Multi-input multi-output multi-point temperature joint control method for inertial measurement system

Abstract

The application discloses a multi-input multi-output multi-point temperature joint control method of an inertial measurement system and belongs to the field of inertial measurement systems, and specifically is: aiming at the fiber-optic gyroscope precision controlled object in an inertial measurement platform, a temperature control system of inertial device cavity heating and refrigeration of the inertial measurement platform is designed; then, based on the gyroscope and the gage table in the temperature control system, a heat conduction model of the inertial measurement system is established; and based on the disturbance and the parameter uncertainty in the heat conduction model, a multi-input multi-output multi-point temperature joint control state space equation is designed; then, a multi-point robust H performance index function is designed, temperature joint control is carried out, and the preparation time of the inertial system and the inertial navigation system accuracy are shortened. Finally, the multi-point robust H performance index function is applied to the heat conduction model, and the heat conduction model is tested according to the influence mechanism of the temperature field on the gyroscope temperature error and the requirement of the gyroscope precision on the temperature control system. The application realizes fast tracking of the temperature field.

Description

Technical Field

[0001] This invention belongs to the field of inertial measurement systems, specifically a multi-input multi-output multi-point temperature joint control method for inertial measurement systems. Background Technology

[0002] The optimization of the temperature field and thermal structure of the inertial measurement system provides a good working environment for the inertial instrument and the platform structure. However, the accuracy of its fiber optic gyroscope is easily affected by the temperature field. Natural temperature and temperature compensation alone are not enough to meet the requirements of high-precision fiber optic inertial measurement systems. Precision temperature control is still the most effective means to achieve high accuracy, high temperature and stability of fiber optic inertial measurement system instruments.

[0003] However, current inertial measurement systems generally rely on the detection of a single temperature point to control the temperature field of the inertial measurement system. Single-point temperature control is difficult to meet the requirements of temperature changes or temperature gradients at different points of the inertial sensor, and it is difficult to meet the accuracy requirements of high-precision fiber optic gyroscopes in inertial measurement systems.

[0004] Based on the above considerations, it is particularly important to study multi-input multi-output multi-point temperature joint control technology. Summary of the Invention

[0005] To address the aforementioned needs, this invention proposes a multi-input multi-output multi-point temperature joint control method for inertial measurement systems (IMS) based on the structural temperature field model of the IMS and utilizing the relationship between the ambient temperature of the inertial platform and the Shupe error of the fiber optic gyroscope. This method employs robust H... ∞ Multiple-input multiple-output precision temperature control technology, based on the error suppression requirements of fiber optic gyroscope Shupe, research the control method of inertial measurement system to improve the performance of inertial measurement system.

[0006] The specific steps of the multi-input multi-output multi-point temperature joint control method for the inertial measurement system are as follows:

[0007] Step 1: Design a temperature control system for heating and cooling the cavity of the inertial device in the inertial measurement platform, specifically for the precision controlled object of the fiber optic gyroscope in the inertial measurement platform.

[0008] The temperature control system is specifically as follows:

[0009] The temperature control objects of the inertial measurement platform are several gyroscopes and corresponding temperature gauges. On the base plate of each gyroscope and temperature gauge, a temperature sensor and a TEC heating and cooling element are placed to form a multi-input multi-output temperature control device. The control data of each temperature control channel is monitored in real time by a host computer.

[0010] The placement of the TEC heating and cooling element and the temperature sensor is designed at the center of the gyroscope's base plate to maintain the symmetry of the temperature field of the gyroscope's fiber optic ring; the specific calculation principle is as follows:

[0011] According to the expression for Shupe's error:

[0012]

[0013] Where β(l) is the propagation constant related to distance l, β0 = 2π / λ0 is the light propagation constant in vacuum, and n is the effective refractive index of the fiber ring. Let be the temperature coefficient of the refractive index of the fiber optic ring, L be the length of the fiber optic ring, and in the fiber optic gyroscope, the incident light is split into two beams, clockwise (CW) and counterclockwise (CCW), which propagate in opposite directions. t is the time it takes for the two beams to travel through the entire fiber optic ring under normal conditions, c is the propagation speed of light in the fiber, T is the temperature of the fiber optic ring, and ΔT(l) is the temperature change at a distance l from the endpoint of the fiber optic ring.

[0014] That is, if the optical fibers on both sides of the midpoint of the optical fiber experience the same temperature change at the same time, the thermally induced phase shift error can cancel each other out.

[0015] Step 2: Based on the gyroscope and accelerator in the temperature control system, establish a heat conduction model for the inertial measurement system;

[0016] The specific steps are as follows:

[0017] Each gyroscope and each gauge are used as temperature nodes to perform heat conduction analysis on the temperature of a single point corresponding to each node of the temperature control system.

[0018] First, for the i-th temperature node r i (x,y,z), temperature T i When only the gain from the heat source's heat supply has an effect, the temperature change at this node is as follows:

[0019]

[0020] Where K i,j Let b be the heat source gain coefficient from the heat source at temperature node j to node i. i Provide heat to the heat source at temperature node i.

[0021] Then, due to the presence of heat conduction factors, the current temperature node is affected by the surrounding nodes, losing / receiving some heat.

[0022] During the temperature measurement cycle, the temperature obtained by the current measurement node is:

[0023]

[0024] Where T+ T is the temperature at the high-temperature point. - The temperature is the lowest point. Heat flows in from the highest point and then flows to the lowest point, so the environment has both warming and cooling effects. The above formula is a comprehensive calculation result.

[0025] Temperature T at the measuring point i Ultimately, it is determined by the sum of the heat generated by the heat source and the heat conducted by the environment.

[0026] Finally, for two adjacent nodes with temperatures T1 and T2 respectively, considering only the heat transfer between them, the rate of change of the temperature T1 of node 1 over time is proportional to the temperature difference T2-T1 between them.

[0027] For node i, the set of its neighboring nodes is denoted as N(i).

[0028]

[0029] Assuming that the current temperature of each node is affected by the temperatures of other nodes, we have the following equation:

[0030]

[0031] The elements R(i) on the diagonal of the coefficient matrix are:

[0032]

[0033] Among them, R o,i The heat transfer coefficient is the temperature at the node and the ambient temperature.

