Four-motor synchronous drive servo system partial failure fault-tolerant control method and system based on current observer

Abstract

The present application belongs to the technical field of fault-tolerant control of multi-motor servo system, and specifically discloses a four-motor synchronous drive servo system partial failure fault-tolerant control method and system based on a current observer. The present application designs a current observer for the fault-tolerant control problem of the four-motor servo system under the condition of actuator partial failure, which is used to observe the effective coefficient and current of each motor to determine the working state of the motor. A command filter is used to process the calculation complexity and reduce the calculation burden in the backstepping design process. A speed synchronization and torque balance signal is designed to ensure that each motor can maintain high synchronization performance after failure. The four-motor synchronous drive servo system partial failure fault-tolerant control method disclosed in the present application can ensure that even if there is a failure, the four-motor system can accurately track the given angular position under the premise of ensuring synchronization performance.

Description

Technical Field

[0001] This invention belongs to the field of fault-tolerant control technology for multi-motor servo systems, and specifically relates to a partial failure-tolerant control method and system for a four-motor synchronous drive servo system based on a current observer. Background Technology

[0002] To address the issues of insufficient power and limited inertia in single-motor systems, more and more scholars are focusing on multi-motor drive systems. Multi-motor synchronous drive systems have gained widespread application due to their ability to drive large loads and guarantee high tracking accuracy. The requirement for reliable and stable operation of four-motor systems has spurred research into fault-tolerant control of actuators. After prolonged use, especially with frequent start / stop and forward / reverse operations, actuators inevitably face wear and performance degradation, reducing the reliability of the four-motor system and leading to a decline in tracking performance. This phenomenon also exists in four-motor servo systems. However, due to the hardware redundancy of four-motor systems, when one motor fails, the tracking performance of the entire system can be maintained through the coordinated control of the other motors. Redundancy provides a possibility for resolving partial failure issues.

[0003] Command filtering backstepping has received widespread attention as a controller design method. Traditional backstepping methods suffer from computational complexity explosion when dealing with repeated derivatives. To mitigate this explosion, command filtering backstepping technology has been widely applied in single-motor systems, dual-motor servo systems, and robotic systems. To address actuator failures and load disturbances in single-motor systems, a discrete-time command filter control method is proposed. Applying this method to a dual-motor servo system with LuGre friction and torque disturbances achieves load tracking and synchronization in a four-motor system. Furthermore, command filtering technology is also widely used in robotic arm systems and typical nonlinear systems. Although many researchers have conducted extensive studies in these areas, command filtering has not yet been applied to fault-tolerant control of multi-motor synchronous drive servo systems. Summary of the Invention

[0004] The purpose of this invention is to propose a fault-tolerant control method for a four-motor synchronous drive servo system based on a current observer. This method ensures that even when a partial failure occurs in a multi-motor synchronous drive servo system, the four-motor system can still accurately track a given angular position while maintaining synchronization performance.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A partial failure-tolerant control method for a four-motor synchronous drive servo system based on a current observer includes the following steps:

[0007] Step 1. Establish a model of the four-motor servo system and obtain the state-space expression of the four-motor system;

[0008] Step 2. Use a current observer as a fault detection link to realize current observation and failure factor estimation; use the command filtering backstepping method to design a fault-tolerant controller for the four-motor system under partial failure faults;

[0009] A filtering error compensation subsystem is employed to eliminate errors caused by using command filtering;

[0010] Step 3. Perform stability analysis on the constructed fault-tolerant controller, taking into account the stability of the current observer, to prove that both the four-motor system and the current observer satisfy Lyapunov stability.

[0011] Step 4. Use a fault-tolerant controller to implement fault-tolerant control for partial failures in the four-motor synchronous drive servo system.

[0012] Furthermore, based on the aforementioned fault-tolerant control method, this invention also proposes a corresponding fault-tolerant control system for a four-motor synchronous drive servo system based on a current observer, which adopts the following technical solution:

[0013] A partially fault-tolerant control system for a four-motor synchronous drive servo system based on a current observer includes:

[0014] The four-motor system model building module establishes a model of the four-motor servo system and obtains the state-space expression of the four-motor system.

