A displacement sensor configuration and fault diagnosis method for an active pointing ultra-static platform

Abstract

A displacement sensor configuration and fault diagnosis method for an active pointing ultra-quiet platform is proposed, applicable to a class of parallel mechanisms with redundant sensors. First, a high-reliability sensor configuration method is proposed, in which the displacement sensors are configured externally to the actuator. Then, for different active pointing ultra-quiet platform configurations, a minimum sensor combination to maintain operation and a reduced configuration control method are proposed. Finally, a hierarchical fault diagnosis method is designed for different displacement sensor combinations to maximize the life of the active pointing ultra-quiet platform under the same conditions.

Description

Technical Field

[0001] The invention belongs to the field of spacecraft attitude control and relates to a configuration of an active pointing ultra-static platform displacement sensor and a fault diagnosis method thereof. Background Art

[0002] As the demand for high-resolution remote sensing and on-orbit services continues to increase, the demand for agile maneuverability of contemporary large satellite platforms continues to increase.

[0003] For satellites equipped with an active-pointing ultra-quiet platform, the operational life of the platform is a crucial factor in determining the satellite's high performance. Improving the reliability of the entire system, while maintaining the reliability of individual components, is crucial for extending the satellite's high-performance operational life.

[0004] The traditional three-out-of-two diagnostic method for a single actuator can only work when all sensors are intact. When one sensor fails, the remaining components cannot be diagnosed, causing the system to exit the working mode prematurely due to the inability to locate the fault.

[0005] Therefore, it is necessary to propose a high-reliability sensor configuration and diagnosis method to significantly improve the reliability of the entire system at the lowest cost and extend the life of the satellite's high-performance operation. Summary of the Invention

[0006] The technical problem solved by the present invention is to overcome the shortcomings of the existing technology and provide a method for configuring and diagnosing displacement sensors for an active pointing ultra-quiet platform. The method can be used for an active pointing ultra-quiet platform with any number of actuators. By configuring displacement sensors between the upper and lower platforms, mutual diagnosis of heterogeneous sensors can be achieved. On the basis of the original 12 or 16 displacement sensors, at least only 3 are configured, reducing the probability of system failure by at least 2 to 5 orders of magnitude, thereby realizing a low-cost and high-reliability design solution.

[0007] The technical solution of the present invention is: a method for configuring and diagnosing displacement sensors of an active pointing ultra-quiet platform, wherein M additional displacement sensors are configured between the upper and lower platforms of the active pointing ultra-quiet platform to directly measure the relative positions of the upper and lower platforms, where M is greater than or equal to 3; fault diagnosis is performed on a total of 2N displacement sensors originally installed in parallel on N actuators between the upper and lower platforms of the active pointing ultra-quiet platform, as well as the newly configured M displacement sensors; and based on the results of the fault diagnosis, it is determined that the active pointing ultra-quiet platform cannot maintain normal operation or the control torque is redistributed to control the active pointing ultra-quiet platform to downgrade its configuration.

[0008] Furthermore, N=6 or 8.

[0009] Furthermore, when N=6, the configuration combination in which the active pointing ultra-quiet platform can maintain normal operation is: if one or two displacement sensors on one actuator fail, M-2 of the M additional displacement sensors configured between the upper and lower platforms fail; when N=8, the configuration combination in which the active pointing ultra-quiet platform can maintain normal operation is: if one or two displacement sensors on three actuators fail, M-2 of the M additional displacement sensors configured between the upper and lower platforms fail.

[0010] Furthermore, when N=6, it is determined that the active pointing ultra-quiet platform cannot maintain normal operation or the control torque is redistributed to control the active pointing ultra-quiet platform to downgrade the configuration. Specifically, when the displacement sensor on one actuator cannot be diagnosed, the Jacobian matrix J from the upper platform real space to the actuator space is converted to p The corresponding row elements in are set to 0, and the control torque is redistributed; when the displacement sensors on the two actuators cannot be diagnosed, it is determined that the active pointing ultra-quiet platform cannot maintain normal operation; when N=8, it is determined that the active pointing ultra-quiet platform cannot maintain normal operation or the control torque is redistributed to control the active pointing ultra-quiet platform to downgrade the configuration. Specifically, when the displacement sensors on 3 or less actuators cannot be diagnosed, the Jacobian matrix J from the upper platform real space to the actuator space is converted to p The corresponding row elements in are set to 0, and the control torque is redistributed; when the displacement sensor on the fourth actuator cannot be diagnosed, it is determined that the active pointing ultra-quiet platform cannot maintain normal operation.

