Compound Disturbance Rejection Control Method and System for Control Moment Gyroscope Frame Servo System

Abstract

The present invention provides a composite anti-interference control method and system for a control moment gyroscope frame servo system, belonging to the technical field of mechatronic system control. According to the analysis of the working principle of the control moment gyroscope, considering the multi-source interference and uncertainty existing in the frame servo system under complex working conditions, a mathematical model of the frame servo system in the presence of multi-source interference is established, and an extended state observer is constructed to estimate the lumped interference with a bounded rate of change. Combining the interference estimation results, a fast terminal sliding mode controller forms a finite-time composite anti-interference control strategy to compensate for and suppress the influence of interference on the system control performance. The present invention effectively attenuates and suppresses the influence of multi-source unknown coupling interference on the servo accuracy of the control moment gyroscope frame servo system; has stronger robustness to unknown interference and can improve the system speed tracking accuracy within a finite time; enables the control moment gyroscope frame servo system to have good servo performance, and the actual angular velocity can accurately track the reference value with high precision.

Description

Technical Field

[0001] The present invention relates to the technical field of electromechanical system control, and in particular to a composite anti-interference control method and system for a control moment gyro frame servo system. Background Art

[0002] As spacecraft missions become increasingly diverse and their structures become more complex, higher demands are placed on the accuracy, stability, and agility of their attitude control systems. This also places even higher demands on the rapid maneuvering response capabilities of spacecraft attitude control systems. Control moment gyro (CMG) systems, with their high output torque, high energy efficiency, and low power consumption, have become the preferred inertial actuator for spacecraft. CMGs primarily consist of a high-speed rotor system and a gimbal servo system. The accuracy of their output torque is determined by the accuracy of the gimbal angular velocity, making it crucial to ensure excellent servo performance in the CMG gimbal servo system. Furthermore, due to the complex and ever-changing operating environment of the CMG and the unique nature of its system architecture, gimbal servo systems often experience multiple sources of interference and uncertainty. These interlocking disturbances can reduce system control accuracy and severely impact the accuracy of spacecraft attitude control. Therefore, studying high-performance control of CMG gimbal speed under complex interference and constraints is extremely challenging. Therefore, designing a simple and effective composite anti-interference control strategy for the CMG gimbal servo system to offset or suppress interference, ensure velocity tracking performance, and improve its anti-interference capability is a challenging task.

[0003] Based on the above analysis, the current anti-interference research on CMG frame servo systems at home and abroad focuses on only considering a single disturbance, and various anti-interference control theories and methods have their own characteristics and limitations. The anti-interference problem of CMG frame servo systems under multi-source unknown coupled interference needs to be solved urgently. Summary of the Invention

[0004] The object of the present invention is to provide a composite anti-interference control method and system for a control moment gyro frame servo system, so as to solve at least one technical problem existing in the above background technology.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a composite anti-interference control method for a control moment gyro frame servo system, comprising:

[0007] Based on the analysis of the working principle of the control moment gyro, the multi-source interference and uncertainty of the frame servo system under complex working conditions are considered, and a mathematical model of the frame servo system with multi-source interference is established. Among them, the coupled interference that cannot be represented in the multi-source interference of the frame servo system is regarded as a lumped interference.

[0008] Construct an extended state observer based on the established framework servo system model to estimate the lumped disturbance with bounded rate of change;

[0009] Combined with the estimation result of the disturbance, design a fast terminal sliding mode controller to form a finite-time composite anti-disturbance control strategy to compensate for and suppress the influence of the disturbance on the system control performance.

[0010] In a second aspect, the present invention provides a composite anti-disturbance control system for a control moment gyroscope framework servo system, including:

[0011] A construction module for analyzing according to the working principle of the control moment gyroscope, considering the multi-source disturbances and uncertainties existing in the framework servo system under complex working conditions, and establishing a mathematical model of the framework servo system in the presence of multi-source disturbances; among them, the coupling disturbance that cannot be characterized in the multi-source disturbances suffered by the framework servo system is regarded as a lumped disturbance;

[0012] An estimation module for constructing an extended state observer based on the established framework servo system model to estimate the lumped disturbance with bounded rate of change;

[0013] A compensation and suppression module for combining the estimation result of the disturbance, designing a fast terminal sliding mode controller to form a finite-time composite anti-disturbance control strategy to compensate for and suppress the influence of the disturbance on the system control performance.

[0014] In a third aspect, the present invention provides a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, the composite anti-disturbance control method for the control moment gyroscope framework servo system as described in the first aspect is implemented.

[0015] In a fourth aspect, the present invention provides a computer device, including a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the composite anti-disturbance control method for the control moment gyroscope framework servo system as described in the first aspect.

[0016] In a fifth aspect, the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device runs, the processor executes the computer program stored in the memory so that the electronic device executes the instructions for implementing the composite anti-disturbance control method for the control moment gyroscope framework servo system as described in the first aspect.

[0017] Advantages of the present invention: effectively attenuate and suppress the influence of multi-source unknown coupling interference on the servo accuracy of the control moment gyroscope frame servo system; have stronger robustness to unknown interference and can improve the system speed tracking accuracy within a limited time; enable the control moment gyroscope frame servo system to have good servo performance, and the actual angular velocity can accurately track the reference value.

[0018] The advantages of the additional aspects of the present invention will be more clearly given in the following description part, or understood through the practice of the present invention. Brief Description of the Drawings

[0019] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0020] Figure 1 It is a flowchart of the composite anti-interference control method for multi-source unknown coupling interference based on the control moment gyroscope frame servo system described in the embodiments of the present invention.

[0021] Figure 2 It is a schematic diagram of the generation of static unbalance interference of the high-speed rotor of the control moment gyroscope described in the embodiments of the present invention.

[0022] Figure 3 It is a schematic diagram of the generation of dynamic unbalance interference of the high-speed rotor of the control moment gyroscope described in the embodiments of the present invention.

[0023] Figure 4 It is a comparison schematic diagram of the constant-speed tracking performance under constant interference in the composite anti-interference control method for multi-source disturbances based on the control moment gyroscope frame servo system described in the embodiments of the present invention.

