input variables I(ji) and output variables O(ji) of the system in the past to predict the changing state of the system temperature O(j) in the short future time, and obtain the predicted value of the heating temperature at the corresponding moment.

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