[0011] Furthermore, when N=6, fault diagnosis is performed on a total of 2N displacement sensors originally installed in parallel on the N actuators between the upper and lower platforms of the active pointing ultra-quiet platform, as well as the newly configured M displacement sensors, specifically:

[0012] (51) When all displacement sensors are intact, three quantities on each actuator are measured:

[0013]

[0014] Perform a two-out-of-three comparison. If one of the quantities differs significantly from the other two, the displacement sensor corresponding to the quantity is judged to be faulty. iA , dL iB are the length changes of the actuators measured by the two displacement sensors on the i-th actuator, u i is the control force of the motor on the i-th actuator, k i is the stiffness of the i-th actuator;

[0015] (52) When a displacement sensor on an actuator fails, the fault diagnosis of the other displacement sensor is performed through the displacement sensor between the upper and lower platforms and the gyroscopes of the upper and lower platforms. Specifically, assuming dL iA Fault, when J P x and dL iB The difference is large, and J P x and dL jA 、dL jB If the difference is small, it is determined that the other displacement sensor on the actuator is faulty. Here, x is the relative state of the upper platform relative to the lower platform measured by the displacement sensor and gyroscope between the upper and lower platforms. Translation is in 1-3 dimensions, and rotation is in 4-6 dimensions. j is the number of the actuator without fault. The two subscripts A and B are used to distinguish two different displacement sensors on the same actuator.

[0016] (53) When there is no situation where both displacement sensors on the actuator are faulty, the displacement sensor of the actuator is used to diagnose the fault of the displacement sensor between the upper platform and the lower platform. Specifically, when invJ P dL and y Pk The difference is large, and invJ P dL and y Pl If the difference is small, it is considered that the displacement sensor k is faulty, where dL is the length variation array of the 6 actuators, measured by the displacement sensor, k = 1, 2, 3 ... M, l = 1, 2, 3 ... M, l ≠ k, invJ P is the matrix J P The pseudo-inverse, invJ P =(J P T J P ) -1 J P T ,y Pk with y Pl Both satisfy the measurement model y P =A pe x (1:3) ,y P is the measurement value of the newly configured displacement sensor, A pe is the installation matrix of the newly configured displacement sensor relative to the lower platform, x (1:3) are the first three dimensions of x.

[0017] Furthermore, when N=8, fault diagnosis is performed on a total of 2N displacement sensors originally installed in parallel on the N actuators between the upper and lower platforms of the active pointing ultra-quiet platform, as well as the newly configured M displacement sensors, specifically:

[0018] (61) When all displacement sensors are intact, three quantities are measured on each actuator:

[0019]

[0020] Perform a two-out-of-three comparison. If one of the quantities differs significantly from the other two, the displacement sensor corresponding to the quantity is considered to be faulty. iA , dL iB are the length changes of the actuators measured by the two displacement sensors on the i-th actuator, u i is the control force of the motor on the i-th actuator, k i is the stiffness of the i-th actuator;

[0021] (62) When a displacement sensor on an actuator fails, the fault diagnosis of another displacement sensor is performed by any of the following two methods. As long as one of the two methods diagnoses a displacement sensor failure, it is considered to be a failure:

[0022] (621) The fault diagnosis of another displacement sensor is performed through the displacement sensor between the upper platform and the lower platform and the gyroscope of the upper platform and the lower platform. Specifically, assuming dL iA Fault, when J P x and dL iB The difference is large, and J P x and dL jA 、dL jB If the difference is small, it is determined that the other displacement sensor on the actuator is faulty. Here, x is the relative state of the upper platform relative to the lower platform measured by the displacement sensor and gyroscope between the upper and lower platforms. Translation is in 1-3 dimensions, and rotation is in 4-6 dimensions. j is the number of the actuator without fault. The two subscripts A and B are used to distinguish two different displacement sensors on the same actuator.