[0015] The controller design module utilizes a current observer as a fault detection element to achieve current observation and failure factor estimation; a fault-tolerant controller for a four-motor system under partial failure faults is designed using the command filtering backstepping method.

[0016] A filtering error compensation subsystem is employed to eliminate errors caused by using command filtering;

[0017] The controller stability analysis module is used to perform stability analysis on the constructed fault-tolerant controller, while also considering the stability of the current observer, to prove that both the four-motor system and the current observer satisfy Lyapunov stability.

[0018] And a fault-tolerant control module, used to implement fault-tolerant control for partial failures of the four-motor synchronous drive servo system.

[0019] Furthermore, based on the aforementioned fault-tolerant control method for a four-motor synchronous drive servo system based on a current observer, this invention also proposes a computer device comprising a memory and one or more processors.

[0020] The memory stores executable code, and when the processor executes the executable code, it implements the steps of the above-mentioned fault-tolerant control method for a four-motor synchronous drive servo system based on a current observer.

[0021] Furthermore, based on the aforementioned fault-tolerant control method for a four-motor synchronous drive servo system based on a current observer, this invention also proposes a computer-readable storage medium on which a program is stored.

[0022] When executed by the processor, this program implements the steps of the above-mentioned fault-tolerant control method for a four-motor synchronous drive servo system based on a current observer.

[0023] The present invention has the following advantages:

[0024] (1) In a four-motor synchronous drive servo system, this invention proposes a fault-tolerant control method based on command filtering backstepping in the case of actuator failure. This method can effectively deal with the failure caused by long-term use of the actuator and reduce the harm to the production process caused by the failure.

[0025] (2) In order to solve the problem of partial failure and to diagnose and estimate the degree of failure when a failure occurs, the present invention designs a method based on current observation technology. This method realizes fault diagnosis and degree estimation by estimating the failure factors in the four-motor system. Specifically, the method infers whether there is a failure in the four-motor system in real time based on the detection results, and can also accurately estimate the degree of failure, so that the four-motor system can achieve more reliable and safer operation.

[0026] (3) Based on considerations for the operation of the servo system, this invention optimizes the speed synchronization and torque balance signals between the four motors. While ensuring the stability of the four-motor system, it improves the efficiency and accuracy of the four-motor system by enhancing synchronization performance. Specifically, this invention makes the speed and torque signals between the four motors more balanced, enabling them to better cooperate and coordinate during the operation of the four-motor system, thereby ensuring that the operation of the entire four-motor system is more stable and efficient. Attached Figure Description

[0027] Figure 1 This is a flowchart of a partial failure-tolerant control method for a four-motor synchronous drive servo system in an embodiment of the present invention.

[0028] Figure 2 This is a control diagram of a four-motor synchronous servo system in an embodiment of the present invention.

[0029] Figure 3 This is a load position diagram under sinusoidal signal input after adopting the control method of the present invention.

[0030] Figure 4 This is a diagram showing the load position tracking error after adopting the control method of the present invention.

[0031] Figure 5 This is a diagram showing the positions of the four motors after adopting the control method of this invention.

[0032] Figure 6 This is a diagram showing the angular positions of the four motors in the PLOE and FTC mode switching areas.

[0033] Figure 7 The diagram shows the rotational speeds of the four motors after adopting the control method of this invention.

[0034] Figure 8 This is a speed diagram of the four motors in the PLOE and FTC mode switching zone.

[0035] Figure 9 The diagram shows the speed synchronization error between the two sets of motors and between the sets after adopting the control method of the present invention. Detailed Implementation

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0037] Example 1

[0038] This embodiment 1 proposes a fault-tolerant control method for a four-motor synchronous drive servo system with partial actuator failure, based on a current observer. Addressing the fault-tolerant control problem of a four-motor servo system under partial actuator failure, this method designs a current observer to observe the effective coefficient and current of each motor to determine the motor's operating state. A command filter is used to handle computational complexity, reducing the computational burden in the reverse design process. Speed ​​synchronization and torque balance signals are designed to ensure that each motor maintains high synchronization performance after a failure occurs.

[0039] like Figure 1 As shown, a partial failure-tolerant control method for a four-motor synchronous drive servo system based on a current observer includes the following steps:

[0040] Step 1. Establish a model of the four-motor servo system and obtain the state-space expression of the four-motor system.

