CN111707412B - On-line identification system and inertia algorithm for the moment of inertia of a large-scale three-axis air-floating table - Google Patents

Abstract

The invention provides an online identification system and an inertia algorithm for the rotational inertia of a large-scale three-axis air bearing table, and belongs to the technical field of control. The invention comprises the following steps: and (3) deducing a design scheme of a three-axis air bearing table rotational inertia identification system and a three-axis air bearing table rotational inertia algorithm. The design scheme of triaxial air bearing table inertia identification system includes: the system comprises a data processing system, a display system, a support and protection system, a three-axis air bearing table attitude measurement and control system, a wireless transmission system, a balance adjusting system and a power supply system. The online identification technology for the rotational inertia of the large three-axis air bearing table can be used for online identification of the rotational inertia of different large-mass air bearing tables for various systems, can be used for online identification of the rotational inertia compared with other existing schemes, and does not need to change a hardware structure in the identification process.

Description

An online identification system and inertia algorithm for the moment of inertia of a large-scale three-axis air-floating table

technical field

The invention relates to an online identification technology for the moment of inertia of a large-scale three-axis air-floating table, and belongs to the technical field of control.

Background technique

The moment of inertia of the triaxial air flotation platform is an important physical quantity for it to complete the simulation task of facing the spacecraft on the ground. After installing all kinds of measuring instruments, the triaxial air flotation table needs to be adjusted and balanced before it can work. This condition determines that the moment of inertia of the triaxial air flotation table is difficult to obtain by directly analyzing the mass. After the air-floating table is installed, its moment of inertia is identified, which provides a basis for the measurement tasks that require the moment of inertia of the air-floating table in other algorithms.

Application publication number: CN105987788A, application publication date October 05, 2016, published the "Online Recognition Device for the Moment of Inertia of the Three-Axis Air Floating Platform", using six mass block moving devices to carry out three equal distances along the three coordinate axes respectively The method of moving is used to complete the online identification of the characteristics of the moment of inertia, and the moment of inertia of the air-floating table is identified under the premise that the position of the center of mass remains unchanged through the equidistant movement of the paired mass blocks. However, it needs to move the mass block on the air flotation table, which cannot be measured without changing the whole of the air flotation table, and it is difficult to ensure that the center of mass of the air flotation table remains at the center of rotation of the air flotation table during the movement process. In the process of measuring, if the center of mass is offset, it will generate a gravitational interference moment and affect the measurement process.

Application publication number: CN102620886A, application publication date on August 1, 2012, announced the "Two-step On-orbit Identification Combined Spacecraft Moment of Inertia Estimation Method" Selecting the rotational inertia of the spacecraft in a certain direction as the benchmark, the rotational inertia was normalized The system state quantity is estimated by filtering through EKF, and the least square method is used for identification, but offline identification is required after the measurement data is obtained, and online identification cannot be carried out.

Master's thesis "Research on Online Identification Algorithm of Satellite and Air-floating Platform Mass Characteristics", author: Wang Shuting, published in June 2006, with thruster as the actuator, an online identification method of the moment of inertia of the air-floating platform considering the disturbance torque is given. However, the moment of inertia of the air-floating table used for simulation is small, and the specific selection method of the input signal is not detailed enough.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the above problems existing in the prior art, and further provide an online identification technology for the moment of inertia of a large-scale three-axis air-floating table.

The purpose of this invention is to realize through the following technical solutions:

The online identification system for the moment of inertia of a large-scale three-axis air-floating platform involved in this embodiment includes a data processing system, a display system, a support and protection system, a three-axis air-floating platform attitude measurement and control system, a wireless transmission system, and a balance adjustment system. and power supply system. The relationship between the above systems is as follows: the data processing system performs data processing on the output signal from the on-stage measurement and control system to identify the moment of inertia, the display system displays the data processed by the data processing system online, and the support and protection system ensures that the triaxial The safety and reliability of the floating platform when working, the attitude measurement and control system of the three-axis air floating platform is used in the environment where the ground micro-interference torque is obtained, the measurement of the spacecraft on the ground and the control of its attitude are simulated on the ground, and the wireless transmission system is used for on-stage measurement and control. The information exchange between the system and the host computer system under the stage, the balance adjustment system ensures that the center of mass of the three-axis air flotation table is coincident with the rotation center of the air flotation ball, and the power supply system supplies power for the attitude measurement and control system and the balance adjustment system of the three-axis air flotation table.

