Frame system fixed time rotating speed tracking control method based on double interference observers

Abstract

The invention discloses a frame system fixed time rotating speed tracking control method based on a double-disturbance observer, and the method comprises the following steps: S1, carrying out the fine analysis of the multi-source disturbance of a frame system and the uncertainty of a model, and building a disturbed frame system mathematical model; s2, considering rotor rotating speed fluctuation, and finely representing matched interference and mismatched interference suffered by the disturbed frame system mathematical model; s3, designing two self-adaptive fixed-time fine interference observers to respectively estimate matched interference and unmatched interference based on the disturbed frame system mathematical model and the interference characterization result; s4, designing an improved fixed time controller with a novel fast terminal sliding mode surface and constructing a composite control strategy in combination with an interference observation result; according to the method, the influence of matching and mismatching interference on the rotating speed tracking performance of the frame system is compensated, the multi-band interference resistance robustness of the system is enhanced, and the rotating speed tracking precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electromechanical system control, and more specifically to a dual disturbance observer fixed-time speed tracking control method based on a framework system under multi-source interference and model uncertainty. Background Art

[0002] In recent years, with the rapid development of aerospace industry, the tasks undertaken by spacecraft have become more diverse and their applications in military and civilian fields have become more extensive. The above demands drive the improvement of high precision, high stability and rapid maneuvering response capabilities of spacecraft attitude control systems. Control torque gyro (CMG) has become the preferred inertial actuator for spacecraft due to its advantages such as large output torque, fast response and high energy efficiency ratio, providing a new way to control motion attitude with high precision and real-time. The working principle of CMG is to generate gyroscopic torque on the frame by rotating the high-speed rotor, thereby controlling the attitude of the spacecraft. Therefore, it is very important to ensure the good servo performance of the frame servo system. However, due to the complex and changeable working environment of CMG and the special system structure, the low-speed frame servo system is more susceptible to multi-source interference and uncertainty such as rotor unbalanced interference torque, friction torque, parameter perturbation, etc. Therefore, it is challenging to study the high-performance control of frame speed under complex interference.

[0003] At present, the research on anti-interference control of frame systems has achieved certain results, but there are still many problems to be solved in the research on fixed-time fine anti-interference control of systems under the coexistence of matched and unmatched interference. Therefore, the present invention proposes a fixed-time speed tracking control method for frame systems based on dual interference observers, which is insensitive to rotor speed fluctuations, effectively compensates for matched and unmatched multi-source interference, and improves the speed tracking accuracy of the system within a fixed time. Summary of the invention

[0004] The object of the present invention is to provide a fixed-time speed tracking control method for a frame system based on a dual disturbance observer, which compensates for the influence of matched and unmatched multi-source interference and ensures fast and accurate speed tracking performance of the system.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions: The fixed-time speed tracking control method of the frame system based on dual disturbance observers includes the following steps: S1, carefully analyze the multi-source interference and model uncertainty of the frame system, and establish a mathematical model of the disturbed frame system; S2, considering the rotor speed fluctuation, finely characterizes the matched and mismatched disturbances suffered by the mathematical model of the disturbed frame system; S3, based on the mathematical model of the disturbed frame system and the interference characterization results, two adaptive fixed-time fine interference observers are designed to estimate the matching interference and mismatching interference respectively; S4, combined with the disturbance observation results, an improved fixed-time controller with a new fast terminal sliding surface is designed and a composite control strategy is constructed.

[0006] Preferably, the mathematical model of the disturbed frame system in step S1 is as follows:

[0007] in, is the frame angular velocity; They are Axis and The stator current, voltage and inductance of the shaft, where the inductance meets the condition under the surface-mounted permanent magnet synchronous motor drive is the stator resistance; is the magnetic link; is the pole pair number; is the moment of inertia; represents electromagnetic torque; is the rotor unbalance interference torque; is the friction torque; in, Can be modeled as a harmonic signal with a frequency equal to the rotor angular velocity , harmonic order ; Integrate the Stribeck characteristic with the hyperbolic tangent function tanh Characterization is as follows:

[0008] in, and are Coulomb friction torque and maximum static friction torque respectively; represents the Stribeck speed; and are the hyperbolic tangent function tanh and the coefficient of viscous friction respectively; Based on a detailed analysis of multi-source interference and model uncertainty, , Shaft current decoupling, i.e. setting Axis reference current ; Therefore, the mathematical model of the disturbed frame system can be simplified as follows:

[0009] in, is the nominal value of the stator inductance; and are the actual values ​​of flux linkage, stator inductance and stator resistance respectively; are the corresponding parameter perturbations respectively; from this, we can infer that the mismatch interference and matching interference .

