Inertial platform multi-point joint temperature control method based on model predictive control

Abstract

The invention particularly relates to a multi-point joint temperature control method for an inertial platform based on model predictive control, which comprises the following steps of: establishing a three-dimensional heat conduction equation model, describing an evolution process of a temperature field by utilizing a state space model, and optimizing power output of a plurality of heat sources by adopting a model predictive control algorithm. Therefore, the temperatures of multiple control points can be accurately adjusted. According to the control method, multiple heat source powers are optimized through a quadratic cost function, temperature errors, heat source power consumption and system constraint conditions are comprehensively considered, and real-time temperature control is carried out through a rolling optimization strategy. Compared with a traditional single-point control method, the method can effectively solve the problem that the precision of the optical fiber cannot be fully exerted, remarkably improves the temperature control precision and energy efficiency, has a wide application prospect, and is particularly suitable for an inertial platform system with precise temperature control requirements.

Description

Technical Field

[0001] The present invention relates to the field of inertial platform temperature control technology, specifically to a multi-point joint temperature control method for inertial platforms based on model predictive control. This method is used to improve the temperature control accuracy of inertial platforms and ensure the stability of the temperature field within the platform. It is suitable for high-precision temperature control and has wide applications in precision equipment, fiber optic sensor systems, aerospace, and other fields. Background Art

[0002] As a crucial component of precision control systems, inertial platforms typically must operate under high precision and stability requirements. The stability of the temperature field is crucial to the accuracy and stability of inertial platforms. Traditional temperature control methods, such as PID control, typically only adjust a single control point and cannot effectively address the complexity of multi-point temperature control and the dynamic changes in the platform's temperature field. Therefore, developing a control method that can handle multi-point temperature control while ensuring stability and precision is crucial.

[0003] Model Predictive Control (MPC), an advanced control method based on system dynamic models, offers significant advantages in multivariable control problems. By predicting the system's future behavior and adjusting control inputs in advance, MPC effectively improves control accuracy and ensures system stability. Combining the characteristics of the temperature field with system constraints, MPC provides an effective solution for multi-point joint temperature control of inertial platforms.

[0004] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0005] Existing temperature control methods, such as PID control, perform well in certain application scenarios. However, they cannot fully address the complexity and constraints of the system when controlling multi-point temperature fields, resulting in low temperature control accuracy and high energy consumption. This paper proposes a multi-point joint temperature control method for inertial platforms based on model predictive control (MPC). This method improves control accuracy, energy efficiency, and system stability, and is suitable for inertial platforms requiring high-precision temperature control.

[0006] Other features and advantages of the present invention will become apparent from the following detailed description, or may be learned in part by practice of the present invention.

[0007] According to a first aspect of the present invention, a multi-point joint temperature control method for an inertial platform based on model predictive control is provided, the method comprising:

[0008] Step 1: Obtain the temperature data of each control point and heat source of the inertial platform;

[0009] Step 2: Based on the heat conduction equation, the temperature distribution model of the inertial platform is established by considering the interaction between heat source input, control point temperature and heat transfer;

[0010] Step 3: Design the cost function and constraints of the model predictive control algorithm, predict future temperature changes based on the current temperature and heat source input, and optimize the heat source input to achieve the temperature control requirements;

[0011] Step 4: Based on the predicted temperature changes, optimize the heat source input power of multiple control points to achieve joint control of multiple point temperatures;

[0012] Step 5: Update the control input through the rolling optimization strategy and continuously adjust the heat source input based on actual feedback to ensure the stability and accuracy of temperature control.

[0013] In some exemplary embodiments, step 2 specifically includes the following steps:

[0014] Step 2.1: Build a basic model of the heat conduction equation

[0015] When the inertial platform is a three-dimensional cube model, the heat conduction equation inside the platform is established to describe the change in temperature distribution. Specifically:

[0016]

[0017] Where T(x,y,z,t) is the temperature at any position (x,y,z) inside the platform at time t, and α is the thermal diffusion coefficient;

[0018] Step 2.2: Consider the effect of heat source input

[0019] The heat source term Q(x, y, z, t) is added to the heat conduction equation to reflect the influence of the heat source on the temperature field inside the platform, and the revised equation is obtained:

[0020]

[0021] Where Q)x,y,z,t) is the heat source input power, C is the specific heat capacity, and ρ is the density;

[0022] Step 2.3: Set the boundary conditions and initial conditions, numerically solve the heat conduction equation modified in step 2.2, and obtain the temperature distribution model of the inertial platform.

[0023] In some exemplary embodiments, the corrected heat conduction equation in step 2.2 is numerically solved using a finite difference method (FDM) or a finite element method (FEM);

[0024] In the finite difference method (FDM), the platform's space and time are discretized, and the differential approximation is used to replace the partial differential operator in the equation. The temperature distribution at each grid point is solved through iteration.

