Spacecraft thermal control method and system based on distributed model predictive control

Abstract

This invention discloses a spacecraft thermal control method and system based on distributed model predictive control, belonging to the field of spacecraft thermal control and automatic control technology. It addresses the problems of excessive computational complexity, poor robustness, and low anti-interference capability in complex space thermal environments found in existing spacecraft thermal control technologies. The method includes: establishing a space-interconnected T-S fuzzy heat transfer model to address the nonlinear characteristics of the thermal properties of spacecraft insulation materials as a function of temperature; introducing model predictive control theory based on tubular constraints to design distributed robust constraint conditions including disturbance boundary estimation; offline solving of the common Lyapunov matrix and feedback gain of each fuzzy subsystem using linear matrix inequalities; and online distributed collaborative optimization calculation of the thermal control input of each subsystem to achieve high-precision and high-stability collaborative control of the spacecraft insulation structure temperature field under multi-source disturbances. This invention is applicable to spacecraft thermal control.

Description

Technical Field

[0001] This application relates to the field of spacecraft thermal control and automatic control technology, and in particular to spacecraft thermal control. Background Technology

[0002] In spacecraft on-orbit operations, thermal insulation structures serve as crucial barriers isolating internal precision instruments from extreme external thermal environments. Their heat transfer processes exhibit significant spatial distribution characteristics and strong nonlinearity. For such complex, large-scale systems, centralized control schemes require handling high-dimensional state variables, resulting in extremely high computational costs. Furthermore, to ensure the real-time performance of centralized control algorithms in online calculations, existing schemes inevitably involve significant simplification of the thermal control system model, neglecting the dynamic differences in local heat conduction. This leads to decreased control accuracy and a series of thermal safety issues.

[0003] Existing spacecraft thermal control technologies mostly employ passive thermal protection designs or proportional-integral-derivative (PID) system thermal control methods based on linear models. However, the key physical parameters (thermal conductivity, specific heat capacity) of spacecraft insulation materials change significantly with temperature, exhibiting strong nonlinear dynamic characteristics. Traditional linear control methods rely on linearized models with a fixed operating point, failing to fully consider the nonlinear characteristics of material parameters drifting with temperature. This makes it difficult to guarantee the stability of the system during large-scale temperature variations, posing a significant threat to the long-term on-orbit safe operation of spacecraft. Another type of model, based on finite element analysis, provides relatively accurate modeling tools for heat transfer processes, but its computational complexity is too high, making it difficult to apply to online active thermal control tasks with high real-time requirements.

[0004] The Takagi-Sugeno (TS) fuzzy model accurately approximates a nonlinear system using a set of locally linear models and their membership functions, making it an effective mathematical tool for handling complex nonlinear problems. Combining distributed model predictive control (DMDC) with the TS fuzzy model, leveraging a distributed architecture to reduce computational burden and utilizing fuzzy rules to handle nonlinearity, presents a potentially effective solution for thermal control of large insulation structures. However, currently, there is no publicly available technical solution combining DMDC and the TS fuzzy model. Existing technologies, when designing distributed controllers, often assume that the subsystem models are accurate, failing to fully consider external disturbances such as solar radiation pressure fluctuations and aerodynamic heating encountered by spacecraft during on-orbit operation, as well as uncertainties in the model structure due to material aging or measurement errors. Existing distributed control strategies exhibit poor robustness under these real-world disturbances, and their algorithm design lacks consideration for ensuring the non-vulnerability of the thermal control system under parameter perturbations.

[0005] Therefore, for spacecraft thermal insulation structures with nonlinear heat transfer characteristics and spatial distribution features, there is an urgent need to provide a robust distributed model predictive control method for heat transfer systems, so as to combine nonlinear approximation based on TS fuzzy models with distributed robust control, thereby effectively improving the anti-interference capability of thermal control systems in complex space thermal environments. Summary of the Invention

[0006] The purpose of this invention is to solve the technical problems of high computational complexity, poor robustness, and low anti-interference ability in complex space thermal environments in existing spacecraft thermal control technologies, and to provide a spacecraft thermal control method and system based on distributed model predictive control.

[0007] The technical problems solved by this invention include:

[0008] 1. The contradiction between accurate nonlinear models and efficient online calculations: In response to the strong nonlinear characteristics of the drastic changes in physical parameters such as thermal conductivity and specific heat capacity of spacecraft thermal insulation materials with temperature, this paper solves the problem that traditional single linear models are severely mismatched over a wide temperature range, while high-precision numerical models (such as finite element methods) have too large a computational load to meet the requirements of airborne real-time control.

