A flexible tether tension peak-to-average ratio suppression control strategy for permanent magnet motor

Abstract

The application discloses a flexible tether tension peak-to-average ratio suppression control strategy of a permanent magnet motor, and is applied to the technical field of flexible transmission driving control. The application introduces state feedback of target object moving speed, and compensates steady-state error caused by load displacement on tether tension. Since motor driving controller is difficult to directly obtain target object moving speed information in actual application, the application adopts state observation on the target object speed, realizes state feedback under the condition that the target object speed information cannot be directly obtained, and gives basic principle and implementation scheme of the method. The proposed state observer can better track the target object speed within the error allowable range, and the tension dynamic response is relatively stable under the state feedback control.

Description

Technical Field

[0001] This invention relates to the technical field of permanent magnet motor drive control, and more particularly to a state feedback control based on a state observer. Background Technology

[0002] The aerospace industry is one of the leading advanced technologies in the national economy, and the peaceful use of outer space is a symbol of social and technological progress and the development of human civilization. With the rapid development of aerospace technology, my country's capabilities in space research, development, and application have continuously improved. To meet the requirements of manned spaceflight, orbital space stations, and near-Earth and deep space exploration missions, various types of spacecraft have been launched. In the unique environment of vacuum and weightlessness outside the atmosphere, electricity is one of the important sources of power for the internal mechanisms of spacecraft. Various aerospace electric servo mechanisms are the foundation and core for spacecraft to complete their corresponding exploration missions. Since the mid-20th century, the theory and application of aerospace servo systems have continuously expanded and extended with the maturity of microelectronics, computer technology, and automatic control technology, reflecting the development trend of permanent magnetization, digital intelligence, and high integration, enabling the realization of increasingly complex motion control needs of various aerospace mechanisms.

[0003] The flexible tether servo system is a novel spacecraft actuation mechanism that uses flexible tethers to construct corresponding transmission mechanisms to achieve actions such as capture and towing. Compared with traditional rigid transmission mechanisms, flexible transmission mechanisms have advantages such as simple structure, low loss, and strong mechanical compatibility, and have broad application prospects in important space missions such as space debris removal and spacecraft docking and separation. However, the special tension characteristics of flexible tethers also pose new requirements for aerospace electric servo systems. The tension generated by the tether is the medium for the exchange of kinetic energy and momentum between the spacecraft and the target object. In flexible tether servo systems, tension control plays a crucial role. Due to the low stiffness of flexible materials, there is a significant hysteresis and time-varying nature between stress and strain changes, making the tension establishment and release process relatively complex. Tension control of flexible tethers is one of the challenges of aerospace flexible tether electric servo systems. Based on the above background, this invention conducts research on space tether tension servo systems. Summary of the Invention

[0004] This invention addresses the shortcomings of traditional PI control in aerospace flexible servo mechanisms by proposing a peak-to-average power ratio (PAPR) suppression tension control strategy for permanent magnet motor tethered servo mechanisms based on state feedback. This strategy uses tether tension and target velocity as state variables to compensate for the steady-state error caused by load displacement on tether tension. Since it is difficult for the motor drive controller to directly obtain target velocity information in practical applications, this invention also designs a state observer for the target velocity and provides parameter design methods and control strategies for the state gain matrix and observer matrix. Simulation and experimental results show that the proposed state observer has a smaller target velocity tracking error, and the dynamic tension response is relatively stable under state feedback control.

[0005] To achieve the above-mentioned objectives, the present invention employs the following technical solution:

[0006] A technique for controlling the peak-to-average power ratio (PAPR) of a flexible tether for a permanent magnet motor, comprising the following steps:

[0007] A. Achieve vector control speed regulation of permanent magnet synchronous motor, that is, realize current and speed dual closed loop according to the given speed command, which can quickly wind and pull flexible ropes.

[0008] B. Select the tether tension and the end load traction speed as state variables, design the state feedback matrix, and construct a state feedback control system.

[0009] C. Based on the dynamic model of motor-tether-load, design a state observer matrix, and calculate the load displacement velocity at the end of the tether by sampling the tension and motor speed.

[0010] D. Use the unique load speed obtained from the state observer as the state variable to obtain the motor speed command after considering the load displacement speed.

