A position sensorless control parameter setting method and device

Abstract

The application discloses a kind of position sensorless control parameter setting method and device, the present application is according to the voltage model of permanent magnet synchronous motor under rotating coordinate system, establish the local transfer function of position sensorless, determine the relationship of damping ratio, natural frequency and position sensorless proportional integral parameter, and the influence of damping ratio and natural frequency on system steady error, using small signal model stability analysis method to carry out system stability analysis, obtain system linear state model, according to the relationship of damping ratio, natural frequency and position sensorless proportional integral parameter, the influence of damping ratio and natural frequency on system steady error, system linear state model, obtain leading eigenvalue trajectory graph, according to leading eigenvalue trajectory graph and preset actual demand, realize control parameter setting, avoid the tedious parameter adjustment in practical application, can significantly improve the motor control performance based on sensorless technology.

Description

Technical Field

[0001] This invention relates to a method and apparatus for tuning control parameters without position sensors, belonging to the field of sensorless control technology. Background Technology

[0002] Permanent magnet synchronous motors have a mainstream advantage in the servo drive field due to their small size, high efficiency, high power density, easy power control, long service life and high reliability. They are widely used in applications requiring high control precision and high reliability, such as aircraft, CNC machine tools, locomotive traction, electric vehicles and home appliances, and have become a research hotspot for scholars in various countries.

[0003] In the field of environmental control systems for multi-electric aircraft, high-speed permanent magnet synchronous motors drive compressor loads to compress air, providing the high-temperature, high-pressure gas required by the system and meeting the gas source requirements. This makes them one of the core components of the environmental control system. For reasons of margin and reliability, the design of the high-speed sensorless control algorithm equipped with the high-speed permanent magnet synchronous motor system is one of the key issues in the environmental control system.

[0004] Due to the characteristics of fan-type loads, sensorless control algorithms do not require frequent speed changes at high speeds; therefore, steady-state performance is more important for the entire system. Secondly, high-speed, high-power operation limits the conditions for algorithm parameter tuning: since the motor load is a compressor load, the inertia from the fan blades to the motor is significant at high speeds. Even small fluctuations in speed caused by suboptimal parameters can easily lead to system oscillations, ultimately damaging the motor bearings. Therefore, the selected algorithm must have a specific parameter tuning scheme. The traditional PI-based d-axis EEMF algorithm is one of the commonly used sensorless control algorithms, but it lacks a corresponding parameter tuning method. Summary of the Invention

[0005] This invention provides a method and apparatus for tuning control parameters without position sensors, which solves the problems disclosed in the background art.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for tuning control parameters without position sensors includes:

[0008] Based on the voltage model of the permanent magnet synchronous motor in the rotating coordinate system, the extended back EMF of the sensorless system in the rotating coordinate system is solved, and the local transfer function of the sensorless system is established.

[0009] Based on the local transfer function of the sensorless system, the relationship between the damping ratio, natural frequency and the proportional-integral parameter of the sensorless system is determined, as well as the influence of the damping ratio and natural frequency on the steady-state error of the system.

[0010] The system stability analysis is performed using the small-signal model stability analysis method to obtain the linear state model of the system.

[0011] Based on the relationship between damping ratio, natural frequency, and sensorless proportional-integral parameters, and the influence of damping ratio and natural frequency on the steady-state error of the system, the dominant eigenvalue locus of the natural frequency of the state transition matrix in the linear state model of the system is obtained.

[0012] Based on the dominant eigenvalue root locus diagram and the preset actual requirements, determine the setpoints for the sensorless control parameters.

[0013] Based on the voltage model of the permanent magnet synchronous motor in the rotating coordinate system, the extended back EMF of the sensorless system in the rotating coordinate system is solved, and the local transfer function of the sensorless system is established, including:

[0014] Based on the voltage model of the permanent magnet synchronous motor in the rotating coordinate system, the extended back EMF in the rotating coordinate system is solved for the sensorless system to obtain the relationship between the γ-axis back EMF and the angle error information.

[0015] Based on the relationship between the γ-axis back electromotive force and the angle error information, a local transfer function without a position sensor is established.

[0016] The local transfer function of a sensorless system includes an open-loop transfer function and a closed-loop transfer function; the open-loop transfer function is a relationship with respect to the proportional-integral parameters of the sensorless system, and the closed-loop transfer function is a relationship with respect to the damping ratio and the natural frequency.