[0009] 2. High-dimensional spatial distribution characteristics of large-scale thermal insulation structures: In view of the significant spatial distribution characteristics of the heat transfer process of large-scale thermal insulation structures, this paper solves the problems of state dimension explosion, heavy communication burden and poor fault tolerance caused by the increase of nodes in centralized control methods.

[0010] 3. Robust control to suppress thermal disturbances and material aging: In response to the external heat flow disturbances and model structure uncertainties caused by material aging in the complex thermal environment of space, this paper solves the problem that existing control strategies are unable to strictly guarantee temperature field constraints and system stability under worst-case disturbance conditions.

[0011] The technical solution adopted by this invention to solve the above problems is: a spacecraft thermal control method based on distributed model predictive control, the method comprising:

[0012] Step 1: Establishing a fuzzy heat transfer model for space interconnection TS: Based on the one-dimensional partial differential equation of heat conduction, the spacecraft's thermal insulation structure is spatially discretized using the finite difference method or the finite element method to obtain a space interconnection system model composed of multiple mutually coupled subsystems; considering the nonlinear characteristics of thermal property parameters changing with temperature, temperature is selected as the antecedent variable, and polyhedral fuzzy rules are established to transform the nonlinear heat transfer dynamics into a set of locally linear space interconnection TS fuzzy system models;

[0013] Step 2: Offline solution of robust control law parameters: Based on the parallel distributed compensation strategy, an optimization problem containing system stability constraints and dissipative performance indicators is constructed; using the linear matrix inequality technique, the common Lyapunov matrix and the corresponding state feedback control gain satisfying all fuzzy rule subsystems are solved offline, thereby transferring the complex robust stability calculation to the offline stage.

[0014] Step 3: Design distributed robust constraints: For the external heat flow disturbances and model uncertainties of the system, define a compact set containing the disturbance boundary; based on the robust positive invariant set theory, calculate the limit boundary of the state estimation error and the impact of the disturbance on the system, and accordingly shrink the temperature constraints of the insulation structure and the heating / cooling capacity constraints of the actuator to construct robust constraints that can tolerate the worst-case disturbance.

[0015] Step 4: Solving the optimization problem online: At each sampling moment, each thermal insulation subsystem acquires the current local temperature state through sensors and exchanges state information with adjacent subsystems; calculates the membership weights of each fuzzy rule based on the current temperature, and uses the offline parameters obtained in Steps 2 and 3: Lyapunov matrix, terminal invariant set, robust positive invariant set, and perturbation reachable set to construct a distributed model predictive control optimization problem; solves this convex optimization problem online to obtain the optimal thermal control input at the current moment, applies it to the actuator, and rolls into the next moment.

[0016] Secondly, the present invention provides a spacecraft thermal control method system based on distributed model predictive control. The system has program modules corresponding to the steps of the spacecraft thermal control method based on distributed model predictive control as described above, and executes the steps in the spacecraft thermal control method based on distributed model predictive control when running.

[0017] Thirdly, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, it executes the steps of a spacecraft thermal control method based on distributed model predictive control as described above.

[0018] Fourthly, the present invention provides a computer-readable storage medium for storing a computer program that executes a spacecraft thermal control method based on distributed model predictive control as described above.

[0019] The beneficial effects of this invention are:

[0020] This invention proposes a nonlinear distributed model predictive control method for thermal control of spacecraft thermal insulation structures. Addressing the nonlinear characteristics of the thermal properties of spacecraft thermal insulation materials as a function of temperature, a space-interconnected TS fuzzy heat transfer model is established. Model predictive control theory based on tubular constraints is introduced, and distributed robust constraint conditions including disturbance boundary estimation are designed. The common Lyapunov matrix and feedback gain of each fuzzy subsystem are solved offline using linear matrix inequalities. The thermal control input of each subsystem is calculated online through distributed collaborative optimization, achieving high-precision and high-stability collaborative control of the temperature field of the spacecraft thermal insulation structure under multi-source disturbances.

[0021] Through the above progressive implementation steps, this invention transforms the strong nonlinear characteristics of spacecraft thermal insulation structures into a computable distributed control framework, stabilizes the offline integrated system and reduces online computing costs, and achieves collaborative control through information exchange.

[0022] 1) This invention solves the "model mismatch" problem in strongly nonlinear heat transfer processes, significantly improving the convergence speed of the system towards the target temperature. Addressing the physical characteristics of spacecraft insulation materials where thermal conductivity and specific heat capacity change drastically with temperature, this invention abandons the traditional single-operating-point linearization method and innovatively establishes a space interconnection TS fuzzy model. By calculating fuzzy membership weights in real time across the entire temperature domain, this invention can adaptively adjust the control law parameters according to the current temperature state. Compared to traditional linear control methods, this invention eliminates the model mismatch risk caused by parameter drift, guiding the system temperature to converge quickly and smoothly from any initial operating condition to the preset zero-point target, greatly shortening the duration of the thermal runaway risk period.

