Self-adaptive precise temperature control method based on global reduced-order perception

Abstract

The invention discloses a global reduced-order perception self-adaptive precise temperature control method. The method comprises the following steps: establishing a heat transfer mathematical model of a precise temperature control object and a thermal environment boundary thereof; performing spatial discretization processing on the heat transfer mathematical model to obtain a heat balance equation; constructing a discrete state space model based on a heat balance equation; carrying out order reduction processing on the discrete state space model based on a Pitot number criterion; arranging a temperature sensor and a heating loop based on the model after order reduction; carrying out dimension expansion processing on the model after order reduction; performing real-time filtering and parameter estimation on the extended state space model by using an extended Kalman filter to obtain posterior estimation values of the temperature and the heat exchange coefficient; and calculating a control quantity according to the posterior estimation value to realize feedforward-feedback composite control. According to the temperature control method provided by the invention, muK-level, high-dynamic and self-adaptive temperature control on the spacecraft precision load instrument under the conditions of sparse sensing and strong noise can be realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of precise control temperature of spacecraft, and particularly relates to a global reduced-order perception adaptive precise control temperature method. BACKGROUND

[0002] In space missions, high-precision load instruments such as space gravitational wave detectors, high-resolution optical remote sensors, synthetic aperture radars, atomic clocks and precise spectrometers, etc., their performance is highly dependent on the thermal stability of the working environment. Temperature fluctuations will cause thermal deformation of optical elements, detector response drift, mechanical structure size instability and electronic system operating point deviation, which will seriously reduce the measurement accuracy and data reliability. For example, the gravitational wave detection mission requires the temperature fluctuation of the core load to be controlled at the μK level to avoid thermal noise interference with ultra-precision interferometric measurement.

[0003] At present, spacecraft thermal control mainly adopts passive thermal insulation as the main strategy and active temperature control as the auxiliary strategy. Passive thermal control can attenuate external thermal disturbances through multi-layer insulation components (MLI), high thermal resistance support structure and phase change material (PCM), although it can provide static thermal stability, but there are obvious limitations: it cannot actively suppress the temperature gradient caused by internal heat sources (such as lasers, electronic equipment waste heat); thermal inertia is large, resulting in thermal response delay; complex structure increases the mass and volume burden.

[0004] In terms of active temperature control, proportional-integral-derivative (PID) controllers are widely used due to their simple structure and engineering maturity. However, PID completely relies on error feedback and does not rely on the physical model of the controlled object, and has weak adaptive ability, making it difficult to cope with nonlinear and time-varying thermal disturbances. The temperature control precision is usually limited to the millikelvin (mK) level, which is difficult to meet the μK level requirement.

[0005] In recent years, control methods based on physical models (such as model predictive control MPC) have shown higher precision potential, but the full-order thermal network model they rely on has high computational complexity, making it difficult to implement real-time operation under the condition of limited on-board computing resources. In addition, spacecraft thermal systems also face three major engineering constraints: temperature sensor sparse distribution, measurement noise suppression bottleneck and strong nonlinear time-varying characteristics of thermal systems. These factors together limit the application of high-precision temperature control technology in the field of space.

[0006] Therefore, there is an urgent need for a new type of precise temperature control method that can break through the mK level temperature control bottleneck and achieve μK level ultra-high precision, and has on-board real-time operation capability, to meet the needs of future space science missions for extreme thermal stability. SUMMARY

[0007] In view of the above-mentioned deficiencies in the field of precise temperature control of spacecraft at present, the application provides a global reduced-order perception adaptive precise temperature control method, which can achieve μK-level precision, fast dynamic response and feasible calculation load of adaptive precise temperature control of spacecraft core load instruments under harsh engineering conditions of sparse sensor distribution, significant measurement noise and strong nonlinear time-varying thermal system through three-level collaborative innovation technologies of high signal-to-noise ratio real-time filtering, global thermal field reconstruction of parameterized reduced-order model and online identification of time-varying parameters.

[0008] To achieve the above-mentioned purpose, the embodiments of the application adopt the following technical solutions:

[0009] A global reduced-order perception adaptive precise temperature control method, the global reduced-order perception adaptive precise temperature control method comprises:

[0010] establishing a heat transfer mathematical model of a precise temperature control object and a thermal environment boundary thereof;

[0011] spatially discretizing the heat transfer mathematical model to obtain a thermal balance equation;

[0012] constructing a discrete state space model based on the thermal balance equation;

[0013] performing reduced-order processing on the discrete state space model based on the Piot number criterion;

[0014] arranging temperature sensors and heating circuits based on the reduced-order model;

[0015] performing dimension expansion processing on the reduced-order model, augmenting time-varying equivalent heat transfer coefficients as part of a system state vector, constructing an extended state space model containing temperature and heat transfer coefficients, and defining statistical characteristics of process noise and measurement noise of the model;

[0016] performing real-time filtering and parameter estimation on the extended state space model by using an extended Kalman filter to obtain posteriori estimation values of temperature and heat transfer coefficients;

[0017] calculating a feedforward control amount based on the posteriori estimation values, combining a feedback control amount to calculate a compound control amount, and outputting to the heating circuit to realize adaptive temperature control of the temperature control object.

[0018] According to an aspect of the application, the heat transfer mathematical model comprises a transient heat conduction equation inside the temperature control object and a heat exchange boundary condition equation of the outer surface of the temperature control object;

[0019] The expression of the transient heat conduction equation is: wherein, is the density of the temperature control object, is the specific heat capacity of the temperature control object, for the temperature control object in 、 、 the thermal conductivity in the direction, the heat generation power per unit volume, the temperature of the object, the time;

[0020] The expression of the heat exchange boundary condition equation is: wherein, the normal direction of the surface of the temperature control object, the heat conduction and exchange coefficient, the temperature of the load cabin plate, the Stefan-Boltzmann constant, the emissivity of the surface of the temperature control object, the radiation angle coefficient between the temperature control object and the load cabin body.