[0024] Figure 5 It is a comparison schematic diagram of the constant-speed tracking performance under unknown coupling interference in the composite anti-interference control method for multi-source disturbances based on the control moment gyroscope frame servo system described in the embodiments of the present invention.

[0025] Figure 6 It is a comparison schematic diagram of the sinusoidal speed tracking performance under unknown coupling interference suffered by the control moment gyroscope frame servo system described in the embodiments of the present invention. Detailed Embodiments

[0026] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0027] For ease of understanding of the present invention, the present invention will be further explained below with reference to specific embodiments in conjunction with the accompanying drawings, and the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0028] Those skilled in the art should understand that the drawings are only schematic diagrams of the embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0029] Embodiment 1

[0030] In this Embodiment 1, first, a composite anti-interference control system for a control moment gyroscope frame servo system is provided, including: a construction module for establishing a mathematical model of the frame servo system in the presence of multi-source interference according to the working principle analysis of the control moment gyroscope, considering the multi-source interference and uncertainties existing in the frame servo system under complex working conditions; wherein, the coupling interference that cannot be characterized among the multi-source interferences suffered by the frame servo system is regarded as lumped interference; an estimation module for constructing an extended state observer based on the established frame servo system model to estimate the lumped interference with a bounded rate of change; a compensation and suppression module for designing a fast terminal sliding mode controller in combination with the estimation result of the interference to form a finite-time composite anti-interference control strategy to compensate for and suppress the influence of the interference on the system control performance.

[0031] In this Embodiment 1, the above system is used to implement a composite anti-interference control method for a control moment gyroscope frame servo system. The coupling interference that is difficult to accurately characterize is regarded as lumped interference, and then an ESO is constructed for estimation for the lumped interference. In combination with the interference estimation result, a fast terminal sliding mode controller (FTSMC) is designed to form a finite-time composite anti-interference control strategy. The method includes the following steps:

[0032] S1. According to the working principle analysis of the control moment gyroscope, considering the multi-source interference and uncertainties existing in the frame servo system under complex working conditions, establish a mathematical model of the frame servo system in the presence of multi-source interference;

[0033] S2. Analyze and model the multi-source interferences suffered by the frame servo system under actual working conditions, and regard the coupling interference that is difficult to accurately characterize as lumped interference for the subsequent design of the control strategy;

[0034] S3. Construct an extended state observer (ESO) based on the established control moment gyroscope (CMG) frame servo system model to estimate the lumped interference with a bounded rate of change;

[0035] S4. Based on the estimated result of the combined interference, design a fast terminal sliding mode controller (FTSMC) to form a finite-time composite anti-interference control strategy, compensating for and suppressing the impact of interference on the system control performance;

[0036] S5. Select a Lyapunov function to prove the stability of the system, and at the same time prove that the tracking error of the system can converge within a finite time, improving the speed tracking accuracy of the system within a finite time.

[0037] In this embodiment, the difficult-to-precisely-characterize coupling interference is regarded as lumped interference, and then an ESO is constructed for estimation aiming at the lumped interference. Based on the estimated result of the interference, a fast terminal sliding mode controller (FTSMC) is designed to form a finite-time composite anti-interference control strategy. The modeling of the frame servo system with multi-source interference in step S1 is as follows:

[0038] In the d-q coordinate system, the frame servo system driven by a surface-mounted PMSM can be modeled as the following formula:

[0039]

[0040] It has been assumed that: the saturation of the motor iron core is ignored, the eddy current and hysteresis losses in the motor are not considered, and the current in the motor is a symmetric three-phase sine wave. Among them, i d and i q are the stator currents on the d-axis and q-axis respectively, u_d and u q are the stator voltages on the d-axis and q-axis respectively. The PMSM structure adopted has a very small difference in the direct and quadrature axis inductances, which can be approximated as L d = L q = L, R s is the stator resistance, n_p is the number of pole pairs, ψ_f is the magnetic flux, J is the moment of inertia, ω is the angular velocity of the frame servo system, and the torque coefficient ds represents the lumped term of multi-source interference.

[0041] Vector control methods are often used in the control of frame servo systems to achieve independent control of magnetic flux and torque. Usually, to eliminate the coupling between the current i d and i q , the d-axis reference current is set to When the d-axis current loop controller works in an ideal state, it can be obtained that: Then the system can be re-described as the following formula:

[0042]

[0043] The coupling interference that is difficult to accurately characterize is regarded as lumped interference, and then an ESO is constructed for estimation for the lumped interference. Combining the interference estimation results, a fast terminal sliding mode controller (FTSMC) is designed to form a finite-time composite anti-interference control strategy. Step S2 further includes the following sub-steps:

[0044] S2.1. Analyze and model the rotor unbalance disturbance suffered by the frame servo system.

[0045] During the processes of machining, manufacturing, and assembly, there are inevitably errors and uneven mass distributions in the high-speed rotor of the control moment gyro, which leads to static and dynamic unbalances of the rotor. The resulting unbalance disturbance is regarded as the main interference source of the frame servo system. When the rotor rotates at high speed, the static unbalance mass generated by the deviation of its geometric center from the inertial center will generate a radial periodic centrifugal inertial force F s in space, and its expression is as follows:

[0046]

[0047] where U s = m s r ms , m s is the lumped static unbalance mass, Ω is the rotational speed of the high-speed rotor flywheel, is the initial phase angle of m s .

[0048] When the rotor rotates at high speed, the dynamic unbalance mass generated by the intersection of its principal inertia axis and the rotation axis will generate an axial periodic inertial torque T d in space, and its expression is as follows:

[0049]

[0050] where U d = m d r md h f , m d is the lumped dynamic unbalance mass, is the initial phase angle of m d .

[0051] The centrifugal force generated by static unbalance will cause fluctuations in the radial frictional torque of the frame servo system, and the centrifugal torque generated by dynamic unbalance will cause axial vibration of the system, thereby affecting the servo accuracy of the frame servo system. The resulting speed fluctuations will be further transmitted to the spacecraft, ultimately affecting the attitude control performance of the spacecraft. It can be seen from the expression of T d that the unbalanced disturbance torque T dis a harmonic interference with a known frequency but unknown amplitude and phase, which can be modeled in the form of an exogenous system:

[0052]

[0053] where the state ξ is defined as V =

[10] .