[0023] 2) This invention overcomes the high-dimensional spatial distribution problem of centralized control, significantly reducing the online computational load and meeting the real-time requirements of airborne systems. Addressing the numerous spatial nodes in the thermal insulation structure of large spacecraft, this invention employs a distributed model predictive control architecture, decomposing the high-dimensional global optimization problem into multiple low-dimensional subsystem parallel optimization problems. Simultaneously, this invention introduces a hybrid computational strategy of "offline design + online solution," transferring complex stability and robustness analysis to the offline stage, greatly reducing the online computational load and enabling the algorithm to run in real-time on the spacecraft's computationally limited onboard processors.

[0024] 3) Enhanced robustness of the system to external environmental disturbances and model structural uncertainties. Compared with conventional control methods that do not consider disturbances, this invention introduces a constraint contraction mechanism based on robust positive invariant sets. By explicitly incorporating external heat flow disturbances such as aerodynamic heating and solar radiation, as well as model parameter perturbations caused by material aging, into the constraint design, this invention ensures that the system's temperature state is always strictly limited within a safe range under worst-case disturbances, effectively suppressing multi-source disturbances and significantly improving the robust stability and operational safety of the thermal control system.

[0025] 4) This invention achieves decoupling between the overall thermal insulation structure and interconnected local thermal insulation structures, exhibiting excellent scalability and modularity. Based on the theory of space interconnected systems, this invention utilizes information interaction between adjacent subsystems to achieve global coordination. This control architecture not only conforms to the space physics characteristics of heat conduction but also possesses good structural flexibility; when the size of the thermal insulation structure increases or the number of subsystems changes, there is no need to redesign the entire controller; only the parameters of local nodes and neighbor relationships need to be adjusted, facilitating the engineering implementation and expansion of the spacecraft thermal control system.

[0026] This invention is applicable to spacecraft thermal control. Attached Figure Description

[0027] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of the space interconnection discretization and distributed control architecture of the spacecraft thermal insulation structure in this embodiment of the invention;

[0029] Figure 2 This is the overall flowchart of a nonlinear distributed model predictive control method for thermal control of spacecraft thermal insulation structures proposed in this invention.

[0030] Figure 3 This is a schematic diagram of the TS fuzzy membership function based on temperature antecedent variables in an embodiment of the present invention;

[0031] Figure 4 This is a schematic diagram of the constraint contraction principle based on robust positive invariant sets in an embodiment of the present invention;

[0032] Figure 5 This is a schematic diagram of the spatiotemporal evolution of temperature at each node of the thermal insulation structure under multi-source interference in an embodiment of the present invention;

[0033] Figure 6 This is a spatiotemporal distribution diagram of the control input in an embodiment of the present invention;

[0034] Figure 7 This is a graph showing the temperature change over time for each subsystem in an embodiment of the present invention. Detailed Implementation

[0035] Combined with appendix Figure 1-7 The implementation of the spacecraft thermal control method based on distributed model predictive control described in this invention is explained as follows:

[0036] Step 1: Establish a TS fuzzy heat transfer model for the spacecraft's thermal insulation structure. The specific steps are as follows: The one-dimensional heat transfer equation is spatially discretized using the finite difference method, constructing a dynamic model composed of mutually coupled subsystems. Temperature is selected as the antecedent variable to establish polyhedral fuzzy rules, transforming the nonlinear heat transfer process caused by temperature variations into a set of locally linear spatial interconnected models.

[0037] Consider the continuous-time one-dimensional transient nonlinear heat transfer control equation, which is of the form of

[0038]

[0039] in, For spacecraft thermal insulation structure Time and space Temperature variable at the location; , These are the material density and specific heat capacity, respectively. for Directional material thermal conductivity; To control the quantity; For disturbance terms; This is the structured uncertainty term for the model.

[0040] By using the finite difference scheme to replace partial differential calculation, the partial differential calculation is transformed into difference calculation.

[0041] The difference scheme for temperature with respect to spatial coordinates is as follows:

[0042]

[0043] Difference scheme of temperature versus time axis

[0044]

[0045] in, For discrete time coordinates, These are discrete spatial coordinates.

[0046] right exist Taylor expansion

[0047]

[0048] Will Substitution , can be obtained

[0049]

[0050] Considering thermal conductivity It is a nonlinear function of the subsystem temperature. The local linear system is represented by a TS fuzzy model established through if-then rules with fuzzy meaning.

