A model predictive compensation large heat flow test control method

Abstract

The application provides a model prediction compensation high heat flux test control method, which takes a graphite heating finite element model as a prediction model for controlling a high heat flux test system, firstly expresses a process of radiation heating of a test piece by a graphite heating element according to a virtual work principle, then establishes a transfer function between input electric power and output radiation heat of a controlled object, and substitutes a time-varying temperature field of graphite heating calculated by the prediction model into closed-loop control of the test system; finally, a time sequence prediction model is established, errors generated by the test system are compared with a test heating target temperature field, and the errors are applied to a controller of the system as input to pre-adjust and compensate parameters of the controller. The model prediction compensation high heat flux test control method provided by the application solves a control problem of large inertia, nonlinearity and time variation of a thermal test system composed of graphite heating elements, and ensures precision of construction of a ground aerodynamic heat simulation test environment.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic thermal simulation testing, and in particular to a model-predictive compensation method for controlling large heat flux tests. Background Technology

[0002] With the development of high Mach number weapons, spacecraft face increasingly harsh thermal environments, and the temperature field distribution characteristics of structural surfaces change rapidly over time, exhibiting highly transient characteristics. In ground tests, graphite heating can be used to conduct megawatt-level heat flux tests to evaluate the thermal protection performance of spacecraft and their structural mechanical response under high-temperature environments. However, the thermal test heating control system composed of graphite heating elements has characteristics such as large inertia, nonlinearity, and time-varying nature, which can easily lead to problems of "over-control" and "under-control". Summary of the Invention

[0003] To address the aforementioned problems, the present invention aims to provide a model-predictive compensation method for high heat flux test control. This method uses a graphite heating finite element model as the predictive model for the control of the high heat flux test system. First, the process of radiative heating of the test specimen by the graphite heating element is expressed based on the principle of virtual work. Then, a transfer function between the input electrical power and output radiant heat of the controlled object is established. The temperature field of graphite heating over time, calculated by the predictive model, is then substituted into the closed-loop control of the test system. Finally, a time-series predictive model is established, compared with the target temperature field of the test heating, and the error generated by the test system is predicted. This error is then used as input to the system controller to pre-adjust and compensate the controller parameters. The specific steps are as follows:

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

[0005] The graphite heating element heats the test piece via radiation during operation. Based on the principle of virtual work, the expression for the virtual work equation for heat conduction is obtained as follows:

[0006]

[0007] Where T is the graphite temperature, R h It is the pyrogen source term for a chemical reaction, P h This is the phase change reaction heat source term, where ρ is the graphite density, k is the thermal conductivity, x and y represent the coordinate positions, Q is the internal heat source of the graphite, i.e., the Joule heat generated by the electric current, and the graphite heating radiation boundary condition is:

[0008]

[0009] In the formula, q0 is the heat flux density, 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 a finite element model for graphite heating.

[0011] The spatial domain is discretized into finite element volumes, denoted by the symbol e. The temperature within each element is represented by the nodal temperature T. i Interpolation yields N i Using the shape function of a two-dimensional rectangular element, the nodal temperature as a function of time is expressed as follows:

[0012]

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

[0014] MV+ST i =F (4)

[0015] Where M is the heat source matrix, V is the derivative matrix of nodal temperature with respect to time, S is the heat conduction matrix, and F is the temperature load array.

[0016]

[0017] in,

[0018]

[0019] c is the electrothermal conversion coefficient, and the internal heat source of graphite is Joule heat generated by electric current.

[0020] Q = r e J 2 (12)

[0021] In the formula, r e Let J be the unit resistivity and J be the current density.

[0022]

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

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

[0025] MV+ST i t+Δt =F t+Δt (14)

[0026] make Substituting into the above equation, we obtain the iterative solution form:

[0027] (M+S)T i t+Δt =ΔtF t+Δt +MT t (15) The temperature field of graphite heating over time was calculated using the Newton iteration method.

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

[0029] Establish the transfer function between the input electrical power and the output radiant heat of the controlled object. During the operation of the graphite heating element, energy conservation yields:

[0030]

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

[0032] q=ε·σ·T 4 ·A (17)

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

[0034] Transform equations (16) and (17) into incremental form:

[0035]

[0036] Substituting equation (18) into equation (19), we get:

[0037]

[0038] In the formula,

[0039]

[0040] Equation (20) is transformed by Laplace to obtain the transfer function between the input electrical power and the output radiant heat of the controlled object, where s is the Laplace operator and τ is the time constant of the heating element:

[0041]

[0042] S5. Establish a model-predictive compensation-based high-heat-flux experimental control system.