[0054] In addition, in order to smoothly estimate the unbalanced disturbance, it is necessary to ensure that the disturbance is observable. Combining the speed equation of the system with the disturbance model gives the following equation:

[0055]

[0056] where the observability matrix is Due to its full rank, T d can be observed.

[0057] S2.2. Analyze the nonlinear friction torque suffered by the frame servo system.

[0058] The friction torque is mainly caused by the relative motion of rotating and transmission components such as bearings and conductive slip rings in the control moment gyro frame servo system, which easily leads to steady-state errors, tracking lags and limit cycles during the speed regulation process of the system. Therefore, the friction torque is one of the main factors affecting the servo accuracy of the system.

[0059] In addition, the gyroscopic torque and cogging torque will also affect the servo accuracy of the frame servo system. However, the factors generating them are complex, and it is difficult to obtain accurate model information of these disturbances. Therefore, in this embodiment, the coupling disturbances that are difficult to accurately characterize in the control moment gyro frame servo system are regarded as lumped disturbance d s For the subsequent control strategy, the coupling disturbances that are difficult to accurately characterize are regarded as lumped disturbances, and then an ESO is constructed for estimation for the lumped disturbances. Combining the disturbance estimation results, a fast terminal sliding mode controller (FTSMC) is designed to form the design of a finite-time composite disturbance rejection control strategy.

[0060] Step S3 further includes the following sub-steps:

[0061] S3.1. For the case where the frame servo system has unknown coupling disturbances, regard the coupling disturbances that are difficult to accurately characterize as lumped disturbances and design as follows:

[0062] This embodiment considers the rotor unbalance disturbing torque, frictional torque and q-axis current regulation error as the disturbances suffered by the frame servo system. For the unknown coupling disturbances that are difficult to accurately model among them, the above disturbances are regarded as lumped disturbance d with a bounded rate of change s for the subsequent design of the controller.

[0063] Define the speed tracking error e = ω* -ω, where ω * is the reference angular velocity of the frame servo system. By differentiating the rotational speed tracking error and dynamically substituting the actual rotational speed into e, the following rotational speed tracking error model can be established

[0064] Assumption 3.1: Assume that the lumped disturbance d s is bounded and differentiable. That is, there exists a known constant ε d > 0 such that the condition is satisfied.

[0065] For the convenience of the subsequent proof of the finite-time stability of the system, the following lemma is given:

[0066] Lemma 3.1: Consider the system f(0) = 0, where is continuous, and x0 is the initial state of the system. If there exists a continuously differentiable positive definite function such that where λ1 > 0, λ2 > 0, 0 < γ < 1. Then the origin of the closed-loop system is semi-globally finite-time stable and the convergence time T(x0) satisfies

[0067]

[0068] S3.2. Based on the established CMG frame servo system model, an extended state observer (ESO) is constructed to estimate the lumped disturbance d with bounded rate of change s , and the design of the extended state disturbance observer is as follows:

[0069] Regarding d s as the extended state of the system. Let x1 = ω, x2 = d s (t), and thus the following second-order model is constructed to describe the speed loop dynamics model of the system:

[0070]

[0071] where

[0072] Then the ESO can be constructed in the following form:

[0073]

[0074] where λ1, λ2 > 0 are the gain values to be designed for the observer, and are the estimated values of the states x1 and x2 respectively.

[0075] By taking the difference between the above two equations, the ESO estimation error model can be obtained:

[0076]

[0077] where are the estimation errors of states x1 and x2 respectively. Let the ESO estimation error model can be re-described in the following form:

[0078]

[0079] Assumption 3.1 ensures that h is bounded. Under this condition, as long as the matrix A - LC is Hurwitz, that is, its eigenvalues are all less than zero, the above system is Bounded-Input Bounded-Output (BIBO) stable.

[0080] In this embodiment, the poles of the observer are configured at -ω o , that is, let: |sI - (A - LC)| = (s + ω o ) 2 . Then the gains of the ESO can be selected according to the following rules, where there is only one adjustable parameter ω o

[0081] λ1 = 2ω o ,

[0082] For the convenience of the subsequent proof of the finite-time stability of the composite controller, the following assumptions are proposed:

[0083] Assumption 3.2: Assume that the estimation error of the lumped disturbance is bounded and differentiable. That is, there exists a known constant such that the condition is satisfied.

[0084] To sum up, based on the comprehensive classification and analysis of the multi-source disturbances suffered by the frame servo system, for the rotor unbalance disturbance, frictional torque, current regulation error and other disturbances suffered by the system which are cross-linked with each other, the coupling disturbance containing difficult-to-precisely-characterize is regarded as a lumped disturbance d s with a bounded rate of change. Since it is difficult to obtain the prior information of the lumped disturbance d s and its derivative, this embodiment constructs an extended state observer to estimate it, and then combines the disturbance estimation effect to propose a finite-time composite anti-disturbance control strategy combining the extended state disturbance observer-based fast terminal sliding mode control (ESO-FTSMC) to improve the accuracy of the multi-source disturbance estimation of the frame servo system.

[0085] The coupling interference that is difficult to accurately characterize is regarded as lumped interference, and then an Extended State Observer (ESO) is constructed for estimation aiming at the lumped interference. Combining with the interference estimation results, a Fast Terminal Sliding Mode Controller (FTSMC) is designed to form a finite-time composite anti-interference control strategy. Step S4 further includes the following sub-steps:

[0086] S4.1. Design of the Fast Terminal Sliding Mode Controller

[0087] Based on the rotational speed tracking error model established in S3.1, the traditional linear sliding mode surface is expressed as where the constant c > 0, which cannot make the system state converge to the equilibrium point in finite time. To achieve finite-time convergence, the Terminal Sliding Mode (TSM) and the Nonsingular Terminal Sliding Mode (NTSM) including nonlinear sliding mode surfaces are designed respectively as follows:

[0088]

[0089] where k, k' > 0, 0 < α < 1, 1 < α' < 2. sig α (x) = sign(x)|x| α , where sign(·) represents the conventional sign function.