[0041] A model of a four-motor servo system is established, as shown in formula (1);

[0042]

[0043] Where the subscript j represents the j-th motor, j = 1, 2, 3, 4;

[0044] θ mω represents the load angle position. m J is the load angular velocity. m For load inertia, b m The coefficient of viscous friction under load;

[0045] u sqj i sqj R sj L sqj θ cj ω j C Tj C ej J j These represent the control voltage, input current, resistance, inductance, angular position, angular velocity, equivalent torque coefficient, back electromotive force coefficient, and moment of inertia applied to the j-th motor, respectively.

[0046] r m k is the reduction ratio between the motor and the load. cmj This represents the elasticity coefficient between the j-th motor and the load;

[0047] β j This represents the failure factor of the j-th motor actuator;

[0048] β j The range of values ​​is 0 ≤ β j ≤1, when β j =0 represents a complete actuator failure, when β j =1 indicates that the actuator is fault-free.

[0049] For ease of derivation, the following state variables are selected:

[0050]

[0051] Combining formulas (1) and (2), the state-space expression of the four-motor system is expressed as:

[0052]

[0053] Where y represents the output of the four-motor system, i.e., the load angle position;

[0054]

[0055]

[0056] Step 2. Use a current observer as a fault detection link to realize current observation and failure factor estimation; use the command filtering backstepping method to design a fault-tolerant controller for the four-motor system under partial failure faults.

[0057] In addition, a filtering error compensation subsystem is employed to eliminate errors caused by using command filtering.

[0058] Define y d This indicates the given position tracked by the four-motor system.

[0059] For the controller design of a four-motor system under abnormal operating conditions, it is necessary to meet the following requirements. and It is continuous, smooth, and bounded, and It is also bounded, and the state variables in the four-motor system are observable.

[0060] Each failure factor β j The values ​​are not all zero at the same time, meaning that the four motor drivers do not fail completely at the same time, j = 1, 2, 3, 4.

[0061] Define the following command filter:

[0062]

[0063] α w Let φ0 represent the input of the command filter, and φ1 represent the output of the command filter. When t ≥ 0, the initial condition that the input signal should satisfy is: φ1=α w =0, φ2=0 and δ1, δ2 are positive numbers; w=1,2,3,4 j 5 j ;

[0064] Wherein, φ1(0), α w (0) and φ2(0) represent φ1 and α respectively. w And the initial value of φ2;

[0065] For any μ > 0, the parameter ω n >0, ζ∈(0,1) satisfies |φ1-α w |≤μ.

[0066] Step 2.1. Design a current observer to detect faults and detect the fault status of the motor.

[0067] For this four-motor system, the following current observer is designed to realize the observation of motor current and the estimation of fault coefficient.

[0068]

[0069] in, This represents the observed value of the motor current obtained through the current observer.

[0070] Indicates the estimated failure factor value, l 1j Indicates control parameters; current error Defined as:

[0071]

[0072] Step 2.2. Design a fault-tolerant controller for actuator partial failure.

[0073] The tracking error of the four-motor system state is defined as shown in formula (7):

[0074]

[0075] Among them, y d This indicates the given position tracked by the four-motor system; e1, e2, e3, e4, and e5 represent the error amounts in each step of the backstepping design process; x ia,c It is the output of the virtual control signal after passing through the command filter, i a =2,3,4 j 5 j j = 1, 2, 3, 4.

[0076] e 41 e 42 e 43 e 44 These represent the error amounts of the first, second, third, and fourth motors in step 2.6, respectively. 51 e 52 e 53 e 54 These represent the error amounts of the first, second, third, and fourth motors in step 2.7, respectively.

[0077] x 4j,c Select the desired tracking signal. Ensure that all four motors maintain the same speed to drive the load.

[0078] Design a synchronization error signal to ensure the synchronization performance between the motors in the four-motor system, as shown in formula (8).

[0079]

[0080] The first and second motors are defined as the first group of motors, and the third and fourth motors are defined as the second group of motors.

[0081] Among them, e s1 e s2 These represent the speed synchronization errors between the first group of motors and the second group of motors, respectively; e s3 This indicates the speed synchronization error between the first group of motors and the second group of motors; e T1 e T2 These represent the torque balance errors between the first group of motors and the second group of motors, respectively; e T3This represents the torque balance error between the first group of motors and the second group of motors.