[0043] A graphite heating finite element model was used as the predictive model for the control of the experimental system, and the predictive model was substituted into the closed-loop control algorithm.

[0044] S6. Calculate the time-domain predicted value and pre-adjust and compensate the controller output.

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

[0046] The time-domain prediction is performed using the autoregressive moving average method, as follows:

[0047] S6.1: Assume the predicted data forms a data sequence O according to the changes over time. t Data sequence O t With each stimulus I in the previous time step l t-1 I t-2 I t-3 , ..., I t-l Related, can be expressed as:

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

[0049] Z in equation (23) I Representing errors, β1, β2, β3, ..., β l For each influencing factor I t-1 I t-2 I t-3 …I t-l The coefficient.

[0050] Data sequence O t It will also be affected by its own changing pattern, and its value O in the previous n steps. t-1 O t-2 O t-3 …O t-n The relevant pattern is expressed by the following formula:

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

[0052] Z in equation (24) O Representing errors, α1, α2, α3, ..., α n The first n steps of the data sequence take O values. t-1 Ot-2 O t-3 …O t-n The coefficient.

[0053] S6.2: Based on the relationships between variables in multiple linear regression analysis, the expression is obtained as follows:

[0054]

[0055] The results were:

[0056]

[0057] S6.3: For the graphite heating system, based on the temperature change data predicted by the model, the transfer function of the heating system is discretized, and the Z-function form of the heating system is obtained through transformation equations:

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

[0059] Transforming the Z-function of the system yields the difference equations for the heating system:

[0060]

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

[0062] The beneficial effects achieved by this invention are as follows: The innovative aspect of the model prediction compensation control method provided by this invention is the introduction of a predictive model as a feedforward link into the original control system, which is an improvement on the original system. It is simple to develop, convenient to operate during the test process, precise in control, and reusable. It solves the problems of large inertia, nonlinearity, and time-varying control of thermal test systems composed of graphite heating elements, and ensures the accuracy of ground aerodynamic thermal simulation test environment construction. Attached Figure Description

[0063] Figure 1 Flowchart of the high heat flux experimental control method for model prediction compensation provided by this invention;

[0064] Figure 2 A schematic diagram of the graphite heating finite element model provided by this invention.

[0065] In the diagram: R represents the target temperature field for the experimental heating; T represents the heating temperature of the graphite; E represents the system error; U represents the control output of the controller, i.e., the voltage intensity; I represents the input variable of the control system; O represents the output variable; T i (t) is the element node temperature at time t, where i = 1, 2, ..., 8; q0 is the heat flux density; Ω represents the element volume domain; and Γ is the graphite boundary. Detailed Implementation

[0066] The adaptive adjustment control method for aerodynamic thermal simulation experiments proposed in this invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of this invention will become clearer from the following description and claims. It should be noted that the drawings are all in a very simplified form and use non-precise ratios, and are only used to facilitate and clarify the illustration of the embodiments of this invention.

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

[0068] like Figure 2 As shown, the graphite heating element heats the test piece via radiation during operation. Based on the principle of virtual work, the expression for the virtual work equation for heat conduction is obtained as follows:

[0069]

[0070] Where T is the graphite temperature, R h It is the pyrogen source term for a chemical reaction, P h This is the phase change reaction heat source term, where ρ is the graphite density, k is the thermal conductivity, x and y represent the coordinate positions, Q is the internal heat source of the graphite, i.e., the Joule heat generated by the electric current, and the graphite heating radiation boundary condition is:

[0071]

[0072] In the formula, q0 is the heat flux density, 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 a finite element model for graphite heating.

[0074] The spatial domain is discretized into finite element volumes, denoted by the symbol e. The temperature within each element is represented by the nodal temperature T. i Interpolation yields N i Using the shape function of a two-dimensional rectangular element, the nodal temperature as a function of time is expressed as follows:

[0075]

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

[0077] MV+ST i =F (4)

[0078] Where M is the heat source matrix, V is the derivative matrix of nodal temperature with respect to time, S is the heat conduction matrix, and F is the temperature load array.

