A method and device for angular displacement servo control of a permanent magnet synchronous motor with limited rotational speed

Abstract

The present invention discloses a speed-limited permanent magnet synchronous motor angular displacement servo control method and device, which relates to the field of servo drive technology, wherein the method comprises the following steps: Step S1: designing a transition process, wherein the transition process comprises three stages: starting, uniform speed operation and braking; determining the time of each stage, and determining the planned motion amount according to the time of each stage, including the expected angular displacement. θ d , expected angular velocity ω d and the expected angular acceleration a d ; Step S2: Design the mechanical loop self-disturbance rejection backstepping controller to achieve the desired angular displacement θ d and the desired angular velocity ω d Through the design of the transition process and the design of the controller, the present invention enables the angular displacement and angular velocity of the motor to accurately track the planned expected angular displacement and expected angular velocity; the design of the closed-loop control system not only improves the stability and accuracy of the device during operation, but also significantly enhances the overall performance of the AC servo system under speed-limited conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of servo drive, and in particular to an angular displacement servo control method and device for a permanent magnet synchronous motor with limited rotational speed. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) play a key role in modern mechatronic drives and are widely used in industrial robots, automated production, electric vehicles, and other fields. The common control methods for PMSMs mainly include: field-oriented control, direct torque control, and constant voltage-frequency ratio control. Among them, field-oriented control is the most commonly used and very efficient control strategy, which has been widely applied in industry. Its principle is to convert the three-phase alternating current of the motor into two-phase direct current through two coordinate transformations (Clark transformation and Park transformation) to achieve precise control of the motor. Field-oriented control usually includes a current loop, an angular velocity loop, and an angular displacement loop, and a PI controller is used to adjust the current, angular velocity, and angular displacement to achieve the required performance. The key of the FOC control algorithm lies in controlling the magnitude and direction of the three-phase input current to generate the maximum torque and efficiency.

[0003] During the angular displacement control process of the motor, a low-pass filter is usually used to plan the transition process of the angular displacement and angular velocity of the motor. However, when the single displacement adjustment amount of the motor is relatively large, the planned peak angular velocity will be relatively large. For the motor controller, since the rotational speed of the motor that it can control has an upper limit, when the planned peak angular velocity exceeds the rotational speed upper limit that the controller can withstand, the closed-loop control system will experience an out-of-control phenomenon. Summary of the Invention

[0004] In view of the above problems, the present invention provides an angular displacement servo control method for a permanent magnet synchronous motor with limited rotational speed, including the following steps:

[0005] Step S1: Design a transition process, which includes three stages: start-up, uniform operation, and braking:

[0006] In the start-up stage, the angular velocity is accelerated from 0 to the maximum allowable rotational speed ω at a constant angular acceleration max ;

[0007] In the middle stage, it runs at a constant speed with the maximum allowable rotational speed ω max ;

[0008] In the braking stage, the angular velocity is decelerated from the maximum allowable rotational speed ω max to 0 at a constant angular acceleration;

[0009] Determine the time of each stage, and determine the planned amount of motion according to the time of each stage, including the expected angular displacement θ d, Desired angular velocity ω d and desired angular acceleration a d .

[0010] Step S2: Based on the motion amounts planned in the above Step S1, design a mechanical loop active disturbance rejection backstepping controller and a current loop controller to achieve accurate tracking of the angular displacement and angular velocity of the permanent magnet synchronous motor with respect to the planned desired angular displacement and desired angular velocity.

[0011] Based on the above technical solution, in the starting and braking phases, the magnitudes of the constant angular accelerations are equal.

[0012] Based on the above technical solution, the times of each phase and the determination of the planned motion amounts include:

[0013] Let the starting and braking durations be τ , the intermediate constant-speed running duration be , the acceleration be , and determine the times of each phase: when , ; when , , is the target angle.

[0014] Define the time point , and determine the planned motion amounts according to the times of each phase, including the desired angular displacement θ d , the desired angular velocity ω d and the desired angular acceleration a d , if , then

[0015] ,

[0016] ,

[0017] ;

[0018] If , then

[0019] ,

[0020] ,

[0021] ;

[0022] If , then

[0023] ,

[0024] ,

[0025] ;

[0026] If , then

[0027] ,

[0028] ,

[0029] .