[0051] The rules of the TS fuzzy model are as follows:

[0052]

[0053] in It is the antecedent variable. For fuzzy sets, For the number of rules, The number of preceding variables.

[0054] The temperature of the subsystem is considered as a state variable.

[0055]

[0056] in The time component of the state represents the subsystem. exist Temperature at any moment; The spatial components of the state represent the subsystem. exist Time to subsystem The effect of temperature.

[0057] The non-minimum state space realization of a locally linear system is as follows

[0058]

[0059]

[0060] in, and These represent the system's time state vector and spatial state vector, respectively. This represents the generalized exogenous input received by the system. and These represent bounded external process disturbances and measurement noise, respectively. This represents the performance output used to evaluate control quality; Indicates the first The local subsystem (or the first) The augmented system parameter matrix (of a local model), where the superscripts of its internal elements are... Refers to the corresponding first in the TS fuzzy model Fuzzy rules; specifically, matrix The block matrices in the data can be categorized into four types: , , The system state matrix represents the internal state evolution and coupling relationships of the system in the time and space dimensions. , , The input matrix represents the uncertain input. External disturbances and control input The driving effect on the spatiotemporal state of the system; , , The output matrix represents the effect of the system's internal spatiotemporal state on its internal output. Performance Evaluation and measurement output The mapping relationship; , As a direct feedforward matrix (or direct transfer matrix), it characterizes the direct interaction paths between each input signal and each output signal; regarding the structured uncertainty component contained in this model, and These represent the internal output signal transmitted by the nominal system to the uncertainty module and the internal input signal received by the nominal system, respectively. , and They represent different spatial nodes ( , and At ) physical parameters and Uncertainty perturbation.

[0061] right The local models are fuzzed together to obtain the complete TS model in the form of:

[0062]

[0063] in, Is it like this? Figure 3 The TS fuzzy membership function shown is as follows:

[0064]

[0065]

[0066] in, It is the first The first fuzzy rule one preceding variable The corresponding membership function, the antecedent variable Defined as: It describes the first Under this rule, the antecedent variable The degree to which a specific vague concept is satisfied. It is the first The membership degree of a fuzzy rule measures the membership of the current antecedent vector. With the The degree of matching of the antecedent conditions of each rule, and the fuzzy weights satisfying the normalization condition: .

[0067] Step 2: Offline solution of robust control law parameters. Specifically, based on a parallel distributed compensation strategy, an optimization problem is constructed that includes system stability and dissipation indices. The Lyapunov matrix and feedback gain, shared by all subsystems, are solved offline using linear matrix inequalities, thus pre-completing the complex stability calculations offline.

[0068] Based on the fuzzy rules of the TS fuzzy model, a parallel distributed compensation strategy is used to design the controller. For the ... Fuzzy rules Design the corresponding local linear state feedback control law:

[0069]

[0070] For the design of the first The feedback gain matrix of each subsystem. The global control law of the system is obtained by weighting the local control laws using fuzzy membership functions:

[0071]

[0072] The normalized membership function determined in step one. For the preceding variable.

[0073] To ensure the robust stability of the closed-loop system and suppress external disturbances, a Lyapunov function is selected.

[0074]

[0075] in, It is a symmetric positive definite matrix. The energy gain is set ( Gain) index That is, it requires the disturbance to To performance output The gain satisfies .

[0076] Meet the indicators Lyapunov matrix It can be obtained from the following formula

[0077]

[0078]

[0079] in, To augment the system's block diagonal form of the Lyapunov matrix; Represents the symmetric positive definite Lyapunov matrix corresponding to the time state ( This is used to ensure the time asymptotic stability of the system and meet a given energy gain specification. ; Represents the non-singular symmetric matrix corresponding to the spatial state ( ), used to characterize the spatial evolution characteristics of the system; For scaling multiplier matrices; This is the identity matrix of the corresponding dimension.

[0080] Since direct solution is nonconvex, a bilinear transformation is introduced to convert the discrete-time system into a continuous-time system.

[0081] Define new optimization variables and : , . Corresponding time state components, Corresponding spatial state components.

[0082] Construct the following linear matrix inequalities

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] The symbol * represents a symmetric term. yes The null basis matrix. The matrix of the continuous domain system after bilinear transformation, and the common Lyapunov matrix. , No. Feedback gain of a fuzzy rule . and These are the penalty (weight) matrices for the system state and control input, respectively. These not only guarantee the convexity of the performance index function, but also serve to balance the convergence rate of the system state with the energy consumption of control.