[0010] Preferably, in step S2, the mismatch interference It is represented as follows:

[0011] in, and Represent the order of harmonics and polynomials respectively; coefficient matrix , , and , specifically, , , , , and ,in , is the nominal rotor speed, For speed fluctuation; for auxiliary status; Represents unknown external input; Similarly, matching interference The same structure as above can be used, just let and ,in for The auxiliary state of , Bounded and there exists a positive constant Make the condition , is satisfied; in addition, suppose there is an unknown positive constant and Make the condition and Be satisfied.

[0012] Preferably, in step S3, based on and The representation form of two adaptive fixed-time fine disturbance observers are designed as follows:

[0013]

[0014] Among them, the sliding mode term , , , ; Exponential power , , and ,in are odd numbers and ; and is an auxiliary variable; and Respectively represent , and An estimated value of and is the observer gain to be designed; For unknown parameters The adaptive laws are designed as follows:

[0015] Among them, the parameters and is the normal number to be selected.

[0016] Preferably, step S4 comprises: S4.1, introduce speed tracking error variable and , construct the following error system:

[0017] S4.2, to compensate for mismatched interference The new fast terminal sliding surface is designed as follows:

[0018] in, and ; In order to ensure that the error system state can reach the sliding surface under any initial conditions, the following reaching law is constructed:

[0019] Among them, the parameters and ; S4.3, combined with the error system, and the sliding surface Combining the derivation with the above reaching law, the improved fixed-time controller is designed as follows: .

[0020] The beneficial effects of the present invention are as follows: The present invention can effectively compensate for the influence of matched and unmatched multi-source interference, improve the rotation speed tracking accuracy of the system within a fixed time and reduce jitter. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1A flow chart of a fixed-time speed tracking control method for a framework system based on dual disturbance observers is shown.

[0022] Figure 2 A schematic diagram showing the disturbance estimation performance of the fixed-time speed tracking control method for the framework system based on dual disturbance observers.

[0023] Figure 3 Schematic diagram showing constant speed tracking performance comparison.

[0024] Figure 4 Schematic diagram showing comparison of sinusoidal speed tracking performance. DETAILED DESCRIPTION

[0025] In order to explain the present invention more clearly, the present invention is further described below in conjunction with preferred embodiments and drawings. It should be understood by those skilled in the art that the content described below is illustrative rather than restrictive, and should not be used to limit the scope of protection of the present invention.

[0026] The fixed-time speed tracking control method of the framework system based on dual disturbance observers provided in this embodiment is used to compensate for the influence of matched and unmatched multi-source interferences and improve the speed tracking accuracy of the system within a fixed time, such as Figure 1 As shown, the method includes: S1. Detailed analysis of the multi-source interference and model uncertainty of the frame system, and establishment of a mathematical model of the disturbed frame system (it should be noted that, in this embodiment, the frame system is the core actuator of the control torque gyro (CMG), which is mainly responsible for accurately controlling the frame angular motion of the gyro rotor, thereby generating the required output torque).

[0027] Specifically, due to the complex operating environment of the control moment gyro (CMG), the frame system is susceptible to interference such as rotor unbalanced torque, friction torque and parameter uncertainty. Based on these interference factors, the mathematical model of the disturbed frame system is designed as follows: in, is the frame angular velocity; and , and , and They are Axis and The stator current, voltage and inductance of the shaft, where the inductance meets the condition when driven by a surface-mounted permanent magnet synchronous motor (PMSM) ; is the stator resistance; is the magnetic link; is the pole pair number; is the moment of inertia; represents electromagnetic torque; is the rotor unbalance interference torque; is the friction torque; in, Can be modeled as a harmonic signal with a frequency equal to the rotor angular velocity , harmonic order ; Integrate the Stribeck characteristic with the hyperbolic tangent function tanh Characterization is as follows: in, and are Coulomb friction torque and maximum static friction torque respectively; represents the Stribeck speed; and are the coefficients of the hyperbolic tangent function tanh and viscous friction respectively; in addition, under the influence of operating temperature, stator winding current and flux saturation effect, the frame system parameters will change significantly; the above multi-source interference and model uncertainty will affect the tracking accuracy of the frame speed; Based on a detailed analysis of multi-source interference and model uncertainty, , Shaft current decoupling, i.e. setting Axis reference current ; Therefore, the mathematical model of the disturbed frame system can be simplified as follows: in, is the nominal value of the stator inductance; , and are the actual values ​​of flux linkage, stator inductance and stator resistance respectively; , and are the corresponding parameter perturbations respectively; from this, we can infer that the mismatch interference and matching interference .

[0028] S2, considering the rotor speed fluctuation, finely characterizes the matched and mismatched disturbances suffered by the mathematical model of the disturbed frame system.