[0030] Based on the above technical solution, the step S2 specifically includes the following steps:

[0031] Step S21: Design a mechanical loop auto-disturbance rejection backstepping controller:

[0032] First, define the angle tracking error: ; and take its derivative: ;

[0033] Construct the virtual control law as ω. In order to achieve , the expected value is: , where , k1 is a positive constant;

[0034] Define the angular velocity tracking error: , take the derivative: , where T l is the unknown load torque or disturbance torque, and J is the moment of inertia referred to the motor shaft;

[0035] Use an extended state observer to estimate the unknown load torque or disturbance torque. Define the disturbance , and design a reduced-order extended state observer to estimate the disturbance σ:

[0036]

[0037] where, 0 < μ << 1, z is the constructed intermediate variable, is 's estimated value. When , ;

[0038] Design the expected torque value:

[0039] ,

[0040] where is a positive constant.

[0041] Step S22, design a PID controller for the current loop to achieve precise regulation of the motor output torque, and adjust the motor output torque to the desired torque , and then achieve :

[0042] Adopt the field-oriented control method with i d =0. According to it can be obtained , which can be written as:

[0043] ,

[0044] where i d is the d-axis current, i q is the q-axis current, Ψ f is the amplitude of the permanent magnet flux linkage of the stator winding, n p is the number of pole pairs on the motor rotor;

[0045] Adopt the PI control algorithm with model compensation to adjust the d-axis and q-axis currents. The input voltages and can be designed as:

[0046]

[0047] where , , , , , represents the switching frequency of the PWM.

[0048] The present invention also provides an angular displacement servo control device for a permanent magnet synchronous motor with limited speed, including:

[0049] A transition module, which is used to design a transition process, and the transition process includes a start, a constant-speed and a braking unit:

[0050] A start unit, which accelerates the angular velocity from 0 to the maximum allowable speed ω max at a constant angular acceleration;

[0051] A constant-speed unit, which runs at a constant speed with the maximum allowable speed ω max ;

[0052] A braking unit, which decelerates the angular velocity from the maximum allowable speed ω maxDecelerate to 0;

[0053] A planning module, which is used to determine the time of each stage and determine the planned motion amount according to the time of each stage, including the expected angular displacement θ d , the expected angular velocity ω d and the expected angular acceleration a d ;

[0054] A controller design module, which is used to design a mechanical loop active disturbance rejection backstepping controller and a current loop controller based on the motion amount planned by the planning module, so as to realize the accurate tracking of the angular displacement and angular velocity of the permanent magnet synchronous motor to the planned expected angular displacement and expected angular velocity.

[0055] On the basis of the above scheme, the magnitudes of the constant angular accelerations in the starting unit and the braking unit are equal and the directions are opposite.

[0056] The present invention also provides a controller, including a memory, a processor, and instructions stored in the memory and executable on the processor, and the processor is used to execute a method for angular displacement servo control of a speed-limited permanent magnet synchronous motor as described above.

[0057] Compared with the prior art, the present invention has the following beneficial effects: Through the design of the transition process and the design of the controller, the angular displacement and angular velocity of the motor can accurately track the planned expected angular displacement and expected angular velocity; The design of the closed-loop control system not only improves the stability and accuracy of the device during operation, but also significantly enhances the overall performance of the AC servo system under speed-limited conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is a timing diagram of the transition process designed by the present invention;

[0059] Figure 2 is a block diagram of the closed-loop system principle of the discrete-time domain robust speed controller proposed by the present invention;

[0060] Figure 3 is a schematic diagram of the experimental results of an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] The following will refer to the drawings to describe in detail the embodiments of a method and device for angular displacement servo control of a speed-limited permanent magnet synchronous motor according to the present invention. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0062] The angular displacement servo system of a surface-mounted permanent magnet synchronous motor (SPMSM) can be written as:

[0063] ,

[0064] where the meanings of the parameters are shown in Table 1:

[0065] Table 1 Meanings of motor parameters

[0066]

[0067] For the angular displacement servo system of a permanent magnet synchronous motor, the control objective is to design the input voltage of the axis and the input voltage of the axis so that the angle of the rotor can be quickly adjusted to the target angle , and at the same time, during the adjustment process, the angular velocity of the motor rotation does not exceed the set value , that is holds for all

[0068] To achieve the control objective, the present invention provides a method for angular displacement servo control of a permanent magnet synchronous motor with limited speed. First, a transition process is designed, as shown in Figure 1 . Let the start and brake durations be τ , and the intermediate constant-speed operation duration be τ mid , then the acceleration is

[0069] ,

[0070] When ,

[0071] ,

[0072] When ,

[0073] .

