A motor selection method based on desired tracking task and controller structure

Abstract

The application belongs to the technical field of motor system control, and discloses a motor selection method based on expected tracking tasks and controller structures, which comprises the following steps: first, a second-order differential equation describing the generalized position and generalized speed characteristics of a motor is established; second, the load and expected trajectory involved in the expected tracking task are determined, and constants are selected to represent the upper and lower bounds of the load and expected trajectory; third, an error variable is defined, and an adaptive tracking controller is designed based on the second-order differential equation; fourth, a Lyapunov function is selected to analyze the upper and lower bounds of the error variable; fifth, based on the controller structure, controller parameters, initial value of the error variable, upper and lower bounds of the error variable, and expected task, the upper and lower bounds of the required control torque of the motor and the upper bound of the power are determined, and motor selection is completed according to the boundary conditions. The application realizes the analysis of the peak torque and maximum power of the motor and the tracking of the expected motor position.

Description

Technical Field

[0001] This invention belongs to the field of motor system control technology, and particularly relates to a control and selection method for a type of motor system with torque control function. Background Technology

[0002] Currently, electric motors operate using three modes: position loop control, speed loop control, and torque loop control. Torque loop control is the most commonly used mode, adjusting the motor's output torque to achieve generalized position tracking of the desired position. However, in industrial applications, motors often need to carry different loads and perform different position tracking tasks. This places different demands on the motor's performance indicators, requiring engineers to analyze and select the appropriate motor model before executing the task.

[0003] However, motor selection currently relies primarily on engineers' practical experience and engineering application testing, lacking theoretical guidance. Furthermore, in most experience-based selections, engineers only consider the tasks the motor needs to perform, neglecting the impact of different controller structures on transient control torque performance. In engineering application testing, motor testing carries certain risks and, as the complexity of the loaded motion task increases, it places additional workload on engineers, resulting in significant resource waste.

[0004] Therefore, there is an urgent need to design a theoretically sound and easily implementable motor selection method for the desired tracking task and controller structure, to support engineers in completing the initial motor selection in the engineering design process, thereby reducing the difficulty, cost and safety risks of selection. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a theoretically sound and easily implemented method for motor selection, based on the desired tracking task and controller structure.

[0006] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows: A motor selection method based on desired tracking task and controller structure includes the following steps: The first step is to establish second-order differential equations describing the generalized position and generalized velocity characteristics of the motor; The second step is to clarify the load and desired trajectory involved in the tracking task, and select constants to represent the upper and lower bounds of the load and the desired trajectory. The third step is to define the error variable and design an adaptive tracking controller based on the second-order differential equation. The fourth step is to analyze the upper and lower bounds of the error variable using the Lyapunov function; The fifth step involves determining the upper and lower bounds of the required control torque and the upper bound of the power of the motor based on the controller structure, controller parameters, initial values ​​of error variables, upper and lower bounds of error variables, and the desired task. The motor selection is then completed based on these boundary conditions.

[0007] Furthermore, the first step, establishing the second-order differential equations describing the generalized position and generalized velocity characteristics of the motor, specifically involves: in, This refers to the generalized position of the motor. It refers to the generalized speed of the electric motor. It is the control torque of the motor. It is the motor's own moment of inertia. It is the unknown but bounded inertia introduced by the mounted load. It is the unknown but bounded drag-noise figure under load, with the initial state being... , .

[0008] Furthermore, the second step specifically involves: S2.1, specify the type, weight, size, mounting method, and operating environment of the load, thereby determining the inertia in the differential equation. and drag-noise figure The range of values ​​for the positive constant is determined. , , and ,make S2.2, the desired trajectory of the tracking task is characterized as follows: in, For the desired generalized position, To achieve the desired generalized speed, For a given time-varying function, Representing time, the initial value of the desired trajectory is expressed as: and ; S2.3, Determine the constants , , and ,make Furthermore, in the third step, the error variable is defined, and the adaptive tracking controller structure is designed based on the second-order differential equation as follows: in, and These are positive controller parameters. It is an error variable, defined as , Yes The online estimate, Yes The online estimate, and These are the initial values ​​of the estimates; estimated value and The update law is designed as follows: in, and It is a positive update law parameter.