[0023] (622) The fault diagnosis of another displacement sensor is carried out through the other 7 actuators. Specifically, assuming that dL iA Fault, when J P(i,:) invJ Pni dL and dL iB The difference is large, and J P(j,:) invJ Pnj dL and dL jA 、dL jB If the difference is small, it is determined that another displacement sensor on actuator i is faulty, where dL is the length variation array of 8 actuators, measured by the displacement sensor, j is the number of the actuator without fault, and J P(i,:) For J P The row vector composed of the i-th row, invJ Pni For JPni The pseudo-inverse is invJ Pni =(J Pni T J Pni ) -1 J Pni T , J Pni For J P The matrix formed by setting the elements in the i-th row to 0;

[0024] (63) When all four displacement sensors on two actuators fail, perform fault diagnosis using the method of step (621);

[0025] (64) When there are at least one displacement sensor on 6 or more actuators that is in good condition, the displacement sensor of the actuator is used to diagnose the fault of the displacement sensor between the upper platform and the lower platform. Specifically: Pu dL and y Pk The difference is large, and invJ Pu dL and y Pl If the difference is small, it is considered that the displacement sensor k is faulty, where k = 1, 2, 3 ... M, l = 1, 2, 3 ... M, l ≠ k, invJ Pu is the matrix J Pu The pseudo-inverse, invJ Pu =(J Pu T J Pu ) -1 J Pu T , J Pu is the Jacobian matrix of the actuators with more than one intact displacement sensor, y Pk with y Pl Both satisfy the measurement model y P =A pe x (1:3) ,y P is the measurement value of the newly configured displacement sensor, A pe is the installation matrix of the newly configured displacement sensor relative to the lower platform, x (1:3) are the first three dimensions of x.

[0026] Furthermore, the large or small difference is compared with the fault diagnosis threshold ErrMax. If it is greater than ErrMax, the difference is determined to be large; if it is less than ErrMax, the difference is determined to be small. ErrMax is selected according to the hardware characteristics of the displacement sensor.

[0027] The advantages of the present invention compared with the prior art are:

[0028] (1) Compared with the existing three-out-of-two diagnosis method for a single actuator, this method fully utilizes the mutual diagnosis characteristics of heterogeneous sensors and redundant degree-of-freedom sensors, and accurately locates the faulty component through multiple means, ensuring the system's working ability and improving reliability;

[0029] (2) Compared with the solution of adding sensors to the actuator, this method is significantly cheaper than the former. When the probability of failure of a single component remains unchanged, the probability of system failure is also significantly lower than the former, thus achieving a low-cost and high-reliability design solution.

[0030] (3) When the number of sensors added to the actuator is the same as the number of sensors between platforms, the probability of system failure of the method of the present invention is low; while ensuring the same probability of system failure, the number of sensors configured between platforms in the method of the present invention is less than the number of sensors added to the actuator. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 1. A diagram comparing the system failure probabilities of two diagnostic methods for six actuators according to an embodiment of the present invention;

[0032] Figure 2 A diagram comparing system failure probabilities of several diagnostic methods for eight actuators in an embodiment of the present invention;

[0033] Figure 3 This is a comparison chart of the system failure probability of adding one displacement sensor to three actuators and adding three displacement sensors between the upper and lower platforms in an 8-actuator configuration according to an embodiment of the present invention;

[0034] Figure 4 : This is a comparison chart of the system failure probability of the configuration with 8 actuators in an embodiment of the present invention, in which one displacement sensor is added to each of the 8 actuators, and in which 6 displacement sensors are added between the upper and lower platforms. DETAILED DESCRIPTION

[0035] Typically, an active pointing ultra-quiet platform consists of an upper platform, a lower platform, and N actuators (typically N = 6 or 8). These actuators are installed in parallel between the upper and lower platforms. Each actuator is equipped with a motor. To control and diagnose each actuator, two displacement sensors are installed on each actuator. Let's number the actuators i, where i = 1, 2, 3, ... 6 or 8. The displacement sensors on each actuator are numbered 1A, 1B, 2A, 2B, and so on, up to NA, NB, where N = 6 or 8.

[0036] Both the upper platform and the lower platform are equipped with gyroscopes. At the same time, one or both of the upper platform and the lower platform are equipped with star sensors for measuring the angular velocity and angle of the upper platform and the lower platform.

[0037] In general, the dynamic model of the active pointing super-static platform is:

[0038]

[0039] Where M is the mass matrix of the upper platform, C is the damping matrix of the upper platform, K is the stiffness matrix of the upper platform, x is the relative state of the upper platform relative to the lower platform, and is a 6-dimensional vector containing relative translation and relative rotation, where translation is in 1 to 3 dimensions and rotation is in 4 to 6 dimensions. p is the Jacobian matrix from the upper platform real space to the actuator space, J p T is the matrix J p is the transpose of , and u is the control force acting on each actuator.