[0034] Taking into account the temperature conduction at the nodes of the inertial measurement system and the heat source gain, the heat balance equation of the inertial measurement system platform system is established based on the heat balance equation, resulting in the following heat conduction model for the inertial measurement system:

[0035] T(k+1)=R·T(k)+K·B(k)

[0036] in:

[0037]

[0038] T1, T2, T3, T4, T5, T6, and T7 represent the temperatures of the X-gyroscope, Y-gyroscope, Z-gyroscope, X-gyroscope accelerometer, Y-gyroscope accelerometer, Z-gyroscope accelerometer, and the inertial measurement system platform, respectively. T8, T9, ..., T n These refer to the temperatures of other components, frames, caps, and other hardware and structural parts on the inertial measurement system.

[0039] R1, R2, R3, R4, R5, R6, R7,…, R nThese include the X-gyroscope, Y-gyroscope, Z-gyroscope, X-gyroscope accelerometer, Y-gyroscope accelerometer, Z-gyroscope accelerometer, inertial measurement system platform, and other hardware and structural components such as the frame and cap on the inertial measurement system. The defined heat transfer coefficient; R i,j K represents the heat transfer coefficient between temperature node i and temperature node j. i,j Let be the heat source gain coefficient from the heat source at temperature node j to node i. i Provide heat to the heat source at temperature node i.

[0040] Step 3: Based on the disturbances and parameter uncertainties in the heat conduction model, design the state-space equations for multi-input multi-output multi-point temperature joint control;

[0041] First, by introducing external disturbances into the heat conduction model, we obtain the model described in the following equation:

[0042] T(k+1)=(R+ΔR)·T(k)+K·B(k)+E·w(k)

[0043] Where ΔR is the deviation of the heat transfer coefficient. E is the interference input, and E is the coefficient matrix of the interference acting on the system.

[0044] Then, design the augmented matrix T. k The Q matrix is ​​as follows:

[0045]

[0046] Therefore, the system shown in the above equation is transformed into an augmented state-space equation:

[0047]

[0048] Finally, in the augmented state-space equations, due to the reference temperature T r The reference temperature T is set by the system. r The transition matrix is ​​set to the identity matrix I:

[0049]

[0050] Step 4: Design a multi-point robust H∞ performance index function for the state-space equation of multi-input multi-output multi-point temperature joint control, and carry out joint temperature control to shorten the preparation time of the inertial system and improve the accuracy of the inertial navigation system.

[0051] The multi-point robust H∞ performance index function is:

[0052]

[0053] The index function consists of the squared residuals between the measured temperature and the ideal temperature, plus quadratic forms of the control input and disturbance input. S is the weight matrix of the heat source supply at each temperature node, and γ... 2 It is the coefficient of influence of interference input on performance indicators.

[0054] Step 5: Apply the multi-point robust H∞ performance index function to the heat conduction model, and conduct experiments on the heat conduction model based on the influence mechanism of the temperature field on the temperature error of the gyroscope and the requirements of the gyroscope accuracy on the temperature control system.

[0055] Compared with existing inertial measurement platform temperature field control methods, the advantages of this invention are:

[0056] 1) This invention presents a multi-input multi-output multi-point temperature joint control method for inertial measurement systems. It performs system analysis on the structure and control objective of an array-type multi-heat-source temperature field system, analyzes the heat conduction effect within the temperature field, and constructs a state-space system model. Robust control design is implemented for the multi-input multi-output temperature field system, considering the system's parameter uncertainties and constructing the control problem as an H∞ optimization problem. The robust heat source control gain is solved to achieve rapid temperature field tracking. Compared to traditional control methods, this method does not require precise system physical model construction, making it highly practical for addressing issues such as difficulty in determining temperature field system parameters and excessively high modeling costs. This method also exhibits strong robustness.

[0057] 2) The multi-input multi-output multi-point temperature joint control method of the inertial measurement system of the present invention, based on considering the relationship between the temperature environment of the inertial platform and the Shupe error of the fiber optic gyroscope, realizes constant temperature control of the inertial measurement system platform structure and instruments, especially achieving the requirements of fast speed and high accuracy of gyroscope-level temperature field control.

[0058] 3) The multi-input multi-output multi-point temperature joint control method of the inertial measurement system of the present invention, based on the objective function of the robust controller updated in real time, can shorten the process of the gyroscope reaching thermal equilibrium after startup during the full-speed heating phase, so that the temperature can be quickly approached when the temperature control point is reached, and then precise temperature control can be achieved. After reaching the temperature control point in a short time, the temperature point configuration is heated with a small current to ensure uniform temperature field distribution inside the platform, so that the gyroscope is minimally affected by the temperature fluctuation of the external environment, and realizes a multi-input multi-output high-precision temperature control system.

[0059] 4) The multi-input multi-output multi-point temperature joint control method for inertial measurement systems of this invention addresses the difficulty of single-point temperature control in inertial measurement systems in meeting the requirements for precise temperature control and temperature gradient at different points. It establishes the thermal balance relationship equation of the inertial measurement system and the Shupe error model of the high-precision fiber optic gyroscope, thereby realizing constant temperature control of the inertial measurement system platform structure and instruments, and meeting the requirements for high-precision inertial devices to achieve the required accuracy in the inertial measurement system. Attached Figure Description

[0060] Figure 1 This is a flowchart of the multi-input multi-output multi-point temperature joint control method for the inertial measurement system of the present invention;

[0061] Figure 2 This is a schematic diagram of a finite element model of an optical fiber ring according to the present invention;

[0062] Figure 3 This is a schematic diagram of a heat transfer network for an inertial measurement system according to the present invention;

[0063] Figure 4 This is a diagram illustrating the effect of a practical six-point multi-input multi-output temperature control according to the present invention. Detailed Implementation

[0064] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are merely some, not all, embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort should fall within the scope of protection of the present invention.

[0065] Based on the optimization of the structural temperature field of an inertial measurement system (IMS), and considering the relationship between inertial platform temperature control and fiber optic gyroscope Shupe error, this invention proposes a multi-input multi-output multi-point joint temperature control method for IMS. It rationally selects the temperature control point, control method, and control algorithm according to the ambient temperature and the temperature of the controlled object, and considers the impact of the platform's overall performance, proposing a robust H-axis control method. ∞ The multi-input multi-output precision temperature control technology enables constant temperature control of the inertial measurement system platform structure and instruments, ensuring accuracy under complex temperature field conditions. In particular, it achieves high speed and high precision in temperature field control at the gyroscope level, solving the problem of shortening the thermal equilibrium process of inertial devices after the inertial measurement system starts up, and enabling it to quickly enter a stable working state.