[0090] The above two sliding mode surfaces are globally finite-time stable at the equilibrium point x = 0. For any initial state x(0), the system state converges to the equilibrium point in finite time under TSM, and the system state converges to the equilibrium point in finite time under NTSM. However, when taking the derivative of s in TSM, a negative exponential power term will appear, resulting in a singularity problem, and the convergence speed of NTSM is slower than that of TSM.

[0091] Therefore, combining the advantages of the above two sliding mode surfaces, a new Fast Terminal Sliding Mode (FTSM) surface is proposed in this embodiment as follows

[0092]

[0093] where k1, k2 > 0, 1 < α1 < 2 < α2, α1 = p / q, and both p and q are odd numbers. When the rotational speed tracking error e is close to the equilibrium point, that is, |e| ≤ 1, the and terms in the sliding mode surface play a dominant role, and the high-order term can be ignored, and its convergence speed is close to that of NTSM. When e is far from the equilibrium point, that is, |e| > 1, the high-order term in the sliding mode surface It plays a leading role and its convergence speed is much faster than NTSM.

[0094] In summary, the FTSM has a faster convergence speed than the NTSM, and the exponential power α1>1 avoids the singularity problem caused by the TSM. Therefore, based on the design of the FTSM, this embodiment selects the FTSMC to control the actual speed of the CMG frame servo system to accurately and quickly track the given reference speed.

[0095] Based on the FTSM designed above, in order to ensure that the frame speed tracking error converges to zero within a finite time, the FTSMC is designed as follows

[0096]

[0097] in:

[0098]

[0099] where u eq represents the equivalent control law, u ss represents the switching control law, k1, k2>0 are the controller parameters to be designed, l1, l2>0 are the reaching law parameters to be designed, 1<α1<2<α2 and 0<α3<1.

[0100] S4.2 Design of composite anti-interference controller based on ESO

[0101] The interference estimation results obtained based on ESO Incorporated into the design of FTSMC, a finite-time composite anti-interference control strategy is formed. The composite FTSMC based on ESO is designed as follows:

[0102]

[0103] in:

[0104]

[0105] in, It is the result of lumped disturbance estimation based on ESO and serves as the feedforward compensation part of the composite anti-disturbance controller.

[0106] The coupled disturbance that is difficult to accurately characterize is regarded as a lumped disturbance. Then, the ESO is constructed for the lumped disturbance and estimated. Combined with the disturbance estimation results, a fast terminal sliding mode controller (FTSMC) is designed to form a finite-time composite anti-disturbance control strategy. Step S5 further includes the following sub-steps:

[0107] S5.1. Based on the error system model, select an appropriate Lyapunov function to prove the stability of the system. The proof is as follows:

[0108] Theorem 5.1: For a frame servo system and a composite control law that satisfy Assumption 3.2, if the controller gains then the actual rotational speed of the system converges to zero within a finite time.

[0109] Proof:

[0110] First, substitute the system and its control law into the sliding mode surface designed in the present invention. The designed sliding mode surface is simplified to the following formula:

[0111]

[0112] Combined with the composite control law, taking the derivative of the above formula can deduce the sliding mode dynamics as the following formula:

[0113]

[0114] The Lyapunov candidate function is chosen as: Taking the derivative of the selected Lyapunov function gives:

[0115]

[0116] where γ1, γ2 > 0. Based on Lemma 3.1, from the above formula, it can be seen that when the controller gains are satisfied, the rotational speed tracking error e can reach the sliding mode surface s = 0 within a finite time. The proof is completed.

[0117] S5.2. Prove that the rotational speed tracking error e of the system can converge to zero within a finite time. The proof is as follows:

[0118] Theorem 5.2: For a control moment gyro frame servo system and a fast terminal sliding mode control law that satisfy Assumption 3.1, if the controller gain l2 > ε d , then the actual rotational speed of the system converges to zero within a finite time.

[0119] Proof:

[0120] First, substitute the frame servo system and its fast terminal sliding mode control law into the sliding mode surface designed in the present invention. The simplification is as follows:

[0121]

[0122] Combined with the control law, taking the derivative of the above formula can deduce the sliding mode dynamics as the following formula:

[0123]

[0124] The Lyapunov candidate function is chosen as: Combined with the above formula, taking the derivative of the selected Lyapunov function gives:

[0125]

[0126] where β1, β2 > 0. It can be seen from the above formula that when the controller gain l2 > ε d is satisfied, the rotational speed tracking error can reach the sliding mode surface s = 0 within a finite time T. Based on Lemma 3.1, T can be expressed as

[0127]

[0128] In summary, the rotational speed tracking error e of the system can converge to zero within a finite time. The proof is completed.

[0129] Although FTSMC can improve the servo accuracy of the perturbed system, under strong disturbances, the switching gain of this controller needs to be set relatively high to effectively suppress the interference, which will introduce large rotational speed fluctuations and chattering in the frame servo system. The prerequisite for the implementation of the composite anti-interference control strategy proposed in this embodiment is the controller gain This gain is less than the gain l2 > ε required for FTSMC implementation d , so compared with the separate feedback control, on this basis, the composite feedforward compensation result based on ESO can reduce the influence of disturbances on the servo accuracy of the system within a finite time and improve the stability of the rotational speed output.

[0130] Embodiment 2

[0131] The composite anti-interference control method for a control moment gyroscope frame servo system with multi-source disturbances provided in this Embodiment 2 is used for high-precision servo control of a control moment gyroscope frame servo system under multi-source disturbances. As Figure 1 shown, the method includes the following steps:

[0132] S1. According to the analysis of the working principle of the control moment gyroscope, considering the multi-source disturbances and uncertainties existing in the frame servo system under complex working conditions, establish a mathematical model of the frame servo system in the presence of multi-source disturbances;

[0133] S2. Analyze the multi-source disturbances suffered by the frame servo system under actual working conditions. Since the disturbances such as rotor unbalance disturbance, frictional torque, and current regulation error suffered by the system are cross-linked with each other, the coupling disturbances that are difficult to accurately characterize are regarded as lumped disturbances for the subsequent design of the control strategy;

[0134] S3. Based on the established CMG frame servo system model, construct an extended state observer (ESO) to estimate the lumped disturbance d with a bounded rate of change s ;

[0135] S4. Based on the estimated results of the interference, design a fast terminal sliding mode controller (FTSMC) to form a finite-time composite anti-interference control strategy to compensate for and suppress the influence of interference on the system control performance;

[0136] S5. Select a Lyapunov function to prove the stability of the system, and at the same time prove that the tracking error of the system can converge within a finite time.