[0017] Based on the sensorless local transfer function, the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters is determined, along with the influence of the damping ratio and natural frequency on the system's steady-state error, including:

[0018] Based on the open-loop transfer function and the closed-loop transfer function, determine the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters;

[0019] Based on the relationship between damping ratio, natural frequency, and sensorless proportional-integral parameters, the influence of damping ratio and natural frequency on the steady-state error of the system is determined.

[0020] The relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters is as follows:

[0021]

[0022] Among them, K pe K is the proportional coefficient without position sensors. ie ζ is the integral coefficient without position sensors, ζ is the damping ratio, and ω is the integral coefficient without position sensors. nE is the natural frequency. ex Extend the back EMF of the d-axis of the permanent magnet synchronous motor;

[0023] The effects of damping ratio and natural frequency on the steady-state error of the system are as follows: when the damping ratio is 1, the larger the natural frequency, the smaller the steady-state error of the system.

[0024] The linear state model of the system is:

[0025]

[0026] Where p is the differential operator, Δx s Δw and Δx are the output vectors. s =[Δi d Δi q Δω r ] T , Δi d Let Δi be the d-axis current disturbance. q Let Δω be the q-axis current disturbance. r This represents the rotor angular velocity disturbance. To estimate the disturbance of angular velocity, Δw1 is the disturbance of the integral value of the input error of the speed PI controller, Δw2 is the disturbance of the integral value of the input error of the d-axis current PI controller, Δw3 is the disturbance of the integral value of the input error of the q-axis current PI controller, Δw4 is the disturbance of the integral value of the input error without position sensor, and Δθ r The angle between the d-axis and the γ-axis. Let A be the state transition matrix. s A x A w B s B r B T F x F w F r All are parameter matrices. K pd K is the proportional coefficient of the d-axis current PI controller. pq The proportional gain of the q-axis current PI controller. K id K represents the integral coefficient of the d-axis current PI controller. is K is the integral coefficient of the speed PI controller. ps K is the proportional coefficient of the speed PI controller. iq i represents the integral coefficient of the q-axis current PI controller. d0 Let i be the steady-state value of the d-axis current. q0 This represents the steady-state value of the q-axis current. This is the given value of the steady-state voltage along the γ-axis. Given a value for the stator resistance, ωc This is the filter cutoff frequency. L d For the d-axis inductance, L q It is the q-axis inductance. P is the number of pole pairs of the motor, and J is the moment of inertia. K pe This is the proportional coefficient without position sensors. Set the value for the q-axis inductance. To estimate the steady-state value of the angular velocity, ω r0 ω is the steady-state value of the rotor angular velocity. e0 Let ψ be the steady-state value of the electric angular velocity. f For permanent magnet flux linkage, R s For stator resistance, parameters ,parameter , i δ0 K is the steady-state value of the delta-axis current. ie The integral coefficient is for sensorless applications. This is the given value for the d-axis current disturbance. ΔT is the given value of the rotor angular velocity disturbance. L This represents the load torque disturbance.

[0027] Based on the relationship between damping ratio, natural frequency, and sensorless proportional-integral parameters, and the influence of damping ratio and natural frequency on the system's steady-state error, the dominant eigenvalue locus of the natural frequency of the state transition matrix in the system's linear state model is obtained, including:

[0028] Based on the relationship between damping ratio, natural frequency and sensorless proportional-integral parameters, and the influence of damping ratio and natural frequency on the steady-state error of the system, all eigenvalues ​​of the natural frequency of the state transition matrix in the linear state model of the system are determined.

[0029] By using the conjugate eigenvalues ​​as the dominant eigenvalues ​​and changing the natural frequency of the state transition matrix, the trajectory map of the dominant eigenvalues ​​can be obtained.

[0030] The sensorless control parameters are natural frequencies; the tuning values ​​of the sensorless control parameters are determined based on the dominant eigenvalue locus and preset actual requirements, including:

[0031] Based on the dominant eigenvalue trajectory plot, determine the first range of natural frequencies when all dominant eigenvalues ​​are located in the left half-plane;

[0032] Based on the preset actual needs, determine the second range of values ​​for the natural frequency;

[0033] Find the intersection of the first and second value ranges to obtain the final range of natural frequencies.

[0034] A sensorless control parameter tuning device, comprising:

[0035] The local transfer function module, based on the voltage model of the permanent magnet synchronous motor in the rotating coordinate system, solves the extended back EMF in the rotating coordinate system for the sensorless system and establishes the local transfer function for the sensorless system.

[0036] The analysis module determines the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters, as well as the impact of the damping ratio and natural frequency on the system's steady-state error, based on the sensorless local transfer function.