[0095] To ensure the recursive feasibility of online optimization, it is necessary to calculate the input constraints. The largest terminal invariant set, where To determine the maximum allowed input, select the terminal set. A subset of Lyapunov functions: .in, This is a boundary parameter that defines the size of the terminal invariant set (i.e., the upper bound of the horizontal cutoff set of the Lyapunov function). Geometrically, it determines the volume of the ellipsoidal invariant set in the state space.

[0096] The maximum value is determined by solving the following convex optimization problem.

[0097]

[0098] The final maximum allowed terminal set parameters This will serve as the terminal constraint boundary for the online optimization problem in step four.

[0099] Step 3: Design distributed robust constraints. The specific steps are: define a compact set of disturbance boundaries for external heat flow disturbances, and utilize, for example... Figure 4 The robust positive invariant set calculation error limit boundary is shown. By shrinking the constraints on temperature and actuator output, robust constraint conditions capable of tolerating worst-case disturbances are constructed to ensure system safety.

[0100] Taking advantage of the structural characteristic that the time evolution of the heat transfer process is affected by disturbances but the spatial coupling is relatively deterministic, the following distributed state observer is designed.

[0101]

[0102] in, This is an estimate of the time state. For actual measurement output, To estimate the output, The observer gain matrix is ​​designed to ensure that the observer error dynamics matrix is ​​within acceptable limits. Schur is stable.

[0103] Define state estimation error

[0104]

[0105] Substituting the observer equations into the system dynamics equations, we obtain the error dynamics equations.

[0106]

[0107] To quantify the cumulative effects of process noise and estimation errors, a compact perturbation set is defined. First, a linear mapping set of external perturbations is defined. ( (The bounded range of the disturbance source).

[0108] Integrated disturbance set Defined as

[0109]

[0110] Among them, symbols Minkowski and, For the bounded set of noise measurements.

[0111] Based on the above error dynamics, even if the initial error is arbitrary, the estimated error sequence can be determined. Ultimately, it will converge and remain within a specific ellipsoidal region. This region is called the minimum robust positive invariant set, denoted as .

[0112]

[0113] This set It describes the maximum deviation boundary between the actual state and the estimated state under the worst-case perturbation.

[0114] To ensure that the real system strictly satisfies the physical constraints when disturbed, the nominal constraints used for online optimization need to be reduced.

[0115] First, define the composite disturbance term introduced by observer error and external disturbance. and its corresponding compact set

[0116]

[0117]

[0118] Next, calculate the first... Shrinking state constraint set during step prediction and input constraint set

[0119]

[0120]

[0121] in, Indicates the difference between Pontryagin and the gold standard. and These are the original temperature constraints of the thermal insulation structure (such as the material's limiting temperature) and the original capability constraints of the actuator; For the closed-loop system at the terminal gain The disturbance under the action can reach the set

[0122]

[0123] Through the above steps, the online optimization problem in step four will be based on the shrunken constraint set. and The solution is then performed. This ensures that as long as the nominal predicted state lies within the contraction constraint, the perturbed true state will necessarily lie within the original constraint. and This achieves the system's hard constraint robustness.

[0124] Step 4: Solve the optimization problem online. The specific steps are: real-time acquisition of local temperature and exchange of information with neighboring subsystems; dynamic synthesis of control parameters based on current membership weights; online solving of a convex optimization problem satisfying robust constraints; obtaining the optimal thermal control input at the current moment and applying it to the actuator to achieve rolling optimization control.

[0125] During the online optimization phase, to increase control degrees of freedom and optimize performance, the control input parameter is parameterized as a combination of "offline state feedback" and "online disturbance compensation." For the subsystem... Its control law is defined as:

[0126]

[0127] in, The robust state feedback gain obtained offline in step two; This is a combination of the current time state estimate obtained by the observer in step three and the current spatial state; This is the sequence of decision variables to be solved for online optimization.

[0128] Each subsystem uses its own time state estimate and spatial state information received from adjacent subsystems (There is a communication delay), building the future An open-loop prediction model for the step.

[0129] Define the performance index of local quadratic forms in the finite time domain

[0130]

[0131] in, Indicates the current moment and spatial nodes Regarding the future The predicted value of the system's time state at any given moment; For the corresponding predictive control input sequence; Predict the terminal's status; For prediction in the time domain.

[0132] The planning objective is to minimize the cost function. To transform this quadratic programming problem into a solvable semidefinite programming problem, a scalar performance upper bound is introduced. , making .

[0133] Using Schul's complement lemma, the performance constraint is transformed into the following linear matrix inequality form:

[0134]

[0135] in, For time state prediction sequences, To control the input sequence; The weight matrix blocks are diagonal matrices of the extended dimension. , , .