[0040] The measurement model of the displacement sensor on each actuator is:

[0041] y i =J p x

[0042] Among them, y i is the measured value of the displacement sensor on each actuator.

[0043] In the present invention, to measure the three-axis relative displacement between the upper and lower platforms, M additional displacement sensors are placed between the upper and lower platforms to directly measure their relative positions. To measure the three-axis relative displacement, M ≥ 3 must be satisfied.

[0044] Correspondingly, the measurement model of the newly configured displacement sensor between the upper and lower platforms is:

[0045] y P =A pe x (1:3)

[0046] Among them, y P is the measurement value of the newly configured displacement sensor between the upper platform and the lower platform, A pe is the installation matrix of the newly configured displacement sensor between the upper platform and the lower platform relative to the lower platform (a matrix of M*3), x (1:3) are the first three dimensions of x.

[0047] On the basis of the above configuration, the present invention provides a minimum displacement sensor combination and a reduced configuration control method for maintaining normal operation for different active pointing ultra-quiet platform configurations.

[0048] In the present invention, the definition of the active pointing ultra-quiet platform being able to maintain normal operation is: there are 5 or more displacement sensors on the actuators that are operating normally and can be diagnosed when a fault occurs.

[0049] In this invention, a displacement sensor failure is defined as being diagnosable when its measured value differs from the combined information from two or more other components on the platform. If a displacement sensor cannot be diagnosed based on the combined information from two or more other components on the platform, the displacement sensor failure is considered undiagnosable.

[0050] For an active pointing ultra-quiet platform configuration with N=6 actuators, the configuration combination that can maintain normal operation is: one or two displacement sensors on one actuator fail, and there are M-2 failures in the displacement sensors between the upper and lower platforms.

[0051] The down-configuration control method is: when the displacement sensor on one actuator cannot be diagnosed, the Jacobian matrix J p The corresponding row elements in are set to 0 and the control torque is redistributed. When the displacement sensors on the two actuators cannot be diagnosed, it is considered that the entire platform cannot maintain operation.

[0052] For the active pointing ultra-quiet platform configuration with N=8 actuators, the configuration combination that can maintain normal operation is: one or two displacement sensors on three actuators fail, and there are M-2 failures in the displacement sensors between the upper and lower platforms.

[0053] The down-configuration control method is: when the displacement sensors on 3 or less actuators cannot be diagnosed, the Jacobian matrix J p The corresponding row elements in are set to 0 and the control torque is redistributed. When the displacement sensor on the fourth actuator cannot be diagnosed, it is considered that the entire platform cannot maintain operation.

[0054] On this basis, a hierarchical fault diagnosis method is designed for different displacement sensor combinations.

[0055] (3.1) For the active pointing ultra-quiet platform configurations with 6 and 8 actuators, when all displacement sensors are intact, the three quantities on each actuator are:

[0056]

[0057] Perform a two-out-of-three comparison. If one of the quantities differs significantly from the other two (the difference is greater than ErrMax, where ErrMax is the fault diagnosis threshold selected based on the hardware characteristics of the displacement sensor), the component corresponding to the quantity is considered to be faulty.

[0058] Among them, dL iA , dL iB are the length changes of the actuators measured by the two displacement sensors on the i-th actuator, u iis the control force of the motor on the i-th actuator, k i is the stiffness of the i-th actuator.

[0059] (3.2) For an active pointing ultra-quiet platform configuration with six actuators, when a displacement sensor on one actuator fails, the fault diagnosis of the other displacement sensor is performed through the displacement sensor between the upper and lower platforms and the gyroscopes of the upper and lower platforms:

[0060] Assume dL iA Fault, when J P x and dL iB The difference is large (the difference is greater than ErrMax, where ErrMax is the fault diagnosis threshold, which is selected according to the hardware characteristics of the displacement sensor), and J P x and dL jA 、dL jB If the difference is small (less than ErrMax, where ErrMax is the fault diagnosis threshold, selected based on the displacement sensor hardware characteristics), the other displacement sensor on the actuator is considered faulty. Here, x is measured by the displacement sensor and gyroscope between the upper and lower platforms, and j is the number of the fault-free actuator.