[0011] Furthermore, in the peak-to-average power ratio (PAPR) suppression control strategy for the flexible tether tension of the permanent magnet motor, step A specifically involves: transforming the mutually coupled three-phase AC quantities into orthogonally decoupled two-phase AC quantities through a transformation from a three-phase natural coordinate system to a two-phase stationary coordinate system; then, achieving static decoupling of the excitation and torque components through a transformation from a two-phase rotating coordinate system to a two-phase stationary coordinate system. Based on this, separate control of the AC motor's excitation and torque can be achieved. Acceleration, speed, and position all need to be adjusted in real-time according to their reference values, and real-time torque control is a prerequisite. In these systems, acceleration is the ratio of the difference between the electromagnetic torque and the group torque to the rotor inertia. Acceleration is also the differential of the motor speed with respect to time; controlling the motor's electromagnetic torque controls the motor speed. Similarly, speed is the differential of position with respect to time; controlling the motor speed controls the rotor's trajectory. Based on the application requirements of small-to-medium power high-performance permanent magnet motor servo systems, the id=0 control method exhibits superior performance. The tension servo system for permanent magnet motors used in space tethering requires high reliability, and the permanent magnet motors used have low power. Furthermore, overly complex online calculation algorithms are not suitable for aerospace applications. Therefore, this invention employs a vector control method with id=0. The electromagnetic torque of the motor is the product of the rotor flux linkage vector and the stator current vector. The amplitude and phase difference between the rotor flux linkage vector and the stator current vector both affect the magnitude and direction of the motor's electromagnetic torque. By selecting the rotor direction as the reference direction, the phase difference between the rotor flux linkage vector and the stator current vector can be oriented.

[0012] Furthermore, in the peak-to-average power ratio (PAPR) suppression control strategy for the flexible tether tension of the permanent magnet motor, the purpose of introducing an integral term in the conventional PI regulator is to eliminate steady-state error and improve control accuracy. However, as analyzed in previous sections, when the tension is set or significantly increased or decreased, the tension will vary greatly in a short period of time. This will lead to a significant difference in the accumulation of the integral term, resulting in a noticeable peak. This is not allowed in the tension control system of the motor-driven flexible rope structure. When the tension reaches a given value, the output value of the integral term is reset to the speed of the target object at this time, so as to quickly adjust the speed reference and maintain the continuity and stability of the tension. Ideally, after the tension reaches a given value, the motor should be controlled to quickly adjust the speed so that the tether and the load are in the same direction and at the same speed. Because the integral term accumulates too much error, even after the tension reaches a given value, the output of the tension loop still has a significant integral desaturation process. The specific method of step B is as follows: First, examine the state equation of the permanent magnet motor tether tension mechanism. Based on the state transition matrix A and the input matrix B, its controllability matrix S = [B AB] can be easily obtained. Design the state feedback configuration to determine its closed-loop response effect. Calculate the characteristic polynomial of the system based on the state torque matrix. In the tension mechanism, the elastic coefficient k of the tethering rope is... r The ratio of the load mass m to σ is 2The response bandwidth ω required based on system performance b Configure the eigenvalues ​​and state gain matrix K of the closed-loop system with the damping ratio μ, and design the state feedback u = -Kx, such that the eigenvalues ​​of the closed-loop system are...

[0013] Furthermore, in the peak-to-average power ratio (PAPR) suppression control strategy for the flexible tether tension of a permanent magnet motor, step C is specifically as follows: Although state feedback can effectively improve system performance, the system's state variables are not necessarily easily measurable quantities. Since the system's output is generally measurable, if the system's output is used to reconstruct the system's state through a state observer, the estimated state value can then be fed back to the input control for system pole placement. This method of reconstructing the state is called state estimation, and the system that reconstructs the state is the state observer. When the system is controllable, the state feedback matrix K and the system observer matrix H can be designed independently. When the initial state of the simulated system is exactly the same as the initial state of the controlled system, the observer can accurately reflect the state changes of the controlled system. In general, there is an error between the initial state of the simulated system and the initial state of the controlled system. As long as the eigenvalues ​​of the state observer matrix (A-HC) have negative real parts, the observation error of the state variables will decay exponentially, and the convergence speed can be adjusted through the pole placement of the observer.

[0014] When selecting the parameters of the H matrix, it is generally desirable for the observer's response speed to be 5 to 10 times that of the state feedback system's response speed. Excessive values ​​can lead to adverse effects such as saturation and increased noise.

[0015] First, calculate the characteristic polynomial of the state observer.

[0016] det[λI-(AH

[11] )]=λ 2 +(H1+H2)λ+(σ 2 -H1 / m+H2k r )

[0017] The observer system matrix can be obtained by comparing the coefficients.