[0137] Among them, in step S1, the modeling of the frame servo system with multi-source interference is as follows:

[0138]

[0139] It has been assumed that: the saturation of the motor iron core is ignored, the eddy current and hysteresis losses in the motor are not considered, and the current in the motor is a symmetric three-phase sine wave. Among them, i d and i q are the stator currents of the d-axis and q-axis respectively, u d and u q are the stator voltages of the d-axis and q-axis respectively. The PMSM structure adopted is surface-mounted, and the difference between the direct and quadrature axis inductances is very small, which can be approximated as L d = L q = L, R s is the stator resistance, n p is the number of pole pairs, ψ f is the magnetic flux, J is the moment of inertia, ω is the angular velocity of the frame servo system, and the torque coefficient d s represents the lumped term of multi-source interference.

[0140] The vector control method is often used in the control of the frame servo system to achieve independent control of the magnetic flux and torque. Usually, to eliminate the coupling between the current i d and i q , the d-axis reference current is set to When the d-axis current loop controller works in an ideal state, we can get Then the system can be redescribed as the following formula

[0141]

[0142] Step S2 further includes the following sub-steps:

[0143] S2.1. Analyze and model the rotor unbalance disturbance suffered by the frame servo system.

[0144] During the processing, manufacturing, and assembly processes, errors and uneven mass distribution inevitably exist in the high-speed rotor of the control moment gyro, resulting in static and dynamic imbalances of the rotor. The resulting imbalance disturbances are regarded as the main interference sources of the frame servo system. Combining Figure 2 with the schematic diagram of the static imbalance interference generation of the high-speed rotor of the control moment gyro shown in s , when the rotor rotates at high speed, the static imbalance mass generated by the deviation of its geometric center from the inertial center will generate a radial periodic centrifugal inertial force F

[0145]

[0146] on the high-speed rotating shaft. Its expression in space is as follows: s where U s =m ms r s , m is the lumped static imbalance mass, Ω is the rotational speed of the high-speed rotor flywheel, s is the initial phase angle of m

[0147] Combining Figure 3 with the schematic diagram of the dynamic imbalance interference generation of the high-speed rotor of the control moment gyro shown in d , when the rotor rotates at high speed, the dynamic imbalance mass generated by the intersection of its principal inertial axis and the rotation axis will generate an axial periodic inertial torque T

[0148]

[0149] on the frame axis. Its expression in space is as follows: d where U d =m md r f h d , m is the lumped dynamic imbalance mass, d is the initial phase angle of m

[0150] The centrifugal force generated by static imbalance will cause fluctuations in the radial frictional torque of the frame servo system, and the centrifugal torque generated by dynamic imbalance will cause axial vibration of the system, thereby affecting the servo accuracy of the frame servo system. The resulting speed fluctuations will be further transmitted to the spacecraft, ultimately affecting the attitude control performance of the spacecraft. From the expression of T d , it can be seen that the unbalanced disturbance torque T d is a harmonic interference with a known frequency but unknown amplitude and phase, which can be modeled in the form of an exogenous system:

[0151]

[0152] where the state ξ is defined as V=

[10] .

[0153] In addition, in order to successfully estimate the unbalanced disturbance, it is necessary to ensure that the disturbance is observable. The speed equation of the system is combined with the disturbance model to obtain the following equation:

[0154]

[0155] Among them, the observable matrix is Due to its full rank, T d Can be observed.

[0156] S2.2. Analysis of the nonlinear friction torque acting on the frame servo system.

[0157] Friction torque is primarily caused by the relative motion of rotating and transmission components, such as bearings and slip rings, in a gyroscopic gimbal servo system. This can lead to steady-state errors, tracking lag, and limit cycles during speed regulation. Therefore, friction torque is a major factor affecting system servo accuracy.

[0158] Furthermore, gyroscopic torque and cogging torque also affect the servo accuracy of the gimbal servo system. However, the factors that generate these disturbances are complex, making it difficult to accurately model them. Therefore, this embodiment treats the coupled disturbances in the control torque gyroscopic gimbal servo system, which are difficult to accurately characterize, as lumped disturbances to facilitate the design of subsequent control strategies.

[0159] Step S3 further includes the following sub-steps:

[0160] S3.1, the frame servo system has unknown coupling interference d s In the case of , the coupled interference that is difficult to accurately characterize is regarded as lumped interference, and the design is as follows:

[0161] This embodiment considers the rotor unbalance disturbance torque, friction torque and q-axis current regulation error as the interferences suffered by the frame servo system. For the unknown coupling interferences that are difficult to accurately model, the above interferences are regarded as lumped interferences with bounded change rates to facilitate the design of subsequent controllers.

[0162] Define the speed tracking error e = ω * -ω, where ω * is the reference angular velocity of the frame servo system. By taking the derivative of the speed tracking error and substituting the actual speed into e, the speed tracking error model can be established as shown below:

[0163]

[0164] Assumption 3.1: Assume that the aggregate interference d s is bounded and differentiable. That is, there is a known constant ε d >0 makes the condition is satisfied.

[0165] For the convenience of proving the finite-time stability of the subsequent system, the following lemma is given:

[0166] Lemma 3.1: Consider the system f(0) = 0, where is continuous and \(x_0\) is the initial state of the system. If there exists a continuously differentiable positive definite function such that where \(\lambda_1\gt0\), \(\lambda_2\gt0\), \(0\lt\gamma\lt1\). Then the origin of the closed-loop system is semi-globally finite-time stable and the convergence time \(T(x_0)\) satisfies

[0167]

[0168] S3.2. Construct an Extended State Observer (ESO) based on the established CMG framework servo system model to estimate the lumped disturbance \(d\) with bounded rate of change s , and the design of the extended state disturbance observer is as follows:

[0169] Regard \(d\) s as the extended state of the system. Let \(x_1=\omega\), \(x_2 = d\) s (t), and thus construct the following second-order model to describe the velocity loop dynamics of the system

[0170]

[0171] where

[0172] Then the ESO can be constructed in the following form

[0173]

[0174] where \(\lambda_1\), \(\lambda_2\gt0\) are the gain values to be designed for the observer, and are the estimated values of states \(x_1\) and \(x_2\) respectively.