[0082] The compensation error for the tracking signal is defined as:

[0083]

[0084] Among them, v i This indicates the compensation error of the tracking signal. It is the filter error compensation signal, i = 1, 2, 3, 4, 5.

[0085] Step 2.3. Define the Lyapunov function:

[0086]

[0087] Combining formulas (3), (7), and (9), the time derivative of V1 is:

[0088]

[0089] Select the virtual control signal α1 and the error compensation signal. for:

[0090]

[0091] Where c1 represents the control parameter for this step in the backstep design process; substituting formula (12) into formula (11), we get:

[0092]

[0093] Step 2.4. Construct the Lyapunov function V2 as follows:

[0094]

[0095] Considering formulas (3), (7) and (9), the derivative of formula (14) is:

[0096]

[0097] The virtual control signal α2 and the filter error signal Designed as follows:

[0098]

[0099] Where c2 represents the control parameter for this step in the backstep design process; α2 and Substituting into formula (15), we get:

[0100]

[0101] Step 2.5. Consider the Lyapunov function V3 as follows:

[0102]

[0103] The derivative of V3 with respect to time is:

[0104]

[0105] The virtual control signal α3 and the filter error signal Designed as follows:

[0106]

[0107] Where c3 represents the control parameter for this step in the backstep design process; combining formulas (19) and (20), we get:

[0108]

[0109] Step 2.6. Select a suitable Lyapunov function V4 as follows:

[0110]

[0111] Then the time derivative of V4 is:

[0112]

[0113] Where, α 4j This refers to the virtual control signal introduced in step 2.6.

[0114] Considering the synchronization between motors, the virtual control signals are divided into two groups, designed as follows:

[0115]

[0116] in,

[0117] c4 represents the control parameter for this step in the backstep design process; combined with α 4j , From formula (23), we get:

[0118]

[0119] Step 2.7. Select Lyapunov function V5 as:

[0120]

[0121] Then the time derivative of V5 is:

[0122]

[0123] Considering the fault factors that occur in formula (27), the actual control law and error compensation signal as shown in formula (28) are designed to ensure the stability of the four-motor servo system.

[0124]

[0125] Where c5 represents the control parameter for this step in the backstep design process.

[0126] α uj This represents the actual control signal for the j-th motor; k T1 k T2 k T3 Control parameters representing torque balance signals.

[0127] γ j =λ 11 k cmj λ 2j λ 4j (29)

[0128] The input design for the four-motor system is as follows:

[0129]

[0130] Where j = 1, 2, 3, 4, the failure factor error Defined as:

[0131]

[0132] Where j = 1, 2, 3, 4; the adaptive update law for the design failure factor is as follows:

[0133]

[0134] Among them, a j It is the gain coefficient, a j >0; P j This represents the adaptive parameter in the adaptive law.

[0135] Based on the nature of the estimation error expressed in formula (31), V5 is simplified to:

[0136]

[0137] Based on the above design process, the filtering error compensation subsystem is as follows:

[0138]

[0139] The design of the fault-tolerant controller under the condition of partial actuator failure is completed. The controller is designed as shown in Equation (30), and the compensation subsystem is shown in Equation (34). When the controller given by Equation (30) and the current observer given by Equation (5) are used, the four motors can achieve stable tracking of the load under the condition of partial actuator failure. Moreover, the designed synchronization signal can better cooperate and coordinate with each other when the four motor system is running, thereby ensuring the stable and efficient operation of the four motor system.

[0140] Step 3. Perform stability analysis on the constructed fault-tolerant controller, taking into account the stability of the current observer, to prove that both the four-motor system and the current observer satisfy Lyapunov stability.

[0141] For the four-motor servo system in formula (1), based on the command filter in formula (4), if the control signal u in formula (30) is selected... sqj The error compensation signal in formula (34), the current observer in formula (5), and the adaptive law of the failure factor in formula (32) then the tracking error e1 and all synchronization error states e s1 e s2 e s3 e T1 e T2 e T3 It can converge to the expected small neighborhood of the origin; after a fault occurs, all signals in the closed-loop system are bounded.

[0142] In a four-motor synchronous drive system, the synchronization performance of the four-motor system and the stability of the current observer are demonstrated.