[0018]

[0019] The present invention, by adopting the above technical solution, has the following beneficial effects:

[0020] 1. The peak-to-average ratio suppression tension control strategy for the flexible tether of the permanent magnet motor disclosed in this invention can control the tension of the flexible tether and the speed of the towed target object respectively. The two are mutually coupled quantities controlled by the speed of the motor winding end, and are controlled as a pair of state-space variables.

[0021] 2. This invention is based on the principle of state feedback control. By introducing state feedback on the target object's moving speed, it compensates for the steady-state error caused by load displacement on the tether tension. In practical applications, the distance between the motor-driven platform and the target object is relatively far, and the controller cannot directly obtain the target object's moving speed. Therefore, this invention introduces state observation of the target object's speed. Since the target object's speed does not change abruptly, the state observer can track the target object's speed well, thus enabling state feedback even when the target object's speed information cannot be directly obtained. The proposed state observer can track the target object's speed well, and the tension dynamic response is relatively stable under the action of state feedback control.

[0022] 3. This method eliminates static errors by configuring a gain feedback matrix, achieving a smooth and stable tension establishment and release. It exhibits better dynamic and steady-state performance, is relatively simple to implement, and requires fewer hardware resources. This method can effectively suppress the peak-to-average power ratio (PAPR) during dynamic processes while ensuring steady-state tension establishment accuracy, and also guarantees relatively stable and smooth motor speed changes. Attached Figure Description

[0023] Figure 1 This is a structural diagram of a permanent magnet synchronous motor flexible tethered electric towing tension control system.

[0024] Figure 2 It is a state variable control model for a flexible tethering mechanism.

[0025] Figure 3 State feedback control structure.

[0026] Figure 4 It is a state feedback control structure that introduces a state observer.

[0027] Figure 5 It employs a permanent magnet motor tension control strategy using a state observer. Detailed Implementation

[0028] The technical solution of the invention will now be described in detail with reference to the accompanying drawings.

[0029] The structure of the permanent magnet synchronous motor flexible tethered electric towing tension control system is as follows: Figure 1 As shown. When there is a speed difference between the winding tether and the load, the flexible tether undergoes elastic deformation due to the stretching process. The deformation of the tether and the magnitude of the resulting tension satisfy the elastic law shown in equation (1):

[0030] T = k r (l s -l f (1)

[0031] Where T is the tension generated by winding the rope, and kr It is the elastic modulus of the rope, which is determined by factors such as the material and size of the rope. s This is the length of the tether that has been wound and stored by the motor. f It is the length of the rope that decreases due to the movement of the load.

[0032] Length of the rope winding section l s The derivative with respect to time is the motor speed, as shown in equation (2):

[0033]

[0034] Among them, v s It is the linear velocity of the outer diameter of the motor load section.

[0035] There is a second-order differential relationship between the load displacement and tension, as shown in equation (3):

[0036]

[0037] Where m is the load mass.

[0038] The characteristic equation of the tension mechanism can be transformed into the form of a state matrix to obtain...

[0039]

[0040] The state variable x, state transition A, and input matrix B are given by equations (5), (6), and (7), respectively. Based on equations (5)-(7), the state variable model of the rope-tying mechanism studied in this invention can be obtained, as follows: Figure 2 As shown.

[0041] x = [T v] f ]T (5)

[0042]

[0043] B = [1 0]T (7)

[0044] When the control input of the system takes the form of a linear function of the state variables

[0045] u=v-Kx (8)

[0046] By negatively feeding the state vector x back to the control input through the undetermined state feedback matrix K, a linear direct state feedback system is formed, the system structure of which is as follows: Figure 3 As shown.

[0047] Equation (8) yields the system dynamic equation with state feedback and the characteristic polynomial of the state transition matrix, respectively.

[0048]

[0049] |λI-(A-BK)|(10)

[0050] As can be seen, after the system introduces state feedback, only the system matrix and its eigenvalues ​​are changed, while the input matrix and output matrix remain unchanged.

[0051] Construct a controlled system with the same structure but which can be implemented using computer simulation.

[0052]

[0053] in: These are the state vector and output vector of the simulation system, respectively.

[0054] Error of state vector Error of the output vector There is a close relationship, and the output of the controlled system is always measurable. Negative feedback is sent to point x to control. If it converges to zero as quickly as possible, then It will converge to zero consistently, thus forming a state feedback implemented using x.