[0021] According to one aspect of the present application, during the spatial discretization process of the mathematical model, the nodes of the heat source concentrated area and the geometric mutation of the temperature control object are encrypted, and the nodes of the heat exchange concentrated area and the boundary mutation of the heat environment boundary are encrypted;

[0022] The heat capacity, self-heat generation and adjacent node heat conduction and exchange coefficient of each temperature control object node are determined, and the radiation and heat conduction and exchange coefficient with the temperature control object of each boundary node are determined;

[0023] After discretization, the state equation describing the thermal dynamic behavior of the system is: wherein, the heat capacity of the i-th node, the temperature of the i-th node, the temperature of the m-th node on the n-th cabin plate, the time, the radiation heat exchange coefficient between the m-th node on the n-th cabin plate and the i-th node of the temperature control object, the heat conduction and exchange coefficient between the m-th node on the n-th cabin plate and the i-th node of the temperature control object, the heat conduction and exchange coefficient between the j-th node inside the temperature control object and the i-th node, the self-heat generation of the i-th node, the active heat compensation control amount applied to the i-th node.

[0024] According to one aspect of the present application, the discrete state space model includes a state vector composed of the temperatures of multiple nodes of the temperature control object, an input vector of the control heat compensation amount, self-heat generation and external disturbance, and corresponding state matrix and input matrix.

[0025] According to one aspect of the present application, the order reduction of the discrete state space model based on the Biot number criterion comprises:

[0026] calculating the Biot number of the discrete object, denoted as Bi;

[0027] performing lumped parameter order reduction on the temperature-controlled object with a Biot number Bi<0.1 to obtain a temperature-controlled object order reduction model, which combines I nodes into one lumped parameter node;

[0028] performing region equivalent order reduction on the thermal environment boundary with a Biot number Bi≥0.1 to obtain a thermal environment boundary order reduction model, which equivalently combines M nodes of each panel into one region node, obtaining an order reduction model with the temperature-controlled object being one-dimensional and the thermal environment boundary being N-dimensional, where N is the number of panels;

[0029] integrating the order reduction model and determining the number of temperature measurement nodes.

[0030] According to one aspect of the present application, the model equation of the temperature-controlled object order reduction model is: wherein, is the radiation coefficient between the mth node on the nth panel and the temperature-controlled object, is the heat conduction exchange coefficient between the mth node on the nth panel and the temperature-controlled object, is the total heat capacity of the temperature-controlled object, is the total heat generation of all nodes of the temperature-controlled object, is the thermal compensation amount of the control system, is the temperature of the temperature-controlled object, is the temperature of the mth node on the nth panel.

[0031] The model equation of the thermal environment boundary order reduction model is: wherein, is the temperature change rate of the temperature-controlled object, is the measured temperature of the nth core panel, is the heat exchange coefficient between the temperature-controlled object and the nth core panel.

[0032] According to one aspect of the present application, the extended state vector of the extended state space model is N+1-dimensional, wherein the first dimension is the temperature of the temperature-controlled object, and the second to N+1 dimensions are the equivalent heat exchange coefficients between each load panel and the temperature-controlled object;

[0033] The process noise and the measurement noise both obey normal distribution with a mean of 0, and their covariance matrices are and respectively, used to characterize the model accuracy and sensor accuracy;

[0034] the and The expression is: wherein, is the variance of the process noise, is the variance of the measurement noise.

[0035] According to an aspect of the present application, the real-time filtering and parameter estimation of the extended state space model by the extended Kalman filter comprises:

[0036] initializing the extended state vector posterior estimate and the posterior error covariance matrix;

[0037] in the prediction stage of the extended Kalman filter, calculating the prior state estimate and the prior error covariance matrix;

[0038] calculating the observation Jacobian matrix, solving the Kalman gain by combining the observation noise covariance, correcting the prior state estimate by the temperature measurement value, and updating the posterior error covariance matrix to obtain the posterior state estimate and the posterior error covariance matrix.

[0039] According to an aspect of the present application, the calculation of the compound control quantity by combining the feedback control quantity comprises:

[0040] extracting the temperature posterior estimate of the temperature-controlled object as the feedback control input;

[0041] estimating the total disturbance heat flow transferred to the temperature-controlled object from the thermal environment boundary based on the posterior estimate of the heat transfer coefficient, the temperature measurement value of each load panel, and the heat generation of the temperature-controlled object itself;

[0042] calculating the feedforward control quantity according to the total disturbance heat flow, which is used to actively offset the foreseeable thermal disturbance;

[0043] superimposing the feedforward control quantity and the feedback control quantity based on the temperature control deviation to generate the compound control quantity, and outputting the compound control quantity to the heating loop to perform power regulation.

[0044] According to an aspect of the present application, the calculation formula of the feedback control quantity is: wherein, is the heat transfer coefficient between the temperature-controlled object and the nth panel, is the target temperature of the temperature-controlled object, is the measured temperature of the nth panel, is the total heat generation of all nodes of the temperature-controlled object, is the feedback gain, is the temperature control deviation;

[0045] The calculation formula of the temperature control deviation is: wherein, is the temperature posterior estimate;

[0046] The composite control quantity needs to meet the power constraint of the heating loop, and when the calculated value exceeds the range of the constraint interval, it is limited within the constraint interval. , ) range, limit in the constraint interval.

[0047] The advantages of the embodiment of the present application are as follows: first, through the reduced-order model and the EKF algorithm, global temperature field high-precision perception based on sparse sensors and muK-level temperature control are realized, and the precision is improved by more than two orders of magnitude compared with the traditional PID control; second, through online identification of time-varying heat transfer coefficients, the nonlinear and time-varying characteristics of the thermal system can be dynamically compensated, and the internal thermal disturbance and external environmental changes have strong robustness and self-adaptive ability; third, the model reduction technology greatly reduces the calculation dimension and complexity, so that it can be run in real time on the limited computing resources of the on-board computer, and the reduction of the number of sensors reduces the system weight, wiring complexity and failure rate, greatly improving the engineering feasibility; fourth, the method can realize fast response without overshoot or with low overshoot, significantly shortens the regulation time, and improves the dynamic performance of the system. Simulation verification shows that the regulation time can be shortened by 51.5% compared with the traditional PI algorithm. Fifth, the method of the present application is not only suitable for space gravitational wave detection, high-resolution remote sensing satellites, deep space probes and other frontier space missions, but also has the potential to migrate and apply to high-tech fields such as semiconductor manufacturing equipment and medical precision instruments. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0049] Figure 1 The flowchart of the adaptive precise temperature control method of the global reduced-order perception according to the present application;

[0050] Figure 2 The structural diagram of the characteristic model of the gravitational wave detection spacecraft according to the present application;

[0051] Figure 3 The reduced-order process diagram of the heat transfer model according to the present application;

[0052] Figure 4 The physical and thermal model diagram of Taiji No. 1 core cabin according to the present application;

[0053] Figure 5 The performance comparison effect diagram of the temperature control method and PI algorithm according to the present application. DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0055] Figure 1 A flowchart of a global order reduction perception adaptive precision temperature control method of the present application is shown. As shown in the figure, Figure 1 , the method comprises the following steps:

[0056] Step S1: establishing a heat transfer mathematical model of the precision temperature control object and the thermal environment boundary thereof.

