A global order reduction perception adaptive precision temperature control method

Abstract

The application discloses a kind of global reduction perception's self-adapting precision temperature control method, the method includes establishing the heat transfer mathematical model of precision temperature control object and its thermal environment boundary;Heat transfer mathematical model is spatially dispersed to obtain heat balance equation;Discrete state space model is constructed based on heat balance equation;The discrete state space model is reduced based on the criterion of Prandtl number processing;Temperature sensor and heating loop are arranged based on the reduced model;The reduced model is expanded to process;Real-time filtering and parameter estimation are carried out to the extended state space model using extended Kalman filter, obtain the posteriori estimation value of temperature and heat transfer coefficient;According to the posteriori estimation value, control quantity is calculated, realizes feedforward-feedback compound control.The temperature control method provided by the application can realize the μK level, high dynamic, adaptive temperature control of spacecraft precision load instrument under the condition of sparse sensing and strong noise.

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 attenuates external thermal disturbance through multi-layer insulation (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 mK level, making it 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: sparse temperature sensor 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 demand for extreme thermal stability of future space science missions. SUMMARY

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

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

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

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

[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 the time-varying equivalent heat transfer coefficient as part of the system state vector, constructing an extended state space model containing temperature and heat transfer coefficient, and defining the statistical characteristics of the process noise and measurement noise of the model;

[0016] 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 transfer coefficient;

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

[0018] According to one 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 a reduced 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 temperature-controlled object order reduction model and the thermal environment boundary 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, The variance of the process noise, The variance of the measurement noise.

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

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

[0037] In the prediction stage of the extended Kalman filter, the prior state estimate and the prior error covariance matrix are calculated;

[0038] The observation Jacobian matrix is calculated, the Kalman gain is solved by combining the observation noise covariance, the prior state estimate is corrected using the temperature measurement value, and the posterior error covariance matrix is updated to obtain the posterior state estimate and the posterior error covariance matrix.

[0039] According to one aspect of the application, the calculation of the composite control quantity combined with the feedback control quantity comprises:

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

[0041] 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, estimate the total disturbance heat flow transferred to the temperature-controlled object from the thermal environment boundary;

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

[0043] Superimpose the feedforward control quantity and the feedback control quantity based on the temperature control deviation to generate the composite control quantity, and output it to the heating loop to perform power regulation.

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

[0045] The calculation formula of the temperature control deviation is: Wherein, 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 μK-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 system has strong robustness and self-adaptive ability to internal thermal disturbance and external environmental changes; 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 be applied 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 drawings needed in the embodiments will be briefly introduced as follows. 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 A flowchart of the adaptive precise temperature control method of the global reduced-order perception according to the present application;

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

[0051] Figure 3 A schematic diagram of the heat transfer model reduction process according to the present application;

[0052] Figure 4 A schematic diagram of the Taiji-1 core cabin and the thermal model according to the present application;

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

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] Figure 1 A flowchart illustrating an adaptive precision temperature control method based on global order reduction sensing, as presented in this invention, is shown. Figure 1 As shown, the method includes the following steps:

[0056] Step S1: Establish a mathematical model of heat transfer for the precision temperature-controlled object and its thermal environment boundary.

[0057] Figure 2 A schematic diagram of the structural features of the gravitational wave detection spacecraft used in this invention is shown. (See attached diagram.) Figure 2 As shown, its thermal control structure, from the outside to the inside, consists of: the platform cabin (including the outer cabin panels and electronic instruments), the payload cabin, and the core payload instruments (i.e., the precision temperature-controlled target object). The temperature control technology used in this invention first requires clearly defining the precision temperature-controlled object and its thermal environment boundaries, which is the basis for establishing a heat transfer mathematical model.

[0058] Among these, precision temperature control targets specifically refer to core payload instruments on spacecraft that have stringent requirements for temperature stability, including gravitational wave detectors, high-resolution optical remote sensors, interferometric synthetic aperture radar, high-precision atomic clocks, and precision spectrometers. The performance of these objects directly determines the effectiveness of the spacecraft's core mission and must be considered the core target for temperature control. Taking a gravitational wave detection spacecraft as an example, the temperature control target is the core payload instrument, which is modeled as a solid structure with continuous homogeneous medium properties and isotropic thermophysical properties.

[0059] The thermal environment boundary, from the outside to the inside, consists of the platform cabin (including the outer cabin panels and electronic instruments), the load cabin (composed of N independent cabin panels), and related supporting components. Here, the load cabin is the direct thermal environment of the temperature-controlled object. The two mainly exchange heat through radiation and conduction. It is necessary to clarify the heat exchange path and key influencing parameters of this type.

[0060] Based on the above definition, a heat transfer mathematical model is further established, which includes the transient heat conduction equation inside the temperature control target and the heat exchange boundary conditions on the outer surface.

[0061] In this approach, the target object for precise temperature control is simplified to a solid structure with continuous and homogeneous dielectric properties, and its thermophysical properties are assumed to be isotropic. Its internal transient heat conduction behavior is described by the classical Fourier law of heat conduction and can be represented 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, as 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, while the right side encompasses the contributions of both conductive 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 surrounding payload cabin is governed by both conduction and radiation mechanisms, mathematically described as: .