[0029] Specifically, considering the rotor speed fluctuation and making full use of the prior frequency information of the rotor unbalance disturbance, the mismatch disturbance It is represented as follows: in, and Represent the order of harmonics and polynomials respectively; coefficient matrix , , and , specifically, , , , , and ,in , is the nominal rotor speed, For speed fluctuation; for auxiliary status; Represents unknown external input; Similarly, matching interference The same structure as above can be used, just let and ,in for Assume that , Bounded and there exists a positive constant Make the condition , is satisfied; in addition, suppose there is an unknown positive constant and Make the condition and Be satisfied.

[0030] S3, based on the mathematical model of the disturbed frame system and the interference characterization results, two adaptive fixed-time fine interference observers (AFxTRDO) are designed to estimate the matched interference and the mismatched interference respectively.

[0031] Specifically, based on and The representation form of two adaptive fixed-time fine disturbance observers AFxTRDO are designed as follows: Among them, the sliding mode term , , , ; Exponential power , , and ,in are odd numbers and ; and is an auxiliary variable; and Respectively represent and An estimated value of , and is the observer gain to be designed; For unknown parameters , The adaptive laws are designed as follows: Among them, the parameters and is the normal number to be selected; In this embodiment, the theory of designing disturbance observer is further verified: using the disturbance estimation error As an example, we construct the Lyapunov function , and take its derivative, , ,in Under the condition that it is a positive number, it can be proved that the speed tracking error At a fixed time Converges to 0 and derives the equivalent interference estimation error . Continue to construct the Lyapunov function: in, and ;

[0032] Function To guide, Dynamics, Substituting the adaptive law (7) into In the derivation formula, For Hurwitz, and Under the condition of , it can be deduced that: in, , is a positive constant; parameter and To be designed; According to the fixed time lemma, At a fixed time , Converges to a bounded set; similarly, we only need to make (5) The second AFxTRDO can be designed to estimate , and in , , , and ,in The interference estimation error is a positive constant. The convergence proof of is similar to the above process, and thus the proof is completed.

[0033] S4, combined with the disturbance observation results, an improved fixed-time controller (MFxTC) with a new fast terminal sliding mode surface is designed and a composite control strategy is constructed.

[0034] Step S4 specifically includes: S4.1, introduce speed tracking error variable and , the following error system can be constructed:

[0035] S4.2, to compensate for mismatched interference The new fast terminal sliding surface is designed as follows:

[0036] in, and ; The double power term ensures that the speed tracking error can converge quickly.

[0037] In order to ensure that the error system state can reach the sliding surface under any initial conditions, the following reaching law is constructed: Among them, the parameters and ; S4.3, combined with the error system, and the sliding surface Combining the derivation with the above reaching law, the improved fixed time controller (MFxTC) is designed as follows: In this embodiment, the controller is further verified theoretically by constructing a Lyapunov function: For the system ,in represents the vector field, combined with the reaching law (13) for the function The derivative is , the system is globally asymptotically stable; according to the fixed time correlation lemma, Fixed time stability; for disturbed systems , where the disturbance According to the fixed time correlation lemma, we can deduce At a fixed time Converges to the set ,in and are all positive real numbers; Continue to construct Lyapunov function , for the function Taking the derivative and applying Young's inequality to the derivative formula yields: in, , for At a fixed time The residual set that converges to the inner for At a fixed time The small area that converges within; According to the fixed time theorem, Converges to a bounded set At a fixed time in, , , ,and ; The error system (11) is stable in actual fixed time under any initial state, and the proof is complete.

[0038] Next, in order to verify the effectiveness of the fixed-time speed tracking control method for the frame system based on dual disturbance observers provided in this embodiment, a simulation experiment is carried out using MATLAB and a detailed description is given.

[0039] The framework system model provided in this embodiment comprehensively considers the influence of multi-source interference, parameter perturbation and rotor speed fluctuation on the system servo performance.

[0040] In the simulation experiment, the frame system model parameters are selected as follows: , , , and ; Set the constant reference speed respectively and sinusoidal reference speed The composite controller adopts the method proposed in this invention, in which the parameters of two adaptive fixed-time fine disturbance observers (AFxTRDO) (5) (6) are designed as follows: , , , , , , , , , , , , , ; The parameters of adaptive laws (7) and (8) are designed as , , , ; The parameters of the sliding surface (12) are selected as , , , ; The parameters of the reaching law (13) are selected as , , , ; Case 1 considers only slow-changing interference and sets ; Case 2 Considering multiple sources of interference, set ; Case 3: Considering multi-source interference with vibration frequency offset ,set up 10% parameter , and The uncertainty caused by the perturbation. Based on the above parameters and interference settings, the system simulation is carried out, and the results are as follows Figure 2-Figure 4 As shown. Among them, Figure 2 The interference estimation performance of the proposed method is presented, indicating that the adaptive fixed-time fine interference observer (AFxTRDO) can make full use of the interference frequency information to accurately and quickly estimate the matched and mismatched interferences with low conservatism; Figure 3 A comparison of constant speed tracking performance under different control methods is given, including sliding mode control based on extended state observer (ESO-SMC), improved fixed time control based on extended state observer (ESO-MFxTC), improved fixed time control based on adaptive fixed time disturbance observer (AFxTDO-MFxTC) and the proposed method. It can be seen that the proposed method effectively suppresses high-frequency and its multiplier interference and is insensitive to frequency offset. The system speed can track the reference speed with high precision within a fixed time and has low jitter. The sinusoidal speed tracking performance comparison under the above control methods is as follows: Figure 4 As shown in the figure, it shows that the proposed method enhances the robustness of the system against multi-band interference, and the speed tracking fluctuation is minimized and the convergence time is the shortest. In summary, the fixed-time speed tracking control method based on the framework system with dual disturbance observers can improve the speed tracking accuracy and weaken the chattering within a fixed time.