[0025] In the finite element method (FEM), the platform area is divided into several small units. The local temperature equation of each unit is constructed and then the temperature equation of each unit is solved by numerical methods to obtain the global temperature field.

[0026] In some exemplary embodiments, the method further comprises:

[0027] By comparing experimental data with model prediction results, the physical parameters in the model are adjusted to ensure the accuracy of the heat conduction model; through error analysis and error correction, the numerical model can better reflect the temperature field changes of the actual platform.

[0028] In some exemplary embodiments, the physical parameters in the adjustment model specifically include thermal diffusion coefficient, specific heat capacity, and heat source power input.

[0029] In some exemplary embodiments, the cost function in step 3 includes temperature error, energy consumption, control input change rate, and temperature change rate, and is specifically expressed as follows:

[0030]

[0031] Among them, the temperature error e i (t) represents the actual temperature T of each control point on the platform i (t) and target temperature T target The difference between i (t) is the heat source input power, λ i is the weight of the temperature error, γ is the weight of the power consumption, N is the number of control points, M is the number of heat sources, α i is the weight of the temperature change rate, and β is the weight of the heat source input change rate;

[0032] By optimizing the cost function J, the MPC algorithm can minimize the temperature error while reducing energy consumption, achieving the best balance between control accuracy and energy utilization.

[0033] In some exemplary embodiments, the constraints in step 3 include:

[0034] Power input constraint for each heat source: For each heat source, set a power input upper limit to ensure that the heat source input power does not exceed its maximum allowable value, thereby preventing equipment overload;

[0035] Temperature constraints for each control point: Set minimum and maximum limits for the temperature of each control point to ensure that the temperature is always within the specified range to avoid damage to the equipment caused by overheating or overcooling;

[0036] Energy consumption upper limit constraint: Ensure that the total power consumption of the system does not exceed a predetermined upper limit to optimize energy efficiency.

[0037] According to a second aspect of the present invention, a storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the method for multi-point joint temperature control of an inertial platform based on model predictive control according to the first aspect is implemented.

[0038] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored. When the computer program is executed by a processor, the method for multi-point joint temperature control of an inertial platform based on model predictive control according to the first aspect is implemented.

[0039] According to a fourth aspect of the present invention, there is provided an electronic device, comprising:

[0040] processor; and

[0041] a memory for storing executable instructions of the processor;

[0042] The processor is configured to implement the multi-point joint temperature control method of an inertial platform based on model predictive control as described in the first aspect above by executing the executable instructions.

[0043] The embodiment of the present invention provides an inertial platform multi-point joint temperature control method based on model predictive control, which significantly improves the accuracy of the inertial platform multi-point joint temperature control by introducing the model predictive control (MPC) algorithm. By optimizing the quadratic cost function and minimizing the temperature error and energy consumption, the present invention achieves the best balance between high precision of temperature control and energy utilization. In addition, combined with multiple constraint designs (such as heat source power limitation, temperature range constraint, temperature change rate limitation, etc.), the stability and safety of the system are effectively guaranteed. The rolling optimization strategy enables the system to dynamically adapt to environmental changes and system errors, thereby ensuring real-time temperature control accuracy and enhancing the robustness of the system. In short, the present invention not only improves the temperature control accuracy, but also optimizes energy consumption, and has high practical value and broad application prospects.

[0044] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The accompanying drawings are incorporated into and constitute a part of this specification, illustrate embodiments consistent with the present invention, and together with the description, serve to explain the principles of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and it is clear that those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0046] Figure 1 This is a flow chart of the platform cavity temperature control of the present invention;

[0047] Figure 2 Validation results for the temperature model;

[0048] Figure 3 This is the temperature change trend result under MPC control;

[0049] Figure 4 It is the result of control input change trend under MPC control;

[0050] Figure 5 This is the temperature change rate trend result under MPC control. DETAILED DESCRIPTION

[0051] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0052] In addition, the accompanying drawings are merely schematic illustrations of the present invention and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the blocks shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0053] In view of the shortcomings and deficiencies of the existing technology, this example embodiment provides a multi-point joint temperature control method for an inertial platform based on model predictive control, which can specifically include the following steps:

[0054] Step 1: Collect the temperature data of each control point and heat source of the inertial platform and use it as the input data of the model;

[0055] Step 2: Based on the heat conduction equation, establish the temperature distribution model of the inertial platform, considering the interaction between heat source input, control point temperature and heat transfer;

[0056] Step 3: Design a model predictive control (MPC) algorithm by designing appropriate cost functions and constraints. This algorithm predicts future temperature changes based on current temperature and heat source input, and optimizes heat source input to achieve temperature control requirements.