[0175] Taking the difference between the above two equations, the ESO estimation error model can be obtained

[0176]

[0177] where are the estimation errors of states \(x_1\) and \(x_2\) respectively. Let The ESO estimation error model can be re-described in the following form

[0178]

[0179] Assumption 3.1 ensures that h is bounded. Under this condition, as long as the matrix A - LC is Hurwitz, that is, its eigenvalues are all less than zero, the above system is Bounded-Input Bounded-Output (BIBO) stable. In this embodiment, the poles of the observer are configured at -ω o where, that is, let: |sI - (A - LC)| = (s + ω o ) 2 . Then the gains of the ESO can be selected according to the following rules, where there is only one adjustable parameter ω o

[0180]

[0181] For the convenience of proving the finite-time stability of the subsequent composite controller, the following assumptions are proposed

[0182] Assumption 3.2: Assume that the estimation error of the lumped disturbance is bounded and differentiable. That is, there exists a known constant such that the condition is satisfied.

[0183] To sum up, based on the comprehensive classification and analysis of the multi-source disturbances suffered by the frame servo system, for the rotor imbalance disturbance, frictional torque, current regulation error and other disturbances suffered by the system that are cross-linked with each other, the coupling disturbances that are difficult to accurately characterize are regarded as lumped disturbances d s with bounded rates of change. Since it is difficult to obtain the prior information of the lumped disturbance d s and its derivative, this scheme constructs an extended state observer to estimate it, and then combines the interference estimation effect to propose a fast terminal sliding mode control (ESO-FTSMC) combined with an extended state disturbance observer to form a finite-time composite anti-interference control strategy to improve the accuracy of the multi-source disturbance estimation of the frame servo system.

[0184] Step S4 further includes the following sub-steps:

[0185] S4.1. Design of the fast terminal sliding mode controller

[0186] Based on the speed tracking error model established in S3.1, the traditional linear sliding surface is expressed as where the constant c > 0, which cannot make the system state converge to the equilibrium point in finite time. To achieve finite-time convergence, the terminal sliding mode (TSM) and non-singular terminal sliding mode (NTSM) including non-linear sliding surfaces are designed as follows:

[0187]

[0188] where \(k,k'\gt0\), \(0\lt\alpha\lt1\), \(1\lt\alpha'\lt2\). sig α (x) = sign(x)|x| α , where sign(·) represents the conventional sign function.

[0189] The above two sliding surfaces are globally finite-time stable at the equilibrium point \(x = 0\). For any initial state \(x(0)\), the system state converges to the equilibrium point in finite time under TSM and converges to the equilibrium point in finite time under NTSM . However, when taking the derivative of \(s\) in TSM, a negative exponent term will appear, resulting in a singularity problem, and the convergence rate of NTSM is slower than that of TSM.

[0190] Therefore, combining the advantages of the above two sliding surfaces, a new fast terminal sliding mode surface (Fast Terminal Sliding Mode, FTSM) is proposed in this embodiment as follows

[0191]

[0192] where \(k_1,k_2\gt0\), \(1\lt\alpha_1\lt2\lt\alpha_2\), \(\alpha_1 = p / q\), and both \(p\) and \(q\) are odd numbers. When the rotational speed tracking error \(e\) is close to the equilibrium point, i.e., \(|e|\leq1\), the and terms in the sliding surface play a dominant role, and the high-order term can be ignored, and its convergence rate is close to that of NTSM. When \(e\) is far from the equilibrium point, i.e., \(|e|\gt1\), the high-order term in the sliding surface plays a dominant role, and its convergence rate is much faster than that of NTSM.

[0193] In summary, FTSM has a faster convergence rate than NTSM, and at the same time, the exponential power \(\alpha_1\gt1\) avoids the singularity problem caused by TSM. Therefore, based on the design of FTSM, this embodiment selects FTSMC to control the actual rotational speed of the CMG frame servo system to accurately and quickly track the given reference rotational speed.

[0194] Based on the above-designed FTSM, to ensure that the frame rotational speed tracking error converges to zero within a finite time, FTSMC is designed in the following form

[0195]

[0196] where:

[0197]

[0198] where \(u\)eq represents the equivalent control law, u ss represents the switching control law, where k1, k2 > 0 are the controller parameters to be designed, l1, l2 > 0 are the reaching law parameters to be designed, 1 < α1 < 2 < α2, and 0 < α3 < 1.

[0199] S4.2. Design of Composite Disturbance Rejection Controller Based on ESO

[0200] The disturbance estimation result obtained based on ESO is incorporated into the design of FTSMC to form a finite-time composite disturbance rejection control strategy. The composite FTSMC based on ESO is designed in the following form:

[0201]

[0202] where:

[0203]

[0204] where is the lumped disturbance estimation result based on ESO and serves as the feedforward compensation part of the composite disturbance rejection controller.

[0205] Step S5 further includes the following sub-steps:

[0206] S5.1. Based on the error system model, select an appropriate Lyapunov function to prove the stability of the system, as shown below:

[0207] Theorem 5.1: For a frame servo system and a composite control law that satisfy Assumption 3.2, if the controller gains then the actual rotational speed of the system converges to zero within a finite time.

[0208] Proof:

[0209] First, substitute the system and its control law into the sliding surface designed in the present invention. The designed sliding surface is simplified to the following formula

[0210]

[0211] Combined with the composite control law, taking the derivative of the above formula can deduce the sliding mode dynamics as the following formula

[0212] [[ID=5-3]]

[0213] The Lyapunov candidate function is selected as: Taking the derivative of the selected Lyapunov function gives

[0214]

[0215] where γ1, γ2 > 0. Based on Lemma 3.1, it can be seen from the above formula that when the controller gain is satisfied, the rotational speed tracking error e can reach the sliding mode surface s = 0 within a finite time. The proof is completed.