[0057] Figure 2 A structural schematic diagram of a characteristic model of a gravitational wave detection spacecraft used in the present application is shown. As shown in the figure, Figure 2 , the thermal control structure thereof is sequentially from outside to inside: a platform cabin body (including an outer cabin plate and electronic instruments), a load cabin body, and core load instruments (i.e. the precision temperature control target object). The temperature control technology used in the present application first needs to clearly define the precision temperature control object and the thermal environment boundary thereof, which is the basis for establishing the heat transfer mathematical model.

[0058] Among them, the precision temperature control object specifically refers to the core load instruments carried by the spacecraft which have strict requirements on temperature stability, including gravitational wave detectors, high-resolution optical remote sensors, synthetic aperture radars, high-precision atomic clocks, precision spectrometers, etc. The performance of such objects directly determines the implementation effect of the core mission of the spacecraft, and needs to be taken as the core target of temperature control. Taking the gravitational wave detection spacecraft as an example, the temperature control object is the core load instrument, which is modeled as a solid structure with continuous and uniform medium characteristics and isotropic thermal physical properties.

[0059] Among them, the thermal environment boundary is sequentially from outside to inside: the platform cabin body (including the outer cabin plate and electronic instruments), the load cabin body (composed of N independent cabin plates) and the associated support components. Here, the load cabin body is the direct thermal environment of the temperature control object, and the two mainly exchange heat through radiation and conduction, and the heat exchange path and key influence parameters thereof need to be clearly defined.

[0060] Based on the above definition, a heat transfer mathematical model including the internal transient heat conduction equation of the temperature control target and the external surface heat exchange boundary condition is further established.

[0061] Among them, the precision temperature control target object is simplified as a solid structure with continuous and uniform medium characteristics, and it is assumed that its thermal physical properties are isotropic. The internal transient heat conduction behavior thereof is described by the classical Fourier heat conduction law, which can be expressed by the following partial differential equation (PDE): .

[0062] wherein:

[0063] is the density of the temperature-controlled object in kg / m 3 ;

[0064] is the specific heat capacity of the temperature-controlled object in J / (kg·K);

[0065] is the thermal conductivity of the temperature-controlled object in the , , direction in W / (m·K);

[0066] is the volumetric heat generation in W / m 3 ;

[0067] is the temperature of the temperature-controlled object, which is a function of space and time in K;

[0068] is the time in s.

[0069] From the partial differential equation of the temperature-controlled object, the left side describes the rate of change of the heat capacity of the object, and the right side encompasses the contributions of heat conduction and internal heat generation.

[0070] wherein the heat exchange boundary condition between the outer surface of the temperature-controlled object and the inner surface of the peripheral load cabin is jointly dominated by conduction and radiation mechanisms, which is mathematically described as: .

[0071] wherein:

[0072] is the normal direction of the surface of the temperature-controlled object;

[0073] is the heat conduction exchange coefficient, the value of which is related to the specific installation method of the temperature-controlled object, in W / (m·K);

[0074] is the temperature of the load cabin plate in K;

[0075] is the Stefan-Boltzmann constant in W / (m 2 ·K 4 );

[0076] is the emissivity of the surface of the temperature-controlled object;

[0077] is the radiation angle coefficient between the temperature control object and the load cabin body.

[0078] From the mathematical description of the thermal environment boundary, this boundary condition accurately connects the internal heat transfer of the temperature control object with the external thermal environment interaction, providing complete physical constraints for subsequent discretization and reduction.

[0079] Through the combination of the partial differential equation of the temperature control object and the condition equation of the thermal environment boundary, the whole-chain thermal behavior from the internal heat source to the external thermal environment interaction is completely described.

[0080] Step S2: Spatially discretize the mathematical model.

[0081] In order to facilitate numerical simulation and subsequent controller design, it is necessary to convert the continuous temperature field (i.e. the mathematical model of the temperature control object and the thermal environment boundary described above) that cannot be directly solved into a thermal balance relationship of a finite number of discrete nodes.

[0082] For the precise temperature control scene of a spacecraft, the discrete objects are clearly divided into two categories: one is the precise load instrument as the temperature control target, and the other is its main heat exchange carrier, i.e. the thermal environment boundary of the load cabin body composed of N independent cabin plates. Discretization needs to be based on the geometric configuration, material properties and heat exchange strength of both, and through grid division to achieve discretization, providing structured input for subsequent model reduction and control calculation.

[0083] Among them, the discretization of the temperature control object needs to follow the thermal physical property adaptation principle, and it is regarded as a continuous homogeneous medium entity, which is divided into I interconnected nodes by structured or unstructured grid division. The node distribution needs to focus on the internal heat source and geometric features: the areas with concentrated heat sources such as lasers, electronic devices, and geometric mutations such as corners and interfaces need to have more nodes to accurately capture local heat flow changes; at the same time, the calculation accuracy and the feasibility of reduction need to be balanced, and the optimal number of nodes I is determined through pre-simulation to ensure that each node has clear thermal capacity , its own heat generation and the heat transfer coefficient with adjacent nodes.

[0084] Among them, the discretization of the thermal environment boundary takes the N independent cabin plates of the load cabin body as the unit, and each cabin plate is further discretized into M nodes according to its size, coupling strength with the temperature control object and boundary condition mutation characteristics, finally forming N×M thermal boundary nodes. When discretizing, the areas where the cabin plate directly contacts or has intensive radiation heat exchange with the temperature control object, as well as the boundary parts where the cabin plate connects with the platform cabin and is exposed to the external space, are preferentially discretized to accurately reflect the characteristics of external thermal disturbance transmission and internal thermal coupling. Each boundary node needs to define the radiation heat exchange coefficient and the heat transfer coefficient with the temperature control object nodes, and record the node temperature as the heat exchange boundary parameter.

