A gain-balanced fault-tolerant control method for redundantly driven multi-degree-of-freedom motion table

Abstract

This invention discloses a gain-balanced fault-tolerant control method for a redundant-driven multi-degree-of-freedom motion table. The method designs corresponding output decoupling matrices for the case of complete failure of any actuator in the redundant-driven multi-degree-of-freedom motion table. These matrices can be switched via a gain balancing module when an actuator fails, thus controlling the logic axis control signal u after the complete failure of a single actuator. cor Reassigning to the remaining actuators produces the same output as before the failure. act This method ensures that the motion table system P can still track the reference position signal r, significantly improving the reliability and fault tolerance of the redundantly driven multi-degree-of-freedom motion table system. This method not only achieves good motion control and high tracking accuracy when the actuators are fault-free, but also provides good fault-tolerant control even when a single actuator of the redundantly driven multi-degree-of-freedom motion table completely fails, guaranteeing the closed-loop stability and tracking accuracy of the motion table system.

Description

Technical Field

[0001] This invention belongs to the field of ultra-precision equipment manufacturing and relates to a gain-balanced fault-tolerant control method for redundant-driven multi-degree-of-freedom motion stages. Background Technology

[0002] my country is a major manufacturing country, but it still lags behind the highest levels of foreign countries in the field of ultra-precision high-end equipment manufacturing. Multi-degree-of-freedom motion stages are key components of high-end manufacturing equipment such as lithography machines and 3D printers, and their performance directly determines the quality and yield of the manufactured products. Generally, multi-degree-of-freedom motion stages have strict requirements for reliability and availability. If production is interrupted or product quality fails due to internal component failure, it will cause serious economic losses.

[0003] During operation, multi-degree-of-freedom motion tables may experience reduced transmission stiffness and output fluctuations due to frictional losses in the moving pairs; demagnetization of permanent magnets, winding losses and insulation failures; disruption of air gap uniformity; or operation under overload or off-design conditions. These factors can lead to actuator output degradation or even complete failure. Such actuator failures significantly reduce the tracking accuracy of the multi-degree-of-freedom motion table, necessitating the design of corresponding fault-tolerant control schemes to mitigate them. Multi-degree-of-freedom motion table control systems typically employ feedforward-feedback composite controllers. However, these control schemes lack fault-tolerant control capabilities and cannot guarantee closed-loop system stability and tracking accuracy in the event of actuator failure. Summary of the Invention

[0004] To address the problem of closed-loop system instability and inability to continue tracking the reference trajectory in a multi-degree-of-freedom motion table after the complete failure of an actuator during operation, this invention provides a gain-balanced fault-tolerant control method for a redundantly driven multi-degree-of-freedom motion table. This method not only achieves good motion control and high tracking accuracy when the actuator is fault-free, but also provides good fault-tolerant control even when a single actuator of the redundantly driven multi-degree-of-freedom motion table completely fails, ensuring the closed-loop stability and tracking accuracy of the motion table system.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A gain-balanced fault-tolerant control method for a redundantly driven multi-degree-of-freedom motion stage includes the following steps:

[0007] Step 1: Design a feedback controller based on frequency domain shaping technology Design of a feedforward controller based on acceleration feedforward technology ;

[0008] Step 2: Using the trajectory generator Generate reference position signal and reference acceleration signal Reference position signal With actual position signal The difference is used to obtain the position tracking error signal. Position tracking error signal After feedback controller Obtain feedback control signal Reference acceleration signal After feedforward controller Obtain feedforward control signal Feedback control signal With feedforward control signal The summation yields the logic axis control signal. ;

[0009] Step 3: Logic axis control signals After passing through the gain balancing module, the output decoupling matrix within it... Converted into actuator control signals ;

[0010] Step 4: Actuator Control Signal The electrical control system converts the output power into the actual force of the actuator. ;

[0011] Step 5: Actual output of the actuator After passing through the motion table system To obtain the actual position signal This forms a closed-loop control.