[0074] Then, the planned motion amount is determined according to the time of each stage, including the expected angular displacement , the expected angular velocity and the expected angular acceleration . Define the time point , then, there is

[0075] If , then

[0076] ,

[0077] ,

[0078] ;

[0079] If , then

[0080] ,

[0081] ,

[0082] ;

[0083] If , then

[0084] ,

[0085] ,

[0086] ;

[0087] If , then

[0088] ,

[0089] ,

[0090] .

[0091] On the basis of designing the transition process, the designed controller realizes the angular displacement and angular velocity of the permanent magnet synchronous motor to accurately track the planned desired angular displacement and desired angular velocity . First, design the mechanical loop active disturbance rejection backstepping controller:

[0092] Define the angle tracking error:

[0093] ,

[0094] Taking the derivative of it, we can get:

[0095] ,

[0096] Let be the virtual control law. In order to achieve , its expected value is:

[0097] ,

[0098] Among them, is a positive constant.

[0099] To achieve , define the angular velocity tracking error:

[0100] ,

[0101] Taking the derivative of it, we can get:

[0102] ,

[0103] Since is the unknown load torque or disturbance torque, which will have an adverse impact on the control performance. To suppress this adverse impact, define the disturbance , and here a reduced-order extended state observer is used to estimate it. The designed reduced-order extended state observer can be written as:

[0104] ,

[0105] Among them, 0 < μ << 1, is the constructed intermediate variable, is 's estimated value. It can be proved that when , .

[0106] Based on the disturbance estimated value of the extended state observer, the desired torque value can be designed:

[0107] ,

[0108] Among them, is a positive constant.

[0109] When the output torque of the motor can be accurately adjusted to , then can be achieved.

[0110] To achieve the accurate adjustment of the motor output torque, design the PID controller of the current loop, and adopt i d = 0 field-oriented control method. Then according to we can obtain , which can be written as

[0111] ,

[0112] For the current regulation of the d-axis and q-axis, adopt the PI control algorithm with model compensation, and can be designed as:

[0113] ,

[0114] wherein, , , , , , represents the switching frequency of PWM.

[0115] Such as Figure 2 shown, first, according to the target angle θ r of the rotor, trajectory planning is carried out, that is, the transient process design is carried out to obtain the expected angular displacement , the expected angular velocity and the expected angular acceleration ; , the P controller is proportional to the angle tracking error. By selecting an appropriate k1 value, the response speed of the controller to the error can be adjusted; by defining the disturbance , and using a reduced-order extended state observer to estimate, based on the disturbance estimated value of the extended state observer, the expected torque value T e * is designed; the field-oriented control method with i d =0 is adopted. According to the motor electromagnetic torque formula: , then i q can be represented by T e * : ; the PI control algorithm with model compensation is adopted to obtain the input voltages and of the d-axis and q-axis, and the Inverse Park transformation is used to convert the calculated and into three-phase voltage signals; the space vector pulse width modulation (SVPWM) module receives the three-phase PWM signals from the Inverse Park transformation module, and the PWM signals control the switching actions of the MOSFETs in each phase of the inverter, thereby generating the AC voltage for driving the motor. At the same time, the generated three-phase AC current signals are converted into two-phase current signals i d and i q by Clark / Park transformation and flow to the PI controller for calculating and , a closed loop is formed; an encoder is used to monitor the angular displacement signal of the motor, calculate the angular velocity, and feedback the angular displacement and angular velocity to the controller to update the error and adjust the output until the angular displacement reaches the expected value.

[0116] In the present invention, the design of the transient process and the controller can significantly improve the stability of the closed-loop system of the AC servo system under the condition of limited rotational speed, ensuring good stability and accuracy even in the face of limited rotational speed during the motor control process.

[0117] In order to verify the feasibility of the trajectory planning method and the controller design method proposed in the present invention, experiments are carried out on a permanent magnet synchronous motor experimental device for demonstration.