[0057] Design a quadratic cost function to minimize temperature error and energy consumption. Cost function design refers to the model predictive control algorithm optimizing the quadratic cost function to minimize temperature error and energy consumption and obtain the optimal heat source input power. The optimization process is calculated using the quadratic cost function, which includes the following four main objectives: temperature error and energy consumption, control input change rate, and temperature change rate. Temperature error e i (t) represents the actual temperature T of each control point on the platform i (t) and target temperature T target The difference between the energy consumption E(t) and the heat source input power P i (t0 is related and is usually measured by the square of the heat source power. By optimizing the cost function J, the MPC algorithm can minimize the temperature error while reducing energy consumption and controlling the rate of change of state and input, achieving the optimal balance between control accuracy and energy utilization.

[0058] Constraints are set to ensure that the heat source power, temperature range, and temperature change rate are within safe limits. Constraint design refers to the consideration of multiple physical limitations and dynamic characteristics within the model predictive control algorithm to ensure system stability and safety. First, an upper limit is set for the power input of each heat source to ensure that the heat source input power does not exceed its maximum allowable value, thereby preventing equipment overload. Furthermore, to ensure that the temperature of each control point on the platform does not exceed the safe range, minimum and maximum limits are set for each control point to ensure that the temperature remains within the specified range and avoid damage to the equipment due to overheating or overcooling. Finally, to achieve efficient energy utilization, energy consumption constraints are designed to ensure that the total power consumption of the system does not exceed a predetermined upper limit, thereby optimizing energy efficiency. These constraints play a crucial role in the model predictive control algorithm, ensuring the accuracy of temperature control and the stable operation of the system.

[0059] Step 4: Based on the predicted temperature changes, optimize the heat source input power of multiple control points to achieve joint control of multiple point temperatures;

[0060] Step 5: Update the control input through a rolling optimization strategy, continuously adjusting the heat source input based on actual feedback to ensure the stability and accuracy of temperature control;

[0061] The rolling optimization strategy dynamically updates the control input to account for changes in the external environment and system errors, ensuring real-time temperature control accuracy. This is a core feature of the MPC algorithm. By updating the optimization calculation at each time step, the system obtains real-time temperature feedback and uses it to update the control input. This allows the system to adapt to changes in external environmental conditions, such as temperature fluctuations and changes in heat source power, while also correcting errors in the model predictions, ensuring that temperature control accuracy remains within the required range.

[0062] The above steps can be broken down into the following steps:

[0063] Step 1: Construct a temperature field model, considering the mutual influence of heat source input, control point temperature and heat conduction.

[0064] Step 2: Use numerical methods to solve the temperature distribution model and obtain the temperature field of the platform.

[0065] Step 3: Establish a system dynamic characteristic model to describe the heat transfer relationship between the heat source and the control point.

[0066] Step 4: Set the target temperature for each control point and calculate the error between the target temperature and the actual temperature.

[0067] Step 5: Design a quadratic cost function to minimize temperature error and energy consumption.

[0068] Step 6: Set constraints to ensure that the heat source power, temperature range, and temperature change rate are within a safe range.

[0069] Step 7: Based on current temperature data and heat source input, predict future temperature changes.

[0070] Step 8: Dynamically adjust the heat source input through the rolling optimization algorithm to optimize temperature control.

[0071] Step 9: Solve the optimization problem and calculate the optimal heat source input power.

[0072] Step 10: Convert the optimized heat source input into a control instruction and adjust the heat source power.

[0073] Step 11: Adjust system input based on real-time feedback to maintain control accuracy.

[0074] Step 12: Dynamically update the control strategy to cope with environmental changes and system errors.

[0075] Step 13: Design energy consumption constraints to ensure that the system power consumption does not exceed a predetermined upper limit.

[0076] Step 14: Monitor the optimized control input to ensure system stability.

[0077] Step 15: Output the optimized heat source input as a control instruction to achieve temperature control.

[0078] Hereinafter, each step of the multi-point joint temperature control method of an inertial platform based on model predictive control in this exemplary embodiment will be described in more detail with reference to the accompanying drawings and embodiments.

[0079] Example 1

[0080] For ease of explanation, the inertial platform is equivalent to a cubic adiabatic cavity. Model predictive control (MPC) is performed based on the heat transfer model of the three-dimensional cubic space to accurately control the multi-point joint temperature. The basic process is as follows Figure 1 shown.

[0081] Step 1: Establish a three-dimensional heat conduction equation

[0082]

[0083] Where T = T(x,y,z,t) is the temperature field, which is a function of position (x,y,z) and time t; is the thermal diffusivity, where k is the thermal conductivity of the material, ρ is the density, and c is the specific heat capacity; Q = Q(x, y, z, t) is the intensity of the heat source per unit volume, which indicates the influence of the heat source inside the object on the temperature.

[0084] Interpret the terms in the three-dimensional heat conduction equation:

[0085] Countdown time item Indicates the rate of change of temperature over time and is a key variable in the control system. It reflects the trend of temperature change over time under the combined action of heat source and heat conduction.