[0009] Furthermore, in the fourth step, the Lyapunov function is selected as follows: in, , , , .

[0010] Furthermore, the fifth step specifically involves: S5.1, the error variable obtained in step four The upper realm Lower Boundary , The upper realm Lower Boundary Controller parameters , , , , and By substituting the upper and lower bounds into the controller structure, the control torque can be obtained. The upper and lower bounds; S5.2, based on the power formula as well as The upper realm Lower Boundary The motor power can be calculated. The upper bound; S5.3, based on control torque upper and lower bounds and motor power The upper limit is used to select the appropriate motor.

[0011] The present invention has the following advantages: 1. This invention designs a motor selection method based on the desired tracking task and controller structure, realizing the analysis of the motor's peak torque and maximum power, as well as the tracking of the desired motor position; 2. The method proposed in this invention can be applied in noisy environments and does not require precise measurement of the physical parameters of the motor and load, thus having broad application prospects. 3. The motor selection method proposed in this invention can analyze and determine the peak torque and maximum power based on the controller and control task without testing, effectively reducing the loss of manpower and material resources caused by testing. 4. This invention can reduce the adverse effects of resistance and parameter uncertainty on tracking error by increasing the controller parameters. Attached Figure Description

[0012] Figure 1. Flowchart of the method; Figure 2. Schematic diagram of generalized position tracking error; Figure 3. Schematic diagram of parameter estimates; Figure 4. Schematic diagram of control torque; Figure 5. Schematic diagram of motor power; Figure 6. Schematic diagram of generalized position tracking error after reducing control parameters. Detailed Implementation

[0013] To better understand the purpose, structure, and function of this invention, the invention will be described in further detail below with reference to the accompanying drawings.

[0014] This invention proposes a motor selection method based on the desired tracking task and controller structure. Specifically, considering a class of motors capable of torque control, an adaptive tracking controller is designed for different load requirements and desired tracking tasks. The peak torque and maximum power that the motor should possess are theoretically analyzed to guide motor selection in practice.

[0015] The technical solution adopted in this invention is: The first step is to establish second-order differential equations describing the generalized position and generalized velocity characteristics of the motor; The second step is to clarify the load and desired trajectory involved in the tracking task, and select constants to represent the upper and lower bounds of the load and the desired trajectory. The third step is to define the error variable and design an adaptive tracking controller based on the second-order differential equation. The fourth step is to analyze the upper and lower bounds of the error variable using the Lyapunov function; The fifth step involves determining the upper and lower bounds of the required control torque and the upper bound of the power of the motor based on the controller structure, controller parameters, initial values ​​of error variables, upper and lower bounds of error variables, and the desired task. The motor selection is then completed based on these boundary conditions.

[0016] Furthermore, in the first step, the second-order differential equations describing the generalized position and generalized velocity characteristics of the motor are established as follows: in, This refers to the generalized position of the motor. It refers to the generalized speed of the electric motor. It is the control torque of the motor. It is the motor's own moment of inertia. It is the unknown but bounded inertia introduced by the mounted load. It is the unknown but bounded drag-noise figure under load, with the initial state being... , ; In the second step, based on the specific application, the load and desired trajectory involved in the tracking task are defined, and constants are selected to represent the upper and lower bounds of the load and the desired trajectory. Specifically, S1. Define the type, weight, size, mounting method, and operating environment of the load to determine the inertia in the differential equation. and drag-noise figure The range of values ​​for the positive constant is determined. , , and ,make S2, the desired trajectory of the tracking task is characterized as follows: in, For the desired generalized position, To achieve the desired generalized speed, For a certain time-varying function, Indicates time, and The initial value for the trajectory.

[0017] S3, Determine the constant , , and ,make The third step involves defining the error variable and designing an adaptive controller based on a second-order mathematical model, as follows: in, and These are positive controller parameters. It is an error variable, defined as , Yes The online estimate, Yes The online estimate, and These are the initial values ​​of the estimates.