[0061] (3.3) For an active pointing ultra-quiet platform configuration with eight actuators, when a displacement sensor on one actuator fails, the fault diagnosis of the other displacement sensor can be performed simultaneously in two ways:

[0062] (3.3.1) Similar to the method in (3.2), the fault diagnosis is performed using the measurement results of the displacement sensor between the upper and lower platforms and the gyroscopes of the upper and lower platforms;

[0063] (3.3.2) Perform fault diagnosis on another displacement sensor using another 7 actuators:

[0064] Assume dL iA Fault, when J P(i,:) invJ Pni dL and dL iB The difference is large (the difference is greater than ErrMax, where ErrMax is the fault diagnosis threshold, which is selected according to the hardware characteristics of the displacement sensor), and J P(j,:) invJ Pnj dL and dL jA 、dL jB When the difference is small (less than ErrMax, where ErrMax is the fault diagnosis threshold, selected according to the hardware characteristics of the displacement sensor), it is considered that another displacement sensor on actuator i is faulty. Where dL is the length change array of 8 actuators, measured by the displacement sensor, j is the number of the actuator without fault, and JP(i,:) For J P The row vector composed of the i-th row, invJ Pni For J Pni The pseudo-inverse of invJ is calculated as Pni =(J Pni T J Pni ) -1 J Pni T , J Pni For J P The matrix with the elements in row i set to 0.

[0065] Simultaneously means that two methods are called one after the other in each control cycle. As long as one of the two methods diagnoses a fault in a displacement sensor, it is considered to be a fault.

[0066] (3.4) For an active pointing ultra-quiet platform configuration with eight actuators, when all four displacement sensors on two actuators fail, a method similar to that in Section (3.2) is used to perform fault diagnosis using the measurement results of the displacement sensors between the upper and lower platforms and the gyroscopes of the upper and lower platforms.

[0067] At this time, there are 6 actuators left. The situation is the same as that of the active pointing ultra-quiet platform of the 6 actuators. The displacement sensors of the 6 actuators can only be diagnosed using the displacement sensors between the platforms.

[0068] (3.5) For the active pointing ultra-quiet platform configuration with six actuators, when both displacement sensors on the actuators are not faulty, the displacement sensors of the actuators are used to diagnose the fault of the displacement sensors between the upper and lower platforms:

[0069] When invJ P dL and y Pk The difference is large, and invJ P dL and y Pl If the difference is small, it is considered that the displacement sensor k is faulty. Where k=1,2,3…M, l=1,2,3…M, l≠k, invJ P is the matrix J P The pseudo-inverse of invJ is calculated as P =(J P T J P ) -1 J P T .

[0070] (3.6) For an active pointing ultra-quiet platform configuration with eight actuators, when at least one displacement sensor on six or more actuators is intact, the displacement sensor of the actuator is used to diagnose the fault of the displacement sensor between the upper and lower platforms:

[0071] When invJ Pu dL and y Pk The difference is large, and invJ Pu dL and y Pl If the difference is small, it is considered that the displacement sensor k is faulty. Where k=1,2,3…M, l=1,2,3…M, l≠k, invJ Pu is the matrix J Pu The pseudo-inverse of invJ is calculated as Pu =(J Pu T J Pu ) -1 J Pu T , J Pu is the Jacobian matrix of the actuators that currently have more than one intact displacement sensor.

[0072] This completes the design of a low-cost and high-reliability solution.

[0073] Example

[0074] Figure 1 The figure shows the system failure probability of the two diagnostic methods under the configuration of 6 actuators. The horizontal axis is the probability of a single sensor failure within a fixed time. They are the system failure probability when only the 2 out of 3 diagnostic method is used and the system failure probability after adding inter-platform sensors. It can be seen that after adding inter-platform sensors, the probability of system failure is reduced by 2-5 orders of magnitude.

[0075] Figure 2 For a configuration with 8 actuators, the system failure probabilities of several diagnostic methods involved in the present invention are shown. From top to bottom, the higher curve represents the system failure probability when only the 2-out-of-3 diagnostic method is used, the lower curve represents the system failure probability when the inter-platform sensor is added, the lower curve represents the system failure probability when the inter-actuator diagnostic method is added, and the bottom curve represents the system failure probability when both the inter-platform sensor and the inter-actuator diagnostic method are added. It can be seen that the addition of the inter-actuator diagnostic method significantly improves the system failure, reducing the probability of system failure by 4-10 orders of magnitude. On this basis, adding the inter-platform sensor can further reduce the system failure probability by 2-5 orders of magnitude.