[0012] Step Six: When an actuator fails, the actual position signal and the actual output of the actuator Fault information is obtained through the fault detection module. Fault information The fault index is obtained after the reconstruction module. ;

[0013] Step 7: Failure Index After passing through the gain balancing module, the fault index is determined within the gain balancing module. Switch to the corresponding output decoupling matrix To ensure the logic axis control signal It can correctly allocate control signals to the remaining actuators that have not yet failed, generating the same actuator control signals as before the failure. This ensures the motion table system The closed-loop stability and tracking accuracy.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] This invention designs corresponding output decoupling matrices for cases where any actuator of a redundantly driven multi-degree-of-freedom motion table completely fails. When an actuator fails, a gain balancing module can be used to switch the logic axis control signal after a single actuator completely fails. Reassigning to the remaining actuators produces the same result as before the failure. To ensure the motion table system It can still track the reference position signal This significantly improves the reliability and fault tolerance of redundantly driven multi-degree-of-freedom motion table systems. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the fault-tolerant control loop based on gain balancing used in this invention.

[0017] Figure 2 This is the frequency response curve of the redundantly driven multi-degree-of-freedom motion stage system in this invention.

[0018] Figure 3 This is the physical layout of the actuators for the redundantly driven multi-degree-of-freedom motion stage in this invention.

[0019] Figure 4 In this invention Reference position signal and reference acceleration signal for degrees of freedom.

[0020] Figure 5 In this invention time The position tracking response and position tracking error signal.

[0021] Figure 6 In this invention From Switch to process The position tracking response and position tracking error signal.

[0022] Figure 7 In this invention From Switch to process The position tracking response and position tracking error signal.

[0023] Figure 8 In this invention From Switch to process The position tracking response and position tracking error signal.

[0024] Figure 9In this invention From Switch to process The position tracking response and position tracking error signal.

[0025] Figure 10 Because the fault-tolerant control scheme proposed in this invention was not adopted, From Switch to process The position tracking response and position tracking error signal. Detailed Implementation

[0026] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0027] This invention provides a gain-balanced fault-tolerant control method for redundantly driven multi-degree-of-freedom motion stages, such as... Figure 1 As shown, the method includes the following steps:

[0028] Step 1: Design a feedback controller based on frequency domain shaping technology Design of a feedforward controller based on acceleration feedforward technology .

[0029] In this step, the feedback controller By PID controller and low-pass filter Composition. First, according to... Figure 2 Frequency response curves of a medium-redundant driven multi-degree-of-freedom motion stage system, and selection of appropriate bandwidth. Given the mass of the motion table system Based on this, select an appropriate PID frequency ratio Calculate the proportional gain Integral frequency Differential frequency and low-pass filter cutoff frequency Low-pass filter damping ratio The value range is generally 0.5 to 1.0.

[0030] PID controller The structure is as follows:

[0031]

[0032] in, It is a Laplace variable; , , .

[0033] low-pass filter The structure is as follows:

[0034]

[0035] in, , .

[0036] Feedback controller The structure is as follows:

[0037]

[0038] Feedforward controller The structure is as follows:

[0039]

[0040] in, This is the feedforward gain, and its value typically ranges from 0.7 to 1.0.

[0041] Step 2: Using the trajectory generator Generate reference position signal and reference acceleration signal Reference position signal With actual position signal The difference is used to obtain the position tracking error signal. Position tracking error signal After feedback controller Obtain feedback control signal Reference acceleration signal After feedforward controller Obtain feedforward control signal Feedback control signal With feedforward control signal The summation yields the logic axis control signal. .

[0042] Step 3: Logic axis control signals After passing through the gain balancing module, the output decoupling matrix within it... Converted into actuator control signals .