[0143] The total Lyapunov function is designed as follows:

[0144]

[0145] Among them, a j Let represent the gain coefficient, then the time derivative of formula (35) is:

[0146]

[0147] Calling formulas (3), (5), and (32) will yield the following formula:

[0148]

[0149] Considering the synchronization performance index of a four-motor system, combining formulas (3), (7), and (8) yields the following equation:

[0150]

[0151] Where, α42 α represents the virtual control signal for the second motor introduced in step 2.6. 41 The virtual control signal for the first motor introduced in step 2.6 is represented by the following inequality:

[0152]

[0153] Where, ε 11 ε 12 ε 13 This indicates a bounded quantity; the speed synchronization error is expressed as:

[0154]

[0155] From formulas (3), (7) and (8), we get:

[0156]

[0157] Based on formulas (33), (37), (40), (41) and Young's inequality, formula (36) is obtained:

[0158]

[0159] Define the following variables:

[0160]

[0161]

[0162]

[0163] Therefore, through equation (42), the designed fault-tolerant controller satisfies the stability in the Lyapunov sense, that is, the control output signal can stably track the control input signal, which meets the requirements of the four-motor servo system.

[0164] Step 4. Use a fault-tolerant controller to implement fault-tolerant control for partial failures in the four-motor synchronous drive servo system.

[0165] Step 4 specifically involves the following steps: After a partial failure occurs in the actuator of the four-motor servo system, the failure factor changes. Fault diagnosis is performed using a current observer to obtain the observed values ​​of the current and failure factor. Then, the control law of the four-motor servo system is reconstructed to enable the four motors to drive the load to accurately track the given signal and have good synchronization performance.

[0166] This invention facilitates position tracking control of a four-motor servo system.

[0167] like Figure 2The diagram shows a composite controlled object consisting of a four-motor synchronous drive servo system based on a current observer, a speed controller, a position controller, a current controller, and an SVPWM inverter, as described in this invention.

[0168] The AC permanent magnet synchronous motor serves as the actuator in the four-motor system. A non-contact multi-pole dual-channel rotary transformer is selected as the load angular position detection sensor to detect the angular positions θ1, θ2, θ3, and θ4 of the four motors.

[0169] The obtained motor angular position and the given signal y d After the difference is calculated, it is input to the position controller.

[0170] In the speed loop, the motor rotary transformer measures the angular position of the motor rotor, and after differential and filtering processing, the motor speed feedback ω1, ω2, ω3, ω4 are obtained, which are compared with the given motor speed. The difference is calculated, and the motor quadrature-axis current is obtained through the speed controller.

[0171] At the same time, according to the vector control method, I is adopted. d =0 control strategy, Set it to 0.

[0172] In the fault detection section, the current observer can be used to observe the motor current and estimate the failure factor of the actuator.

[0173] Observations obtained from the observer Used for designing fault-tolerant controllers.

[0174] The current observations are processed to obtain a current control signal, which is then converted into a PWM signal by an SVPWM inverter and input to a three-phase inverter to obtain the permanent magnet synchronous motor input voltage u. sq1 ,u sq2 ,u sq3 ,u sq4 This enables motor feedback control.

[0175] The following simulation of the proposed fault-tolerant control method for a four-motor synchronous drive servo system based on a current observer in a virtual environment verifies the feasibility of the proposed control method:

[0176] Motor parameters:

[0177] J j =0.80352 kg·m 2 C Tj = 0.641 N·m / A, L sqj =0.0375H, R sj =1.3Ω, C ej=64.17V / rad (j=1,2,3,4).

[0178] Load parameters: J m =20kg·m 2 b m = 0.5 N·m·s / rad, r m =8.5.

[0179] The remaining parameters are as follows: c1 = 500, c2 = 800, c3 = 500, c4 = 300, c5 = 400; k cm1 =k cm2 =k cm3 =k cm4 =10,k cm =40,k s1 =0.15,k s2 =0.17,k s3 =0.11, k T1 =0.16,k T2 =0.2,k T3 =0.2; ω n =10 4 , ζ=0.8, a1=a2=a3=a4=10.

[0180] Figures 3 to 9 The effects of the method of the present invention are demonstrated, wherein:

[0181] Figure 3 This shows how the load position tracks the given signal relative to the given signal.