[0136] To ensure the recursive feasibility and robust stability of the closed-loop system, the optimization problem must simultaneously satisfy the following constraints:

[0137] (1) Process constraints after contraction: The predicted state sequence and control input sequence must be within the robust contraction constraint set calculated in step three: This ensures that even with external disturbances and estimation errors, the actual system state and inputs will not violate physical limitations.

[0138] (2) Terminal ellipsoid constraint: Terminal prediction state We must proceed to the maximum permissible terminal invariant set calculated in step two. .

[0139] Considering the above objectives and constraints, the subsystem exist Solve the following semidefinite programming problem at any time:

[0140]

[0141]

[0142]

[0143]

[0144] Solve this convex optimization problem to obtain the optimal sequence of decision variables. Take the first element of the sequence. According to the formula The system calculates the actual control input at the current moment and applies it to the actuators of the spacecraft's thermal insulation structure. Then, the system scrolls to... Repeat the above measurement and optimization process at any time.

[0145] Example: In this example, the structure is as follows Figure 1 One-dimensional spacecraft thermal insulation structure as Figure 2 The controller design shown.

[0146] Based on the system model established in step one, consider a long, straight section of spacecraft thermal insulation material, whose heat conduction process follows a one-dimensional nonlinear partial differential equation. Material density... Specific heat capacity nominal nonlinear thermal conductivity Spatial sampling interval The thermal insulation structure is divided into A series of interconnected subsystems. Time sampling interval. The variation range of the thermal conductivity parameter is as follows: The system is subjected to random disturbances, with the upper bound of the disturbance amplitude being... State constraints: Input constraints: .

[0147] In step two, select the state weight matrix. Control input weights System gain index Using the YALMIP toolbox and MOSEK solver in MATLAB, the linear matrix inequalities described in this invention are solved. .

[0148] In step four, online prediction of the time domain is performed. Total number of simulation steps Each subsystem is solved separately. And communicate. The spatiotemporal evolution of system temperature is as follows: Figure 5 As shown, the spatiotemporal distribution of the control input is as follows: Figure 6 The temperature change curves of each subsystem over time are shown in Figure 7 As shown in the figure, this embodiment verifies that the nonlinear distributed model predictive control method proposed in this invention has the advantages of high precision, strong robustness, and computational efficiency in solving the thermal control problem of spacecraft thermal insulation structures.

Claims

1. A spacecraft thermal control method based on distributed model predictive control, characterized in that, The method includes: Step 1: Establishing a fuzzy heat transfer model for space interconnection TS: Based on the one-dimensional partial differential equation of heat conduction, the spacecraft's thermal insulation structure is spatially discretized using the finite difference method or the finite element method to obtain a space interconnection system model composed of multiple mutually coupled subsystems; considering the nonlinear characteristics of thermal property parameters changing with temperature, temperature is selected as the antecedent variable, and polyhedral fuzzy rules are established to transform the nonlinear heat transfer dynamics into a set of locally linear space interconnection TS fuzzy system models; Step 2: Offline solution of robust control law parameters: Based on the parallel distributed compensation strategy, an optimization problem containing system stability constraints and dissipative performance indicators is constructed; using the linear matrix inequality technique, the common Lyapunov matrix and the corresponding state feedback control gain satisfying all fuzzy rule subsystems are solved offline, and the Lyapunov matrix and terminal invariant set are obtained, thus transferring the complex robust stability calculation to the offline stage. Step 3: Design Distributed Robust Constraints: Addressing the external heat flow disturbances and model uncertainties of the system, define a compact set containing the disturbance boundary; based on robust positive invariant set theory, calculate the limit boundary of the state estimation error and the impact of the disturbance on the system; accordingly, shrink the temperature constraints of the insulation structure and the heating / cooling capacity constraints of the actuator to obtain the robust positive invariant set and the disturbance reachable set, and construct robust constraint conditions that can tolerate worst-case disturbances. Step 4: Solving the optimization problem online: At each sampling moment, each thermal insulation subsystem acquires the current local temperature state through sensors and exchanges state information with adjacent subsystems; calculates the membership weights of each fuzzy rule based on the current temperature, and constructs a distributed model predictive control optimization problem using the Lyapunov matrix, terminal invariant set, robust positive invariant set, and perturbation reachable set obtained in Steps 2 and 3; solves this convex optimization problem online to obtain the optimal thermal control input at the current moment, applies it to the actuator, and rolls into the next moment.