[0043] In this step, the logic axis control signal Including motion table system Three-degree-of-freedom motion logic axis control signals Actuator control signals It includes control signals for the four actuators of the motion table. Output decoupling matrix under nominal conditions (no actuator failure) The design is based on the physical layout of the actuators in the motion table system, and the specific steps are as follows:

[0044] Step 31: As Figure 3 As shown, the logic axis control signal under nominal conditions With actuator control signals The transformation relationship (also known as the inverse decoupling relationship) between them is as follows:

[0045]

[0046] The inverse decoupling matrix in the nominal case is defined as:

[0047]

[0048] in, The distance between actuator 1, actuator 2 and the X-axis of the coordinate system of the center of mass of the motion table system. The distance between actuator 1, actuator 2 and the Y-axis of the coordinate system of the center of mass of the motion table system. The distance between actuator 3 and the X-axis of the coordinate system of the center of mass of the motion table system.

[0049] Step 32: Inverse decoupling relationship can be obtained to find the output decoupling relationship under the nominal condition, but... Since it's not a square matrix, it cannot be directly inverted; it must be "dimension reduced." The control quantity for actuator 4 is defined as:

[0050]

[0051] The original inverse decoupling relationship can now be rewritten as:

[0052]

[0053] Step 33: Definition:

[0054]

[0055] right By inverting the matrix and adding the control input of actuator 4 to the fourth row, the output decoupling matrix under nominal conditions can be obtained. for:

[0056]

[0057] Step 4: Actuator Control Signal The electrical control system converts the output power into the actual force of the actuator. .

[0058] Step 5: Actual output of the actuator After passing through the motion table system To obtain the actual position signal This forms a closed-loop control system.

[0059] In this step, the transfer function of the motion table system for:

[0060]

[0061] in, This is the inverse decoupling matrix defined in step three; for The mass of a free-degree motion, for Moment of inertia of a motion with degrees of freedom for Moment of inertia of a motion with degrees of freedom.

[0062] Step Six: When an actuator fails, the actual position signal and the actual output of the actuator Fault information is obtained through the fault detection module. Fault information The fault index is obtained after the reconstruction module. .

[0063] In this step, fault information is defined. , This indicates the current fault status (i.e., the index of the actuator that failed). It represents the degree of actuator failure, a mapping from no faults to complete failure, and The present invention defines This indicates that the actuator has completely failed. A failure index is defined. ,in These correspond to five different fault scenarios: Fault 1, no actuator fails; Fault 2, actuator 4 fails; Fault 3, actuator 1 fails; Fault 4, actuator 2 fails; Fault 5, actuator 3 fails.

[0064] Step 7: Failure Index After passing through the gain balancing module, the fault index is determined within the gain balancing module. Switch to the corresponding output decoupling matrix To ensure the logic axis control signal It can correctly allocate control signals to the remaining actuators that have not yet failed, generating the same actuator control signals as before the failure. This ensures the motion table system The closed-loop stability and tracking accuracy.

[0065] In this step, the output decoupling matrix The design should be carried out according to the following method:

[0066] According to the invention description, there are a total of 5 fault conditions, therefore 5 output decoupling matrices need to be designed. :

[0067] (1) At that time, corresponding to the nominal case without actuator failure, the output decoupling matrix The design has already been completed in step three.

[0068] (2) When actuator 4 fails, the inverse decoupling relationship is as follows:

[0069]

[0070] Inverse decoupling matrix for:

[0071]

[0072] Following the calculation method in step three, the output decoupling matrix is... for:

[0073]

[0074] (3) When actuator 1 fails, the inverse decoupling relationship is as follows:

[0075]

[0076] Inverse decoupling matrix for:

[0077]

[0078] Following the calculation method in step three, the output decoupling matrix is... for:

[0079]

[0080] (4) When actuator 2 fails, the inverse decoupling relationship is as follows:

[0081]

[0082] Inverse decoupling matrix for:

[0083]

[0084] Following the calculation method in step three, the output decoupling matrix is... for:

[0085]

[0086] (5) When actuator 3 fails, the inverse decoupling relationship is as follows:

[0087]

[0088] Inverse decoupling matrix for:

[0089]

[0090] Following the calculation method in step three, the output decoupling matrix is... for:

[0091]

[0092] Example:

[0093] The following is combined Figures 1 to 10 The technical solution of this embodiment is explained. Let... , , .