[0066] The proposed multi-input multi-output multi-point temperature joint control method for inertial measurement systems, based on the error suppression requirements of fiber optic gyroscopes (Shupe), studies the control methods and algorithms of inertial measurement systems to improve their performance. It is a robust H... ∞ Multiple-input multiple-output precision temperature control technology; such as Figure 1 As shown, the specific steps are as follows:

[0067] Step 1: Design a temperature control system for heating and cooling the cavity of the inertial device in the inertial measurement platform, specifically for the precision controlled object of the fiber optic gyroscope in the inertial measurement platform.

[0068] The temperature control system is specifically as follows:

[0069] The temperature control objects of the inertial measurement platform are several gyroscopes and corresponding temperature gauges. On the base plate of each gyroscope and temperature gauge, a temperature sensor and a TEC heating and cooling element are placed to form a multi-input multi-output temperature control device. The control data of each temperature control channel is monitored in real time by a host computer.

[0070] The placement of the TEC heating and cooling element and the temperature sensor is designed at the center of the gyroscope's base plate to maintain the symmetry of the temperature field of the gyroscope's fiber optic ring; the specific calculation principle is as follows:

[0071] The study on temperature field optimization of the high-precision fiber optic inertial measurement system includes the generation mechanism of Shupe error in fiber optic gyroscopes and its mathematical model, as well as the heat conduction model of the inertial measurement system.

[0072] The aforementioned fiber optic gyroscope Shupe error generation mechanism and mathematical model are specifically based on the temperature field distribution and variation law inside the inertial measurement system. The focus is on the variation mechanism of Shupe error with temperature field in high-precision fiber optic inertial measurement system, and the temperature field control requirements of fiber optic gyroscope are analyzed.

[0073] As the sensitive core of the fiber optic gyroscope, the Shupe error is decomposed into two parts: the inherent temperature error of the fiber optic ring and the error introduced during the optical path assembly process. Based on the mechanism of temperature affecting the refractive index of the fiber, a theoretical analysis of the temperature error of the entire optical path is conducted to verify the main cause of the temperature performance degradation of the fiber optic gyroscope. Based on the results of physical field simulation analysis, and taking into account the non-reciprocal phase error caused by the change in fiber refractive index due to thermal stress in the Shupe error, a temperature error model of the fiber optic gyroscope system is established.

[0074] The error generation mechanism and mathematical model principle of the fiber optic gyroscope Shupe are as follows:

[0075] According to the Sagnac effect, the interference phase difference in a fiber optic gyroscope is:

[0076]

[0077] Where L and D are the length and average diameter of the fiber optic loop, respectively, Ω is the gyroscope rotation speed, c is the speed of light, and λ is the wavelength of light.

[0078] In systems subject to temperature disturbances:

[0079] Δφ s =Δφ s0 +Δφ sd

[0080] Δφ s0 Let Δφ be the phase difference of the Sagnac interference under ideal conditions. sdThe error signals caused by the temperature environment are mainly optical power fluctuations, Shupe errors and polarization errors, which affect the zero bias stability of the gyroscope; among them, Shupe errors are the main error source.

[0081] When studying the model of Shupe error, the finite element analysis method was used to model and analyze the fiber optic loop.

[0082] The finite element analysis method, such as Figure 2 As shown, light A is input from micro-segment fiber 1. Then, the phase shift calculation function and stress influence function in the micro-segment fiber model are used to calculate the state of the light after passing through micro-segment fiber 1. The light is then input into micro-segment fiber 2 and propagates sequentially until it is output from port B. Finally, the phase shift of light A after passing through the fiber loop can be obtained. Similarly, the phase shift of light B after passing through the fiber loop is calculated using the same method. Then, the phase difference between the two beams after passing through the fiber loop can be obtained by interfering the two beams.

[0083] When a temperature disturbance exists at an asymmetrical location in an optical fiber ring, two beams of light traveling in opposite directions will experience a non-reciprocal phase shift when passing through the disturbance point at different times. The length of the optical fiber ring is L, and the phase delay caused by the light passing through this optical path is:

[0084]

[0085] Where β(l) is the propagation constant related to distance l, β0=2π / λ0 is the light propagation constant in vacuum, where λ0 is the wavelength of light. n(l) is the refractive index related to distance l.

[0086] When the ambient temperature of the fiber optic ring changes, the refractive index of the fiber and the coefficient of thermal expansion of the fiber material will change accordingly, thereby altering the phase difference of light transmission. At this time:

[0087]

[0088] Where n is the effective refractive index of the fiber ring. Let be the temperature coefficient of the refractive index of the fiber optic ring, α be the coefficient of thermal expansion of the fiber optic ring, T be the temperature of the fiber optic ring, and ΔT(l) be the temperature change at a distance l from the endpoint of the fiber optic ring. Changes in temperature lead to changes in the refractive index of the fiber optic ring, which in turn causes a phase change in light.

[0089] In a fiber optic gyroscope, the incident light is split into two beams, one clockwise (CW) and the other counterclockwise (CCW), which propagate in opposite directions. Assuming that under normal conditions the two beams traverse the entire fiber optic loop over time t, the CW beam passes point l at t1 = l / c, and the CCW beam passes point l at t2 = t - (Ll) / c, where c is the propagation speed of light in the fiber.

[0090] As can be seen from the above, the phase delay of CCW light propagating in the fiber optic loop is:

[0091]

[0092] The phase delay generated by CW light is:

[0093]

[0094] Since the temperature of segment dl is time-varying, the phase delay produced by clockwise and counterclockwise light passing through this segment at different times is also different. To obtain the phase difference produced by clockwise and counterclockwise light when a temperature disturbance occurs at point l, the above equation is subtracted:

[0095]

[0096] That is, the Shupe error of an interferometric fiber optic gyroscope is related to the rate of change of the temperature field.

[0097] Meanwhile, consider the segment dl of CCW light passing through point Ll at t1 = l / c:

[0098]

[0099] Subtracting the above equation, we obtain another expression for the Shupe error:

[0100]

[0101] That is, if the fibers on both sides of the midpoint of the fiber optic cable experience the same temperature change at the same time, the thermally induced phase shift error can cancel each other out. Therefore, the TEC heating and cooling element and temperature sensor controlling the gyroscope should be placed at the center of the gyroscope's base plate to maintain the symmetry of the temperature field of the fiber optic ring. The above formula provides a theoretical basis for designing a more reasonable cavity structure. Based on the temperature error generation mechanism of fiber optic gyroscopes and the requirements for the temperature field, the heat conduction model and temperature control method of the inertial measurement platform were further studied.