[0216] S5.2. Prove that the rotational speed tracking error e of the system can converge to zero within a finite time, and the proof is as follows:

[0217] Theorem 5.2: Based on the control moment gyro frame servo system that satisfies Assumption 3.1 and the fast terminal sliding mode control law, if the controller gain l2 > ε d , then the actual rotational speed of the system converges to zero within a finite time.

[0218] Proof:

[0219] First, substitute the frame servo system and its fast terminal sliding mode control law into the sliding mode surface designed in this embodiment and simplify as follows

[0220]

[0221] Combined with the control law, differentiating the above formula can deduce the sliding mode dynamics as the following formula

[0222]

[0223] The Lyapunov candidate function is selected as: Differentiating the selected Lyapunov function combined with the above formula gives

[0224]

[0225] where β1, β2 > 0. It can be seen from the above formula that under the condition that the controller gain l2 > ε d is satisfied, the rotational speed tracking error can reach the sliding mode surface s = 0 within a finite time T. Based on Lemma 3.1, T can be expressed as

[0226]

[0227] In summary, the rotational speed tracking error e of the system can converge to zero within a finite time.

[0228] Although FTSMC can improve the servo accuracy of the perturbed system, under strong disturbances, the switching gain of this controller needs to be set relatively high to effectively suppress the interference, which will introduce large rotational speed fluctuations and chattering in the frame servo system. The prerequisite for the composite anti-interference control strategy proposed in this embodiment is the controller gain This gain is less than the gain l2 > ε required for FTSMC to achieve d, therefore, compared with the separate feedback control, on this basis, the compound feedforward compensation result based on ESO can reduce the influence of disturbances on the servo accuracy of the system within a limited time and improve the stability of the rotational speed output.

[0229] Next, in order to verify the effectiveness of the compound disturbance rejection control method for the multi-source disturbances of the control moment gyroscope frame servo system provided in this embodiment, MATLAB is used for simulation experiments and detailed descriptions are made.

[0230] The control moment gyroscope frame servo system model provided in this embodiment comprehensively considers the influence of multi-source disturbances such as rotor imbalance disturbance, frictional torque, and current regulation error on the frame servo system. Among them, there are unknown coupling disturbances that are difficult to accurately model. The above disturbances can be regarded as lumped disturbances with bounded rates of change, and an ESO is constructed to estimate the lumped disturbance d with bounded rate of change s , and then, combined with the estimation result of the disturbance, an FTSMC is designed to form a finite-time compound disturbance rejection control strategy to compensate for and suppress the influence of the disturbance on the system control performance, so that the following two-stage frame servo system has good servo performance, that is: the actual angular velocity accurately tracks the reference value, and has stronger robustness to unknown disturbances.

[0231] Stage 1: Startup stage

[0232] In the simulation experiment, the control moment gyroscope frame servo system model is used to verify the effectiveness of the proposed compound disturbance rejection controller based on the extended state observer. The parameters used in the frame servo system model are: J = 0.001 kg·m 2 , L = 0.0085 H, R s = 2.785 Ω, ψ f = 0.175 Wb and n p = 4. In addition, the reference rotational speed ω r = 2° / , and the simulation step size is configured as 10 -5 s.

[0233] The design of the compound disturbance rejection controller adopts the method proposed in the present invention. Among them, the controller parameters should be adjusted by comprehensively considering standards such as system stability, dynamic performance, and robustness against multi-source unknown disturbances. The control performance of the algorithm proposed in this embodiment highly depends on the selection of the controller gain. Among them, k1, k2 > 0 are the controller parameters to be designed, l1, l2 > 0 are the reaching law parameters to be designed, and the settings of the controller parameters are: k1 = 3, k2 = 10000, α1 = 1.3, α2 = 3, α3 = 0.5, l1 = 5000, l2 = 0.5

[0234] Stage 2: Stage under the action of multi-source disturbances

[0235] In the following simulation experiments, the focus is on the finite-time composite disturbance rejection control strategy of the proposed fast terminal sliding mode control (ES-FTSMC) combined with an extended state disturbance observer under the action of multi-source disturbances, to ensure the high-precision servo performance of the frame servo system. Using the system model parameters, reference speed, and controller parameters in Stage 1, the lumped disturbance is set to two cases: constant disturbance and coupled disturbance. The specific disturbances are assumed to be the following two cases:

[0236] Case 1: d s is set as a constant disturbance. Stage 1 represents the time period of 5 ≤ t < 15 s, and d s (Nm) = 10 is applied; Stage 2 represents the time period of 15 ≤ t < 20 s, and d s (Nm) = 5 is applied.

[0237] Case 2: d s is set as a coupled disturbance. Stage 1 and Stage 2 respectively represent the application of d s during the two time periods of 0 ≤ t < 10 s and 10 ≤ t < 20 s, and the specific application form is as follows

[0238]

[0239] Based on the above parameters, the composite control strategy proposed in this embodiment is respectively simulated and verified through Stages 1 and 2, and Figure 4 、 Figure 5 and Figure 6 are obtained. Among them, Figure 4 shows the comparison schematic diagram of the constant-speed tracking performance of the frame servo system under constant disturbance, Figure 5 shows the comparison schematic diagram of the constant-speed tracking performance of the frame servo system under unknown coupled disturbance, Figure 6 shows the comparison schematic diagram of the sinusoidal speed tracking performance of the frame servo system under unknown coupled disturbance. It can be seen from the simulation schematic diagrams that the proposed composite disturbance rejection controller has good transient and steady-state performance. The designed extended state observer can accurately estimate the unknown coupled disturbance in the presence of multi-source disturbances, and the disturbance estimation result can be introduced into the design process of the composite control law proposed in the present invention, so as to use the proposed composite disturbance rejection control strategy to achieve the attenuation and suppression of multi-source unknown coupled disturbances, and ensure the high-precision servo performance of the frame servo system.

[0240] Through the above analysis, the effectiveness of the composite disturbance rejection control strategy for the multi-source disturbance of the control moment gyro frame servo system provided in this embodiment is proved.

[0241] Embodiment 3

[0242] Embodiment 3 provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the composite anti-interference control method for the control moment gyroscope frame servo system as described above.