[0094] 1. Design the feedback controller as follows: and feedforward controller Since the three-degree-of-freedom controller structures are exactly the same, this embodiment only uses... Taking the design of a controller with degrees of freedom as an example, Both degrees of freedom are designed using the same method:

[0095] Combination Figure 2 Frequency response curves of a medium-redundant driven multi-degree-of-freedom motion table system, and selection of control bandwidth. PID frequency ratio Low-pass filter damping ratio proportional gain Integral frequency Differential frequency and low-pass filter frequency Based on step one, the transfer function of the feedback controller can be obtained as follows:

[0096]

[0097] Take feedforward gain The transfer function of the feedforward controller is:

[0098]

[0099] 2. Combining Figure 3The physical layout of the actuators in a medium-redundant driven multi-degree-of-freedom motion table is designed with different failure indices as follows. Corresponding output decoupling matrix :

[0100] According to step seven, combined with Figure 3 Substituting the actuator coordinates, we can obtain:

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] 3. Since the three degrees of freedom motion of the motion table system has been completely decoupled in this embodiment, and the control loop structure of each degree of freedom is exactly the same, in order to more concisely prove the effectiveness of the fault-tolerant control method proposed in this invention, only the reference position signal and reference acceleration signal of the Z degree of freedom are given, and the change in tracking accuracy after the failure of a single actuator is measured based on the position tracking error signal of the Z degree of freedom.

[0107] use Figure 4 shown Reference position signal of degrees of freedom as well as Reference acceleration signal for degrees of freedom First The system is running normally under normal conditions. Figure 5 In this invention Position tracking error curve at that time.

[0108] exist The output channel of any one actuator is cut off at any time to simulate the complete failure of that actuator. Figure 6 In this invention Position tracking error curve at time, Figure 7 In this invention Position tracking error curve at time, Figure 8 In this invention Position tracking error curve at time, Figure 9 In this invention Position tracking error curve at that time. Figure 10 Because the fault-tolerant control method proposed in this invention was not adopted, when actuator 4 completely fails ( Position error tracking curve.

[0109] from Figures 5 to 10 It can be observed that, after applying this invention, when a single actuator completely fails, Position tracking error relative to nominal condition The position tracking error remained largely unchanged; however, without this invention, when a single actuator completely failed, the position tracking error could not converge, the closed-loop system lost stability, and the original tracking accuracy could not be guaranteed. Therefore, this invention, based on redundant drive, has a good fault-tolerant control effect for the failure of a single actuator, improving the reliability and fault tolerance of the multi-degree-of-freedom motion table.

Claims

1. A gain-balanced fault-tolerant control method for a redundantly driven multi-degree-of-freedom motion stage, characterized in that... The method includes the following steps: Step 1: Design a feedback controller based on frequency domain shaping technology Design of a feedforward controller based on acceleration feedforward technology ; Step 2: Using the trajectory generator Generate reference position signal and reference acceleration signal Reference position signal With actual position signal The difference is used to obtain the position tracking error signal. Position tracking error signal After feedback controller Obtain feedback control signal Reference acceleration signal After feedforward controller Obtain feedforward control signal Feedback control signal With feedforward control signal The summation yields the logic axis control signal. ; Step 3: Logic axis control signals After passing through the gain balancing module, the output decoupling matrix within it... Converted into actuator control signals The specific steps are as follows: Step 31: Logic axis control signals under nominal conditions With actuator control signals The transformation relationship between them, i.e., the inverse decoupling relationship, is as follows: The inverse decoupling matrix in the nominal case is defined as: in, For motion table system Three-degree-of-freedom motion logic axis control signals For the control signals of the four actuators of the motion table, The distance between actuator 1, actuator 2 and the X-axis of the coordinate system of the center of mass of the motion table system. The distance between actuator 1, actuator 2 and the Y-axis of the coordinate system of the center of mass of the motion table system. The distance between actuator 3 and the X-axis of the coordinate system of the center of mass of the motion table system; Step 32: Define the control variable for actuator 4 as follows: The original inverse decoupling relationship is now rewritten as: Step 33: Definition: right Inverse the matrix and add the control input of actuator 4 to the fourth row to obtain the output decoupling matrix under nominal conditions. for: ； Step 4: Actuator Control Signal The electrical control system converts the output power into the actual force of the actuator. ; Step 5: Actual output of the actuator After passing through the motion table system To obtain the actual position signal This forms a closed-loop control. Step Six: When an actuator fails, the actual position signal and the actual output of the actuator Fault information is obtained through the fault detection module. Fault information The fault index is obtained after the reconstruction module. ; Step 7: Failure Index After passing through the gain balancing module, the fault index is determined within the gain balancing module. Switch to the corresponding output decoupling matrix To ensure the logic axis control signal It can correctly allocate control signals to the remaining actuators that have not yet failed, generating the same actuator control signals as before the failure. This ensures the motion table system The closed-loop stability and tracking accuracy.