[0102] Step 2: Based on the gyroscope and accelerator in the temperature control system, establish a heat conduction model for the inertial measurement system;

[0103] The inertial measurement platform heat conduction model and temperature control method include an inertial measurement system multi-input multi-output multi-point temperature joint control system model and a multi-point temperature joint control method based on robust control.

[0104] The principle of the multi-input multi-output multi-point temperature joint control system model of the inertial measurement system is as follows:

[0105] To ensure precise multi-point temperature control of the inertial measurement system, an optimization model is established with temperature tracking accuracy and tracking performance as indicators. First, the operating mechanism of the temperature-controlled object in the inertial measurement system is analyzed. Based on the law of conservation of energy, a heat transfer mathematical model of the inertial instrument heat transfer coupling network is established, and the state equation of the multi-input multi-output temperature control system is also established.

[0106] This study analyzes the temperature field distribution and variation within an inertial measurement system (IMS) through conjugate heat transfer theory analysis, multiphysics coupling numerical methods, and thermophysical parameter research. Based on fundamental thermodynamic equations, a heat conduction model of the IMS is established. Emphasis is placed on the heat source components providing thermal power and their effects in the thermal field. The models of electronic devices and inertial components with different power levels are simplified step by step. Referring to conjugate heat transfer theory analysis, the convective heat from low-power components and the heat dissipation generated during operation are reasonably omitted.

[0107] In the inertial measurement system, each gyroscope and each gauging unit are used as temperature nodes to perform heat conduction analysis on the temperature of a single point corresponding to each node of the temperature control system.

[0108] First, r i (x, y, z) represents the physical location coordinates of the i-th temperature node, where the temperature is T. i Assuming the medium within a node region is completely mixed and the heat distribution within the region is uniform, its heat is affected by three factors: firstly, the direct influence of the heat source, causing its temperature to rise; secondly, due to the existence of heat conduction, some heat is lost / received due to the influence of surrounding nodes; and thirdly, the influence of neighboring temperature nodes.

[0109] According to the heat conduction equation, the rate of change of the temperature at the state node with time is:

[0110]

[0111] Where f(r,t) is the heat source function, t is time, and a is a constant coefficient, where the heat transfer constant coefficient a = K / (C·ρ), K is the thermal conductivity coefficient of the medium W / (m·K), C is the specific heat capacity of the heat transfer medium J / (Kg·K), and ρ is the density of the heat transfer medium K. g / m 3 .

[0112] The heat source function and temperature gradient are specifically expressed as follows:

[0113]

[0114] f(r,t)=∑b n (t)δ(rr n (9)

[0115] Where b n(t) represents the heat source coefficient at time t, and the heat source coefficient and point source function δ(rr) n By multiplying and summing these, we can obtain the heat gain of the node.

[0116] The boundary conditions for equation (8) are:

[0117]

[0118] According to the mathematical equations, the solution to equation (8) is:

[0119]

[0120] Where G is the Green's function of the heat conduction equation, r i The coordinates of the physical location of node i are used for measurement.

[0121]

[0122] From equation (11), we can see that the first term on the right side of the equation is the temperature contribution from the heat source to r(x,y,z), denoted as u1, and the second term is the temperature change caused by the ambient temperature, denoted as u2. Substituting equation (12) into equation (11), according to the properties of the impulse function, we can obtain the following equation:

[0123]

[0124] The above formula describes the influence of surrounding heat source input nodes on the temperature of the current measurement node. For the i-th measurement point, only |r i -r n |<4a 2 In the case of t, due to the near-linear property of the exponential function near the origin, it can be simplified to the following equation:

[0125]

[0126] Without considering temperature conduction from adjacent nodes, when only the gain effect of heat supply from the heat source is considered, the temperature change of this node is as follows:

[0127]

[0128] Where K i,j Let b be the heat source gain coefficient from the heat source at temperature node j to node i. i Provide heat to the heat source at temperature node i.

[0129] Then, due to heat conduction, the current temperature node is affected by surrounding nodes, losing / receiving some heat. The temperature of the current measurement node is influenced not only by the heat contribution from the heat source but also by the temperatures of surrounding measurement nodes and the external environment. According to the law of heat conduction, the rate of temperature change at a point is proportional to the surrounding temperature gradient. Heat flows in and out simultaneously; when the temperature is high in a certain direction, heat flows in and the temperature rises; when the temperature is low in a certain direction, heat flows out and the temperature falls. Therefore, within a certain temperature measurement period, the temperature obtained by the current measurement node is:

[0130]

[0131] Where T + T is the temperature at the high-temperature point. - The temperature is the lowest point. Heat flows in from the highest point and then flows to the lowest point, so the environment has both warming and cooling effects. The above formula is a comprehensive calculation result.

[0132] Temperature T at the measuring point i Ultimately, it is determined by the sum of the heat generated by the heat source and the heat conducted by the environment.

[0133] Finally, for two adjacent nodes with temperatures T1 and T2 respectively, considering only the heat transfer between them, the rate of change of the temperature T1 of node 1 over time is proportional to the temperature difference T2-T1 between them.

[0134] For node i, only the heat transfer between its neighboring nodes is considered, and the set of neighboring nodes is denoted as N(i).

[0135]

[0136] Assuming that the current temperature of each node is affected by the temperatures of other nodes, we have the following equation:

[0137]

[0138] The elements R(i) on the diagonal of the coefficient matrix are:

[0139]

[0140] Among them, R o,i The heat transfer coefficient is the temperature at the node and the ambient temperature.

[0141] To achieve precise multi-point temperature control while ensuring that the inertial measurement system meets constraints, an optimization model is established with temperature tracking accuracy and tracking performance as indicators. The operating mechanism of the temperature control object in the inertial measurement system is analyzed, and a heat transfer mathematical model of the inertial instrument heat transfer coupling network is established based on the law of conservation of energy. The heat transfer mathematical model is then simplified according to the principle of equivalence.

[0142] Taking into account the temperature conduction at the nodes of the inertial measurement system and the heat source gain, that is, combining equations (15) and (18) according to the heat balance equation, the heat balance equation of the inertial measurement system platform system can be established, and the state space equation of the heat transfer network of the inertial measurement system can be obtained:

[0143]

[0144] The above equation can be simplified, and the heat conduction model of the inertial measurement system is as follows:

[0145] T(k+1)=R·T(k)+K·B(k) (21)

[0146] T1, T2, T3, T4, T5, T6, and T7 represent the temperatures of the X-gyroscope, Y-gyroscope, Z-gyroscope, X-gyroscope accelerometer, Y-gyroscope accelerometer, Z-gyroscope accelerometer, and the inertial measurement system platform, respectively. T8, T9, ..., T n These refer to the temperatures of other components, frames, caps, and other hardware and structural parts on the inertial measurement system.