Three-axis air-floating table moment of inertia algorithm:

One algorithm for moment of inertia measurement

The scheme of identifying the moment of inertia is as follows: use the flywheel as the actuator of the system to input to the air flotation table, measure the angular velocity through the gyroscope as the output of the system, and establish the following dynamic equation:

Among them, J _f is the moment of inertia of the flywheel, ω _f is the rotational speed of the flywheel, J is the moment of inertia of the air-floating table, and ω is the angular velocity of the air-bearing table. In formula (2), since the moment of inertia is large and the attitude control is always performed at a small angle during the identification process, eliminating the small amount in the formula and modifying the position of the input and output can be obtained:

Among them, J ^-1 is the inverse matrix of the moment of inertia matrix. Both the matrix and the moment of inertia matrix are 3×3 symmetric matrices. Transforming the matrix can get:

J ^-1 = [J ₁₁ ^-1 J ₂₂ ^-1 J ₃₃ ^-1 J ₁₂ ^-1 J ₁₃ ^-1 J ₂₃ ^-1 ] ^T (5)

The inverse of each value of the moment of inertia is represented by symbols. After identifying each value in formula (5), it needs to be converted into a 3×3 symmetric matrix and then inverse to obtain the actual moment of inertia matrix.

Through the above analysis, the least squares method for identifying the moment of inertia is obtained. By inverting the formal transformation formula, it can satisfy the characteristic of the least squares method to estimate the minimum variance of the output, so that the identification accuracy is higher.

Moment of inertia measurement recursive algorithm

The standard formulation of the least squares method has been obtained in the above derivation. Repeated measurement with this formula requires many calculations and a long time, and also needs to be converted to the method of recursive least squares to identify the moment of inertia online. Through the above derivation, the following types of least squares formula are obtained:

Y=Φθ,θ=(Φ ^T Φ) ^-1 Φ ^T Y (6)

Where Y is the output angular acceleration, Φ is the torque input obtained from the flywheel speed, and θ is the deformation form of the moment of inertia matrix. The recursive formula is derived as follows:

We order:

P(k)=(Φ ^T (k)Φ(k)) ^-1 ,θ(k)=P(k)Φ ^T (k)Y(k) (8)

Bringing formula (7) and formula (8) into formula (6) can get:

Using the matrix inversion lemma for formula (10), we can get:

Bringing the above formula into formula (6), the recursive formula of the least square method can be obtained:

Among them, take P(0)=10 ¹⁰ I, θ(0)=0 to satisfy the principle of recursive least squares. Considering that the system noise and moment of inertia parameters will change with time with factors such as disturbance torque and temperature, based on the recursive least squares method, the recursive least squares method with fading memory is used to achieve higher-precision identification. The least squares recursion formula of fading memory is as follows:

Among them, λ is the forgetting factor, which takes a value from 0 to 1. The specific value of the forgetting factor can be selected by simulating the estimation of the moment of inertia. The moment of inertia can be obtained by online identification by bringing the values in the primary identification method derived from the system attitude into formula (13).

The invention is an online identification technology for the moment of inertia of a large-scale three-axis air flotation table, which can perform online identification of the moment of inertia of different large-mass air flotation tables used in various systems. The moment of inertia is identified, and there is no need to change the hardware structure during the identification process.

Description of drawings

FIG. 1 is a schematic structural diagram of the online identification system for the moment of inertia of the large-scale three-axis air flotation table according to the present invention.

Figure 2 is a schematic diagram of the structure of the triaxial air flotation table.

3 is a schematic diagram of a data processing system and a display system,

The reference signs in the figure, 1 is the data processing system, 2 is the display system, 3 is the support and protection system, 4 is the attitude measurement and control system of the three-axis air-floating table, 5 is the wireless transmission system, 6 is the balance adjustment system, and 7 is the power supply system.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and provides a detailed implementation manner, but the protection scope of the present invention is not limited to the following embodiments.

Example 1

As shown in Figure 1 to Figure 3, the online identification technology for the moment of inertia of a large-scale three-axis air-floating table involved in this embodiment includes: the design scheme of the identification system for the moment of inertia of the three-axis air-floating table and the algorithm for the moment of inertia of the three-axis air-floating table Derive.