[0085] After discretization, the thermodynamic behavior of the system can be described by the following state equation: .

[0086] wherein:

[0087] Ci is the heat capacity of the ith node, with the unit of J / K;

[0088] Ti is the temperature of the ith node, with the unit of K;

[0089] Tnm is the temperature of the mth node on the nth panel, with the unit of K;

[0090] t is time, with the unit of s;

[0091] hnm,i is the radiation heat exchange coefficient between the mth node on the nth panel and the ith node of the temperature-controlled object, with the unit of W / K 4 ;

[0092] knm,i is the conduction heat exchange coefficient between the mth node on the nth panel and the ith node of the temperature-controlled object, with the unit of W / K;

[0093] kj,i is the conduction heat exchange coefficient between the jth node and the ith node inside the temperature-controlled object, with the unit of W / K;

[0094] Qi is the self-heating amount of the ith node, with the unit of W;

[0095] Ci is the active heat compensation control amount applied to the ith node, with the unit of W.

[0096] After discretization, the continuous heat transfer partial differential equation is converted into a system of ordinary differential equations, and the heat balance relationship of each node of the temperature-controlled object can be described by the balance formula of the conduction between nodes, the radiation and conduction heat exchange with the boundary, the self-heating, and the control compensation amount, thereby establishing a high-dimensional model basis for subsequent model reduction according to the Biot number criterion, and clearly defining the dynamic correlation between the system state, input, and output.

[0097] Step S3: Construct a discrete state space model to clearly define the boundary temperature, self-heating amount, control heat compensation amount, system state matrix, and input matrix.

[0098] Step S3.1: Clearly define the physical definition and numerical source of the core parameters.

[0099] Quantification and definition of three types of basic parameters: boundary temperature, self-heating, and control heat compensation. The boundary temperature corresponds to the N x M node temperatures of the thermal environment boundary discretization in step S2 (n = 1, 2,..., N; m = 1, 2,..., M), representing the real-time temperature of the nth load cabin plate mth node, the initial value is taken from the thermal simulation steady-state result, and is collected in real time by the temperature sensor in orbit, which is the core driving parameter of heat exchange between the temperature control object and the external thermal environment. The self-heating is the heat generation power of I discrete nodes of the temperature control object (i = 1, 2,..., I), reflecting the internal laser, electronic devices, etc. in the corresponding node per unit time heating, determined by load power consumption test, dynamic heating node needs to use time-varying function description, which is the main disturbance source of internal temperature fluctuation.

[0100] The control heat compensation is the active heating power of the I temperature control nodes , which is the adjustment output of the control system, needs to meet the power constraint of the execution component, and is used to compensate for internal and external thermal disturbances.

[0101] Step S3.2: Define the system state vector and input vector.

[0102] Specifically, the physical parameters are converted into a modeled vector consistent with the control theory. The state vector selects the temperature of the I nodes of the temperature control object to construct, to complete the real-time thermal state information of the temperature control object, and is the core target of model tracking and regulation. The input vector adopts a composite form, which needs to consider control input, internal disturbance input and external disturbance input, to comprehensively cover various input factors affecting state changes.

[0103] Step S3.3: Derive the system state matrix and input matrix.

[0104] Based on the heat balance equation set in step S2, the parameter association is converted into a matrix form. The state matrix is I x I dimension, used to describe the thermal coupling characteristics between node temperatures. The input matrix is I x 3I dimension block matrix, which associates the relationship between control compensation, self-heating, external disturbance and temperature change rate.

[0105] Step S3.4: Generate a discrete state space model.

[0106] Complete the conversion from continuous model to discrete model to form the final form that can be calculated in real time. First, based on the state matrix and input matrix, construct the continuous-time state space equation. Then, use the Euler discretization or Runge-Kutta method, combined with the discrete time step, to convert it into a discrete form, thereby providing a standardized mathematical basis for subsequent model reduction, parameter estimation and controller design.

[0107] Step S4: Perform order reduction on the discretized model based on the Biot number criterion to reduce the number of temperature measurement nodes.

[0108] Step S4.1: Calculate the Biot number of the discretized object.

[0109] Specifically, for the two types of core objects (temperature control objects and thermal environment boundaries) obtained by discretization in step S2, the Biot number is calculated to determine the order reduction basis.

[0110] For the temperature control object, since high thermal conductivity materials are used and the interface heat transfer is reduced through thermal insulation measures, the calculated Bi is less than 0.1; for the thermal environment boundary composed of N load cabin plates, the thermal conductivity of the plate material is of the same order of magnitude as the interface heat transfer coefficient, and the calculated Bi is greater than or equal to 0.1, providing criterion support for differentiated order reduction.

[0111] Step S4.2: Perform lumped parameter order reduction on the temperature control object.

[0112] This step combines the I discrete nodes into a single lumped parameter node for the temperature control object with Bi less than 0.1. Since Bi greater than or equal to 0.1 means that the internal thermal resistance of the temperature control object is much smaller than the surface heat transfer resistance, the internal temperature gradient can be ignored, and the temperature of each node is approximately uniform. The order reduction operation directly integrates the thermal physical parameters of the I nodes: the node heat capacity is summed to obtain the total heat capacity , the self-heating amount is summed to obtain the total heating amount , the control heat compensation amount is integrated into the total compensation amount , and the heat transfer coefficient with the thermal environment boundary is combined, reducing the model dimension of the temperature control object from I dimensions to 1 dimension, retaining only one core temperature measurement node.

[0113] Step S4.3: Perform regional equivalent order reduction on the thermal environment boundary.

[0114] This step equivalently reduces the N×M discrete nodes to N regional nodes for the thermal environment boundary with Bi greater than or equal to 0.1. Since Bi greater than or equal to 0.1 indicates that there is a significant temperature gradient inside the plate, it cannot be directly combined into a single node, but the internal details of the plate can be ignored to retain the regional characteristics. The order reduction operation equivalently reduces the M nodes of each plate to a regional node, taking the temperature of the center temperature measurement point of the plate as the equivalent temperature of the regional node , and calculates the comprehensive heat transfer coefficient between the temperature control object and each plate regional node , reducing the model dimension of the thermal environment boundary from N×M dimensions to N dimensions, and only one temperature measurement node needs to be arranged for each plate.

[0115] Step S4.4: Integrate the order reduction model and determine the number of temperature measurement nodes.