[0147] R1, R2, R3, R4, R5, R6, R7,…, R n These include the X-gyroscope, Y-gyroscope, Z-gyroscope, X-gyroscope accelerometer, Y-gyroscope accelerometer, Z-gyroscope accelerometer, inertial measurement system platform, and other hardware and structural components such as the frame and cap on the inertial measurement system. The defined heat transfer coefficient; R i,j K represents the heat transfer coefficient between temperature node i and temperature node j. i,j Let be the heat source gain coefficient from the heat source at temperature node j to node i. i Provide heat to the heat source at temperature node i.

[0148] Step 3: Based on the disturbances and parameter uncertainties in the heat conduction model, design the state-space equations for multi-input multi-output multi-point temperature joint control;

[0149] In the aforementioned array-type multi-input multi-output temperature field control system, there may be a significant number of uncertainties. Although the parameters of the model in an ideal system can be considered deterministic and known, in a real temperature field system, various parameters may be affected by multiple factors. On the one hand, the temperature field system parameters may change over time; on the other hand, the system state is not perfectly accurate, and the system should operate normally under the presence of disturbances and errors.

[0150] For the heat conduction model represented by equation (21), external disturbances are introduced into the heat conduction model to consider the effects of random disturbances and parameter uncertainties in the real environment on the inertial measurement system model.

[0151] The model is obtained as shown in the following formula:

[0152] T(k+1)=(R+ΔR)·T(k)+K·B(k)+E·w(k) (22)

[0153] Where ΔR is the deviation of the heat transfer coefficient. E is the interference input, and E is the coefficient matrix of the interference acting on the system.

[0154] Then, the control objective of the temperature field system is to adjust the heat source gain matrix K so that all measurement points reach the expected target temperature, that is, to find a suitable control law so that T reaches the reference temperature T. r The augmented matrices T and Q are designed as follows:

[0155]

[0156] Therefore, the system shown in the above equation is transformed into an augmented state-space equation:

[0157]

[0158] Finally, in the augmented state-space equations, due to the reference temperature T r The reference temperature T is set by the system. r The transition matrix is ​​set to the identity matrix I:

[0159]

[0160] Step 4: Design a multi-point robust H∞ performance index function for the state-space equation of multi-input multi-output multi-point temperature joint control, and carry out joint temperature control to shorten the preparation time of the inertial system and improve the accuracy of the inertial navigation system.

[0161] For the discrete system shown in equation (24), the multi-point robust H∞ performance index function is:

[0162]

[0163] Where Q is the weight matrix of each temperature point, S is the weight matrix of the heat source supply at each temperature node, and γ is the influence coefficient of the disturbance input on the performance index.

[0164] The index function consists of the squared residual between the measured temperature and the ideal temperature, as well as the quadratic forms of the control input and the disturbance input.

[0165] Step 5: Apply the multi-point robust H∞ performance index function to the heat conduction model, and conduct experiments on the heat conduction model based on the influence mechanism of the temperature field on the temperature error of the gyroscope and the requirements of the gyroscope accuracy on the temperature control system.

[0166] Considering the parameter uncertainties and disturbances caused by complex temperature environments, a multi-point temperature joint control method is designed based on robust H∞ control.

[0167] During gyroscope operation, the stability of gyroscope drift is closely related to temperature. The temperature sensitivity of inertial devices and the temperature field within the platform both affect the accuracy of the navigation system. In short, temperature fluctuations cause changes in gyroscope drift and the platform system's operational accuracy. In applications, it is desirable for the gyroscope to reach thermal equilibrium in the shortest possible time after startup, allowing the inertial navigation system to quickly enter a stable operating state. Therefore, it is necessary to research a practical and effective temperature control system to shorten the inertial system's preparation time and improve its accuracy, while ensuring the system's operational accuracy.

[0168] To ensure the optimal working condition of inertial instruments in an inertial measurement system and achieve precise control of the system temperature, a multi-point temperature joint control technology for inertial measurement systems with multiple inputs and multiple outputs is proposed.

[0169] for

[0170]

[0171] Where, ΔR w =HFE,F T F≤1, H and E are both constant matrices describing the change of parameters with temperature.

[0172] Consider the objective function:

[0173]

[0174] For any

[0175] Take the Lyapunov-Krasovskii function: have

[0176]

[0177] Where P represents the weight of each temperature point.

[0178]

[0179]

[0180]

[0181] It can be seen that E{V(k+1)-αV(k)+J(k)}<0,

[0182] If and only if

[0183] According to Schur's lemma, this is equivalent to:

[0184]

[0185] On the other hand, equation (28) can

[0186]

[0187] in

[0188]

[0189] M = [0 0 0 H] T P],

[0190] N = [E 0 0 0],

[0191] Equation (29) is equivalent to:

[0192]

[0193]

[0194]

[0195] Therefore, based on the above proof, a robust H∞ control design method for an array-type multi-heat source temperature field system suitable for inertial measurement systems was obtained, and the design of multi-input multi-output multi-point temperature joint control technology was completed.

[0196] as follows:

[0197] Theorem 1: For the closed-loop system equation (27) to be robustly mean-square exponentially stable for any parameter uncertainty, there exists a positive definite matrix P∈R n×n The feedback gain matrix K and the positive number ε make...

[0198]

[0199] Furthermore, the estimated value of state decay is

[0200]

[0201] in

[0202]

[0203] Example:

[0204] The specific design process of the multi-input multi-output multi-point temperature joint control technology for the inertial measurement system is as follows:

[0205] The first step is to consider the precision controlled object of the fiber optic gyroscope in the inertial measurement platform and design a temperature control system for heating and cooling the cavity of the inertial device in the inertial measurement platform.

[0206] According to the expression for Shupe's error

[0207]

[0208] If the fibers on both sides of the midpoint of the fiber optic cable experience the same temperature change at the same time, the thermally induced phase shift error can cancel each other out. Therefore, the TEC heating / cooling element and temperature sensor controlling the gyroscope should be placed at the center of the gyroscope's base plate to maintain the symmetry of the temperature field in the fiber optic ring. The above formula serves as the theoretical basis for designing a more rational temperature control system for heating and cooling fiber optic gyroscopes.