The design scheme of the moment of inertia identification system of the three-axis air-floating platform, including data processing system 1, display system 2, support and protection system 3, attitude measurement and control system of the three-axis air-floating platform 4, wireless transmission system 5, balance adjustment system 6 and Power supply system 7. The relationship between the above seven systems is as follows: data processing system 1 performs data processing on the output signal from the on-stage measurement and control system to identify the moment of inertia, display system 2 displays the data processed by data processing system 1 online, supports and protects the system 3. To ensure the safety and reliability of the three-axis air flotation platform when working, the attitude measurement and control system of the three-axis air flotation platform 4 is used to obtain the environment of the ground micro-interference torque, simulate the measurement of the spacecraft on the ground and its attitude control, wireless transmission System 5 is used to exchange information with the on-stage measurement and control system and the off-stage host computer system. Balance adjustment system 6 ensures that the center of mass of the three-axis air flotation table is coincident with the rotation center of the air flotation ball. The power supply system 7 is the attitude measurement and control system of the three-axis air flotation table. 4 and balancing system 6 for power supply.

Example 2

The derivation of the moment of inertia algorithm of the three-axis air-floating table:

One algorithm for moment of inertia measurement

The scheme of identifying the moment of inertia is as follows: use the flywheel as the actuator of the system to input to the air flotation table, measure the angular velocity through the gyroscope as the output of the system, and establish the following dynamic equation:

Among them, J _f is the moment of inertia of the flywheel, ω _f is the rotational speed of the flywheel, J is the moment of inertia of the air-floating table, and ω is the angular velocity of the air-bearing table. In formula (2), since the moment of inertia is large and the attitude control is always performed at a small angle during the identification process, eliminating the small amount in the formula and modifying the position of the input and output can be obtained:

Among them, J ^-1 is the inverse matrix of the moment of inertia matrix. Both the matrix and the moment of inertia matrix are 3×3 symmetric matrices. Transforming the matrix can get:

J ^-1 = [J ₁₁ ^-1 J ₂₂ ^-1 J ₃₃ ^-1 J ₁₂ ^-1 J ₁₃ ^-1 J ₂₃ ^-1 ] ^T (5)

The inverse of each value of the moment of inertia is represented by symbols. After identifying each value in formula (5), it needs to be converted into a 3×3 symmetric matrix and then inverse to obtain the actual moment of inertia matrix.

Through the above analysis, the least squares method for identifying the moment of inertia is obtained. By inverting the formal transformation formula, it can satisfy the characteristic of the least squares method to estimate the minimum variance of the output, so that the identification accuracy is higher.

Moment of inertia measurement recursive algorithm

The standard formulation of the least squares method has been obtained in the above derivation. Repeated measurement with this formula requires many calculations and a long time, and also needs to be converted to the method of recursive least squares to identify the moment of inertia online. Through the above derivation, the following types of least squares formula are obtained:

Y=Φθ,θ=(Φ ^T Φ) ^-1 Φ ^T Y (6)

Where Y is the output angular acceleration, Φ is the torque input obtained from the flywheel speed, and θ is the deformation form of the moment of inertia matrix. The recursive formula is derived as follows:

We order:

P(k)=(Φ ^T (k)Φ(k)) ^-1 ,θ(k)=P(k)Φ ^T (k)Y(k) (8)

Bringing formula (7) and formula (8) into formula (6) can get:

Using the matrix inversion lemma for formula (10), we can get:

Bringing the above formula into formula (6), the recursive formula of the least square method can be obtained:

Among them, take P(0)=10 ¹⁰ I, θ(0)=0 to satisfy the principle of recursive least squares. Considering that the system noise and moment of inertia parameters will change with time with disturbance torque and temperature factors, based on the recursive least squares method, the recursive least squares method with fading memory is used to achieve higher accuracy identification. The least squares recursion formula of fading memory is as follows:

Among them, λ is the forgetting factor, which takes a value from 0 to 1. The specific value of the forgetting factor can be selected by simulating the estimation of the moment of inertia. The moment of inertia can be obtained by online identification by bringing the values in the primary identification method derived from the system attitude into formula (13).

Input signal selection method for identification

The system uses the given input signal to obtain the output signal and uses the above algorithm to identify the moment of inertia, the most critical of which is the selection of the input signal. The selection of the input signal should meet the following requirements:

1) The order of the input signal is higher than the order of the system.

2) The signal needs to be able to be simulated with the flywheel in the actual project.

3) The input signal can make the air-floating table with a large moment of inertia generate a suitable attitude change to obtain the output signal for easy identification.

According to the above conditions, there are two ways to select the input signal. One is to use multiple sinusoidal signals with different frequencies to superimpose as the input signal; the other is to use the high-order pseudo-random m-sequence as the excitation command for the flywheel as the input signal.

Example 3

The identification of the moment of inertia of the three-axis air flotation table in this system is a prerequisite for the air flotation table to complete other tasks. Because the three-axis air flotation table needs to be adjusted and balanced before it works, the moment of inertia will change, so as long as the routine The system composed of the three-axis air-floating table has the devices and functions described in this system, and the moment of inertia of the three-axis air-floating table can be identified after other systems complete the required hardware installation and adjustment and balance.