[0079]

[0080] in,

[0081]

[0082] c is the electrothermal conversion coefficient, and the internal heat source of graphite is Joule heat generated by electric current.

[0083] Q = r e J 2 (12)

[0084] In the formula, r e Let J be the unit resistivity and J be the current density.

[0085]

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

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

[0088] MV+ST i t+Δt =F t+Δt (14)

[0089] make Substituting into the above equation, we obtain the iterative solution form:

[0090] (M+S)T i t+Δt =ΔtF t+Δt +MT t (15) The temperature field of graphite heating over time was calculated using the Newton iteration method.

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

[0092] Establish the transfer function between the input electrical power and the output radiant heat of the controlled object. During the operation of the graphite heating element, energy conservation yields:

[0093]

[0094] In the formula, P is the input electrical power of the graphite heating element, c is the electrothermal conversion coefficient, and C pLet m be the specific heat capacity of the graphite material, m be the mass of the heating element, and q be the heat radiated outward by the heating element. The expression is as follows:

[0095] q=ε·σ·T 4 ·A (17)

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

[0097] Transform equations (16) and (17) into incremental form:

[0098]

[0099] Substituting equation (18) into equation (19), we get:

[0100]

[0101] In the formula,

[0102]

[0103] Equation (20) is transformed by Laplace to obtain the transfer function between the input electrical power and the output radiant heat of the controlled object, where s is the Laplace operator and τ is the time constant of the heating element:

[0104]

[0105] S5. Establish a model-predictive compensation-based high-heat-flux experimental control system.

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

[0107] S6. Calculate the time-domain predicted value and pre-adjust and compensate the controller output.

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

[0109] The time-domain prediction is performed using the autoregressive moving average method, as follows:

[0110] S6.1: Assume the predicted data forms a data sequence O according to the changes over time. t Data sequence O t With each stimulus I in the previous time step l t-1 I t-2 I t-3 , ..., I t-l Related, can be expressed as:

[0111] O t =β1I t-1 +β2I t-2 +β3I t-3 +…+β l I t-l +Z I (twenty three)

[0112] Z in equation (23) I Representing errors, β1, β2, β3, ..., β l For each influencing factor I t-1 I t-2 I t-3 …I t-l The coefficient.

[0113] Data sequence O t It will also be affected by its own changing pattern, and its value O in the previous n steps. t-1 O t-2 O t-3 …O t-n The relevant pattern is expressed by the following formula:

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

[0115] Z in equation (24) O Representing errors, α1, α2, α3, ..., α n The first n steps of the data sequence take O values. t-1 O t-2 O t-3 …O t-n The coefficient.

[0116] S6.2: Based on the relationships between variables in multiple linear regression analysis, the expression is obtained as follows:

[0117]

[0118] The results were:

[0119]

[0120] S6.3: For the graphite heating system, based on the temperature change data predicted by the model, the transfer function of the heating system is discretized, and the Z-function form of the heating system is obtained through transformation equations:

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

[0122] Transforming the Z-function of the system yields the difference equations for the heating system:

[0123]

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

[0125] The contents not described in detail in this specification are prior art known to those skilled in the art. It will be apparent 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 invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