[0118] The control objective is to make the angular displacement of the permanent magnet synchronous motor first adjust forward from 0 rad to 100 rad, with the angular velocity not exceeding 20 rad / s during the process. The time for the angular velocity to accelerate from 0 rad / s to 20 rad / s is 0.5 s, and the time for decelerating from 20 rad / s to 0 rad / s is 0.5 s. Then, it adjusts backward from 100 rad to 0 rad, with the angular velocity not exceeding -20 rad / s during the process, and the acceleration and deceleration time of the angular velocity is also 0.5 s. The experimental results are as Figure 3 shown.

[0119] In the figure, a1 is the first stage of the actual angular displacement, representing that the actual angular displacement can smoothly transition from 0 rad to 100 rad. a2 is the second stage of the actual angular displacement, representing that the displacement does not change. a3 is the third stage of the actual angular displacement, indicating that the angular displacement transitions back from 100 rad to 0 rad. In the figure, b1 and b2 are the actual angular velocity change processes when the motor rotates forward and backward respectively. It can be seen that the actual angular velocity does not exceed the limit of ±20 rad / s during the whole motion process. In the figure, A1 and A2 are the processes of the planned angular displacement transitioning from 0 rad to 100 rad and from 100 rad back to 0 rad, and B1 and B2 are the planned angular velocity change processes when the motor rotates forward and backward respectively. C1, C2, C3, and C4 are the change processes when the planned angular acceleration is not 0, and each stage of the angular acceleration is a fixed value. According to the results, it is found that there is good consistency between the planned angular displacement and angular velocity and the actual angular displacement and angular velocity.

[0120] Specifically, the motor can perform smooth transitions according to the planned angular displacement, angular velocity, and angular acceleration. At the same time, the angular velocity does not exceed the limit of ±20 rad / s, and the angular displacement and angular velocity can also well track the planned trajectory. This shows that the present invention can achieve smooth adjustment of the angular displacement, meet the requirements of the control target, and can effectively control the angular velocity of the motor so that it does not exceed the set limit value. Therefore, the experimental results verify the feasibility and effectiveness of the transition process design method and the controller design method proposed by the present invention.

[0121] The present invention also provides an angular displacement servo control device for a permanent magnet synchronous motor with limited speed, including:

[0122] A transition module, which is used to design a transition process, and the transition process includes a start, a constant speed, and a braking unit:

[0123] A start unit, which accelerates the angular velocity from 0 to the maximum allowable speed ω with a constant angular acceleration max ;

[0124] A constant speed unit, which operates at a constant speed with the maximum allowable speed ω max constantly;

[0125] A braking unit, which decelerates the angular velocity from the maximum allowable speed ω max to 0 with a constant angular acceleration;

[0126] A planning module, which is used to determine the time of each stage and determine the planned amount of motion according to the time of each stage, including the desired angular displacement θ d , the desired angular velocity ω d and the desired angular acceleration a d ;

[0127] A controller design module, which is used to design a mechanical loop active disturbance rejection backstepping controller design and a current loop controller based on the amount of motion planned by the planning module, so as to achieve precise tracking of the angular displacement and angular velocity of the permanent magnet synchronous motor to the planned desired angular displacement and desired angular velocity.

[0128] Specifically, the magnitudes of the constant angular accelerations in the start unit and the braking unit are equal and the directions are opposite.

[0129] The present invention also provides a controller, which includes a memory, a processor, and instructions stored in the memory and executable on the processor. The processor is configured to execute a method for angular displacement servo control of a speed-limited permanent magnet synchronous motor as described above. Among them, the instructions can be stored in a computer-readable storage medium, and when executed by the processor, the steps in the above-mentioned various method embodiments can be implemented.

[0130] The present invention has been described with reference to the above-mentioned preferred embodiments, but the scope of the present invention is not limited to such embodiments. The scope of the present invention is determined by the following claims and may include various revisions and modifications within the equivalent scope of the present invention.