[0086] Spatial second-order derivative term Represents the rate at which heat diffuses in all spatial directions. Based on Fourier's law of heat conduction, the direction of heat flow is consistent with the temperature gradient, with higher temperature areas transferring heat to lower temperature areas.

[0087] Thermal diffusivity α: controls the speed of heat diffusion. For materials with a larger thermal diffusivity, temperature changes propagate faster in space.

[0088] Heat source term This term represents the effect of a heat source on temperature. Q is the amount of heat generated or absorbed per unit volume, which has an additional effect on the temperature distribution. When there are multiple heat sources in a system, Q can be considered the sum of the effects of each source.

[0089] Solving the three-dimensional heat conduction equation above requires appropriate boundary conditions and initial conditions. These conditions should be set appropriately based on the physical characteristics of the inertial platform and its operating environment. Common boundary conditions include constant temperature, adiabatic, or convection. The initial condition is generally the initial temperature field of the platform at a specific moment. First, the following settings are given:

[0090] Initial conditions: At t = 0, the initial temperature distribution of each point in the entire space needs to be given

[0091] T(x,y,z,0)=T0(x,y,z) (2)

[0092] Boundary conditions: Boundary conditions can be classified as constant temperature boundary conditions, constant heat flux boundary conditions or convection boundary conditions.

[0093] Constant temperature boundary condition (Dirichlet boundary condition): The temperature on the specified boundary is T = T b .

[0094] Neumann boundary condition: specifies the heat flow on the boundary Where n represents the normal vector of the boundary.

[0095] Convective boundary condition (Robin boundary condition): represents the convective heat transfer between the boundary and the environment, usually in the form of Where h is the convective heat transfer coefficient, T ∞ is the ambient temperature.

[0096] Since analytical solutions to the three-dimensional heat conduction equation are usually difficult to obtain under complex boundary conditions, numerical methods are often used to solve them. Common numerical methods include:

[0097] Finite Difference Method (FDM): Discretize continuous space and time, use difference formulas to approximate partial derivatives, and thus obtain a numerical solution to the temperature field.

[0098] Finite Element Method (FEM): The spatial region is divided into grids or cells, and the temperature field is approximated by constructing an interpolation function.

[0099] Finite Volume Method (FVM): The control volume is divided into small volume units, and the energy conservation equation is used to calculate the heat change of each unit.

[0100] Model calibration and validation. By comparing experimental data with model predictions, we adjust the model's physical parameters (such as thermal diffusivity, specific heat capacity, and heat source power input) to ensure the accuracy of the heat conduction model. Through error analysis and correction, we ensure that the numerical model better reflects the actual platform temperature field changes.

[0101] Step 2: Spatial discretization

[0102] Applying the finite difference method in space, the second-order partial derivative of temperature in the x-direction can be expressed as follows

[0103]

[0104] Similarly, the second-order derivatives in the y and z directions are:

[0105]

[0106] Discretizing the time derivative and assuming the time step is Δt, we can approximate:

[0107]

[0108] Substituting the heat conduction equation and sorting it out, we can get the discretized temperature update formula:

[0109]

[0110] Step 3: Construct the state vector

[0111] Reorganize the temperature T(i, j, k, t) at each discrete spatial point into a state vector x(t), where each element of x(t) corresponds to the temperature value at a grid point. If there are N grid points, then x(t) is an N x 1 vector. This allows us to represent the state of the temperature field at each time step.

[0112] Step 4: Construct the system matrix A and input matrix B of the state space model

[0113] State transfer matrix A: All coefficients in the temperature update formula of the matrixed influence relationship of neighboring points are organized into matrix A. Each row of this matrix corresponds to a grid point, and its elements represent the heat transfer relationship with its neighboring points.

[0114] Input matrix B: If there is an external heat source acting on the system, the relationship between the heat source and the temperature of each grid point can be matrixed through matrix B.

[0115] In the discretized equation, if for all T ( i,j,k ) values ​​are renumbered, the temperature evolution equation can be written as:

[0116] x(t+Δt)=Ax(t)+Bu(t) (8)

[0117] in:

[0118] A is the state transfer matrix, which represents the temperature influence relationship between each node and its adjacent nodes;

[0119] B is the input matrix, which represents the effect of heat source on temperature change;

[0120] u(t) is the input vector, which represents the intensity of the heat source at different positions.

[0121] Step 5: Construct the output matrix C and direct transfer matrix D

[0122] For the control system, if we only need to observe the temperature of certain specific points, we can define the output matrix C and the direct transfer matrix D:

[0123] Output matrix: Select the grid points to be observed and construct the matrix C so that y(t) = Cx(t) represents the temperature of the output temperature point.

[0124] Direct transfer matrix D: In a heat conduction system, the direct transfer term is usually zero.

[0125] Therefore, the final state-space model is:

[0126]

[0127] Where: x(t) represents the current state of the temperature field.

[0128] u(t) represents the power input of the heat source.