The system adopts the structure of the measurement and control system on the platform, the calculation and display control of the host computer system on the platform, the wireless communication between the monitoring and control system on the platform and the host computer system on the platform. The off-stage host computer system sends commands, the on-stage measurement and control system controls the flywheel to generate control torque, the gyroscope measures the attitude change, and the off-stage host computer system runs the identification algorithm and displays the data. The moment of inertia identification technology given by this method can identify the triaxial air flotation table used in most systems, so the composition of the system will be different according to different air flotation table systems, and only some necessary systems will be described later. composition. The detailed system composition is as follows:

Attitude measurement and control system of three-axis air-floating table

The attitude measurement and control system of the three-axis air flotation table consists of an air flotation ball, an instrument platform, a flywheel, and a gyroscope. The flywheel and gyroscope should be installed orthogonally in the three directions of the table coordinate system, and the external air supply will connect the air flotation ball and the instrument. The platform is held up, and the environment of the ground micro-interference moment is obtained. In this environment, the spacecraft can be simulated on the ground and its attitude can be measured and controlled, and the working environment of the air flotation platform to be identified is obtained.

Support and Protection System

The safety of the instrument platform and the air-floating ball bearing, the core components of the triaxial air-floating table, is one of the key issues of the system, which ensures the safety and reliability of the tri-axial air-floating table during operation.

The protection system is composed of an umbrella-shaped support under the instrument platform, and the opening angle of the umbrella-shaped part is controlled by controlling the motor, thereby controlling the angle variation range of the instrument platform.

The support system consists of three synchronous jacks and their drive control systems. In the non-working state, the jacks are raised synchronously, so that the air-floating ball is separated from the bearing seat to protect the system. In the working state, after the air flotation table system is supplied with air, put down the jack to make it in working state.

balance system

To complete the simulation of the spacecraft, the triaxial air flotation table needs its center of mass to coincide with the rotation center of the air flotation ball. The identification task of this system is also based on this basis, so the air flotation table needs to be adjusted and balanced first.

The balance adjustment system consists of multiple counterweight blocks and linear modules. During rough balance adjustment, observe the inclination of the air flotation table to adjust the position of the counterweight blocks. After rough adjustment, adjust the position of the slider through the linear module. Fine-tune the balance to ensure the balance of the air flotation table.

power supply system

In order to completely isolate the air flotation stage system from the understage to complete the identification task, the air flotation stage cannot have any wired connection with the understage, so the power supply system needs to use lithium batteries and secondary power supplies to supply power to each equipment on the stage.

wireless transmission system

In the case of ensuring the independence of the air flotation table system, it is necessary to issue instructions to the equipment on the air flotation table, and obtain the data on the stage. The IPC on the stage sends the collected data to the substage through the wireless transmission system, and the substage performs the data processing and display work.

Offstage data processing and display system

The host computer under the platform sends the flywheel command to the platform to generate the input signal to act on the system, and performs data processing on the output signal from the platform to identify the moment of inertia, and displays it online at the same time.

Specific measurement steps

1. Install hardware equipment as required, and adjust the counterweight to make the center of mass of the air flotation table close to the geometric center of the air flotation ball.

2. The power supply system in the on-stage measurement and control system is powered on, the off-stage host computer system and the support and protection system are powered on, and the on-stage monitoring and control system is connected by communication with the off-stage host computer system.

3. Supply air to the triaxial air flotation table to make it float.

4. Open the umbrella support and lower the jack.

5. Precisely adjust the balance of the air flotation table.

6. Send the flywheel command to the on-stage measurement and control system to start the identification task.

7. On-line identification and display of the moment of inertia of the host computer system under the stage.

8. After the identification, raise the jack, retract the umbrella support, and stop the air supply to the air flotation table.