[0209] In this embodiment, the temperature control objects of the inertial measurement platform are three gyroscopes and three temperature gauges. Each of the three gyroscopes and three temperature gauges in the system has a temperature sensor and a TEC heating element placed on its base plate, forming a multi-input multi-output temperature control device. The control data of each temperature control channel is monitored in real time by the host computer.

[0210] The second step is to establish a heat conduction model for the inertial measurement system.

[0211] A schematic diagram of the heat transfer network of an inertial measurement system is shown below. Figure 3 As shown, in an inertial measurement system, each gyroscope and each accelerator are considered as temperature nodes. First, a heat conduction analysis is performed on the temperature of a single point within the temperature field for each node. Considering the point temperature node r... i (x,y,z), the temperature of the i-th measurement node is T. i Assuming the medium within the node region is completely mixed and the heat distribution within the region is uniform, its heat is affected by three factors. First, the direct influence of the heat source causes its temperature to rise. Second, due to the presence of heat conduction, some heat is lost or received due to the influence of surrounding nodes.

[0212] Based on the derivation of equations (8) to (12), we can obtain the formula describing the influence of the surrounding heat source input node on the temperature of the current measurement node:

[0213]

[0214] For the i-th measurement point, only |r is considered i -r n |<4a 2 In the case of t, due to the near-linear property of the exponential function near the origin, it can be simplified to the following equation:

[0215]

[0216] Without considering temperature conduction between adjacent nodes and only taking into account the heat source gain, the temperature change can be written as follows:

[0217]

[0218] Where K i,j is the heat source gain coefficient from heat source j to node i.

[0219] The temperature of the current measurement node is influenced not only by the heat contribution from the heat source but also by the temperatures of surrounding measurement nodes and the external environment. According to the law of heat conduction, the rate of temperature change at a point is proportional to the surrounding temperature gradient. Heat flows in and out simultaneously; when the temperature is higher in a certain direction, heat flows in and the temperature rises; when the temperature is lower in a certain direction, heat flows out and the temperature falls. Therefore, within a certain temperature measurement period, the temperature obtained at a certain measurement point is:

[0220]

[0221] Where T + T is the temperature at the high-temperature point. - The temperature is the lowest point. Heat flows in from the highest point and then flows to the lowest point, so the environment has both warming and cooling effects. The above formula is a comprehensive calculation result.

[0222] For two adjacent nodes with temperatures T1 and T2, considering only the heat transfer between them, the rate of change of node 1's temperature T1 over time is proportional to the temperature difference T2-T1 between them. For node i, considering only the heat transfer between its adjacent nodes, the set of adjacent nodes of node i is denoted as N(i).

[0223]

[0224] Assuming that the current temperature of each node is affected by the temperatures of other nodes, we have the following equation:

[0225]

[0226] Among them, the elements R on the diagonal of the coefficient matrix i for:

[0227]

[0228] Among them, R o,i The heat transfer coefficient is the temperature at the node and the ambient temperature.

[0229] Taking into account the temperature conduction at the nodes of the inertial measurement system and the heat source gain, the heat balance equation for the inertial measurement system platform is established based on the heat balance equation. This yields:

[0230]

[0231] The above equation can be simplified, and the heat conduction model of the inertial measurement system is as follows:

[0232] T(k+1)=R·T(k)+K·B(k)

[0233] Therefore, a model of the heat conduction system of the inertial measurement system was established.

[0234] The third step is to consider the disturbances and parameter uncertainties in the heat conduction system model of the real inertial measurement system and design the multi-input multi-output multi-point temperature joint control state equation.

[0235] In the aforementioned array-type multi-input multi-output temperature field control system, there may be a significant number of uncertainties. Although the parameters of the model in an ideal system can be considered deterministic and known, in a real temperature field system, various parameters may be affected by multiple factors. On the one hand, the temperature field system parameters may change over time; on the other hand, the system state is not perfectly accurate, and the system should operate normally under the presence of disturbances and errors.

[0236] For the heat conduction model, external disturbances are introduced into the system equations. Considering the effects of random disturbances and parameter uncertainties in the real environment on the inertial measurement system model, the following model is obtained:

[0237] T(k+1)=(R+ΔR)·T(k)+K·B(k)+E·w(k)

[0238] in E is the interference input, and E is the coefficient matrix of the interference acting on the system.

[0239] The control objective of the temperature field system is to adjust the heat source gain matrix K so that all measurement points reach the expected target temperature, i.e., to find a suitable control law that makes T... k Reaching reference temperature T r Design augmented matrix T k The Q matrix is ​​as follows:

[0240]

[0241] Therefore, the system shown in the above equation is transformed into an augmented state-space equation:

[0242]

[0243] In the augmented state-space equations, due to the reference temperature T r The reference temperature T is set by the system. r The transition matrix is ​​set to the identity matrix I:

[0244]

[0245] The fourth step is to consider the disturbances and parameter uncertainties in the heat conduction model of the inertial measurement system and design a multi-input multi-output multi-point robust H∞ temperature joint control method.

[0246] for Design the performance index function for the discrete system shown:

[0247]

[0248] The index function consists of the squared residual between the measured temperature and the ideal temperature, as well as the quadratic forms of the control input and the disturbance input.

[0249] The fifth step involves calculating system parameters and conducting experiments based on the influence mechanism of the temperature field on the temperature error of the gyroscope, the requirements of the gyroscope accuracy on the temperature control system, and the theoretical model and control method mentioned above, to verify the actual effect of the multi-input multi-output multi-point temperature joint control technology model of the inertial measurement system.

[0250] Based on the Shupe error requirement of 0.0002 deg / h for fiber optic gyroscopes, the temperature control requirement is that the steady-state temperature change under a multi-input multi-output temperature control system should not exceed 0.02℃ / min. Design its H∞ performance index function, where Q and S are identity matrices. In the inertial measurement platform structure, the thermal conductivity parameter R is 0.7, the thermal conductivity parameter fluctuation ΔR is 0.07, and the coefficient E of the disturbance effect on the system is 0.01.

[0251] According to Theorem 1, the feedback gain matrix K of the multi-input multi-output temperature control system is obtained:

[0252]

[0253] After conducting the experiment and collecting data, the specific error effect graph is as follows: Figure 4 As shown, according to the objective function of the robust controller updated in real time, the full-speed heating segment can shorten the process of the gyroscope reaching thermal equilibrium after startup, so that the temperature can quickly approach the temperature control point before achieving precise temperature control. After reaching the temperature control point in a short time, the temperature point configuration is heated with a small temperature control current to ensure uniform temperature field distribution inside the platform. This minimizes the impact of temperature fluctuations in the external environment on the gyroscope, meeting the temperature control requirement that the temperature change in the steady state of the system does not exceed 0.02℃ / min under the multi-input multi-output temperature control system. This realizes a multi-input multi-output high-precision temperature control system.