[0055] The state observer and control structure that implements state feedback based on the above principles are as follows: Figure 4 As shown.

[0056] The eigenvalues ​​of the calculated system state transition matrix are λ. 1,2 =±σ i It can be seen that since the eigenvalues ​​of the flexible tether tension mechanism model are imaginary, it is prone to oscillations without changing the feedback poles, and the degree of oscillation is related to the tether elastic coefficient k. r It is related to the load mass m. The larger the elastic coefficient of the tether or the smaller the load mass, the more likely it is to cause instability in the dynamic process.

[0057] Based on the response bandwidth ω required by system performance b Given the damping ratio μ, configure the eigenvalues ​​and state gain matrix K of the closed-loop system, and design the state feedback u = -Kx, such that the eigenvalues ​​of the closed-loop system are: First, calculate the characteristic polynomial of the state observer.

[0058] det[λI-(AH

[11] )]=λ 2 +(H1+H2)λ+(σ 2 -H1 / m+H2k r (12)

[0059] The observer system matrix can be obtained by comparing the coefficients.

[0060]

[0061] Figure 5 This is a block diagram of the peak-to-average power ratio (PAPR) suppression strategy based on state observation proposed in this invention. It mainly includes the mathematical model of the control system, the state feedback matrix K, and the observer system matrix H.

Claims

1. A peak-to-average power ratio (PAPR) suppression control strategy for flexible tether tension in a permanent magnet motor, characterized in that, Includes the following steps: A. The vector control speed regulation of the permanent magnet synchronous motor is adopted, that is, the current and speed are closed-loop according to the given speed command, which can quickly wind and pull the flexible rope. B. Select the tether tension and the end load traction speed as state variables, design the state feedback matrix, that is, the state gain matrix K, and construct the state feedback control system. C. Based on the dynamic model of motor-tether-load, design a state observer calculation method, and calculate the load displacement velocity at the end of the tether by sampling the tension and motor speed. D. Using the load displacement velocity obtained in step C as a state variable, obtain the motor speed command after considering the load displacement velocity to achieve high-performance control of the tether tension.

2. The peak-to-average power ratio suppression control strategy for flexible tether tension of a permanent magnet motor according to claim 1, characterized in that, The specific method of step A is as follows: the three-phase AC quantities that are coupled to each other are transformed into two-phase AC quantities that are orthogonally decoupled by transforming the three-phase natural coordinate system to the two-phase stationary coordinate system. Then, the excitation component and the torque component are statically decoupled by transforming the two-phase rotating coordinate system to the two-phase stationary coordinate system. The excitation current and torque current of the motor are controlled according to the principle of magnetic field orientation, so as to achieve the purpose of controlling the motor torque.

3. The peak-to-average power ratio suppression control strategy for flexible tether tension of a permanent magnet motor according to claim 2, characterized in that, The specific method for step B is as follows: First, examine the state equation of the permanent magnet motor tether tension mechanism. Based on the state transition matrix A and the input matrix B, its controllability matrix S = [B AB] can be easily obtained. Design the state feedback configuration to determine its closed-loop response effect. Calculate the characteristic polynomial of the system based on the state transition matrix. In the tension mechanism, the elastic coefficient of the tethering rope is k. r The ratio of the load mass m to σ is 2 The response bandwidth ω required based on system performance b Configure the eigenvalues ​​and state gain matrix K of the closed-loop system with the damping ratio μ, and design the state feedback u = -Kx, such that the eigenvalues ​​of the closed-loop system are... x is a state variable.

4. The peak-to-average power ratio suppression control strategy for flexible tether tension of a permanent magnet motor according to claim 3, characterized in that, The specific method for step C is as follows: Under the condition that the system is controllable, the state feedback matrix K and the system observer matrix H are designed independently, based on the dynamic equations of the state observer in state feedback control. First, by selecting the H matrix parameters, the characteristic polynomial of the state observer is calculated: det[λI-(AH[1 1])]=λ 2 +(H1+H2)λ+(σ 2 -H1 / m+H2k r ) The observer system matrix can be obtained by comparing the coefficients. in, This is the output vector of the state observer. This is the state vector of the state observer.

5. The peak-to-average power ratio suppression control strategy for flexible tether tension of a permanent magnet motor according to claim 1 or 4, characterized in that, The specific method of step D is as follows: based on the motor speed given value obtained in steps B and C, the speed of the permanent magnet motor is controlled by vector control technology, and the tension is controlled by winding up the rope.

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