[0116] Specifically, the reduced order results of the two types of objects are integrated to form a low-dimensional model and the final temperature measurement node configuration is determined.

[0117] In the embodiment of the present application, the reduced order model equation of the temperature control object is described as: .

[0118] Among them:

[0119] is the radiation coefficient between the mth node on the nth panel and the temperature control object, with the unit of W / K4;

[0120] is the heat conduction heat exchange coefficient between the mth node on the nth panel and the temperature control object, with the unit of W / K;

[0121] is the total heat capacity of the temperature control object, with the unit of J / K;

[0122] is the total heat generation of all nodes of the temperature control object, with the unit of W;

[0123] is the heat compensation of the control system, with the unit of W;

[0124] is the temperature of the temperature control object;

[0125] is the temperature of the mth node on the nth panel.

[0126] In the embodiment of the present application, the reduced order model equation of the thermal environment boundary is: .

[0127] Among them:

[0128] is the temperature change rate of the temperature control object, with the unit of K / s;

[0129] is the measured temperature of the nth core panel, with the unit of K;

[0130] is the heat exchange coefficient between the temperature control object and the nth core panel, with the unit of W / K.

[0131] According to the above two types of reduced order strategies, for the temperature control object with Bi << 0.1, the multiple nodes after discretization are combined into a single lumped parameter node, and the order is directly reduced from multi-dimensional to 1-dimensional; for the N thermal boundary regions with Bi >= 0.1, such as Figure 3As shown, the M nodes originally discrete in each region are equivalent to one node in the region, and the order of the thermal environment boundary is reduced from N x M to N. After order reduction, the number of temperature measurement points is sharply reduced from N x M + 1 to N + 1, and only sensors need to be arranged at the equivalent nodes of the temperature control object body and each thermal boundary region, which not only solves the engineering problem of sparse sensor arrangement, but also greatly reduces the model calculation complexity, laying a foundation for subsequent on-orbit real-time processing.

[0132] Step S5: arranging temperature sensors and heating circuits based on the reduced-order model.

[0133] Specifically, according to the reduced-order mathematical model, the arrangement of temperature sensors needs to strictly match the model reduction results and the core heat exchange path. The order reduction process realizes dimension reduction through the Peclet number criterion: the temperature control object is reduced to a single lumped parameter node because Bi << 0.1, so only one precise temperature sensor needs to be arranged at the geometric center of the object to represent the equivalent temperature of the whole domain; the load cabin plate is reduced to N dimensions because Bi ≥ 0.1, so one sensor needs to be arranged at the geometric center of each of the N core cabin plates or at the region with the largest heat exchange area with the temperature control object, finally reducing the number of temperature measurement points from N x M + 1 to N + 1. The sensors are selected to be of high signal-to-noise ratio and low drift type, and the probes are pasted to the measured surface through thermal paste, and the signal line is shielded twisted pair to resist interference, and real-time digital filtering technology is used to further improve the measurement accuracy.

[0134] The arrangement of heating circuits needs to be adapted to the sensing points and temperature control requirements, and the strategy of global coverage and partition control is adopted. Thin film heaters are uniformly applied to the outer surface of the temperature control object, covering an area of not less than 80%, and the density of heating elements is increased for local high heat flow regions such as lasers and electronic devices; heating circuits are uniformly arranged along the contour on the outer surface of the load cabin plate to form a stable thermal boundary. The circuits are designed with independent driving channels according to the temperature control object and the load cabin plate, the temperature control object circuit is responsible for fine compensation of μK level, the cabin plate circuit suppresses external disturbances in advance, and the heating power is limited within the upper and lower limits of the execution components, ensuring that the thermal compensation accurately matches the dynamic regulation requirements of the reduced-order model.

[0135] Step S6: performing dimension expansion on the reduced-order model to increase the heat exchange coefficients between the state variables and constructing an extended state space model.

[0136] Specifically, the reduced-order physical model is converted into a mathematical framework suitable for real-time operation of a digital controller and capable of sensing the global thermal state through algorithms. The core is to expand the state to make the key time-varying parameters that cannot be directly measured estimable, thereby realizing global sensing under the condition of sparse sensors. This process can be divided into the following sub-steps:

[0137] Step S6.1, model discretization.

[0138] Transform the continuous time-domain model into a discrete model form suitable for sampling and computation by digital computers.

[0139] Specifically, a numerical discretization method is used to discretize the reduced-order model equations of the thermal environment boundary. The discretization results in a difference equation that can predict the current state based on the previous state and input. The calculation formula is: .

[0140] in:

[0141] Discrete time step;

[0142] : The estimated temperature of the object under temperature control at time k;

[0143] The sampling period of the control system;

[0144] : The temperature of the nth panel measured at time k-1;

[0145] : The equivalent heat transfer coefficient between the temperature-controlled object and the nth compartment at time k-1;

[0146] : The total heat generated by all nodes of the temperature-controlled object at time k-1, in W;

[0147] : The thermal compensation of the control system at time k-1, in W.

[0148] Step S6.2, State Dimension Expansion.

[0149] Specifically, the time-varying equivalent heat transfer coefficient, which was originally used as a model parameter, is... This is augmented to be part of the system state vector. Thus, the system state is no longer just temperature, but an extended state vector containing temperature and various heat transfer coefficients. This transforms the parameter identification problem into a state estimation problem, laying the foundation for using advanced estimation techniques such as Kalman filtering.

[0150] Define the expanded state vector X as: .

[0151] in:

[0152] The temperature of the controlled object at time k is... The unit is K;

[0153] (n = 2, …, N + 1): the equivalent heat transfer coefficient between the (n-1)th load cabin panel and the temperature-controlled object at the kth moment , with the unit of W / K;

[0154] : the measured temperature of the (n-1)th load cabin panel at the (k-1)th moment;

[0155] : the process noise of the nth state equation, with the unit of K.

[0156] After expansion, the dimension of the system state vector increases to N+1, where (n = 2, …, N + 1) is a slowly varying variable, which can be approximately equal to the value at the last moment. The temperature of the temperature-controlled object is the actual temperature measurement value in the system state space, and the equation is: .

[0157] wherein:

[0158] is the temperature measurement value of the temperature-controlled object, with the unit of K;

[0159] is the measurement noise, with the unit of K.

[0160] Step S6.3, constructing a parameterized nonlinear state space model.

