Method and system for compensating zero-crossing friction torque of reaction flywheel

Abstract

The invention relates to the technical field of permanent magnet synchronous motor control, in particular to a zero-crossing friction torque compensation method and system for a reaction flywheel, and the method comprises the following steps: constructing a friction model which is continuous and differentiable; constructing an extended state observer; acquiring a first angular velocity of a reaction flywheel and a feedback current signal of the permanent magnet synchronous motor to the extended state observer, and calculating by the extended state observer to obtain a second angular velocity and system lumped disturbance; the friction model calculates friction torque according to the second angular velocity; calculating a feed-forward compensation vector in combination with the friction torque and the system lumped disturbance; performing feed-forward compensation according to the feed-forward compensation vector; according to the method, the improved friction torque model and the extended state observer are utilized, and the zero-crossing friction torque is accurately calculated and compensated by accurately estimating the rotating speed and calculating the friction torque.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor control, and more particularly to a method and system for compensating the zero-crossing friction torque of a reaction flywheel. Background Art

[0002] Reaction flywheels have the advantages of high output control torque accuracy, simple system structure, and no need to consume working fluid. They are widely used in high-precision, high-stability and long-term spacecraft. Reaction flywheels change the magnitude and direction of the angular momentum output by the flywheel rotor by controlling the acceleration and deceleration of the rotor, thereby outputting torque, and directly applying the generated torque to the spacecraft to achieve the purpose of attitude stability and attitude maneuvering of the spacecraft. It is an important inertial actuator for spacecraft attitude control. Permanent magnet synchronous motors have the significant advantages of simple structure, reliable operation, small size, light weight, high efficiency, and flexible shape and size of the motor, and have gradually become the ideal drive motor for reaction flywheels.

[0003] Since the reaction flywheel achieves torque output through the acceleration and deceleration of the rotor, the rotor of the reaction flywheel needs to change its rotation direction frequently. However, the friction torque generated by the bearing when the rotor rotates will bring additional disturbances, especially when the rotor changes its rotation direction, the friction torque shows serious nonlinearity, at this time the disturbance is more serious and leads to a decrease in the speed and output torque accuracy. In addition, due to the limited accuracy of the angular position encoder used in the system, in the ultra-low speed range, the angular position update period of the rotor will be much smaller than the period of the speed controller. At this time, when the rotor angular velocity is calculated by differential, it will cause serious angular velocity errors. When using angular velocity information with errors for friction torque compensation, it will cause reverse compensation of torque or serious speed oscillation. From the above analysis, it can be seen that in order to improve the zero-crossing friction torque compensation effect, it is necessary to improve the accuracy of friction estimation and speed measurement at the same time. Summary of the invention

[0004] In view of this, the present invention provides a method and system for compensating the zero-crossing friction torque of a reaction flywheel, which improves the zero-crossing friction torque compensation effect and improves the accuracy of friction estimation and rotation speed measurement.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A method for compensating a reaction flywheel zero friction torque comprises the following steps:

[0007] A friction model is constructed, wherein the friction model is continuously differentiable.

[0008] Constructing the extended state observer.

[0009] The first angular velocity of the reaction flywheel and the feedback current signal of the permanent magnet synchronous motor are collected and sent to the extended state observer, and the extended state observer calculates the second angular velocity and the system lumped disturbance.

[0010] The friction model calculates the friction torque according to the second angular velocity; calculates the feedforward compensation amount by combining the friction torque and the system lumped disturbance; and performs feedforward compensation according to the feedforward compensation vector.

[0011] Preferably, the step of collecting the first angular velocity of the reaction flywheel comprises:

[0012] The rotor angular position of the permanent magnet synchronous motor is monitored to obtain a pulse signal related to the rotor angular position, and the first angular velocity is obtained by differentiating the pulse signal.

[0013] Preferably, the inverse trigonometric function is used to approximate the sign function in the Stribeck model, and the friction model is obtained as follows:

[0014]

[0015] Among them, T fS is the Stribeck friction torque, ω s is the Sterbeck rate, T st is the maximum static friction torque, T c is the Coulomb friction torque, B v is the viscous friction coefficient, ω is the mechanical angular velocity of the rotor, and λ is the friction model accuracy coefficient, which is used to reflect the error relationship between the improved model and the original model. The larger its value is, the smaller the deviation from the original model is, and the higher the accuracy is.

[0016] Preferably, the extended state observer is:

[0017]

[0018] Among them, z1 represents the estimate of ω, and z2 represents the lumped disturbance e1=z1-x1 is the estimation error, β1 and β2 are the observer gains.

[0019] Preferably, the observer gain is adaptively adjusted according to the system reference speed.