[0037] The system linear state model module uses the small-signal model stability analysis method to perform system stability analysis and obtain the system linear state model.

[0038] The eigenvalue trajectory module obtains the dominant eigenvalue trajectory of the natural frequency of the state transition matrix in the linear state model of the system based on the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters, as well as the influence of the damping ratio and natural frequency on the steady-state error of the system.

[0039] The tuning module determines the tuning values ​​of the sensorless control parameters based on the dominant characteristic root locus diagram and the preset actual requirements.

[0040] A computer-readable storage medium storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform a sensorless control parameter tuning method.

[0041] The beneficial effects achieved by this invention are as follows: 1. Based on the voltage model of the permanent magnet synchronous motor in the rotating coordinate system, this invention establishes the sensorless local transfer function, determines the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters, and the influence of the damping ratio and natural frequency on the system steady-state error. It then employs a small-signal model stability analysis method to perform system stability analysis, obtaining the system linear state model. Based on the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters, the influence of the damping ratio and natural frequency on the system steady-state error, and the system linear state model, it obtains the dominant eigenvalue locus. Based on the dominant eigenvalue locus and... 1. This invention achieves control parameter tuning based on pre-defined actual needs, avoiding cumbersome parameter adjustments in practical applications and significantly improving the motor control performance based on sensorless technology; 2. This invention performs control parameter tuning by determining the relationship between damping ratio, natural frequency, and sensorless proportional-integral parameters, as well as the influence of damping ratio and natural frequency on the system's steady-state error, effectively preventing system oscillations; 3. This invention uses a small-signal model stability analysis method for system stability analysis, reducing the difficulty of sensorless control parameter tuning under harsh operating conditions, decreasing the complexity of parameter adjustments in practical applications, and enhancing system robustness and practicality. Attached Figure Description

[0042] Figure 1 This is a flowchart of the method of the present invention;

[0043] Figure 2 This is a schematic diagram of a rotating coordinate system;

[0044] Figure 3 This is a block diagram of a sensorless control algorithm.

[0045] Figure 4 A comparison chart of underdamped and critically damped systems;

[0046] Figure 5 A comparison diagram of overdamped and critically damped systems;

[0047] Figure 6 The eigenvalue locus is a plot of eigenvalues ​​with varying natural frequencies. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0049] like Figure 1 As shown, a method for tuning control parameters without a position sensor includes the following steps:

[0050] Step 1: Based on the voltage model of the permanent magnet synchronous motor in the rotating coordinate system, solve the extended back EMF of the sensorless system in the rotating coordinate system and establish the local transfer function of the sensorless system.

[0051] Step 2: Based on the local transfer function of the sensorless system, determine the relationship between the damping ratio, natural frequency, and the proportional-integral parameters of the sensorless system, as well as the influence of the damping ratio and natural frequency on the steady-state error of the system.

[0052] Step 3: Perform system stability analysis using the small-signal model stability analysis method to obtain the system's linear state model;

[0053] Step 4: Based on the relationship between damping ratio, natural frequency and sensorless proportional-integral parameters, and the influence of damping ratio and natural frequency on the steady-state error of the system, obtain the dominant eigenvalue locus of the natural frequency of the state transition matrix in the linear state model of the system.

[0054] Step 5: Determine the sensorless control parameter settings based on the dominant eigenvalue trajectory diagram and the preset actual requirements.

[0055] The above method establishes a sensorless local transfer function based on the voltage model of the permanent magnet synchronous motor in the rotating coordinate system, determines the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters, and the influence of the damping ratio and natural frequency on the steady-state error of the system. It then employs a small-signal model stability analysis method to perform system stability analysis, obtaining a linear state model of the system. Based on the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters, the influence of the damping ratio and natural frequency on the steady-state error of the system, and the linear state model of the system, it obtains the dominant eigenvalue locus. According to the dominant eigenvalue locus and the preset actual requirements, the control parameters are tuned, avoiding cumbersome parameter adjustments in practical applications and significantly improving the control performance of motors based on sensorless technology.

[0056] In step 1 above, a mathematical model of the permanent magnet synchronous motor (high-speed permanent magnet synchronous motor) in a rotating coordinate system can be performed first to obtain the voltage model in the rotating coordinate system. Based on the voltage model of the permanent magnet synchronous motor in the rotating coordinate system, the extended back EMF of the sensorless system in the rotating coordinate system is solved to obtain the relationship between the γ-axis back EMF and the angle error information. Based on the relationship between the γ-axis back EMF and the angle error information, the local transfer function of the sensorless system is established.