[0161] Specifically, based on the expanded state vector, the nonlinear process equation and the linear observation equation of the system are constructed respectively, to provide a complete and formally specified mathematical model for the subsequent extended Kalman filter (EKF), including the process model describing how the state evolves and the observation model describing the relationship between the measurement value and the state.

[0162] Step S6.4: defining the statistical properties of the process noise and the measurement noise.

[0163] In order for the EKF filter to work optimally, the statistical properties of the process noise and the measurement noise need to be defined or assumed.

[0164] wherein the process noise w and the measurement v both obey a normal distribution, i.e.: That is, it is assumed that the process noise w and the measurement noise v both obey a normal distribution with a mean of 0. Their covariance matrices and are key tuning matrices in the EKF algorithm, and their values reflect the designer's prior knowledge of the model accuracy and sensor accuracy.

[0165] wherein, and The expressions are as follows:

[0166] where, is the variance of process noise, is the variance of measurement noise.

[0167] Step S6.5: Linearization and calculation of Jacobian matrix.

[0168] The extended state space model is a nonlinear system, while the standard Kalman filter is only applicable to linear systems, so it needs to be linearized, which is the key step of the extended Kalman filter (EKF).

[0169] where the calculated Jacobian matrix is:

[0170] .

[0171] Through the above several sub-steps, a nonlinear time-varying system with unknown parameters is successfully converted into an extended state dimension nonlinear system model. This model perfectly lays the foundation for the next step of applying the EKF algorithm to estimate the global temperature state and the key time-varying parameters.

[0172] Step S7: Real-time filtering and parameter estimation of the extended state space model using the extended Kalman filter to obtain the posteriori estimation value of temperature and heat transfer coefficient.

[0173] Through the prediction and update iteration process of the extended Kalman filter (EKF), the cooperative estimation of temperature and heat transfer coefficient in the extended state space model is realized, and the measurement noise and model uncertainty are suppressed. The specific process is as follows:

[0174] First, initialize the initial posteriori estimation value of the extended state vector and initialize the posteriori error covariance matrix. Enter the prediction stage, and calculate the priori state estimation and priori error covariance matrix according to the state transition function.

[0175] where:

[0176] The calculation formula of the predicted value is: where, is the posteriori state estimation at the k-1 time;

[0177] The priori state estimation error is calculated using the covariance matrix calculation formula, and the calculation formula is: where, is the Jacobian matrix; .

[0178] Then calculate the Jacobian matrix of the state transition function, and combine the process noise covariance matrix​ The prior error covariance matrix is updated, and a preliminary prediction of the current state is completed.

[0179] Subsequently, an update phase is entered, in which the prior estimate is corrected based on the measured data of the sensor. First, the Jacobian matrix of the observation function is calculated (the manner of calculating the Jacobian matrix has been described above), and the Kalman gain is solved in combination with the observation noise covariance; then, the residual error is calculated using the temperature measurement value of the temperature control object, and the posterior state estimate is obtained by weighting correction through the Kalman gain, and the posterior error covariance matrix is updated synchronously.

[0180] Wherein:

[0181] The extended Kalman gain matrix is calculated as:

[0182] The posterior state estimate calculation formula is:

[0183] The formula for updating the posterior state estimate error covariance matrix is:

[0184] Finally, the above process is iteratively executed, and the temperature posterior estimate value of the temperature control object and the heat exchange coefficient posterior estimate value are extracted from the posterior state estimate, so as to realize the dual goals of filtering and denoising and online parameter identification.

[0185] Step S8: Calculate the control quantity according to the posterior estimate value, and realize the front-end feedback composite control.

[0186] Firstly, the core input parameters of control calculation need to be determined and the temperature control deviation needs to be quantified. Two types of key parameters need to be accurately extracted from the posterior state vector output in step S7: one is the temperature posterior estimate value of the temperature control object, which has been suppressed by the extended Kalman filter and can truly reflect the actual temperature state of the temperature control object; the other is the heat exchange coefficient posterior estimate value between the temperature control object and the N load cabin plates, which can dynamically represent the time-varying characteristics of heat exchange strength.

[0187] At the same time, the temperature control target value is determined according to the spacecraft mission requirements The temperature control deviation is calculated by the following formula, and the deviation value is the core basis for feedback control correction of temperature deviation, which is directly related to the adjustment direction and strength of the control quantity. The calculation formula of the temperature control deviation is: (wherein, is the temperature control target temperature, is the temperature posterior estimate value).

[0188] ​​​Based on the extracted posteriori estimation, a feedforward control amount is constructed to achieve active compensation for foreseeable thermal disturbance. The core logic of feedforward control is to apply reverse compensation in advance using known thermal disturbance information to offset its impact on the temperature-controlled object. Combined with the thermal balance relationship of the reduced-order model, the calculation of the feedforward control amount needs to integrate parameters such as heat exchange coefficient, cabin plate temperature and internal heat: the heat flow between the temperature-controlled object and the cabin plate is quantified to quantify the heat flow transmitted from the thermal environment of each cabin plate to the temperature-controlled object, and after superimposing the heat generation of the temperature-controlled object, the total disturbance heat load to be compensated is obtained, and finally the feedforward control amount is used to actively offset the load to avoid temperature fluctuations caused by disturbance.

[0189] The real-time deviation is corrected by the feedback control amount, and the final execution instruction is formed by combining the feedforward control. The feedback control adopts proportional regulation strategy, and the temperature-controlled deviation The feedback control amount is calculated to correct the unforeseen disturbance not covered by the feedforward control. The calculation formula of the feedback control amount is: .

[0190] In the formula:

[0191] : heat exchange coefficient between the temperature-controlled object and the nth cabin plate.

[0192] : temperature-controlled target temperature;

[0193] : measured temperature of the nth cabin plate;

[0194] : total heat generation of all nodes of the temperature-controlled object;

[0195] : belongs to the feedback control part, is the feedback gain, is the temperature-controlled deviation.

[0196] At the same time, due to the physical limitations of the actuator, the control amount cannot exceed its working range , . If u obtained by the above calculation exceeds this range, it will be limited to and to ensure the safe and reliable operation of the actuator, that is, .

[0197] Finally, the feedforward control amount and the feedback control amount are superimposed to obtain the composite control amount, and the composite control amount is output to the heating loop to realize accurate heat compensation for the temperature-controlled object through power regulation, and complete the feedforward-feedback composite control closed loop.