[0018] estimated value and The update law is designed as follows: in, and It is a positive update law parameter.

[0019] The fourth step involves selecting a Lyapunov function to analyze the upper and lower bounds of the error variable. The selected Lyapunov function is as follows: in, , , , .

[0020] Will , and Substituting the time derivative of the Lyapunov function In this study, the upper and lower bounds of the error variable are analyzed.

[0021] The fifth step, based on the controller structure, controller parameters, initial values ​​of error variables, upper and lower bounds of error variables, and the desired task, determines the upper and lower bounds of the required control torque and the upper bound of the power for the motor, and completes the motor selection based on these boundary conditions. Specifically, S1, the error variable obtained in step four The upper realm Lower Boundary , The upper realm Lower Boundary Controller parameters , , , , and By substituting the upper and lower bounds into the controller structure, the control torque can be obtained. The upper and lower bounds; S2, based on the power formula as well as The upper realm Lower Boundary The motor power can be calculated. The upper bound; S3, based on control torque upper and lower bounds and motor power The upper limit is used to select the appropriate motor.

[0022] Example 1 The technical solution of the present invention will be further described below with reference to specific parameters or scenarios.

[0023] This embodiment provides a motor selection method based on the desired tracking task and controller structure. A flowchart of the method is shown below. Figure 1 As shown, it includes the following steps: The first step is to establish second-order differential equations describing the generalized position and generalized velocity characteristics of the motor; The second step is to clarify the load and desired trajectory involved in the tracking task, and select constants to represent the upper and lower bounds of the load and the desired trajectory. The third step is to define the error variable and design an adaptive tracking controller based on the second-order differential equation. The fourth step is to analyze the upper and lower bounds of the error variable using the Lyapunov function; The fifth step involves determining the upper and lower bounds of the required control torque and the upper bound of the power of the motor based on the controller structure, controller parameters, initial values ​​of error variables, upper and lower bounds of error variables, and the desired task. The motor selection is then completed based on these boundary conditions.

[0024] In the first step, the second-order differential equations describing the generalized position and generalized velocity characteristics of the motor are established: The initial state is , , Drag-noise figure for: In the second step, based on the specific application, the load and desired trajectory involved in the control task are defined, and constants are selected to represent the upper and lower bounds of the complexity and the desired trajectory. Specifically, S1. Define the type, weight, size, mounting method, and operating environment of the load to determine the inertia in the differential equation. and drag coefficient The range of values ​​for the positive constant is determined. , , and ,make S2, the desired trajectory of the tracking task is characterized as follows: in, and ,constant , , and ,Right now In the third step, error variables are defined. The adaptive controller is designed based on a second-order mathematical model as follows: Among them, controller parameters and Obviously, .

[0025] estimated value and The update law is designed as follows: Among them, the update law parameters and , and .

[0026] In the fourth step, the following Lyapunov function is selected to analyze the tracking performance of the motor.

[0027] in, , .

[0028] Will , and Substituting the time derivative of the Lyapunov function From this, we can obtain: Obviously, ,Right now because By solving the ordinary differential equation, we can know that The fifth step, based on the controller structure, controller parameters, initial values ​​of error variables, upper and lower bounds of error variables, and the desired task, determines the upper and lower bounds of the required control torque and the upper bound of the power for the motor, and completes the motor selection based on these boundary conditions. Specifically, S1, the error variable obtained in step four The upper realm Lower Boundary , The upper realm Lower Boundary Controller parameters , , , , and By substituting the upper and lower bounds into the controller structure, the control torque can be obtained. The upper and lower bounds are: S2, based on the power formula as well as The upper realm Lower Boundary The motor power can be calculated. The upper bound is: S3, based on control torque upper and lower bounds and motor power The upper limit is used to select the appropriate motor.

[0029] To further verify the above example, simulations were performed using MATLAB. The differential equations were solved numerically using the fourth-order Runge-Kutta method, with a calculation step size of 0.005 seconds and a simulation duration of 40 seconds. The simulation results are attached. Figure 2-6 As shown.