[0182] Depend on Figure 3 It can be seen that when a partial actuator failure occurs before 5 seconds without fault tolerance, the load position tracking effect of the given signal is poor. After implementing fault-tolerant control, the load tracking accuracy is effectively improved.

[0183] Figure 4 The load position tracking error reflects the tracking performance of the four-motor system.

[0184] Depend on Figure 4 It can be seen that once fault-tolerant control is implemented, the tracking error of the four-motor system is reduced and the tracking performance is enhanced.

[0185] Figures 5 to 8 The figures show the angular positions and angular velocities of the four motors in two different scenarios, with the transition phase highlighted. Figures 5 to 8 It can be seen that the angular position and angular velocity information of the four motors after the fault occurred and after fault-tolerant control was implemented were obtained, and the indicators during the transition phase were magnified for observation. Among them, Figures 5 to 8Motor 1, Motor 2, Motor 3 and Motor 4 represent the first motor, the second motor, the third motor and the fourth motor, respectively.

[0186] Figure 9 This represents the speed synchronization error between the two groups of motors and between groups. Group 1 refers to the first group of motors, consisting of motor 1 and motor 2, and Group 2 refers to the second group of motors, consisting of motor 3 and motor 4.

[0187] from Figure 9 It can be seen that after implementing fault-tolerant control on the four-motor servo system, the speed synchronization error and inter-group error of the motors have been reduced, and the fault-tolerant method has achieved positive results. This invention has practical significance.

[0188] Example 2

[0189] This embodiment 2 describes a fault-tolerant control system for partial failure of a four-motor synchronous drive servo system based on a current observer, which is based on the same inventive concept as the fault-tolerant control method in embodiment 1 above.

[0190] Partial fault-tolerant control of a four-motor synchronous drive servo system based on a current observer, including:

[0191] The four-motor system model building module is used to build a model of a four-motor servo system and obtain the state-space expression of the four-motor system.

[0192] The controller design module utilizes a current observer as a fault detection element to achieve current observation and failure factor estimation; a fault-tolerant controller for a four-motor system under partial failure faults is designed using the command filtering backstepping method.

[0193] A filtering error compensation subsystem is employed to eliminate errors caused by using command filtering;

[0194] The controller stability analysis module is used to perform stability analysis on the constructed fault-tolerant controller, while also considering the stability of the current observer, to prove that both the four-motor system and the current observer satisfy Lyapunov stability.

[0195] And a fault-tolerant control module, used to implement fault-tolerant control for partial failures of the four-motor synchronous drive servo system.

[0196] It should be noted that, in this embodiment, the implementation process of the functions and roles of each functional module in the four-motor fault-tolerant control system is detailed in the implementation process of the corresponding steps in the method of the above embodiment 1, and will not be repeated here.

[0197] Example 3

[0198] This embodiment 3 describes a computer device that includes a memory and one or more processors.

[0199] The memory stores executable code, which, when executed by the processor, is used to implement the steps of the fault-tolerant control method for the four-motor synchronous drive servo system in Embodiment 1 above.

[0200] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0201] Example 4

[0202] This embodiment 4 describes a computer-readable storage medium on which a program is stored. When executed by a processor, the program is used to implement the steps of the partial failure-tolerant control method for the four-motor synchronous drive servo system in embodiment 1 above.

[0203] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0204] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A partial failure-tolerant fault control method for a four-motor synchronous drive servo system based on a current observer. Its features are, Includes the following steps: Step 1. Establish a model of the four-motor servo system and obtain the state-space expression of the four-motor system; Step 2. Use a current observer as a fault detection link to achieve current observation and failure factor estimation; use the command filtering backstepping method to design a fault-tolerant controller for the four-motor system under partial failure faults; A filtering error compensation subsystem is employed to eliminate errors caused by using command filtering; For this four-motor system, the following current observer is designed to realize the observation of motor current and the estimation of fault coefficient; （5） in, This represents the observed value of the motor current obtained through the current observer; This represents the estimated failure factor. Indicates control parameters; , , , , , They respectively represent the application to the first The control voltage, input current, resistance, inductance, angular velocity, and back electromotive force coefficient of the motor; For current error; ， ， ； ； Current error Defined as: （6） Step 3. Perform stability analysis on the constructed fault-tolerant controller, taking into account the stability of the current observer, to prove that both the four-motor system and the current observer satisfy Lyapunov stability. Step 4. Implement fault-tolerant control for partial failures in the four-motor synchronous drive servo system using a fault-tolerant controller.