[0198] It is understandable that adaptive control of the equipment temperature can be achieved by repeatedly executing the above logical process from steps S1 to S8.

[0199] To verify the superior performance of the temperature control method of this invention, it was rigorously compared with the classic PI control algorithm widely used in the aerospace field during design simulation. The experiment relied on the verified high-fidelity thermal model of the entire Taiji-1 satellite (…). Figure 4 The document shows a detailed structural diagram of the Taiji-1 core module (both physical and thermal models), and sets stringent test conditions: applying a thermal disturbance of ±1K to the core module plate and introducing 0.005mK Gaussian white noise into the temperature measurement to simulate the real on-orbit environment. Figure 5 The dynamic response processes of the two algorithms in dealing with a step change in the temperature control target (from 293.15K to 293.16K) were clearly recorded and compared, and the results fully demonstrate the significant advantages of the method of the present invention.

[0200] from Figure 5 The temperature response curve in (a) quantifies the comprehensive superiority of the algorithm of this invention in both dynamic performance and steady-state accuracy. The adaptive algorithm proposed in this invention exhibits excellent consistency, achieving a smooth transition without overshoot. Its settling time is only 1837 seconds, and the steady-state error is suppressed to a level of 0.005 mK, which is comparable to the sensor measurement noise level, indicating that the algorithm has reached the theoretical accuracy limit. In contrast, the traditional PI controller exhibits significant overshoot, with a settling time as long as 3790 seconds and a steady-state error of 0.57 mK. Quantitative comparison shows that the algorithm of this invention completely eliminates overshoot, shortens the settling time by 51.5%, and improves the steady-state control accuracy by two orders of magnitude (114 times). This proves that the adaptive method based on the reduced-order model and online parameter estimation can provide a deeper understanding of the system dynamics, thus offering performance far exceeding that of traditional methods based on error feedback.

[0201] Figure 5 The heater power response curve in (b) further reveals the underlying mechanism of the performance difference. While both algorithms can respond instantaneously to step commands, their subsequent power regulation strategies are drastically different. The adaptive algorithm initiates power descent at 1295 seconds, approximately 115 seconds earlier than the PI algorithm. This indicates that its EKF-based prediction mechanism can anticipate system temperature changes earlier, thus taking proactive action to achieve advance compensation. Furthermore, the adaptive algorithm's power curve exhibits higher peaks and deeper troughs; this greater modulation amplitude is key to its ability to quickly offset disturbances and avoid overshoot. The slight fluctuations in the power curve are an external manifestation of the algorithm's continuous online parameter fine-tuning to combat noise and nonlinear disturbances. In contrast, the PI algorithm's power regulation is slow and conservative, leading to the aforementioned performance gap.

[0202] In summary, Figure 5 The comparative experimental data of the application effectively prove that the method provided by the application overcomes the time delay and overshoot bottleneck of the traditional thermal control system, and through the fusion of global reduced-order perception and adaptive feedforward-compensation mechanism, more accurate and more advanced control instructions can be output, and finally the ultra-precise temperature stable control is realized in time domain and frequency domain, which provides a reliable technical solution for future ultra-high precision space missions.

[0203] The advantages of the embodiment of the application are as follows: first, through the reduced-order model and the EKF algorithm, global temperature field high-precision perception based on sparse sensors and muK-level temperature control are realized, and the precision is improved by more than two orders of magnitude compared with the traditional PID control; second, through online identification of time-varying heat transfer coefficients, the nonlinear and time-varying characteristics of the thermal system can be dynamically compensated, and the internal thermal disturbance and external environmental changes have strong robustness and adaptive ability; third, the model reduction technology greatly reduces the calculation dimension and complexity, so that it can be run in real time on the limited computing resources of the on-board computer, and the reduction of the number of sensors reduces the system weight, wiring complexity and failure rate, greatly improving the engineering feasibility; fourth, no overshoot or low overshoot fast response can be realized, the adjustment time is significantly shortened, and the dynamic performance of the system is improved, and simulation verification shows that the adjustment time can be shortened by 51.5% compared with the traditional PI algorithm; fifth, the method of the application is not only suitable for space gravitational wave detection, high-resolution remote sensing satellites, deep space probes and other frontier space missions, but also has the potential to migrate to high-tech fields such as semiconductor manufacturing equipment and medical precision instruments.

[0204] In summary, the temperature control method provided by the application realizes global temperature field high-precision reconstruction based on sparse sensors and muK-level precision temperature control by fusing reduced-order model perception and adaptive compensation technology, while meeting the stringent requirements of on-board platforms for calculation complexity and reliability, and has important application value.

[0205] The above describes only the specific implementation of the application, but the protection scope of the application is not limited thereto, any changes or replacements that can be easily thought of by those skilled in the art within the technical range disclosed by the application should be covered within the protection scope of the application. Therefore, the protection scope of the application should be subject to the protection scope of the claims.

Claims

1. A globally reduced-order perceptual adaptive fine temperature control method, characterized in that, The global order reduction perception adaptive precision temperature control method comprises: establishing a heat transfer mathematical model of a precision temperature control object and its thermal environment boundary; spatially discretizing the heat transfer mathematical model to obtain a thermal balance equation; constructing a discrete state space model based on the thermal balance equation; performing order reduction on the discrete state space model based on the Biot number criterion, wherein the thermal environment boundary is taken as N cabin plates of a spacecraft load cabin as discrete units, and the equivalent heat exchange relationship between each cabin plate and the temperature control object is retained after order reduction; arranging temperature sensors and heating circuits based on the reduced model, and arranging temperature sensors at the equivalent nodes of the N cabin plates and the lumped nodes of the temperature control object after order reduction; performing dimension expansion on the reduced model, augmenting the time-varying equivalent heat exchange coefficient into part of the system state vector, constructing an extended state space model containing temperature and heat exchange coefficient, and defining the statistical characteristics of the process noise and measurement noise of the model; using an extended Kalman filter to perform real-time filtering and parameter estimation on the extended state space model to obtain posteriori estimation values of temperature and heat exchange coefficient; calculating a feedforward control amount based on the posteriori estimation values, combining a feedback control amount to calculate a composite control amount, and outputting the composite control amount to the heating circuit to achieve adaptive temperature control of the temperature control object.