[0129] y(t) represents the temperature value at the sampling point.

[0130] A, B, and C respectively describe the state transition, the impact of input on state, and the mapping relationship from state to output.

[0131] Δt represents the sampling time interval of the system.

[0132] In temperature field control, the input u(t) represents the power output of multiple controllable heat sources, and the output y(t) represents the temperature values ​​of multiple control points in the temperature field.

[0133] Step 6: Design the prediction horizon and control interval

[0134] The prediction horizon, Np, is the time period used in the MPC algorithm to predict future system behavior. Properly designing the prediction horizon can balance control performance and computational complexity, thereby achieving optimal control. Key points in predictive horizon design include the following:

[0135] System response characteristics: Select an appropriate prediction horizon based on the response characteristics of the controlled system. If the system's dynamic response is fast, the prediction horizon can be shorter; if the system's response is slow, the prediction horizon should be extended to capture more future changes.

[0136] Control objective: The control objective determines the length of the prediction horizon. If the system needs to preemptively adjust for future disturbances, a longer prediction horizon is required. If only the control effect at the current moment is of concern, a shorter prediction horizon can be used.

[0137] Computational resource limitations: Longer prediction horizons increase computational complexity and real-time requirements, so system computing resources should be considered during design. Optimize the length of the prediction horizon through experimentation or simulation.

[0138] In MPC control, the length of the prediction horizon, Np, can be set by balancing control accuracy with computational complexity. This is often determined through trial and error or optimization. Based on engineering experience, Np is typically set to 10 for the first test, with subsequent adjustments and optimizations.

[0139] The control interval Tc is the time step of the controller update in the MPC algorithm, which determines the update frequency of the control input after each optimization calculation. The control interval design should consider the following factors:

[0140] System dynamic response speed: If the system's dynamic response is fast, a shorter control interval is required so that the system can quickly respond to changes in control input; for systems with slower response, the control interval can be appropriately increased.

[0141] Computational efficiency: A shorter control interval increases the calculation frequency and the pressure of real-time calculations. Therefore, if computing resources allow, a shorter control interval can be appropriately selected. If resources are limited, the control interval can be increased and the calculation frequency can be reduced.

[0142] Control stability and accuracy: The control interval should be designed to ensure sufficient control accuracy at the system update frequency. Excessively long control intervals can cause system response lags, affecting control accuracy; while excessively short control intervals can reduce the system's adaptability to real-time disturbances.

[0143] A reasonable control interval design not only helps ensure smooth changes in the control input but also avoids computational pressure on the system caused by excessively high frequencies. Generally, the choice of control interval and prediction horizon are interrelated. Shorter control intervals typically require more frequent calculations and updates, while longer control intervals can reduce the calculation frequency but require a corresponding increase in the prediction horizon. To match the prediction horizon Np = 10, the time interval dt = 0.01s was used in the first experiment. This can be adjusted later based on temperature control requirements.

[0144] Step 7: Cost function design

[0145] The cost function needs to balance multiple control objectives, including: minimizing the output temperature error to ensure that the temperature is close to the desired reference value; minimizing the control input energy to reduce power consumption; minimizing the input change rate to ensure the smoothness of the control input and avoid excessive fluctuations; and minimizing the temperature change rate to avoid instability caused by rapid temperature changes.

[0146] For multi-input, multi-point temperature control problems, the following four key components need to be considered when designing the cost function:

[0147] (1) Output error term

[0148] Output error is the difference between the actual temperature of the system at each moment and the reference temperature. The goal of this term is to make the output temperature as close to the reference temperature as possible. Its mathematical expression is:

[0149]

[0150] in:

[0151] Cx(t+k) is the output temperature at time t+k.

[0152] y ref (t+k) is the reference temperature at time t+k.

[0153] Q is a positive definite weight matrix that determines the weight of the output error in the cost function.

[0154] (2) Control input energy term

[0155] The control input energy term is used to limit the size of the control input to prevent excessive input power and thus reduce energy consumption. Its mathematical expression is:

[0156]

[0157] in:

[0158] u(t+k) is the control input (ie, power value) at time t+k.

[0159] R is a positive definite weight matrix used to regulate the influence of the control input.

[0160] (3) Control input change rate term

[0161] The rate of change of the control input is used to limit the sharp fluctuations of the control input, ensuring smooth input changes and avoiding discontinuous or sharp changes. Its mathematical expression is:

[0162]

[0163] in:

[0164] Δu(t+k) is the change in the control input between adjacent moments.

[0165] S is a positive definite weight matrix used to adjust the influence of the input change rate.

[0166] (4) Temperature change rate term

[0167] The temperature change rate is used to constrain the temperature change rate to prevent the temperature field from changing too quickly, thereby avoiding system instability. Its mathematical expression is:

[0168]

[0169] in:

[0170] Δy(t+k) is the change in temperature field between adjacent moments.