[0020] Preferably, the step of performing feedforward compensation according to the feedforward compensation vector comprises:

[0021] Calculate the feedforward compensation:

[0022]

[0023] in, is the q-axis reference current fed forward to the current loop, k i is the coefficient related to the current;

[0024] The permanent magnet synchronous motor output torque:

[0025]

[0026] Where p is the number of motor pole pairs, ψ d is the permanent magnet flux, i q is the q-axis current of the motor.

[0027] A reaction flywheel zero-crossing friction torque compensation system, comprising: a friction model, an extended state observer, a current detector, an angular velocity detector and a current loop controller;

[0028] The current detector and the angular velocity detector are used to obtain a feedback current signal of the permanent magnet synchronous motor and a first angular velocity of a reaction flywheel, respectively;

[0029] The extended state observer is used to perform state expansion according to the feedback current signal and the first angular velocity to obtain a second angular velocity and a lumped disturbance;

[0030] The friction model is used to calculate the friction torque according to the second angular velocity, and calculate the feedforward compensation amount in combination with the lumped disturbance;

[0031] The current loop controller combines the feedforward compensation amount to form a driving current that acts on the reaction flywheel of the permanent magnet synchronous motor.

[0032] Preferably, a speed loop controller is further included, wherein the speed loop controller is used to calculate a reference current loop signal according to the second angular velocity and a reference angular velocity, and input the calculated reference current loop signal into the current loop controller.

[0033] Preferably, the current loop controller calculates the drive current by combining the feedforward compensation amount, the current loop reference signal and the feedback current signal.

[0034] Preferably, the angular velocity detector includes an angular velocity encoder and a differential module;

[0035] The angular velocity encoder is used to monitor the rotor angular position of the permanent magnet synchronous motor and output a pulse signal;

[0036] The differential module is used to differentiate the pulse signal to obtain the first angular velocity.

[0037] It can be seen from the above technical solutions that, compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. The present invention utilizes an improved friction torque model and an extended state observer to accurately estimate the rotation speed and calculate the friction torque, so that the zero-crossing friction torque can be accurately calculated and compensated.

[0039] 2. In order to facilitate the setting of the gain of the expanded state observer, the present invention adopts a bandwidth configuration method and sets the gain of the observer to a value that changes with the speed, thereby ensuring that the observer has sensitive observation performance while avoiding an excessively high observer bandwidth, which helps to reduce the introduction of high-frequency noise.

[0040] 3. The present invention improves the traditional friction model, eliminates the non-differentiable factors in the traditional model, obtains a continuously differentiable friction model, reduces the adverse effect of the step change of the friction torque calculation value at the zero-crossing moment, and reduces the torque reverse compensation and speed fluctuation caused by the speed measurement error. At the same time, by using an extended state observer with adaptive gain to observe the speed and the system lumped disturbance, the speed observation accuracy is improved, and a more accurate friction torque calculation result is obtained, thereby improving the accuracy of the reaction flywheel output torque. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0042] Figure 1 Schematic diagram of the process of the reaction flywheel zero friction torque compensation method in an embodiment of the present invention.

[0043] Figure 2 This is a simulation diagram of the relationship between the coefficient λ of the improved model and the model accuracy in an embodiment of the present invention.

[0044] Figure 3 Schematic diagram of the structure of the extended state observer in an embodiment of the present invention.

[0045] Figure 4 1 is a Bode diagram of the expanded observer with different bandwidths in an embodiment of the present invention.

[0046] Figure 5 4 is a block diagram of a control system of a reaction flywheel permanent magnet synchronous motor in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] Example 1

[0049] like Figure 1 As shown, the embodiment of the present invention discloses a method for compensating the zero friction torque of a reaction flywheel, comprising the following steps:

[0050] S1: constructing a friction model, wherein the friction model is continuously differentiable;

[0051] S2: Construct an extended state observer;

[0052] S3: collecting the first angular velocity of the reaction flywheel and the feedback current signal of the permanent magnet synchronous motor to the extended state observer, and the extended state observer calculates the second angular velocity and the system lumped disturbance;

[0053] S4: Calculating the friction torque according to the second angular velocity using the friction model;

[0054] S5: Calculate a feedforward compensation amount by combining the friction torque and the system lumped disturbance; and perform feedforward compensation according to the feedforward compensation vector.

[0055] In the traditional Stribeck friction model, there are two factors that cannot be differentiated, namely, the absolute value and the sign function, and both exhibit step characteristics at the zero-crossing moment. Therefore, at the zero-crossing point, a small speed deviation may also cause reverse compensation and overcompensation of the friction torque, thereby causing serious fluctuations in the speed. In order to reduce the large step of the torque compensation value at the zero-crossing point and the speed fluctuation, this embodiment constructs a continuously differentiable friction model.