2. The partial failure-tolerant fault control method for a four-motor synchronous drive servo system according to claim 1, characterized in that, Step 1 specifically involves: A model of a four-motor servo system is established, as shown in formula (1); （1） Where the subscript j represents the j-th motor, ; The load angle position, For the load angular velocity, For load inertia, The coefficient of viscous friction under load; , , They respectively represent the application to the first The angular position, equivalent torque coefficient, and moment of inertia of the motor; This is the reduction ratio between the motor and the load. Indicates the first The elasticity coefficient between the motor and the load; Indicates the first Failure factors of the trolley motor actuator; for ease of derivation, the following state variables are selected: （2） Combining formulas (1) and (2), the state-space expression of the four-motor system is expressed as: （3） in, This indicates the output of the four-motor system, i.e., the load angle position. , , , , , , , .

3. The partial failure-tolerant control method for a four-motor synchronous drive servo system according to claim 2, characterized in that, Step 2 specifically involves: Define the following command filter: (4) This indicates the input to the command filter. Indicates the output of the command filter; when When the input signal meets the initial condition, it should be: , ; , and , It is a positive number; ; in, , as well as They represent , as well as The initial value; For any ,parameter , satisfy ; Step 2.

1. Design a current observer for fault detection to detect the fault status of the motor; For this four-motor system, the following current observer is designed to realize the observation of motor current and the estimation of fault coefficient, as shown in formula (5) and formula (6); Step 2.

2. Design a fault-tolerant controller for actuator partial failure; The tracking error of the four-motor system state is defined as shown in formula (7): （7） in, This indicates the given position tracked by the four-motor system; , , , , These represent the error amounts in each step of the backstepping design process; It is the output of the virtual control signal after passing through the command filter. , ; , , , These represent the error amounts of the first, second, third, and fourth motors in step 2.6, respectively. , , , These represent the error amounts of the first, second, third, and fourth motors in step 2.7, respectively. Select the desired tracking signal. This ensures that all four motors maintain the same speed to drive the load. Design a synchronization error signal to ensure the synchronization performance between the motors in the four-motor system, as shown in formula (8); （8） The first and second motors are defined as the first group of motors, and the third and fourth motors are defined as the second group of motors. , These represent the speed synchronization error between the first group of motors and the second group of motors, respectively. This indicates the speed synchronization error between the first group of motors and the second group of motors; , These represent the torque balance error between the first group of motors and the second group of motors, respectively. This represents the torque balance error between the first group of motors and the second group of motors. The compensation error for the tracking signal is defined as: （9） in, This indicates the compensation error of the tracking signal. It is a filtering error compensation signal. ; Step 2.

3. Definition function: (10) Combining formulas (3), (7) and (9), then The time derivative is: (11) Select virtual control signal and error compensation signal for: (12) in, This represents the control parameter for this step in the backstep design process; substituting formula (12) into formula (11), we get: (13) Step 2.

4. Construction function for: (14) Considering formulas (3), (7) and (9), the derivative of formula (14) is: (15) virtual control signal and filter error signal Designed as follows: （16） in, This indicates the control parameters for this step in the backstep design process; and Substituting into formula (15), we get: (17) Step 2.

5. Consider function for: （18） The derivative with respect to time is: （19） virtual control signal and filter error signal Designed as follows: （20） in, This represents the control parameters for this step in the backstep design process; combining formulas (19) and (20), we get: （21） Step 2.

6. Select the appropriate function for: （22） but The time derivative is: （23） in, This refers to the virtual control signal introduced in step 2.6; Considering the synchronization between motors, the virtual control signals are divided into two groups, designed as follows: (24) in, ; This indicates the control parameters for this step in the backstep design process; combined with , From formula (23), we get: （25） Step 2.