[0076] Figure 3In the configuration of 8 actuators, the system failure probability of adding one displacement sensor to 3 actuators is compared with that of adding 3 displacement sensors between the upper and lower platforms. It can be seen that adding sensors between platforms reduces the system failure probability by 0-4 orders of magnitude compared to adding sensors on the actuators, which proves the high reliability of the method of the present invention.

[0077] Figure 4 In the configuration of 8 actuators, the system failure probability of adding one displacement sensor to each of the 8 actuators is compared with that of adding 6 displacement sensors between the upper and lower platforms. It can be seen that the system failure probability of the two schemes is almost the same, which proves the low cost of the method of the present invention.

[0078] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for configuring and diagnosing a displacement sensor for an active pointing ultra-static platform, characterized by: M additional displacement sensors are configured between the upper and lower platforms of the active pointing ultra-quiet platform to directly measure the relative positions of the upper and lower platforms, M ≥ 3; Fault diagnosis was performed on a total of 2N displacement sensors originally installed in parallel on the N actuators between the upper and lower platforms of the active pointing ultra-quiet platform, as well as on the newly configured M displacement sensors. According to the results of the fault diagnosis, it is determined that the active pointing super-quiet platform cannot maintain normal operation or the control torque is redistributed to control the active pointing super-quiet platform to downgrade the configuration; The N is 6 or 8. When N is 6, the configuration combination in which the active pointing ultra-quiet platform can maintain normal operation is: if one or two displacement sensors on one actuator fail, M-2 of the M additional displacement sensors configured between the upper and lower platforms fail; when N is 8, the configuration combination in which the active pointing ultra-quiet platform can maintain normal operation is: if one or two displacement sensors on three actuators fail, M-2 of the M additional displacement sensors configured between the upper and lower platforms fail.

2. The method for configuring and diagnosing a displacement sensor for an active pointing ultra-static platform according to claim 1, characterized in that: When N=6, it is determined that the active pointing ultra-quiet platform cannot maintain normal operation or the control torque is redistributed to control the active pointing ultra-quiet platform to downgrade the configuration. Specifically, when the displacement sensor on one actuator cannot be diagnosed, the Jacobian matrix J from the upper platform real space to the actuator space is converted to p The corresponding row elements in are set to 0, and the control torque is redistributed; when the displacement sensors on the two actuators cannot be diagnosed, it is determined that the active pointing ultra-quiet platform cannot maintain normal operation; when N=8, it is determined that the active pointing ultra-quiet platform cannot maintain normal operation or the control torque is redistributed to control the active pointing ultra-quiet platform to downgrade the configuration. Specifically, when the displacement sensors on 3 or less actuators cannot be diagnosed, the Jacobian matrix J from the upper platform real space to the actuator space is converted to p Set the corresponding row elements in to 0 and redistribute the control torque; When the displacement sensor on the fourth actuator cannot be diagnosed, it is determined that the active pointing ultra-quiet platform cannot maintain normal operation.

3. The method for configuring and diagnosing a displacement sensor for an active pointing ultra-static platform according to claim 2, characterized in that: When N=6, the fault diagnosis is performed on the 2N displacement sensors originally installed in parallel on the N actuators between the upper and lower platforms of the active pointing ultra-quiet platform, as well as the newly configured M displacement sensors, specifically: (51) When all displacement sensors are intact, three quantities on each actuator are measured: Perform a two-out-of-three comparison. If one of the quantities differs significantly from the other two, the displacement sensor corresponding to the quantity is judged to be faulty. iA , dL iB are the length changes of the actuators measured by the two displacement sensors on the i-th actuator, u i is the control force of the motor on the i-th actuator, k i is the stiffness of the i-th actuator; (52) When a displacement sensor on an actuator fails, the fault diagnosis of the other displacement sensor is performed through the displacement sensor between the upper and lower platforms and the gyroscopes of the upper and lower platforms. Specifically, assuming dL iA Fault, when J P x and dL iB The difference is large, and J P x and dL jA 、dL jB If the difference is small, it is determined that the other displacement sensor on the actuator is faulty. Here, x is the relative state of the upper platform relative to the lower platform measured by the displacement sensor and gyroscope between the upper and lower platforms. Translation is in 1-3 dimensions, and rotation is in 4-6 dimensions. j is the number of the actuator without fault. The two subscripts A and B are used to distinguish two different displacement sensors on the same actuator. (53) When there is no situation where both displacement sensors on the actuator are faulty, the displacement sensor of the actuator is used to diagnose the fault of the displacement sensor between the upper platform and the lower platform. Specifically, when invJ P dL and y Pk The difference is large, and invJ P dL and y Pl If the difference is small, it is considered that the displacement sensor k is faulty, where dL is the length variation array of the 6 actuators, measured by the displacement sensor, k = 1, 2, 3 ... M, l = 1, 2, 3 ... M, l ≠ k, invJ P is the matrix J P The pseudo-inverse, invJ P =(J P T J P ) -1 J P T ,y Pk with y Pl Both satisfy the measurement model y P =A pe x (1:3) ,y P is the measurement value of the newly configured displacement sensor, A pe is the installation matrix of the newly configured displacement sensor relative to the lower platform, x (1:3) are the first three dimensions of x.