[0057] like Figure 2 As shown, γ-δ is defined as the coordinate system for estimating the rotation axis, with rotational angular velocity... Rotate counterclockwise, the angle between the d-axis and the γ-axis is Δθ. rThe voltage model of a permanent magnet synchronous motor is transformed to the γ-δ coordinate system using a coordinate transformation matrix, as shown in the following formula:

[0058]

[0059] in, To estimate the angular velocity, ω r Let ω be the rotor angular velocity, p be the differential operator, and ψ be the angular velocity. f For permanent magnet flux linkage, R s L is the stator resistance. d For the d-axis inductance, L q For q-axis inductance, i γ For the γ-axis current, i δ For the delta-axis current, u γ For the γ-axis voltage, u δ Let i be the δ-axis voltage. d For d-axis current, The differential of the q-axis current, Δθ r The angle between the d-axis and the γ-axis.

[0060] Define the extended back electromotive force in the rotating axis coordinate system as:

[0061]

[0062] Among them, E ex Extended back EMF for the d-axis of a permanent magnet synchronous motor, hereinafter referred to as extended back EMF, e γ To extend the component of the back potential on the γ-axis, e δ To extend the component of the back potential on the δ axis, L d For the d-axis inductance, L q For q-axis inductance, ψ f For permanent magnet flux linkage, ω r Let i be the rotor angular velocity. d For d-axis current, This is the differential of the q-axis current.

[0063] The position information can be obtained by using the extended back potential of equations (1) and (2).

[0064] During normal operation without position sensors, Δθ r Since the term is approximately 0, equation (2) can be expressed as:

[0065]

[0066] Ignoring the differential term in the back potential, the γ-axis back potential can be further expressed as:

[0067] e γ =u γ -R s i γ+ω e L d i δ (4)

[0068] Among them, u γ For the γ-axis voltage, i γ R is the γ-axis current. s For stator resistance, i δ Let ω be the delta-axis current. e L is the electric angular velocity. d It is the d-axis inductance.

[0069] Equation (3) shows that the γ-axis back EMF contains angular error information. Therefore, equation (4) is the relationship between the γ-axis back EMF and the angular error information. By using the angular error to reconstruct the position information through the phase-locked loop, the rotor position information can be calculated.

[0070] The local transfer function of a sensorless system includes an open-loop transfer function and a closed-loop transfer function; the open-loop transfer function is a relationship with respect to the proportional-integral parameters of the sensorless system, and the closed-loop transfer function is a relationship with respect to the damping ratio and the natural frequency.

[0071] Based on the relationship between the γ-axis back electromotive force and the angle error information, Figure 3 Therefore, the open-loop transfer function can be expressed as:

[0072]

[0073] Among them, K pe K is the proportional coefficient without position sensors. ie is the integral coefficient without a position sensor, and s is the complex frequency.

[0074] As can be seen from the open-loop transfer function, the sensorless system is a typical Type II system. However, in actual engineering, the speed is usually given by a ramp. Therefore, the main analysis focuses on the response of the sensorless system during the ramp-up process of the motor speed and during steady-state operation.

[0075] Replacing the PI loop parameters with the relationship between the damping ratio and the natural frequency, the closed-loop transfer function can be expressed as:

[0076]

[0077] Where ξ is the damping ratio, ω n It is the natural frequency.

[0078] Given the open-loop and closed-loop transfer functions, the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters can be determined. Based on this relationship, the influence of the damping ratio and natural frequency on the steady-state error of the system can be determined.

[0079] According to equations (5) and (6), the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameter is as follows:

[0080]

[0081] Where ζ is the damping ratio, ω n It is the natural frequency.

[0082] When determining the damping ratio ζ, it is desirable to have stable observations during position observation, without overshoot or oscillation, and to allow for a certain angular lag. According to the pole distribution characteristics, when the critical damping or overdamped state is selected, the system time response has no overshoot and meets the requirements. In this case, the damping ratio is selected as ζ = 1 or ζ > 1.

[0083] Given a unit ramp and a natural frequency ω as input speed. n It is 1 rad / s, by Figure 4 It can be seen that when 0 < ζ < 1, the system exhibits oscillations and converges slowly; when ζ = 1, the system has no oscillations, exhibits monotonically increasing behavior, and converges quickly. Therefore, selecting ζ = 1 is more suitable. Figure 5 It can be seen that when ζ > 1, the adjustment time is faster and there is no oscillation. However, compared with ζ = 1, the convergence is slower. Considering all factors, the damping ratio ζ = 1 is better for the sensorless system. That is, when the speed input is a unit ramp, the system has no oscillation, monotonically increases and converges quickly when the damping ratio ζ = 1 is selected.