7. Select function for: （26） but The time derivative is: （27） Considering the fault factors that appear in formula (27), the real control law and error compensation signal as shown in formula (28) are designed to ensure the stability of the four-motor servo system. (28) in, This indicates the control parameters for this step in the backstep design process; Indicates the first The actual control signal of the motor; , , Control parameters representing torque balance signals; （29） The input design for the four-motor system is as follows: （30） in, Failure factor error Defined as: （31） in, The adaptive update law for the design failure factor is as follows: （32） in, It is the gain coefficient. ; This represents the adaptive parameter in the adaptive law; Based on the nature of the estimation error expressed in formula (31), Simplified to: (33) Based on the above design process, the filtering error compensation subsystem is as follows: (34) The design of the fault-tolerant controller under the condition of partial actuator failure is completed. The controller is designed as shown in Equation (30), and the compensation subsystem is shown in Equation (34). When the controller given by Equation (30) and the current observer given by Equation (5) are used, the four motors can achieve stable tracking of the load under the condition of partial actuator failure. Furthermore, the designed synchronization signal can better cooperate and coordinate with each other when the four motor system is running, ensuring the stable and efficient operation of the four motor system.

4. The partial failure-tolerant fault control method for a four-motor synchronous drive servo system according to claim 3, characterized in that, Step 3 specifically involves: In a four-motor synchronous drive system, proof is provided considering the synchronization performance of the four-motor system and the stability of the current observer. The total Lyapunov function is designed as follows: （35） The time derivative of formula (35) is: （36） Calling formulas (3), (5), and (32) will yield the following formula: （37） Considering the synchronization performance index of a four-motor system, combining formulas (3), (7), and (8) yields the following equation: （38） in, This represents the virtual control signal for the second motor introduced in step 2.

6. The virtual control signal for the first motor introduced in step 2.6 is represented by the following inequality: （39） in, , , This indicates a bounded quantity; the speed synchronization error is expressed as: （40） From formulas (3), (7) and (8), we get: (41) According to formulas (33), (37), (40), (41) and Young's inequality, formula (36) is obtained: （42） Define the following variables: ； ； ； Therefore, through equation (42), the designed fault-tolerant controller satisfies the stability in the Lyapunov sense, that is, the control output signal can stably track the control input signal, which meets the requirements of the four-motor servo system.

5. The partial failure-tolerant control method for a four-motor synchronous drive servo system according to claim 2, characterized in that, In step 1, The range of values ​​is ; when This indicates a complete actuator failure, when This indicates that the actuator is fault-free.

6. The partial failure-tolerant control method for a four-motor synchronous drive servo system according to claim 1, characterized in that, Step 4 specifically involves the following steps: After a partial failure occurs in the actuator of the four-motor servo system, the failure factor changes. The current and failure factor are obtained through fault diagnosis using a current observer. Then, the control law of the four-motor system is reconstructed to enable the four-motor drive load to accurately track the given signal and achieve good synchronization performance.

7. The partial failure-tolerant fault control method for a four-motor synchronous drive servo system according to claim 1, characterized in that, The fault-tolerant control method for partial failure of the four-motor synchronous drive servo system is applied to the position tracking control of the four-motor synchronous drive servo system.

8. A partially fault-tolerant control system for a four-motor synchronous drive servo system based on a current observer, characterized in that, Includes the following functional modules: The four-motor system model building module is used to build a model of a four-motor servo system and obtain the state-space expression of the four-motor system. The controller design module utilizes a current observer as a fault detection component to achieve current observation and failure factor estimation. Design a fault-tolerant controller for a four-motor system under partial failure faults using command filtering backstepping method; A filtering error compensation subsystem is employed to eliminate errors caused by using command filtering; The controller stability analysis module is used to perform stability analysis on the constructed fault-tolerant controller, while also considering the stability of the current observer, to prove that both the four-motor system and the current observer satisfy Lyapunov stability. And a fault-tolerant control module, used to implement fault-tolerant control for partial failures of the four-motor synchronous drive servo system.

9. A computer device comprising a memory and one or more processors; said memory storing executable code, characterized in that, When the processor executes the executable code, it implements the steps of the partial failure-tolerant control method for a four-motor synchronous drive servo system as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a program stored thereon; characterized in that, When the program is executed by the processor, it is used to implement the steps of the partial failure-tolerant control method for the four-motor synchronous drive servo system as described in any one of claims 1 to 7.

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