2. The spacecraft thermal control method based on distributed model predictive control according to claim 1, characterized in that: Step one specifically includes: Consider the continuous-time one-dimensional transient nonlinear heat transfer control equation, which is of the form of in, For spacecraft thermal insulation structure Time and space Temperature variable at the location; , These are the material density and specific heat capacity, respectively. for Directional material thermal conductivity; To control the quantity; For disturbance terms; This is to structure the uncertainty terms in the model; The partial differential equation is replaced by a finite difference scheme, which transforms the partial differential equation into a difference calculation. The difference scheme for temperature with respect to spatial coordinates is as follows: Difference scheme of temperature versus time axis in, For discrete time coordinates, For discrete spatial coordinates; right exist Taylor expansion Will Substitution , can be obtained Considering thermal conductivity It is a nonlinear function of the subsystem temperature. The local linear system is represented by a TS fuzzy model established through if-then rules with fuzzy meaning. The rules of the TS fuzzy model are as follows: in It is the antecedent variable. For fuzzy sets, For the number of rules, The number of preceding variables; The temperature of the subsystem is considered as a state variable; in The time component of the state represents the subsystem. exist Temperature at any moment; The spatial components of the state represent the subsystem. exist Time to subsystem The effect of temperature; The non-minimum state space realization of a locally linear system is as follows in, and These represent the system's time state vector and spatial state vector, respectively. This represents the generalized exogenous input received by the system. and These represent bounded external process disturbances and measurement noise, respectively. This represents the performance output used to evaluate control quality; Indicates the first A local subsystem or the first The augmented system parameter matrix of a local model, with superscripts of its internal elements. Refers to the corresponding first in the TS fuzzy model Fuzzy rules; specifically, matrix The block matrices in the data can be categorized into four types: , , The system state matrix represents the internal state evolution and coupling relationships of the system in the time and space dimensions. , , The input matrix represents the uncertain input. External disturbances and control input The driving effect on the spatiotemporal state of the system; , , The output matrix represents the effect of the system's internal spatiotemporal state on its internal output. Performance Evaluation and measurement output The mapping relationship; , As a direct feedforward matrix or direct transfer matrix, it characterizes the direct interaction paths between each input signal and each output signal; regarding the structured uncertainty component contained in this model, and These represent the internal output signal transmitted by the nominal system to the uncertainty module and the internal input signal received by the nominal system, respectively. , and Representing different spatial nodes , and Physical parameters at the location and Uncertainty perturbation momentum; right The local models are fuzzed together to obtain the complete TS model in the form of: in in, It is the first The first fuzzy rule one preceding variable The corresponding membership function, the antecedent variable Defined as: It describes the first Under this rule, the antecedent variable The degree to which a specific fuzzy concept is satisfied; It is the first The membership degree of a fuzzy rule measures the membership of the current antecedent vector. With the The degree of matching of the antecedent conditions of each rule, and the fuzzy weights satisfying the normalization condition: .

3. The spacecraft thermal control method based on distributed model predictive control according to claim 1, characterized in that: Step two specifically includes: Based on the fuzzy rules of the TS fuzzy model, a parallel distributed compensation strategy is used to design the controller; for the ... Fuzzy rules Design the corresponding local linear state feedback control law: For the design of the first The feedback gain matrix of each subsystem; the global control law of the system is obtained by weighting the local control laws through fuzzy membership functions: The normalized membership function determined in step one. For the preceding variable; To ensure the robust stability of the closed-loop system and suppress external disturbances, a Lyapunov function is selected. in, It is a symmetric positive definite matrix, which sets the energy gain index. That is, it requires the disturbance to To performance output The gain satisfies ; Meet the indicators Lyapunov matrix It can be obtained from the following formula in, To augment the system's block diagonal form of the Lyapunov matrix; This represents the symmetric positive definite Lyapunov matrix corresponding to the time state. This is used to ensure the time asymptotic stability of the system and meet a given energy gain specification. ; This represents a non-singular symmetric matrix corresponding to a spatial state. , used to characterize the spatial evolution characteristics of the system; For scaling multiplier matrices; For the corresponding dimension of the identity matrix; Since direct solution is nonconvex, a bilinear transformation is introduced to transform the discrete-time system into a continuous-time system. Define new optimization variables and : , ; Corresponding time state components, Corresponding spatial state components; Construct the following linear matrix inequalities The symbol * represents a symmetric term. yes The null basis matrix; The matrix of the continuous domain system after bilinear transformation, and the common Lyapunov matrix. , No. Feedback gain of a fuzzy rule ; and These are the penalty (weight) matrices for the system state and control input, respectively. They not only guarantee the convexity of the performance index function, but also serve to balance the convergence speed of the system state with the consumption of control energy. To ensure the recursive feasibility of online optimization, it is necessary to calculate the input constraints. The largest terminal invariant set, where To determine the maximum allowed input; select the terminal set. A subset of Lyapunov functions: ； in, The boundary parameter that defines the size of the terminal invariant set, namely the upper bound of the level cut of the Lyapunov function, geometrically determines the volume of the ellipsoidal invariant set in the state space. The maximum value is determined by solving the following convex optimization problem. The final maximum allowed terminal set parameters This will serve as the terminal constraint boundary for the online optimization problem in step four.