2. The redundant drive multi-degree-of-freedom motion stage gain balancing fault-tolerant control method according to claim 1, characterized in that... In step one, the feedback controller By PID controller and low-pass filter Composition, in which: The PID controller The structure is as follows: in, It is a Laplace variable. It is proportional gain. It is the integral frequency. It is the differential frequency; The low-pass filter The structure is as follows: in, It is the cutoff frequency of the low-pass filter. It is the damping ratio of the low-pass filter; The feedback controller The structure is as follows: 。 3. The redundant drive multi-degree-of-freedom motion stage gain balancing fault-tolerant control method according to claim 2, characterized in that... The , , , , , It's bandwidth. It's the quality of the motion table system. It is the PID frequency ratio.

4. The redundant drive multi-degree-of-freedom motion stage gain balancing fault-tolerant control method according to claim 1, characterized in that... In step one, the feedforward controller The structure is as follows: in, For feedforward gain, It is a Laplace variable.

5. The redundant drive multi-degree-of-freedom motion stage gain balancing fault-tolerant control method according to claim 4, characterized in that... The The value range is 0.7 to 1.

0.

6. The redundant-drive multi-degree-of-freedom motion stage gain balancing fault-tolerant control method according to claim 1, characterized in that... In step five, the transfer function of the motion table system for: in, It is the inverse decoupling matrix; for The mass of a free-degree motion, for Moment of inertia of a motion with degrees of freedom for Moment of inertia of a motion with degrees of freedom It is a Laplace variable.

7. The redundant drive multi-degree-of-freedom motion stage gain balancing fault-tolerant control method according to claim 1, characterized in that... In step six, fault information is defined. , Indicates the current fault status. This indicates the degree of actuator failure, a mapping from no faults to complete failure; definition This indicates that the actuator has completely failed; a failure index is defined. ,in These correspond to five different fault scenarios: Fault 1, no actuator fails; Fault 2, actuator 4 fails; Fault 3, actuator 1 fails; Fault 4, actuator 2 fails; Fault 5, actuator 3 fails.

8. The redundant drive multi-degree-of-freedom motion stage gain balancing fault-tolerant control method according to claim 1, characterized in that... In step seven, the output decoupling matrix The design should be carried out according to the following method: (1) At that time, corresponding to the nominal case without actuator failure, the output decoupling matrix The design has already been completed in step three; (2) When actuator 4 fails, the inverse decoupling relationship is as follows: Inverse decoupling matrix for: Following the calculation method in step three, the output decoupling matrix is... for: (3) When actuator 1 fails, the inverse decoupling relationship is as follows: Inverse decoupling matrix for: Following the calculation method in step three, the output decoupling matrix is... for: (4) When actuator 2 fails, the inverse decoupling relationship is as follows: Inverse decoupling matrix for: Following the calculation method in step three, the output decoupling matrix is... for: (5) When actuator 3 fails, the inverse decoupling relationship is as follows: Inverse decoupling matrix for: Following the calculation method in step three, the output decoupling matrix is... for: 。

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