[0071] wherein:

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

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

[0074] is the temperature of the payload cabin panel, 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] where:

[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 of the ith node, with the unit of W;

[0095] ui 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. The heat balance relationship of each node of the temperature-controlled object can be described by the balance of the conduction between nodes, the radiation and conduction heat exchange with the boundary, the self-heating, and the control compensation amount. This establishes the dynamic relationship between the system state, input, and output, and lays the foundation for subsequent model reduction based on the Poincare number criterion.

[0097] Step S3: Construct a discrete state space model to clearly define the boundary temperature, self-heating, 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] Quantitative 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 the 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 and needs to meet the power constraints 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, which is 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, a continuous-time state space equation is constructed. Then, using the Euler discretization or Runge-Kutta method, combined with the discrete time step, it is converted 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) discretized in step S2, the Biot number is calculated to determine the order reduction basis.

[0110] For temperature control objects, 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 a criterion 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 with the center temperature measurement point temperature 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: .

[0118] Wherein:

[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] Wherein:

[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] where:

[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 to make the EKF filter 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 the normal distribution, i.e.: . That is, it is assumed that the process noise w and the measurement noise v both obey the 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 are expressed 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, the posterior state estimate is obtained by weighted 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 formula for calculating the posterior state estimate is:

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

[0184] Finally, the above process is iteratively executed to extract the posterior estimate value of the temperature of the temperature control object and the posterior estimate value of the heat exchange coefficient, 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] First, the core input parameters for 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 posterior estimate value of the temperature 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 posterior estimate value of the heat exchange coefficient between the temperature control object and the N load cabin plates, which can dynamically represent the time-varying characteristics of the 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 posterior estimate value of the temperature).

[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 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 application are as follows: first, through the reduced-order model and EKF algorithm, global temperature field high-precision perception and muK-level temperature control based on sparse sensors 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 coefficient, the nonlinear and time-varying characteristics of the thermal system can be dynamically compensated, and the internal thermal disturbance and external environmental change 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, 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 and muK-level precision temperature control based on sparse sensors through fusion of 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 is only a specific embodiment of the application, but the protection scope of the application is not limited thereto, any changes or replacements within the technical scope disclosed by the application can be easily thought of by those skilled in the art, which 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. An adaptive precision temperature control method based on global order reduction sensing, characterized in that, The adaptive precision temperature control method based on global order reduction sensing includes: Establish a mathematical model of heat transfer for the precision temperature-controlled object and its thermal environment boundary; The heat transfer mathematical model is spatially discretized to obtain the heat balance equation; A discrete state-space model is constructed based on the aforementioned thermal balance equation; The discrete state space model is reduced in order based on the Bishop number criterion, wherein the thermal environment boundary is taken as the N compartments of the spacecraft payload cabin as discrete units, and the equivalent heat transfer relationship between each compartment and the temperature control object is retained after the order reduction. Temperature sensors and heating circuits are arranged based on the reduced discrete state space model. Temperature sensors are arranged at the equivalent nodes of the N compartments and the total node of the temperature control object set after the reduction. The dimension of the reduced discrete state-space model is expanded by incorporating the time-varying equivalent heat transfer coefficient into the system state vector, thus constructing an extended state-space model that includes temperature and heat transfer coefficient, and defining the statistical characteristics of process noise and measurement noise of the model. The extended state-space model is filtered and its parameters are estimated in real time using an extended Kalman filter to obtain posterior estimates of temperature and heat transfer coefficient. The feedforward control quantity is calculated based on the posterior estimate, and the composite control quantity is calculated by combining the feedback control quantity. The result is then output to the heating circuit to achieve adaptive temperature control of the object being controlled.

2. The adaptive precision temperature control method with global order reduction sensing according to claim 1, characterized in that, The heat transfer mathematical model includes the transient heat conduction equation inside the temperature-controlled object and the heat exchange boundary condition equation on the outer surface of the temperature-controlled object. The expression for the transient heat conduction equation is: ,in, For the density of the object being temperature controlled, The specific heat capacity of the object being temperature controlled. For the temperature-controlled object , , Thermal conductivity in the direction, The heat output per unit volume To control the temperature of the object, For time; The expression for the heat exchange boundary condition equation is: ,in, The normal direction of the surface of the object being controlled. The thermal conductivity and heat transfer coefficient, For the load compartment temperature, The Stefan-Boltzmann constant is given. To control the emissivity of the surface of the object, This is the radiation angle coefficient between the temperature-controlled object and the load chamber.