[0171] T is a positive definite weight matrix, which is used to adjust the influence of the temperature change rate.

[0172] Taking the above four parts into consideration, the final cost function can be expressed as:

[0173]

[0174] in:

[0175] Np is the length of the prediction time domain.

[0176] Cx(t+k)-y ref (t+k) is the output error term.

[0177] u(t+k) is the control input.

[0178] Δu(t+k) is the rate of change of the control input.

[0179] Δy(t+k) is the rate of temperature change.

[0180] Step 8: Matrix the cost function

[0181] Writing the cost function in matrix form is beneficial for optimizing the subsequent problems. To write the cost function in matrix form, we first define the following vector:

[0182] Output error vector E y : Contains the output error term E at each moment k y (k) = Cx(t+k)-y ref (t+k), that is

[0183]

[0184] Control input vector U: Contains the control input term u(t+k) at each moment.

[0185]

[0186] Input change rate vector ΔU: contains the input change rate at each moment Δu(t+k)=u(t+k)-u(t+k-1), that is,

[0187]

[0188] Temperature change rate vector ΔY: contains the temperature change rate at each moment Δy(t+k)=y(t+k)-y(t+k-1), that is,

[0189]

[0190] Substituting the above vector into the original cost function expression, we can obtain the following matrix form cost function:

[0191]

[0192] In this formula, E y , U, ΔU and ΔY are all vectors of size Np×1, while Q, R, S and T are all symmetric positive definite matrices.

[0193] Expand each item of the matrix cost function in detail:

[0194] Output error term

[0195]

[0196] Control input item U T RU:

[0197]

[0198] Input change rate ΔU T SΔU:

[0199]

[0200] Temperature change rate ΔY T TΔY:

[0201]

[0202] Step 9: Heat source input power and temperature constraint design

[0203] During the control process, it is necessary to constrain the input power of the heat source and the temperature of each control point of the platform. The input power of the heat source needs to meet certain power limit conditions to avoid overload or damage to the equipment. Set the maximum power input of each heat source to P max and the minimum power input is P min ,Right now:

[0204] P min ≤P input ≤P max (twenty four)

[0205] At the same time, in order to ensure the temperature control accuracy, the temperature of each control point of the platform must also meet the set temperature range. Set the minimum temperature of the control point to T min and the maximum temperature is T max ,Right now:

[0206] T min ≤T control (t)≤T max (25)

[0207] These constraints ensure the feasibility and safety of the system in actual operation and avoid overheating or overcooling.

[0208] Step 10: Quadratic programming optimization solution

[0209] After steps 7 and 8, the optimization problem is transformed into a constrained quadratic programming (QP) problem:

[0210]

[0211] Au≤b(27)

[0212] Where A is the constraint matrix and b is the constraint vector.

[0213] Quadratic programming problems are usually solved by numerical optimization methods. Commonly used solvers include:

[0214] OSQP (Operator Splitting Quadratic Program): Applicable to real-time control problems, especially for large-scale optimization problems.

[0215] quadprog(MATLAB): A built-in function provided by MATLAB for solving quadratic programming problems, suitable for small to medium-sized optimization problems.

[0216] CVXPY (Python): An optimization modeling tool in Python that supports constructing and solving quadratic programming problems.

[0217] Here we use quadprog, and we can perform optimization and solution through the following steps:

[0218] Define the matrices and vectors of the optimization problem: construct the matrix H, f, constraint matrix A and constraint vector b based on the cost function and constraints.

[0219] Call the optimization solver: Input the constructed matrix and vector into the QP solver to obtain the optimal control input sequence u(t).

[0220] Obtaining an optimal solution: The optimization solver returns an optimal solution, which is the best sequence of control inputs that minimizes the cost function and satisfies the constraints.

[0221] Step 11: Rolling Optimization

[0222] Rolling optimization is a core strategy in model predictive control. It allows the system to reoptimize control inputs based on the current state within each control cycle, executing only the first instance of the optimal control input. This strategy ensures that the system can continuously adapt to dynamic environments and cope with unforeseen disturbances. The following are the specific steps of rolling optimization.

[0223] Step 11.1: System Status Update

[0224] During each control cycle, the system's current state x(t) must first be updated through measurement or estimation. This serves as the initial state for the optimization problem and provides a basis for subsequent optimization. The accuracy of the current state is crucial to the performance of the rolling optimization process and can be obtained using temperature sensors and state estimation methods.

[0225] Step 11.2: Re-solve the optimization problem

[0226] At each control cycle, the entire optimization problem is re-solved using the current system state x(t) as the initial condition. The cost function, constraints, and prediction horizon Np all need to be updated to obtain a new control input sequence.

[0227] Step 11.3: Calculation of Control Inputs

[0228] After the optimization solution, we get an optimal control input sequence {u(t),u(t+1),...,u(t+N p -1)}, but only the first control input is executed:

[0229] u opt (t) = argmin u J(u)(28)

[0230] This step is the key step of rolling optimization. Although the control inputs at multiple moments are obtained during the optimization process, due to the rolling update of the time domain, we only execute the first control input at the current moment and use the remaining control inputs as the initial control inputs for the next optimization.