4. The spacecraft thermal control method based on distributed model predictive control according to claim 1, characterized in that: Step three specifically includes: Taking advantage of the structural characteristic that the time evolution of the heat transfer process is affected by disturbances but the spatial coupling is relatively deterministic, the following distributed state observer is designed. in, This is an estimate of the time state. For actual measurement output, To estimate the output, The observer gain matrix is ​​designed to ensure that the observer error dynamics matrix is ​​within acceptable limits. Schur is stable; Define state estimation error Substituting the observer equations into the system dynamics equations, we obtain the error dynamics equations. To quantify the cumulative effects of process noise and estimation errors, a compact perturbation set is defined; first, a linear mapping set of external perturbations is defined. , The bounded range of the disturbance source; Integrated disturbance set Defined as Among them, symbols Minkowski and, For the bounded set of noise measurements; Based on the above error dynamics, even if the initial error is arbitrary, the estimated error sequence can be determined. Ultimately, it will converge and remain within a specific ellipsoidal region; this region is called the minimum robust positive invariant set, denoted as . This set It describes the maximum deviation boundary between the actual state and the estimated state under the worst-case perturbation.

5. A spacecraft thermal control method based on distributed model predictive control according to claim 4, characterized in that: To ensure that the real system strictly satisfies the physical constraints when disturbed, the nominal constraints used for online optimization need to be reduced. First, define the composite disturbance term introduced by observer error and external disturbance. and its corresponding compact set Next, calculate the first... Shrinking state constraint set during step prediction and input constraint set in, Indicates the difference between Pontryagin and the gold standard. and These are the original temperature constraints of the thermal insulation structure and the original capability constraints of the actuator, respectively. For the closed-loop system at the terminal gain The disturbance under the action can reach the set ； in, The state feedback control law gain exists within this. make Stablize.

6. The spacecraft thermal control method based on distributed model predictive control according to claim 1, characterized in that: Step four specifically includes: For subsystems Its control law is defined as: in, The robust state feedback gain obtained offline in step two; This is a combination of the current time state estimate obtained by the observer in step three and the current spatial state; The sequence of decision variables to be solved for online optimization; Each subsystem uses its own time state estimate and spatial state information received from adjacent subsystems Building the Future An open-loop prediction model for the step; Define the performance index of local quadratic forms in the finite time domain in, Indicates the current moment and spatial nodes Regarding the future The predicted value of the system's time state at any given moment; For the corresponding predictive control input sequence; Predict the terminal's status; For prediction in the time domain; The planning objective is to minimize the cost function. To transform this quadratic programming problem into a solvable semidefinite programming problem, a scalar performance upper bound is introduced. , making ; Using Schul's complement lemma, the performance constraint is transformed into the following linear matrix inequality form: in, For time state prediction sequences, To control the input sequence; The weight matrix blocks are diagonal matrices of the extended dimension. , , .

7. A spacecraft thermal control method based on distributed model predictive control according to claim 6, characterized in that: Step four also includes: To ensure the recursive feasibility and robust stability of the closed-loop system, the optimization problem must simultaneously satisfy the following constraints: Post-shrinkage process constraints: The predicted state sequence and control input sequence must be within the robust shrinkage constraint set calculated in step three. This ensures that even with external disturbances and estimation errors, the actual system state and inputs will not violate physical constraints; Terminal ellipsoid constraints: Terminal predicted state We must proceed to the maximum permissible terminal invariant set calculated in step two. ; Considering the above objectives and constraints, the subsystem exist Solve the following semidefinite programming problem at any time: Solve this convex optimization problem to obtain the optimal sequence of decision variables. Take the first element of the sequence. According to the formula The system calculates the actual control input at the current moment and applies it to the actuators of the spacecraft's thermal insulation structure; subsequently, the system rolls to... Repeat the above measurement and optimization process at any time.

8. A spacecraft thermal control method system based on distributed model predictive control, characterized in that: The system has a program module corresponding to the steps of any one of claims 1-7, and executes the steps in the spacecraft thermal control method based on distributed model predictive control when it is run.

9. A computer device, characterized in that: It includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, it performs the steps of a spacecraft thermal control method based on distributed model predictive control as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that: The storage medium is used to store a computer program that executes a spacecraft thermal control method based on distributed model predictive control according to any one of claims 1-7.

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