[0056] In this embodiment, the electromagnetic torque equation output by the permanent magnet synchronous motor is:

[0057]

[0058] Where p is the number of motor pole pairs, ψ d is the permanent magnet flux, i q is the q-axis current of the motor.

[0059] The dynamic equation of the reaction flywheel can be expressed as:

[0060]

[0061] Where J is the moment of inertia of the reaction flywheel rotor, is the angular acceleration of the rotor, T f is the friction torque of the rotor, T d is the uncertainty disturbance.

[0062] The present invention drives the torque output by the permanent magnet synchronous motor by adjusting the q-axis current of the motor through feedforward compensation, thereby controlling the angular acceleration of the reaction flywheel rotor and outputting the torque.

[0063] In order to further implement the above technical solution, the construction process of the continuously differentiable friction model is as follows:

[0064] The symbolic function is approximated by using inverse trigonometric functions, namely:

[0065]

[0066] In order to improve the fitting accuracy and reduce the model deviation before and after improvement, the parameter λ is introduced, and the fitting equation is obtained as follows:

[0067]

[0068] The above approximation can eliminate the non-differentiable symbolic function terms in the model, and the improved model expression is:

[0069]

[0070] Among them, the simulation results of parameter λ and fitting accuracy are as follows Figure 2 As shown, by adjusting the size of the parameter λ, the fitting function matches the reference friction value.

[0071] In order to further implement the above technical solution, the present invention constructs an extended state observer to observe the rotor speed and lumped disturbance of the permanent magnet synchronous motor.

[0072] Specifically, the dynamic equation of the reaction flywheel is As a second-order system, the speed ω of the reaction flywheel and the variables related to the uncertainty disturbance They are defined as two state variables of the system: x1 and x2. At this time, the two-dimensional state variables can be obtained: Define f as the derivative of the variable related to the uncertainty disturbance, that is: Define u as the input quantity of the system and y is the output quantity and y=x1.

[0073] Therefore, the linear control system can be expressed as:

[0074]

[0075] Combining the above analysis, we can see that is the state transfer matrix, is the input matrix, C =

[10] is the output matrix, is the disturbance matrix of the system.

[0076] Based on the linear control system equation, use the formula Construct an extended state observer, where Y and U are the matrix forms of the system output y and the system input u respectively. The obtained extended state observer is expressed as:

[0077]

[0078] Where Z = [z1, z2] T , L = [β1, β2] T z1 represents the estimate of ω, and z2 represents the lumped disturbance The estimate of; e1 = z1-x1 is the estimation deviation,: β1 = 2ω eso and is the observer gain.

[0079] Furthermore, compared with the traditional extended state observer structure, the designed observer adds an adaptive link to the traditional extended state observer structure. Figure 3 , where the reference speed of the system is ω ref As the input of the adaptive link, it represents the target speed that the reaction flywheel is expected to reach, which can generally be given to the control system by the host computer or other means. The main content of the adaptive rule is to change the bandwidth ω of the extended state observer according to the reference speed eso .

[0080]

[0081] With the reference speed ω ref The increase of the observer bandwidth ω eso It increases accordingly, but the lower limit of the bandwidth is 5 rad / s due to the gain of the observer β1=2ω eso and Yes eso function, therefore, the designed extended state observer can realize adaptive adjustment of the gain.

[0082] The simulation results of the relationship between the amplitude-phase characteristics and bandwidth of the observer are as follows: Figure 4 As shown, it can be seen that as the bandwidth increases, the lag caused by the observer decreases, so the observer has better dynamic characteristics.

[0083] In order to further implement the above technical solution, the first angular velocity of the reaction flywheel is collected, and the steps include: monitoring the rotor angular position of the permanent magnet synchronous motor to obtain a pulse signal related to the rotor angular position, and obtaining the first angular velocity by differentiating the pulse signal.

[0084] Example 2

[0085] Based on the same inventive concept, Figure 5 An embodiment of the present invention discloses a reaction flywheel zero-crossing friction torque compensation system, including a friction model, an extended state observer, a current detector, an angular velocity detector and a current loop controller.

[0086] The current detector and the angular velocity detector are used to obtain the feedback current signal of the permanent magnet synchronous motor and the first angular velocity of the reaction flywheel respectively; the extended state observer is used to perform state expansion according to the feedback current signal and the first angular velocity to obtain the second angular velocity and the lumped disturbance; the friction model is used to calculate the friction torque according to the second angular velocity, and calculate the feedforward compensation amount in combination with the lumped disturbance; the current loop controller forms a driving current in combination with the feedforward compensation amount to act on the reaction flywheel of the permanent magnet synchronous motor.