2. The globally reduced-order perceptually adaptive fine temperature control method of claim 1, wherein, The heat transfer mathematical model comprises a transient heat conduction equation inside the temperature control object and a heat exchange boundary condition equation on the outer surface of the temperature control object; The expression of the transient heat conduction equation is: wherein, is the density of the temperature-controlled object, is the specific heat capacity of the temperature-controlled object, is the thermal conductivity of the temperature-controlled object in the direction of the heat flow, , , is the thermal conductivity of the temperature-controlled object in the direction of the heat flow, is the heat generation power per volume, is the temperature of the temperature-controlled object, is the time; The expression of the heat exchange boundary condition equation is: wherein, is the normal direction of the temperature-controlled object surface, is the heat conduction and heat exchange coefficient, is the temperature of the load cabin plate, is the Stefan-Boltzmann constant, is the emissivity of the temperature-controlled object surface, is the radiation angle coefficient between the temperature-controlled object and the load cabin body.

3. The globally reduced-order perceptually adaptive fine temperature control method of claim 1, wherein, During the spatial discretization process of the heat transfer mathematical model, nodes need to be added to the heat source concentration area and geometric mutation of the temperature control object, and nodes need to be added to the heat exchange concentration area and boundary mutation of the thermal environment boundary; The heat capacity, self-heating amount and adjacent node heat exchange coefficient of each temperature control object node need to be determined, and the radiation and heat exchange coefficient of each boundary node with the temperature control object need to be determined; After discretization, the state equation describing the thermal dynamic behavior of the system is: where, Ci is the heat capacity of the ith node, Ti is the temperature of the ith node, Tnm is the temperature of the mth node on the nth panel, t is time, hnm is the radiation heat transfer coefficient between the mth node on the nth panel and the ith node of the temperature-controlled object, kmn is the conductive heat transfer coefficient between the mth node on the nth panel and the ith node of the temperature-controlled object, kj is the conductive heat transfer coefficient between the jth node inside the temperature-controlled object and the ith node, Qi is the self-heating amount of the ith node of the temperature-controlled object, ui is the active heat compensation control amount applied to the ith node.

4. The globally reduced-order perceptually adaptive fine temperature control method of claim 1, wherein, The discrete state space model comprises a state vector composed of the temperatures of multiple nodes of the temperature control object, an input vector of control heat compensation, self-heating and external disturbance, and corresponding state and input matrices.

5. The globally reduced-order perceptually adaptive fine temperature control method of claim 1, wherein, The order reduction of the discrete state space model based on the Biot number criterion comprises: calculating the Biot number of the discrete object, denoted as Bi; performing lumped parameter order reduction on the temperature control object with a Biot number Bi<0.1 to obtain a temperature control object order reduction model, wherein the temperature control object order reduction model combines I nodes into one lumped parameter node; performing regional equivalent order reduction on the thermal environment boundary with a Biot number Bi≥0.1 to obtain a thermal environment boundary order reduction model, wherein the thermal environment boundary order reduction model equivalently combines M nodes of each cabin plate into one regional node, obtaining a temperature control object with one dimension and a thermal environment boundary with N dimensions, wherein N is the number of cabin plates; integrating the order reduction model and determining the number of temperature measurement nodes.

6. The globally reduced-order perceptually adaptive fine temperature control method of claim 5, wherein, The model equation of the temperature control object reduced order model is: wherein, is the radiation coefficient between the mth node on the nth hatch plate and the temperature control object, is the heat conduction heat exchange coefficient between the mth node on the nth hatch plate and the temperature control object, is the total heat capacity of the temperature control object, is the total heat generation of all nodes of the temperature control object, is the heat compensation amount of the control system, is the temperature of the temperature control object, is the temperature of the mth node on the nth hatch plate; The model equation of the thermal environment boundary reduced order model is: wherein, is a temperature change rate of the temperature control object, is a measured temperature of the nth core panel, is a heat exchange coefficient between the temperature control object and the nth core panel.

7. The globally reduced-order perceptually adaptive fine temperature control method of claim 1, wherein, The extended state vector of the extended state space model is N+1 dimensional, wherein the first dimension is the temperature of the temperature control object, and the second to N+1 dimensions are the equivalent heat exchange coefficients between each load cabin plate and the temperature control object; The process noise and the measurement noise are both subject to normal distribution with mean value 0, and their covariance matrices are and for characterizing model accuracy and sensor precision; The and The expression is: wherein, is the variance of the process noise, is the variance of the measurement noise.

8. The globally reduced-order perceptually adaptive fine temperature control method of claim 7, wherein, The real-time filtering and parameter estimation of the extended state space model using the extended Kalman filter comprises: initializing the posteriori estimation value of the extended state vector and the posteriori error covariance matrix; In the prediction stage of the extended Kalman filter, a prior state estimation and a prior error covariance matrix are calculated; An observation Jacobian matrix is calculated, a Kalman gain is solved in combination with an observation noise covariance, the prior state estimation is corrected by using a temperature measurement value, and a posterior error covariance matrix is updated to obtain a posterior state estimation and the posterior error covariance matrix.

9. The globally reduced-order perceptually adaptive fine temperature control method according to any one of claims 1 to 8, characterized in that, The calculation of the composite control amount based on the feedback control amount comprises: extracting a temperature posterior estimation value of the temperature-controlled object as a feedback control input; estimating a total disturbance heat flow transferred to the temperature-controlled object from the thermal environment boundary based on the heat exchange coefficient posterior estimation value, the temperature measurement value of each load cabin panel, and the heat generation of the temperature-controlled object itself; calculating a feedforward control amount according to the total disturbance heat flow, which is used to actively offset foreseeable thermal disturbances; superimposing the feedforward control amount and a feedback control amount based on the temperature-controlled deviation to generate a composite control amount, and outputting the composite control amount to the heating loop for power regulation.

10. The globally reduced-order perceptually adaptive fine temperature control method of claim 9, wherein, The calculation formula of the feedback control quantity is: Wherein, is the heat exchange coefficient between the temperature control object and the nth hatch plate, is the temperature control target temperature, is the measured temperature of the nth hatch plate, is the total heat generation of all nodes of the temperature control object, is the feedback gain, is the temperature control deviation; The calculation formula of the temperature control deviation is: wherein, is a temperature posterior estimate value; The composite control quantity must meet the power constraints of the heating circuit. When the calculated value exceeds ( , When the range is specified, it is limited to the constraint interval.

Images