3. The adaptive precision temperature control method with global order reduction sensing according to claim 1, characterized in that, During the spatial discretization of the heat transfer mathematical model, it is necessary to densify the nodes in the concentrated heat source area and geometric change points of the temperature control object, and densify the nodes in the dense heat transfer area and boundary change points of the thermal environment boundary. Each temperature-controlled node needs to determine its heat capacity, its own heat generation, and the thermal conductivity of adjacent nodes. Each boundary node needs to determine its radiation and thermal conductivity with the temperature-controlled object. After discretization, the state equation describing the thermodynamic behavior of the system is: ,in, Let i be the heat capacity of the i-th node. Let be the temperature of the i-th node. Let be the temperature of the m-th node on the n-th deck. For time, Let be the radiative heat transfer coefficient between the m-th node on the n-th compartment and the i-th node of the temperature-controlled object. Let be the thermal conductivity between the m-th node on the n-th compartment and the i-th node of the temperature-controlled object. Let be the thermal conductivity between the j-th node and the i-th node inside the temperature-controlled object. Let be the heat generated by the i-th node of the temperature-controlled object. This is the active thermal compensation control quantity applied to the i-th node.

4. The adaptive precision temperature control method with global order reduction sensing according to claim 1, characterized in that, The discrete state-space model includes a state vector consisting of the temperatures of multiple nodes of the temperature-controlled object, the control heat compensation amount, the self-generated heat, the input vector of external disturbances, and the corresponding state matrix and input matrix.

5. The adaptive precision temperature control method with global order reduction sensing according to claim 1, characterized in that, The order reduction process of the discrete state-space model based on the Biot number criterion includes: Calculate the Bivouac number of the discrete object, denoted as Bi; For temperature control objects with Bi < 0.1, lumped parameter reduction is performed to obtain a reduced-order model of the temperature control object, wherein the reduced-order model of the temperature control object merges I nodes into 1 lumped parameter node; For thermal environment boundaries with Bi ≥ 0.1, a region equivalent reduction model is performed to obtain a thermal environment boundary reduction model. The thermal environment boundary reduction model converts the M nodes of each compartment into one region node, resulting in a reduction model with a 1-dimensional temperature control object and an N-dimensional thermal environment boundary, where N is the number of compartments. The reduced-order model of the temperature-controlled object and the reduced-order model of the thermal environment boundary are integrated, and the number of temperature measurement nodes is determined.

6. The adaptive precision temperature control method with global order reduction sensing according to claim 5, characterized in that, The model equations for the reduced-order model of the temperature-controlled object are as follows: ,in, Let be the radiation coefficient between the m-th node on the n-th compartment and the temperature-controlled object. Let be the thermal conductivity between the m-th node on the n-th compartment and the temperature-controlled object. The total heat capacity of the object being temperature controlled. The total heat generated by all nodes of the temperature-controlled object. This is the thermal compensation amount for the control system. To control the temperature of the object, Let be the temperature of the m-th node on the n-th deck; The model equations of the thermal environment boundary order reduction model are as follows: ,in, The rate of temperature change of the object being controlled. The measured temperature of the nth core module. The heat transfer coefficient between the temperature-controlled object and the nth core compartment plate.

7. The adaptive precision temperature control method with global order reduction sensing according to claim 1, characterized in that, The extended state vector of the extended state space model is N+1 dimensional, where the first dimension is the temperature of the temperature-controlled object, and the second to N+1 dimensions are the equivalent heat transfer coefficients between each load compartment and the temperature-controlled object, respectively. Both the process noise and the measurement noise follow a normal distribution with a mean of 0, and their covariance matrices are respectively... and It is used to characterize model accuracy and sensor precision; The and The expression is: ,in, Let Variance be the process noise. To measure the variance of noise.

8. The adaptive precision temperature control method with global order reduction sensing according to claim 7, characterized in that, The real-time filtering and parameter estimation of the extended state-space model using an extended Kalman filter includes: Initialize the posterior estimate of the extended state vector and the posterior error covariance matrix; In the prediction phase of the extended Kalman filter, the prior state estimate and the prior error covariance matrix are calculated. The observation Jacobian matrix is ​​calculated, and the Kalman gain is solved by combining the observation noise covariance. The prior state estimate is corrected and the posterior error covariance matrix is ​​updated using the temperature measurement value, thus obtaining the posterior state estimate and the posterior error covariance matrix.

9. The adaptive precision temperature control method with global order reduction sensing according to any one of claims 1 to 8, characterized in that, The calculation of the composite control quantity by combining the feedback control quantity includes: Extract the a posteriori estimate of the temperature of the object to be controlled as the input for feedback control; Based on the a posteriori estimate of the heat transfer coefficient, the measured temperature of each load compartment, and the heat generation of the temperature-controlled object itself, the total disturbance heat flow transferred from the thermal environment boundary to the temperature-controlled object is estimated. The feedforward control quantity is calculated based on the total disturbance heat flow to actively counteract foreseeable thermal disturbances. The feedforward control quantity is superimposed with the feedback control quantity based on the temperature control deviation to generate a composite control quantity, which is then output to the heating circuit to perform power regulation.

10. The adaptive precision temperature control method with global order reduction sensing according to claim 9, characterized in that, The formula for calculating the feedback control quantity is: ,in, Let be the heat transfer coefficient between the temperature-controlled object and the nth compartment plate. To control the target temperature, The measured temperature of the nth compartment. The total heat generated by all nodes of the temperature-controlled object. For feedback gain, Temperature control deviation; The formula for calculating the temperature control deviation is: ,in, This is a posterior estimate of the temperature. 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.

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