[0243] Embodiment 4

[0244] Embodiment 4 provides a computer device, including a memory and a processor, where the processor communicates with the memory, the memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the composite anti-interference control method for the control moment gyroscope frame servo system as described above.

[0245] Embodiment 5

[0246] Embodiment 5 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device runs, the processor executes the computer program stored in the memory so that the electronic device executes the instructions for implementing the composite anti-interference control method for the control moment gyroscope frame servo system as described above.

[0247] Although the specific embodiments of the present invention are described above in conjunction with the accompanying drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that based on the technical solutions disclosed in the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts should be covered within the protection scope of the present invention.

Claims

1. A composite anti-interference control method for a control moment gyroscope frame servo system, characterized in that including: According to the working principle analysis of the control moment gyro, considering the multi-source interference and uncertainty existing in the gimbal servo system under complex working conditions, a mathematical model of the gimbal servo system in the presence of multi-source interference is established; among them, the coupling interference that cannot be characterized in the multi-source interference received by the gimbal servo system is regarded as lumped interference; Based on the established gimbal servo system model, an extended state observer is constructed to estimate the lumped interference with a bounded rate of change; Combined with the estimated results of the interference, a fast terminal sliding mode controller is designed to form a finite-time composite anti-interference control strategy to compensate for and suppress the influence of the interference on the system control performance; The terminal sliding mode control is as follows: where k1, k2 > 0, 1 < α1 < 2 < α2, α1 = p / q, and both p and q are odd numbers; when the rotational speed tracking error e is relatively close to the equilibrium point, i.e., |e| ≤ 1, the terms and in the sliding mode surface play a dominant role, and the high-order term can be ignored. When e is relatively far from the equilibrium point, i.e., |e| > 1, the high-order term in the sliding mode surface plays a dominant role; To ensure that the gimbal speed tracking error converges to zero within a finite time, the terminal sliding mode control is in the following form: where, where, u eq represents the equivalent control law, u ss represents the switching control law, k1, k2 > 0 are controller parameters to be designed, l1, l2 > 0 are reaching law parameters to be designed, 1 < α1 < 2 < α2 and 0 < α3 < 1; The interference estimation result obtained based on the extended state disturbance observer is incorporated into the design of the terminal sliding mode control to form a finite-time composite anti-interference control strategy: where, Among them, is the lumped interference estimation result based on ESO, which serves as the feedforward compensation part of the composite anti-interference controller.

2. The composite anti-interference control method of the control moment gyro frame servo system according to claim 1, characterized in that, The mathematical model of the gimbal servo system in the presence of multi-source interference is as follows: where, i d and i q are the stator currents of the d-axis and q-axis respectively, u d and u q are the stator voltages of the d-axis and q-axis respectively, L d and L q are the inductances of the d-axis and q-axis respectively, R s is the stator resistance, n p is the number of pole pairs, ψ f is the magnetic flux linkage, J is the moment of inertia, ω is the angular velocity of the frame servo system, k t is the torque coefficient, d s represents the lumped term of multi-source interference; To eliminate the coupling between the current i d and i q the d-axis reference current is set to When the d-axis current loop controller operates ideally, we can obtain Then the mathematical model of the frame servo system can be re-described as:

3. The composite anti-interference control method for the control moment gyroscope frame servo system according to claim 1, wherein, The design of the extended state interference observer is as follows: Regard d s as the expanded state of the system, and let x1 = ω, x2 = d s (t), thus constructing the following second-order model to describe the speed-loop dynamics of the system: Among them Then the extended state interference observer is constructed in the following form: where λ1, λ2 > 0 are the gain values to be designed for the observer, and are the estimated values of states x1 and x2, respectively; Then, the estimation error model is: wherein are the estimation errors of states x1 and x2 respectively; Let the estimation error model is reformulated as follows:

4. A composite anti-interference control system for a control moment gyro frame servo system, characterized in that, including: A construction module for establishing a mathematical model of the gimbal servo system in the presence of multi-source interference according to the working principle analysis of the control moment gyro, considering the multi-source interference and uncertainty existing in the gimbal servo system under complex working conditions; among them, the coupling interference that cannot be characterized in the multi-source interference received by the gimbal servo system is regarded as lumped interference; An estimation module for constructing an extended state observer based on the established gimbal servo system model to estimate the lumped interference with a bounded rate of change; A compensation and suppression module for designing a fast terminal sliding mode controller to form a finite-time composite anti-interference control strategy in combination with the estimated results of the interference, to compensate for and suppress the influence of the interference on the system control performance; where, the terminal sliding mode control is as follows: where k1, k2 > 0, 1 < α1 < 2 < α2, α1 = p / q, and both p and q are odd numbers; when the rotational speed tracking error e is relatively close to the equilibrium point, i.e., |e| ≤ 1, the terms and in the sliding mode surface play a dominant role, and the high-order term can be ignored. When e is relatively far from the equilibrium point, i.e., |e| > 1, the high-order term in the sliding mode surface plays a dominant role; To ensure that the gimbal speed tracking error converges to zero within a finite time, the terminal sliding mode control is in the following form: where, where, u eq represents the equivalent control law, and u ss represents the switching control law. k1, k2 > 0 are controller parameters to be designed, l1, l2 > 0 are reaching law parameters to be designed, 1 < α1 < 2 < α2 and 0 < α3 < 1; The disturbance estimation result obtained based on the extended state disturbance observer is incorporated into the design of the terminal sliding mode control to form a finite-time composite anti-disturbance control strategy: where, Among them, is the lumped interference estimation result based on ESO and serves as the feedforward compensation part of the composite anti-interference controller.

5. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the composite anti-interference control method of the control moment gyro gimbal servo system as described in any one of claims 1-3 is implemented.

6. A computer device, characterized in that, including a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the composite anti-interference control method of the control moment gyro gimbal servo system as described in any one of claims 1-3.

7. An electronic device, characterized in that, including: A processor, a memory, and a computer program; among them, the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device runs, the processor executes the computer program stored in the memory so that the electronic device executes the instructions for implementing the composite anti-interference control method of the control moment gyro gimbal servo system as described in any one of claims 1-3.

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