9. Turn off the power and end all work.

The above are only preferred specific embodiments of the present invention, and these specific embodiments are based on different implementations under the overall concept of the present invention, and the protection scope of the present invention is not limited to this. Anyone familiar with the technical field Changes or substitutions that can be easily conceived by a skilled person within the technical scope disclosed in the present invention shall be included within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (3)

1. a large-scale three-axis air-floating table moment of inertia online identification system is characterized in that, comprising: data processing system (1), display system (2), support and protection system (3), three-axis air-floating table attitude measurement and control System (4), wireless transmission system (5), balance adjustment system (6) and power supply system (7), the relationship between the above-mentioned seven systems is as follows: the output from the data processing system (1) to the on-stage measurement and control system Signal data processing to identify the moment of inertia, display system (2) online display of the data processed by the data processing system (1), support and protection system (3) to ensure the safety and reliability of the three-axis air flotation table when working, and the protection system It consists of an umbrella-shaped support under the instrument platform, and the support system consists of three synchronous jacks and their drive control systems; the attitude measurement and control system (4) of the three-axis air-floating platform is used to obtain the environment of the ground micro-interference torque, and simulate the aerospace on the ground. The measurement of the device and the control of its attitude, the wireless transmission system (5) is used for information exchange between the on-stage measurement and control system and the off-stage host computer system, and the balance adjustment system (6) ensures that the center of mass of the three-axis air flotation stage and the air flotation ball rotate. The centers are coincident, and the power supply system (7) supplies power to the attitude measurement and control system (4) and the balance adjustment system (6) of the three-axis air-floating table. 2. a three-axis air-floating platform moment of inertia algorithm using a large-scale three-axis air-floating platform moment of inertia online identification system according to claim 1 is characterized in that, the moment of inertia is measured once algorithm, and the scheme of identifying the moment of inertia is as follows : The flywheel is used as the actuator of the system to input to the air flotation table, and the angular velocity is measured by the gyroscope as the output of the system, thus establishing the following dynamic equation:

Among them, J _f is the moment of inertia of the flywheel, ω _f is the rotational speed of the flywheel, J is the moment of inertia of the air-floating table, and ω is the angular velocity of the air-bearing table. The attitude control is performed at a small angle, so eliminating the small amount in the formula and modifying the position of the input and output can be obtained:

Among them, J ^-1 is the inverse matrix of the moment of inertia matrix. Both the matrix and the moment of inertia matrix are 3×3 symmetric matrices. Transforming the matrix can get:

J ^-1 = [J ₁₁ ^-1 J ₂₂ ^-1 J ₃₃ ^-1 J ₁₂ ^-1 J ₁₃ ^-1 J ₂₃ ^-1 ] ^T (5) The inverse of each value of the moment of inertia is represented by symbols. After identifying the values in formula (5), it needs to be converted into a 3×3 symmetric matrix and then inverse to obtain the actual moment of inertia matrix; Through the above analysis, the least squares representation of the moment of inertia is obtained, and the inverse form transformation formula can satisfy the characteristic of the least squares estimation of the output of the minimum variance, so that the identification accuracy is higher; Recursive algorithm for moment of inertia measurement. The standard formula of least squares method has been obtained in the above derivation. Repeated measurement with this formula requires many calculations and long time. It also needs to be converted to recursive least squares method to identify moment of inertia online. Through the above derivation, the following types of least squares formula are obtained: Y=Φθ,θ=(Φ ^T Φ) ^-1 Φ ^T Y (6) Among them, Y is the output angular acceleration, Φ is the torque input obtained from the speed of the flywheel, and θ is the deformation form of the moment of inertia matrix. The recursive formula is derived as follows: We order:

P(k)=(Φ ^T (k)Φ(k)) ^-1 ,θ(k)=P(k)Φ ^T (k)Y(k) (8) Bringing formula (7) and formula (8) into formula (6) can get:

Using the matrix inversion lemma for formula (10), we can get:

Bringing the above formula into formula (6), the recursive formula of the least square method can be obtained:

Among them, take P(0)=1010I, θ(0)=0 to satisfy the principle of recursive least squares. Considering that the system noise and moment of inertia parameters will change with time as disturbance torque and temperature factors, in the recursive least squares On the basis, the recursive least squares method of fading memory is used to achieve higher precision identification. The recursive formula of the least squares method of fading memory is as follows:

Among them, λ is the forgetting factor, which takes a value from 0 to 1. By simulating the estimation of the moment of inertia, a specific value can be selected for the forgetting factor, and each value in the primary identification method derived from the system attitude is brought into formula (13) The moment of inertia can be obtained by online identification. 3. The moment of inertia algorithm of the three-axis air-floating table according to claim 2, is characterized in that, the input signal for identification is selected to meet the following requirements: 1) The order of the input signal is higher than the order of the system; 2) The signal needs to be simulated by the flywheel in the actual project; 3) The input signal can make the air-floating table with a large moment of inertia generate a suitable attitude change to obtain the output signal for easy identification; Therefore, the input signal is to use a plurality of sinusoidal signals with different frequencies for superposition or to use a high-order pseudo-random m-sequence as the excitation for the flywheel command as the input signal.

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