[0231] Step 11.4: Control Input Execution

[0232] The calculated optimal control input u opt (t) is executed into the system to drive the system to achieve the target temperature. The control input can be a control variable such as heating power, cooling power, etc.

[0233] u(t)=u opt (t)(29)

[0234] Step 11.5: Update the forecast horizon

[0235] After each control cycle, the prediction horizon is updated, and the current state x(t+1) is used as the initial state for the next control cycle. This rolling optimization continuously adjusts the control strategy, allowing the system to continuously optimize in a dynamic environment.

[0236] t←t+1(30)

[0237] Step 11.6: Adjust parameters in real time

[0238] Control inputs must be adjusted in real time based on environmental changes, model uncertainties, and external disturbances. Each optimization problem solution and control input execution are based on the latest system state and model. This rolling optimization allows the control system to flexibly respond to various situations, ensuring system performance and stability.

[0239] Substitute the specific physical parameters into the grid node number N*N=125, the cube cavity side length L=1.0m, the node spacing dx=L / (N-1)=0.2m, and the thermal diffusion coefficient α=0.01m 2 / s, time interval dt = 1min, and ambient temperature is set to 20℃. In order to verify the thermal stability of the model, the initial temperature of each point in the cavity is set to have a random error (0-0.02℃), allowing the cavity to automatically transfer heat. Eight temperature observation points are evenly selected, and their distribution is shown in Table 1. The temperature changes are observed. The results are as follows Figure 2 As shown, the temperature at each point will tend to the ambient temperature.

[0240] Table 1 Coordinates of temperature observation points

[0241] (2,2,4) (3,2,3) (4,2,2) (2,3,2) (2,4,4) (4,3,3) (4,4,4) (3,4,2)

[0242] Density ρ = 7850 kg / m 3, specific heat capacity c = 500 J / (kg·℃), the number of heat sources is 8, evenly distributed in the cavity. There are 27 temperature observation points, evenly distributed in the cavity, as shown in Table 2. Q = I, R = 0.1I, S = 0.01I, T = 0.01I. The external environment temperature is 20℃ and changes at 0.06℃ / min. When there is an initial temperature error (0-0.02℃), MPC control is used. The temperature change trend of each point is as follows Figure 3 As shown, the control input change trend is as follows Figure 4 As shown, the temperature change rate trend of each point is as follows Figure 5 shown.

[0243] Table 2 Coordinates of temperature observation points

[0244] (2，2，2) (2，2，3) (2，2，4) (2，3，2) (2，3，3) (2，3，4) (2，4，2) (2，4，3) (2，4，4) (3，2，2) (3，2，3) (3，2，4) (3，3，2) (3，3，3) (3，3，4) (3，4，2) (3，4，3) (3，4，4) (4，2，2) (4，2，3) (4，2，4) (4，3，2) (4，3，3) (4，3，4) (4，4，2) (4，4，3) (4，4，4)

[0245] This invention discloses a temperature field control method based on Model Predictive Control (MPC), suitable for precise regulation of multi-input, multi-point temperature field control systems. By constructing state-space equations and a prediction model, the method achieves dynamic optimization control of the temperature field. The invention includes the following core steps: system modeling and discretization, prediction model construction, prediction time domain and control interval design, cost function design, matrix optimization solution, rolling optimization, and real-time control input solution based on quadratic programming.

[0246] The cost function, expressed as a matrix norm, comprehensively considers factors such as output temperature error, control input energy, input rate of change, and temperature rate of change, with the goal of minimizing the objective function. Quadratic programming is used to solve the optimal control input, and a rolling optimization strategy is employed, where only the first control input from each optimization result is executed to adapt to dynamic changes in system state and external disturbances in real time.

[0247] The present invention has the following advantages:

[0248] It achieves precise control of multi-input and multi-point temperature fields and can dynamically adapt to complex environments.

[0249] During the optimization process, temperature error, energy consumption, input smoothness and temperature change rate are comprehensively considered to ensure the efficiency and stability of the control system.

[0250] Through rolling optimization and real-time solution of quadratic programming, the robustness of the control strategy is improved, making it suitable for real-time temperature control needs in industrial processes.

[0251] The above-mentioned model predictive control-based multi-point joint temperature control method for an inertial platform is applied to a multi-point joint temperature control system for an inertial platform. The multi-point joint temperature control system for an inertial platform includes multiple heat source units, temperature sensor units, a control unit, and an execution unit. Through real-time feedback and optimization control, the input of the control system is the temperature of each point, the measuring element is the temperature sensor, and the execution element is the power of the heat source, thereby achieving coordinated regulation of the temperature of multiple control points. Constraint design is also used to meet a series of control indicators such as the temperature change rate and temperature change range. Compared with traditional single-point control systems, the present invention can effectively solve the problem of insufficient optical fiber precision, significantly improve temperature control accuracy and energy efficiency, and has broad application prospects. It is particularly suitable for inertial platform systems that require precise temperature control.