Claims

1. A speed-limited permanent magnet synchronous motor angular displacement servo control method, characterized in that: The following steps are involved: Step S1: Design a transition process, which includes three stages: starting, running at a constant speed, and braking: During the startup phase, the angular velocity is accelerated from 0 to the maximum allowable speed ω at a constant angular acceleration. max ; In the intermediate stage, at the maximum permissible speed ω max Constant operation; During the braking phase, the angular velocity is increased from the maximum allowable speed ω at a constant angular acceleration. max decelerate to 0; Determine the time of each phase and determine the planned movement amount based on the time of each phase, including the expected angular displacement θ d , expected angular velocity ω d and the expected angular acceleration a d ; The time and amount of exercise planned for each stage include: Let the starting and braking time be τ , the intermediate uniform speed running time is , the acceleration is , determine the time of each stage: when hour, ;when hour, , is the target angle; Define time points , determine the planned movement amount according to the time of each stage, including the expected angular displacement θ d , expected angular velocity ω d and the expected angular acceleration a d ,like ,but ， ， ； like ,but ， ， ； like ,but ， ， ； like ,but ， ， ； Step S2: Based on the movement volume planned in step S1, a mechanical loop anti-disturbance backstepping controller and a current loop controller are designed to achieve accurate tracking of the planned desired angular displacement and desired angular velocity of the permanent magnet synchronous motor by the angular displacement and angular velocity.

2. The method for controlling the angular displacement servo of a permanent magnet synchronous motor with limited speed according to claim 1, characterized in that: During the starting and braking phases, the constant angular accelerations are equal in magnitude and opposite in direction.

3. The method for controlling the angular displacement servo of a permanent magnet synchronous motor with limited speed according to claim 1, characterized in that: Step S2 specifically includes the following steps: Step S21: Design a mechanical loop anti-disturbance backstepping controller: First, define the angular tracking error: ; and take its derivative: ; Construct a virtual control law as ω, in order to achieve , the expected value is: ,in, , k1 is a positive constant; Define angular velocity tracking error: , find the derivative: , where T l is the unknown load torque or interference torque, and J is the moment of inertia converted to the motor shaft; Use the extended state observer to estimate the unknown load torque or disturbance torque and define the disturbance , design a reduced-order extended state observer to estimate disturbances σ : Where 0 < μ << 1, z is the constructed intermediate variable, yes The estimated value of , ; Design expected torque value: ， in, is a positive constant; Step S22, designing a PID controller of the current loop to achieve precise regulation of the motor output torque, Adjust to the desired torque , and thus achieve ,include: use i d =0 magnetic field oriented control method, according to Available : ， in, i d is the d-axis current, i q is the q-axis current, Ψ f is the stator winding permanent magnet flux amplitude, n p is the number of magnetic pole pairs on the motor rotor; The PI control algorithm with model compensation is used to adjust the d-axis and q-axis currents and input voltage and Can be designed as: in, , , , , , Indicates the switching frequency of PWM.

4. A speed-limited permanent magnet synchronous motor angular displacement servo control device, characterized in that: include: Transition module, the transition module is used to design the transition process, the transition process includes starting, constant speed and braking units: A starting unit, wherein the starting unit accelerates the angular velocity from 0 to the maximum allowable rotation speed ω at a constant angular acceleration max ; The uniform speed unit has a maximum allowable rotation speed ω max Constant operation; The brake unit completes the angular velocity from the maximum allowable speed ω at a constant angular acceleration max decelerate to 0; A planning module, which is used to determine the time of each stage and determine the planned movement amount according to the time of each stage, including the expected angular displacement θ d , expected angular velocity ω d and the expected angular acceleration a d ,include: Let the starting and braking time be τ , the intermediate uniform speed running time is , the acceleration is , determine the time of each stage: when hour, ;when hour, , is the target angle; Define time points , determine the planned movement amount according to the time of each stage, including the expected angular displacement θ d , expected angular velocity ω d and the expected angular acceleration a d ,like ,but ， ， ； like ,but ， ， ； like ,but ， ， ； like ,but ， ， ； A controller design module is used to design a mechanical loop self-disturbance rejection backstepping controller and a current loop controller based on the movement volume planned by the planning module, so as to achieve accurate tracking of the planned desired angular displacement and desired angular velocity of the permanent magnet synchronous motor by the angular displacement and angular velocity.

5. The angular displacement servo control device of a permanent magnet synchronous motor with limited speed according to claim 4, characterized in that: The constant angular accelerations in the starting unit and the braking unit are equal in magnitude and opposite in direction.

6. A controller comprising a memory, a processor, and instructions stored in the memory and executable on the processor, characterized in that: The processor is used to execute a speed-limited permanent magnet synchronous motor angular displacement servo control method as described in any one of claims 1-3.

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