[0087] In order to further implement the above technical solution, a speed loop controller is further included, wherein the speed loop controller is used to calculate a reference current loop signal according to the second angular velocity and the reference angular velocity, and input the reference current loop signal to the current loop controller. The current loop controller calculates the drive current by combining the feedforward compensation amount, the current loop reference signal and the feedback current signal.

[0088] In order to further implement the above technical solution, the angular velocity detector includes an angular velocity encoder and a differential module; the angular velocity encoder is used to monitor the rotor angular position of the permanent magnet synchronous motor and output a pulse signal; the differential module is used to differentiate the pulse signal to obtain a first angular velocity.

[0089] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0090] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for compensating the zero friction torque of a reaction flywheel, It is characterized in that The following steps are involved: constructing a friction model, wherein the friction model is continuously differentiable; Constructing an extended state observer; The first angular velocity of the reaction flywheel and the feedback current signal of the permanent magnet synchronous motor are collected and sent to the extended state observer, and the extended state observer calculates the second angular velocity and the system lumped disturbance; The friction model calculates the friction torque according to the second angular velocity; Calculating a feedforward compensation amount by combining the friction torque and the system lumped disturbance; Feedforward compensation is performed according to the feedforward compensation vector.

2. A method for compensating the zero friction torque of a reaction flywheel according to claim 1, It is characterized in that The step of collecting the first angular velocity of the reaction flywheel comprises: The rotor angular position of the permanent magnet synchronous motor is monitored to obtain a pulse signal related to the rotor angular position, and the first angular velocity is obtained by differentiating the pulse signal.

3. A method for compensating the zero friction torque of a reaction flywheel according to claim 1, It is characterized in that The inverse trigonometric function is used to approximate the symbol function in the Stribeck model, and the friction model is obtained as follows: Among them, T fS is the Stribeck friction torque, ω s is the Sterbeck rate, T st is the maximum static friction torque, T c is the Coulomb friction torque, B v is the viscous friction coefficient, ω is the mechanical angular velocity of the rotor, and λ is the friction model accuracy coefficient.

4. A method for compensating the zero friction torque of a reaction flywheel according to claim 1, It is characterized in that The extended state observer is: Among them, z 1 represents the estimate of ω, z 2 Represents the lumped disturbance Estimation of 1 =z 1 -x 1 is the estimated bias, β 1 and β 2 is the observer gain.

5. A method for compensating the zero friction torque of a reaction flywheel according to claim 4, It is characterized in that The observer gain is adaptively adjusted according to the system reference speed.

6. A method for compensating the zero friction torque of a reaction flywheel according to claim 1, It is characterized in that The step of performing feedforward compensation according to the feedforward compensation vector comprises: Calculate the feedforward compensation: in, is the q-axis reference current fed forward to the current loop, k i is the coefficient related to the current; The permanent magnet synchronous motor output torque: Where p is the number of motor pole pairs, ψ d is the permanent magnet flux, i q is the q-axis current of the motor.

7. A reaction flywheel zero friction torque compensation system, It is characterized in that include: Friction model, extended state observer, current detector, angular velocity detector and current loop controller; The current detector and the angular velocity detector are used to obtain a feedback current signal of the permanent magnet synchronous motor and a first angular velocity of a reaction flywheel, respectively; The extended state observer is used to perform state expansion according to the feedback current signal and the first angular velocity to obtain a second angular velocity and a lumped disturbance; The friction model is used to calculate the friction torque according to the second angular velocity, and calculate the feedforward compensation amount in combination with the lumped disturbance; The current loop controller combines the feedforward compensation amount to form a driving current that acts on the reaction flywheel of the permanent magnet synchronous motor.

8. A reaction flywheel zero friction torque compensation system according to claim 7, It is characterized in that It also includes a speed loop controller, which is used to calculate a reference current loop signal according to the second angular velocity and a reference angular velocity, and input the reference current loop signal into the current loop controller.

9. A reaction flywheel zero friction torque compensation system according to claim 8, It is characterized in that The current loop controller calculates the drive current by combining the feedforward compensation amount, the current loop reference signal and the feedback current signal.

10. A reaction flywheel zero friction torque compensation system according to claim 7, It is characterized in that The angular velocity detector includes an angular velocity encoder and a differential module; The angular velocity encoder is used to monitor the rotor angular position of the permanent magnet synchronous motor and output a pulse signal; The differential module is used to differentiate the pulse signal to obtain the first angular velocity.

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