[0254] Compared with existing temperature control methods for inertial measurement platforms, this embodiment designs and implements a robust control method for an array-type multi-heat-source temperature field system. It performs a system analysis of the array-type multi-heat-source temperature field system structure and control objectives, analyzes the heat conduction effect within the temperature field, and constructs a state-space system model. Robust control tracking design is implemented for the multi-input multi-output temperature field system, constructing the control problem as an H∞ optimization problem. Robust heat source gain is solved online using alternative methods, achieving rapid temperature field tracking. Compared to traditional control methods, it does not require precise system physical model construction, making it highly practical for addressing issues such as difficulty in determining temperature field system parameters and excessively high modeling costs. This method exhibits strong robustness. Furthermore, based on the relationship between inertial platform temperature control and fiber optic gyroscope Shupe error, a multi-input multi-output multi-point temperature field precision control method is proposed to achieve constant temperature control of the inertial measurement system platform structure and instruments, especially meeting the requirements of fast and high-precision gyroscope-level temperature field control.

[0255] For traditional inertial measurement systems, temperature control devices are typically employed because temperature has a significant impact on system accuracy. However, these devices often monitor and control only one or a limited number of points within the system, treating areas outside the control node as having the same temperature as the nearest control node. This leads to insufficient understanding of localized system temperatures. If, due to continuous operation or malfunction, the temperature difference between areas outside the control node and their surroundings becomes significant, it will have a substantial impact on the overall system accuracy.

[0256] The multi-input multi-output multi-point temperature joint control method proposed in this invention addresses the aforementioned issues. Temperature control devices are installed at key points on the inertial system to ensure comprehensive temperature control of the entire system. To achieve higher temperature control accuracy, this method considers not only the heating and cooling effects of a single temperature control node but also the heat transfer from surrounding temperature control nodes, external disturbances, and parameter uncertainties. This results in a highly efficient, stable, and rapid temperature control system, giving this method a significant advantage in improving the overall accuracy of the inertial system.

[0257] Based on the relationship between the temperature environment of the inertial platform and the Shupe error of the fiber optic gyroscope, this paper proposes a method for achieving constant temperature control of the inertial measurement system (IMS) platform structure and instruments, meeting the requirements of fast and high-precision gyroscope-level temperature field control. According to the objective function of the robust controller updated in real time, the full-speed heating phase shortens the process of the gyroscope reaching thermal equilibrium after startup, allowing the temperature to quickly approach the temperature control point before achieving precise temperature control. After reaching the temperature control point in a short time, a smaller current is used to heat the temperature point configuration, ensuring a uniform temperature field distribution within the platform and minimizing the impact of external environmental temperature fluctuations on the gyroscope. This achieves a high-precision multi-input multi-output (MIMO) temperature control system. The proposed robust H∞ MIMO temperature field control technology addresses the challenge of single-point temperature control in IMS systems failing to meet the requirements for precise control of temperature variations and temperature gradients at different points. It establishes the thermal equilibrium equation of the IMS and a high-precision fiber optic gyroscope Shupe error model, enabling constant temperature control of the IMS platform structure and instruments, meeting the accuracy requirements of high-precision inertial devices in IMS systems. Experimental results verify the effectiveness and practicality of the proposed temperature control scheme.

[0258] This document describes the principles and implementation methods of the present invention through specific examples. The above embodiments are merely illustrative of the methods and core ideas of the present invention. Those skilled in the art may find variations in implementation and application based on the principles of the present invention. Therefore, the content of this specification should not be construed as limiting the present invention.

Claims

1. A multi-input multi-output multi-point temperature joint control method for an inertial measurement system, characterized in that, This includes temperature control methods and heat conduction models; The temperature control method described above is based on the Shupe error generation mechanism of fiber optic gyroscopes and mathematical models. It is a design method for a temperature control system for heating and cooling the working environment of inertial devices in an inertial measurement platform. Considering the disturbances and parameter uncertainties present in the heat conduction model of a real inertial measurement system, a multi-input multi-output multi-point robust H-type system is designed. ∞ The temperature joint control state equation is verified based on the influence mechanism of the temperature field on the temperature error of the gyroscope and the requirements of the gyroscope accuracy on the temperature control system. The specific steps are as follows: Step 1: Design a temperature control system for heating and cooling the cavity of the inertial device in the inertial measurement platform, specifically for the precision controlled object of the fiber optic gyroscope in the inertial measurement platform. The temperature control involves at least three gyroscopes and at least three corresponding temperature-controlled electrodes; the specific calculation principle is as follows: When a temperature disturbance exists at an asymmetrical location in the fiber optic loop, two beams of light propagating in opposite directions will experience a non-reciprocal phase shift when passing through the disturbance point at different times. Through derivation, the expression for the Shupe error is obtained: in The propagation constant is related to the distance l. Let be the light propagation constant in vacuum, and n be the effective refractive index of the fiber optic ring. Let be the temperature coefficient of the refractive index of the fiber optic ring, L be the length of the fiber optic ring, and T be the temperature of the fiber optic ring. In a fiber optic gyroscope, the incident light is split into two beams, one clockwise (CW) and the other counterclockwise (CCW), which propagate in opposite directions. t is the time it takes for the two beams to traverse the entire fiber optic ring under normal conditions, c is the speed of light in the fiber, and T is the temperature of the fiber optic ring. This represents the temperature change at a distance l from the endpoint of the fiber optic ring. When the optical fibers on both sides of the midpoint of the optical fiber experience the same temperature change at the same time, the thermally induced phase shift error can cancel each other out. Step 2: Based on the gyroscope and accelerator in the temperature control system, establish a heat conduction model for the inertial measurement system; The specific steps are as follows: Each gyroscope and each accelerator are used as temperature nodes. Heat conduction analysis is performed on the temperature of a single point corresponding to each node of the temperature control system. The influence of heating and cooling of a certain temperature control node on the temperature is not only considered, but also the heat transfer of surrounding temperature control nodes, as well as external disturbances and parameter uncertainties are taken into account, forming a highly efficient, stable and fast temperature control system. Taking into account both the temperature conduction at the nodes of the inertial measurement system and the heat source gain, a heat balance equation is established, resulting in the following heat conduction model for the inertial measurement system: in: , , , , , , These are the temperatures of the X-gyroscope, Y-gyroscope, Z-gyroscope, X-gyroscope accelerometer, Y-gyroscope accelerometer, Z-gyroscope accelerometer, and the inertial measurement system platform, respectively. , ... These are the temperatures of other components, frames, caps, and various hardware and structural parts of the inertial measurement system; , , , , , , ... These include the X-gyroscope, Y-gyroscope, Z-gyroscope, X-gyroscope accelerometer, Y-gyroscope accelerometer, Z-gyroscope accelerometer, inertial measurement system platform, other components on the inertial measurement system, frame, cap, and various hardware and structural parts. The defined heat transfer coefficient; The heat transfer coefficient between the node temperature and the ambient temperature; Temperature node With temperature node The heat transfer coefficient between them; is the heat source gain coefficient from the heat source at temperature node j to node i; Temperature node The heat source provides heat; Step 3: Based on the disturbances and parameter uncertainties in the heat conduction model, design the state-space equations for a multi-input multi-output multi-point temperature joint control system; First, random disturbances and parameter uncertainties in the real environment are introduced into the heat conduction model, resulting in the model described in the following equation: in It's a deviation in the heat transfer coefficient. It is interference input. It is the coefficient matrix of the disturbance acting on the system; Then, the control objective of the temperature field system is to adjust the heat source gain matrix K so that all measurement points reach the expected target temperature, i.e., to find a suitable control law that... Reaching the reference temperature Design augmented matrix The Q matrix is ​​as follows: Therefore, the system shown in the above equation is transformed into an augmented state-space equation: Finally, in the augmented form of the state-space equations, due to the reference temperature... The reference temperature is set by the system. The transition matrix is ​​set to the identity matrix. : Step 4: Design the robustness of the multi-point temperature control system based on the state-space equations of the multi-input multi-output multi-point temperature joint control system. The performance index function is used to perform multi-input multi-output temperature joint control in order to shorten the warm-up preparation time of the inertial system and improve the accuracy of the inertial navigation system. Robustness of multi-point temperature control system The performance index function is: The index function consists of the squared residual between the measured temperature and the ideal temperature, as well as the quadratic forms of the control input and the disturbance input; It is the weight matrix for each temperature point. It is a weight matrix of the heat source supply at each temperature node. It is the coefficient of influence of interference input on performance indicators; Step 5: Improve the robustness of the multi-point temperature control system The performance index function is applied to the heat conduction model, and based on the influence mechanism of the temperature field on the gyroscope temperature error, the requirements of gyroscope accuracy on the temperature control system, and the proposed robustness... Feedback gain matrix The solution method yields the feedback gain matrix. The temperature control effect was tested by substituting it into a multi-input multi-output multi-point temperature joint control system.