[0030] Appendix Figure 2 and attached Figure 6 The generalized tracking error generated by the proposed method, wherein, appended Figure 6 The control parameters used are Comparison Appendix Figure 2 and attached Figure 6 The tracking results show that the parameters Reduced time-varying perturbation The impact on tracking performance is significantly increased. (See attached image) Figure 3 The diagram illustrates the parameter estimates. As can be seen from the results, due to discrete calculations, the estimated parameter values ​​slightly exceed the set upper bound, but the deviation is small. With decreasing calculation step size, the estimated values ​​can generally be kept within the given range, which helps in determining the upper and lower bounds of the control torque. (Appendix) Figure 4The diagram illustrates the controlled torque. The results show that the peak torque did not exceed 25, which is less than the theoretically calculated 61.2140. (Attached) Figure 5 The diagram shows the motor power. As can be seen from the results, the maximum motor power is less than 20 watts, which is less than the theoretically calculated 401 watts.

[0031] The simulation results above verify the effectiveness of this method and its beneficial effects.

[0032] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art will be able to make various modifications and improvements without departing from the principles of the present invention, and these modifications and improvements should also be considered to fall within the scope of protection of the present invention.

Claims

1. A motor selection method based on desired tracking task and controller structure, characterized in that, Includes the following steps: The first step is to establish second-order differential equations describing the generalized position and generalized velocity characteristics of the motor; The second step is to clarify the load and desired trajectory involved in the tracking task, and select constants to represent the upper and lower bounds of the load and the desired trajectory. The third step is to define the error variable and design an adaptive tracking controller based on the second-order differential equation. The fourth step is to analyze the upper and lower bounds of the error variable using the Lyapunov function; The fifth step involves determining the upper and lower bounds of the required control torque and the upper bound of the power of the motor based on the controller structure, controller parameters, initial values ​​of error variables, upper and lower bounds of error variables, and the desired task. The motor selection is then completed based on these boundary conditions.

2. The motor selection method based on the desired tracking task and controller structure according to claim 1, characterized in that, The first step, establishing the second-order differential equations describing the generalized position and generalized velocity characteristics of the motor, specifically involves: in, This refers to the generalized position of the motor. It refers to the generalized speed of the electric motor. It is the control torque of the motor. It is the motor's own moment of inertia. It is the unknown but bounded inertia introduced by the mounted load. It is the unknown but bounded drag-noise figure under load, with the initial state being... , .

3. The motor selection method based on the desired tracking task and controller structure according to claim 2, characterized in that, The second step is as follows: S2.1, specify the type, weight, size, mounting method, and operating environment of the load, thereby determining the inertia in the differential equation. and drag-noise figure The range of values ​​for the positive constant is determined. , , and ,make S2.2, the desired trajectory of the tracking task is characterized as follows: in, For the desired generalized position, To achieve the desired generalized speed, For a given time-varying function, Representing time, the initial value of the desired trajectory is expressed as: and ; S2.3, Determine the constants , , and ,make 。 4. The motor selection method based on the desired tracking task and controller structure according to claim 3, characterized in that, The third step involves defining the error variable and designing the adaptive tracking controller structure based on the second-order differential equation as follows: in, and These are positive controller parameters. It is an error variable, defined as , Yes The online estimate, Yes The online estimate, and These are the initial values ​​of the estimates; estimated value and The update law is designed as follows: in, and It is a positive update law parameter.

5. The motor selection method based on the desired tracking task and controller structure according to claim 4, characterized in that, In the fourth step, the Lyapunov function is selected as follows: in, , , , .

6. The motor selection method based on the desired tracking task and controller structure according to claim 5, characterized in that, The fifth step specifically involves, S5.1, the error variable obtained in step four The upper realm Lower Boundary , The upper realm Lower Boundary Controller parameters , , , , and By substituting the upper and lower bounds into the controller structure, the control torque can be obtained. The upper and lower bounds; S5.2, based on the power formula as well as The upper realm Lower Boundary The motor power can be calculated. The upper bound; S5.3, based on control torque upper and lower bounds and motor power The upper limit is used to select the appropriate motor.

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