4. The method for configuring and diagnosing a displacement sensor for an active pointing ultra-static platform according to claim 2, wherein: When N=8, the fault diagnosis is performed on the 2N displacement sensors originally installed in parallel on the N actuators between the upper and lower platforms of the active pointing ultra-quiet platform, as well as the newly configured M displacement sensors, specifically: (61) When all displacement sensors are intact, three quantities are measured on each actuator: Perform a two-out-of-three comparison. If one of the quantities differs significantly from the other two, the displacement sensor corresponding to the quantity is considered to be faulty. iA , dL iB are the length changes of the actuators measured by the two displacement sensors on the i-th actuator, u i is the control force of the motor on the i-th actuator, k i is the stiffness of the i-th actuator; (62) When a displacement sensor on an actuator fails, the fault diagnosis of another displacement sensor is performed by any of the following two methods. As long as one of the two methods diagnoses a displacement sensor failure, it is considered to be a failure: (621) The fault diagnosis of another displacement sensor is performed through the displacement sensor between the upper platform and the lower platform and the gyroscope of the upper platform and the lower platform. Specifically, assuming dL iA Fault, when J P x and dL iB The difference is large, and J P x and dL jA 、dL jB If the difference is small, it is determined that the other displacement sensor on the actuator is faulty. Here, x is the relative state of the upper platform relative to the lower platform measured by the displacement sensor and gyroscope between the upper and lower platforms. Translation is in 1-3 dimensions, and rotation is in 4-6 dimensions. j is the number of the actuator without fault. The two subscripts A and B are used to distinguish two different displacement sensors on the same actuator. (622) The fault diagnosis of another displacement sensor is carried out through the other 7 actuators. Specifically, assuming that dL iA Fault, when J P(i,:) invJ Pni dL and dL iB The difference is large, and J P(j,:) invJ Pnj dL and dL jA 、dL jB If the difference is small, it is determined that another displacement sensor on actuator i is faulty, where dL is the length variation array of 8 actuators, measured by the displacement sensor, j is the number of the actuator without fault, and J P(i,:) For J P The row vector composed of the i-th row, invJ Pni For J Pni The pseudo-inverse is invJ Pni =(J Pni T J Pni ) -1 J Pni T , J Pni For J P The matrix formed by setting the elements in the i-th row to 0; (63) When all four displacement sensors on two actuators fail, perform fault diagnosis using the method of step (621); (64) When there are at least one displacement sensor on 6 or more actuators that is in good condition, the displacement sensor of the actuator is used to diagnose the fault of the displacement sensor between the upper platform and the lower platform. Specifically: Pu dL and y Pk The difference is large, and invJ Pu dL and y Pl If the difference is small, it is considered that the displacement sensor k is faulty, where k = 1, 2, 3 ... M, l = 1, 2, 3 ... M, l ≠ k, invJ Pu is the matrix J Pu The pseudo-inverse, invJ Pu =(J Pu T J Pu ) -1 J Pu T , J Pu is the Jacobian matrix of the actuators with more than one intact displacement sensor, y Pk with y Pl Both satisfy the measurement model y P =A pe x (1:3) ,y P is the measurement value of the newly configured displacement sensor, A pe is the installation matrix of the newly configured displacement sensor relative to the lower platform, x (1:3) are the first three dimensions of x.

5. The method for configuring and diagnosing a displacement sensor for an active pointing ultra-static platform according to claim 3 or 4, characterized in that: The large or small difference is compared with the fault diagnosis threshold ErrMax. If it is greater than ErrMax, the difference is determined to be large; if it is less than ErrMax, the difference is determined to be small. ErrMax is selected according to the hardware characteristics of the displacement sensor.

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