Claims

1. A model predictive, compensating, high heat flux test control method, characterized by, The method first expresses the process of radiation heating of the test piece by the graphite heating element according to the virtual work principle, then establishes the transfer function between the input electric power and the output radiation heat of the controlled object, and substitutes the time-varying temperature field of the graphite heating calculated by the prediction model into the closed-loop control of the test system, finally establishes the time series prediction model, compares the test heating target temperature field, and the error generated by the test system, and applies the error as input to the controller of the system, and pre-adjusts and compensates the controller parameters, The specific steps of the method are as follows: S1, establish a heat conduction virtual work equation 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: where T is the graphite temperature, R h is the chemical reaction heat source term, P h is the phase change reaction heat source term, p is the graphite density, k is the thermal conductivity, x and y represent the coordinate position, and Q is the heat source within the graphite, i.e., the Joule heat generated by the current. The graphite heating radiation boundary condition is: In the formula, q0 is the heat flux density, 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, establish a graphite heating finite element model The space domain is discretized into finite element bodies, and the symbol e represents a finite element body. The temperature T of a node of the element body is i The interpolation is obtained as N i The shape function of a two-dimensional rectangular element is used, and the function expression of the node temperature with time is: Substituting the above equation into equation (1), T i the finite element solution equation of the above equation: MV+ST i = F (4) Wherein, M is the heat source matrix, V is the derivative matrix of the node temperature with respect to time, S is the heat conduction matrix, and F is the temperature load array; Wherein, C is the electric heating conversion coefficient, and the internal heat source of the graphite is the Joule heat generated by the current: Q = r e J 2 (12) where r e is the specific resistance of the cell, J is the current density: S3, solve the dynamic heat transfer field finite element model The solution adopts the backward Euler method, and the expression is as follows: MV+ST i t+Δt = F t+Δt (14) Let Substituting into the above equation, we obtain the iterative form: (M + S)T i t+Δt = AtF t+Δt + MT t (15) Using Newton iteration method, the temperature field of graphite heating with time is calculated; S4, establish the transfer function of the controlled object The transfer function between the input electric power and the output radiation heat of the controlled object is established, and during the operation of the graphite heating element, the energy conservation can be obtained: where P is the input electric power of the graphite heating element, c is the electric heat conversion coefficient, C p is the specific heat capacity of the graphite material, m is the mass of the heating element, and q is the heat radiated outward by the heating element, expressed as follows: q = ε - σ - 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 formula (16) and formula (17) into incremental form: Substitute formula (18) into formula (19) to obtain: In the formula, Take Laplace transform of formula (20) to obtain the transfer function between the input electric power and the output radiation heat of the controlled object: Wherein, s is the Laplace operator, and τ is the time constant of the heating element; S5, establish a large heat flow test control system of model prediction compensation The graphite heating finite element model is used as the prediction model of the test system control, and the prediction model is substituted into the closed-loop control algorithm; S6, calculate the time domain prediction value, and pre-adjust and compensate the controller output The prediction value of the heating temperature at each time is obtained by relying on the prediction model analysis, the error generated by the test system is compared with the test heating target temperature field, and the error is applied as input to the controller of the system, and the output control quantity U is pre-adjusted and compensated by the controller, so as to improve the control precision of the graphite heating system; S7, compare the test heating target temperature field, the error generated by the test system, and apply the error as input to the controller of the system, pre-adjust the controller parameters, and improve the control precision of the graphite heating system.

2. The model predictive, compensating, high heat flux test control method of claim 1, wherein, The calculation of the time domain prediction value adopts the autoregressive moving average method for time domain prediction.

3. The model predictive, compensating, high heat flux test control method of claim 1, wherein, The specific process of calculating the time domain prediction value in S6 by using the autoregressive moving average method for time domain prediction is as follows: S6.1: Assume that the predicted data forms a data sequence O t , data sequence O t , in relation to each stimulus I t-1 , I t-2 , I t-3 ,..., I t-l of the previous time instant, can be expressed as: O t = β1I t-1 + β2I t-2 + β3I t-3 + … + β l I t-l + Z I (23) Z in formula (23) I representing errors, β1, β2, β3,..., β l are coefficients for each influencing factor I t-1 , I t-2 , I t-3 ... t-l ​ Data sequence O t At the same time, it is affected by its own variation law, and each value O t-1 , O t-2 , O t-3 … O t-n related to the previous n steps, and the law is represented by the following formula: O t = α1O t-1 + α2O t-2 + α3O t-3 + … + α n O t-n + Z O (24) Z in formula (24) O representing errors, a1, a2, a3,..., a n , O t-1 , O t-2 , O t-3 , O t-n coefficients; S6.2: According to the relationship between variables in multiple linear regression analysis, the expression is obtained: After sorting, we get: S6.3: For the graphite heating system, the transfer function of the heating system is discretized according to the model predicted temperature change data, and the Z function form of the heating system is obtained by transformation equation: Z [O (jT - nT)] = Z -n O(Z) (27) The Z function of the system is transformed to obtain the difference equation of the heating system: S6.4: Establish a time series prediction model for the heating system, use the input variables I(j-i) and output variables O(j-i) of the system at past time to predict the change state of the system temperature O(j) in the future short time, and obtain the predicted value of the heating temperature at the corresponding time.

Images