[0041] The above analysis proves the effectiveness of the fixed-time speed tracking control method for the framework system based on dual disturbance observers provided in this embodiment.

[0042] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not limitations on the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the protection scope of the present invention.

Claims

1. A fixed-time speed tracking control method for a frame system based on dual disturbance observers, characterized in that: The steps include: S1, carefully analyze the multi-source interference and model uncertainty of the frame system, and establish a mathematical model of the disturbed frame system; S2, considering the rotor speed fluctuation, finely characterizes the matched and mismatched disturbances suffered by the mathematical model of the disturbed frame system; S3, based on the mathematical model of the disturbed frame system and the interference characterization results, two adaptive fixed-time fine interference observers are designed to estimate the matching interference and mismatching interference respectively; S4, combined with the disturbance observation results, an improved fixed-time controller with a new fast terminal sliding surface is designed and a composite control strategy is constructed.

2. The method according to claim 1, characterized in that The mathematical model of the disturbed frame system in step S1 is as follows: ， in, is the frame angular velocity; and , and , and They are Axis and The stator current, voltage and inductance of the shaft, where the inductance meets the condition under the surface-mounted permanent magnet synchronous motor drive ; is the stator resistance; is the magnetic link; is the pole pair number; is the moment of inertia; represents electromagnetic torque; is the rotor unbalance interference torque; is the friction torque; in, Can be modeled as a harmonic signal with a frequency equal to the rotor angular velocity , harmonic order ; Integrate the Stribeck characteristic with the hyperbolic tangent function tanh Characterization is as follows: ， in, and are Coulomb friction torque and maximum static friction torque respectively; represents the Stribeck speed; and are the hyperbolic tangent function tanh and the coefficient of viscous friction respectively; Based on a detailed analysis of multi-source interference and model uncertainty, , Shaft current decoupling, i.e. setting Axis reference current ; Therefore, the mathematical model of the disturbed frame system can be simplified as follows: ， in, is the nominal value of the stator inductance; , and are the actual values ​​of flux linkage, stator inductance and stator resistance respectively; , and are the corresponding parameter perturbations respectively; thus, the mismatch interference is deduced and matching interference .

3. The fixed time speed tracking control method of the frame system based on dual disturbance observer according to claim 2 is characterized in that: In step S2, the rotor speed fluctuation is considered, and the mismatch interference It is represented as follows: ， in, and Represent the order of harmonics and polynomials respectively; coefficient matrix , , and , specifically, , , , , and ,in , is the nominal rotor speed, For speed fluctuation; for auxiliary status; Represents unknown external input; Similarly, matching interference The same structure as above can be used, just let and ,in for The auxiliary state of , Bounded and there exists a positive constant Make the condition , is satisfied; in addition, suppose there is an unknown positive constant and Make the condition and Be satisfied.

4. The method according to claim 3, characterized in that: In step S3, based on and The representation form of two adaptive fixed-time fine disturbance observers are designed as follows: ， ， Among them, the sliding mode term , , , ; Exponential power , , and ,in , , , are odd numbers and , ; and is an auxiliary variable; , , , , , , and Respectively represent , , , , , , and An estimated value of , and is the observer gain to be designed; For unknown parameters , The adaptive laws are designed as follows: ， Among them, the parameters is the normal number to be selected.

5. The method according to claim 4, characterized in that Step S4 includes: S4.1, introduce speed tracking error variable and , construct the following error system: ， S4.2, to compensate for mismatched interference The new fast terminal sliding surface is designed as follows: ， in, and ; In order to ensure that the error system state can reach the sliding surface under any initial conditions, the following reaching law is constructed: ， Among them, the parameters and ; S4.3, combined with the error system, and the sliding surface Combining the derivation with the above reaching law, the improved fixed-time controller is designed as follows: 。

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