2. The multi-input multi-output multi-point temperature joint control method for an inertial measurement system as described in claim 1, characterized in that, The temperature control system is specifically as follows: Each gyroscope and the base plate of the meter are equipped with a temperature sensor and a TEC heating and cooling element, forming a multi-input multi-output temperature control device. The control data of each temperature control channel is monitored in real time by the host computer. The placement of the TEC heating and cooling element and the temperature sensor is designed at the center of the gyroscope structure base plate to maintain the symmetry of the temperature field of the gyroscope fiber optic ring.

3. The multi-input multi-output multi-point temperature joint control method for an inertial measurement system as described in claim 1, characterized in that, In step two, the temperature of a single node is affected by: the gain of heat supplied by the heat source, the heat conducted by the surrounding environment, and the temperature of neighboring nodes. Specifically as follows: For the i-th temperature node The temperature is When only the gain from the heat source's heat supply has an effect, the temperature change at this node is as follows: in Let be the heat source gain coefficient from the heat source at temperature node j to node i. Provide heat to the heat source at temperature node i; Then, due to the presence of heat conduction factors, the current temperature node is affected by the surrounding nodes, losing / receiving some heat; During the temperature measurement cycle, the temperature obtained by the current measurement node is: in The temperature at the high-temperature point. The temperature is the lowest point. Heat flows in from the highest point and then flows to the lowest point, so the environment has both warming and cooling effects. The above formula is a comprehensive calculation result. Finally, for two adjacent nodes, the temperatures are respectively and Considering only the heat transfer between the two, the temperature of node 1 is... Rate of change over time and temperature difference between the two Proportional; For node i, the set of its neighboring nodes is denoted as . ; Assuming that the current temperature of each node is affected by the temperatures of other nodes, we have the following equation: Among them, the elements on the diagonal of the coefficient matrix for: 。 4. The multi-input multi-output multi-point temperature joint control method for an inertial measurement system as described in claim 1, characterized in that, In step three, considering random disturbances and parameter uncertainties, a robust array-type multi-heat-source temperature field system suitable for inertial measurement systems is proposed. Feedback gain matrix of control system The design methodology realizes the design of a high-precision joint control technology for multi-input, multi-output, and multi-point temperature; specifically: consider , and Both are constant coefficient matrices, describing the uncertainty of system parameters caused by temperature changes; Consider the robustness of multi-point temperature control systems Performance metric function, for any Based on the proof, a robust array-type multi-heat-source temperature field system suitable for inertial measurement systems has been obtained. The control design methodology was used to complete the design of a multi-input multi-output multi-point temperature joint control technology. To make the closed-loop system For any parameter uncertainty, it satisfies robust mean-square exponential stability and has a positive definite matrix. and positive numbers The feedback gain matrix K makes Furthermore, the estimated value of state decay is in, , , .

5. The multi-input multi-output multi-point temperature joint control method for an inertial measurement system as described in claim 1, characterized in that, The temperature control system suffers from random disturbances and parameter uncertainties, hence the proposed feedback gain matrix. The design methodology still ensures high-precision control of the multi-input multi-output temperature control system. This includes considering the mechanism of Shupe error variation with temperature field in high-precision fiber optic inertial measurement systems, establishing a model of temperature field distribution and variation within the inertial measurement system, analyzing the temperature error model of fiber optic gyroscopes, and focusing on the design method of feedback gain matrix K for multi-input multi-output multi-point temperature joint control system. The design method is used to design a temperature control system for heating and cooling of an array-type multi-heat source temperature field system.

6. The multi-input multi-output multi-point temperature joint control method for an inertial measurement system as described in claim 1, characterized in that, The heat conduction model includes consideration of the direct influence of heat supply from the heat source on a single temperature node and the influence of surrounding nodes. Based on this, the state-space equation of the heat transfer network of the inertial measurement system is obtained, and a multi-point heat conduction system model of the inertial measurement system is established.

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