[0252] Other embodiments of the present invention will readily occur to those skilled in the art after considering the specification and practicing the invention herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the invention being indicated by the claims.

[0253] It should be understood that the present invention is not limited to the exact construction described above and shown in the drawings and that various modifications and variations can be made without departing from the scope thereof, which is limited only by the appended claims.

Claims

1. A multi-point joint temperature control method for an inertial platform based on model predictive control, characterized in that: The method comprises: Step 1: Obtain the temperature data of each control point and heat source of the inertial platform; Step 2: Based on the heat conduction equation, the temperature distribution model of the inertial platform is established by considering the interaction between heat source input, control point temperature and heat transfer; Step 3: Design the cost function and constraints of the model predictive control algorithm to predict future temperature changes based on the current temperature and heat source input, and optimize the heat source input to achieve the temperature control requirements; Step 4: Based on the predicted temperature changes, optimize the heat source input power of multiple control points to achieve joint control of multiple point temperatures; Step 5: Update the control input through the rolling optimization strategy and continuously adjust the heat source input based on actual feedback to ensure the stability and accuracy of temperature control.

2. The method according to claim 1, characterized in that The step 2 specifically includes the following steps: Step 2.1: Build a basic model of the heat conduction equation When the inertial platform is a three-dimensional cube model, the heat conduction equation inside the platform is established to describe the change in temperature distribution. Specifically: Where T(x,y,z,t) is the temperature at any position (x,y,z) inside the platform at time t, and α is the thermal diffusion coefficient; Step 2.2: Consider the effect of heat source input The heat source term Q(x, y, z, t) is added to the heat conduction equation to reflect the influence of the heat source on the temperature field inside the platform, and the revised equation is obtained: Where Q(x,y,z,t) is the heat source input power, C is the specific heat capacity, and ρ is the density; Step 2.3: Set the boundary conditions and initial conditions, numerically solve the heat conduction equation modified in step 2.2, and obtain the temperature distribution model of the inertial platform.

3. The method according to claim 2, characterized in that Use the finite difference method (FDM) or the finite element method (FEM) to numerically solve the heat conduction equation corrected in step 2.2; In the finite difference method (FDM), the platform's space and time are discretized, and the differential approximation is used to replace the partial differential operator in the equation. The temperature distribution at each grid point is solved through iteration. In the finite element method (FEM), the platform area is divided into several small units. The local temperature equation of each unit is constructed and then the temperature equation of each unit is solved by numerical methods to obtain the global temperature field.

4. The method according to claim 2, characterized in that The method further comprises: By comparing experimental data with model prediction results, the physical parameters in the model are adjusted to ensure the accuracy of the heat conduction model; through error analysis and error correction, the numerical model can better reflect the temperature field changes of the actual platform.

5. The method according to claim 4, characterized in that The physical parameters in the adjustment model specifically include thermal diffusion coefficient, specific heat capacity, and heat source power input.

6. The method according to claim 1, characterized in that The cost function in step 3 includes temperature error, energy consumption, control input change rate and temperature change rate, which is specifically expressed as follows: Among them, the temperature error e i (t) represents the actual temperature T of each control point on the platform i (t) and target temperature T target The difference between i (t) is the heat source input power, λ i is the weight of the temperature error, γ is the weight of the power consumption, N is the number of control points, M is the number of heat sources, α i is the weight of the temperature change rate, and β is the weight of the heat source input change rate; By optimizing the cost function J, the MPC algorithm can minimize the temperature error while reducing energy consumption, achieving the best balance between control accuracy and energy utilization.

7. The method according to claim 1, characterized in that The constraints in step 3 include: Power input constraint for each heat source: For each heat source, set a power input upper limit to ensure that the heat source input power does not exceed its maximum allowable value, thereby preventing equipment overload; Temperature constraints for each control point: Set minimum and maximum limits for the temperature of each control point to ensure that the temperature is always within the specified range to avoid damage to the equipment caused by overheating or overcooling; Energy consumption upper limit constraint: Ensure that the total power consumption of the system does not exceed a predetermined upper limit to optimize energy efficiency.

8. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the multi-point joint temperature control method of an inertial platform based on model predictive control according to any one of claims 1 to 7 is implemented.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the multi-point joint temperature control method of an inertial platform based on model predictive control according to any one of claims 1 to 7 is implemented.

10. An electronic device, characterized in that: include: processor; as well as a memory for storing executable instructions of the processor; The processor is configured to execute the inertial platform multi-point joint temperature control method based on model predictive control according to any one of claims 1 to 7 by executing the executable instructions.

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