[0084] From equation (6), the acceleration time response function of the second-order system can be obtained. The unit acceleration response time function in the state ζ=1 is as follows:

[0085]

[0086] Where t is the time variable and e is the natural constant.

[0087] As shown in equation (8), when the angle is given, the decay term of the time response function under acceleration is positively correlated with the natural frequency ω. n The larger the value, the faster the decay, and the faster the response without a position sensor; for Type II systems, the acceleration response has a steady-state error, when the input acceleration function C(t) = Rt 2 When the steady-state error is reached, it can be expressed as:

[0088]

[0089] Where R is the given slope of the rotational speed;

[0090] Therefore, we can conclude that: with a damping ratio of 1, the larger the natural frequency, the faster the sensorless response and the smaller the system steady-state error; for sensorless systems, given a damping ratio ζ = 1, choosing a larger ω... n The system is superior.

[0091] The observer's local conclusions are not entirely applicable to the system, ω n An increase in the value of the position sensor will affect the system, and it is necessary to seek to analyze the parameter design of the sensorless algorithm at the system level.

[0092] The system stability analysis is performed using the small-signal model method to obtain the linear state model of the system, as follows:

[0093] First, establish the state model of the high-speed permanent magnet synchronous motor, the state model of the speed loop PI controller, the d-axis current loop PI controller, the q-axis current loop PI controller, and the state model of speed estimation without position sensors.

[0094] State model of high-speed permanent magnet synchronous motor:

[0095]

[0096] Where p is the differential operator, ψ f For permanent magnet flux linkage, R s L is the stator resistance. d For the d-axis inductance, L q For q-axis inductance, ω r Let i be the rotor angular velocity. d Let i be the d-axis current. q Let ω be the q-axis current, ω be the mechanical angular velocity, P be the number of pole pairs of the motor, J be the moment of inertia, and T be the moment of inertia. L This represents the load torque.

[0097] Speed ​​loop PI controller state model:

[0098]

[0099] Among them, K ps K is the proportional coefficient of the speed PI controller. is For the integral coefficient of the speed PI controller, Let ω be the rotational angular velocity of the γ-axis, and w1 be the integral value of the input error of the speed PI controller. For a given rotational speed, This is the output of the speed PI controller.

[0100] d-axis current loop PI controller state model:

[0101]

[0102] Among them, K pd K is the proportional coefficient of the d-axis current PI controller. id i represents the integral coefficient of the d-axis current PI controller. γ w1 represents the γ-axis current, and w2 represents the integral value of the input error of the PI controller for the d-axis current. Given the d-axis current, This is the output of the d-axis current PI controller.

[0103] q-axis current loop PI controller state model:

[0104]

[0105] Among them, K pq K is the proportional coefficient of the q-axis current PI controller. iq i represents the integral coefficient of the q-axis current PI controller. δ w3 is the delta-axis current, and w3 is the integral value of the input error of the q-axis current PI controller. Given the q-axis current, This is the output of the q-axis current PI controller.

[0106] Sensorless rotational speed estimation state model:

[0107]

[0108] in, To estimate the rotational speed before filtering, For the γ-axis back potential calculated by equation (14), K pe K is the scaling factor for the position observer. ie w4 is the integral coefficient of the position observer, and w4 is the integral value of the input error of the position observer.

[0109] A first-order low-pass filter is introduced to reduce high-frequency noise in the estimated rotational speed. The estimated speed value is output after passing through the low-pass filter.

[0110]

[0111] Where, ω c This is the filter cutoff frequency. To estimate the rotational speed before filtering, This is the estimated rotational speed of the position observer after filtering.

[0112] The error expression for angles without position estimation is as follows:

[0113]

[0114] Where p is the differential operator, Δθ r The angle between the d-axis and the γ-axis. The estimated rotational speed of the filtered position observer, ω r ω is the rotor angular velocity.

[0115] The voltage along the rotating coordinate axis and the voltage along the dq axis have the following relationship:

[0116]

[0117] Among them, u d For the d-axis voltage, u q Let i be the q-axis voltage. d Let i be the d-axis current. q Let i be the q-axis current. γ For the γ-axis current, i δ For delta-axis current, The given value for the γ-axis voltage. Given the δ-axis voltage, Δθ r The angle between the d-axis and the γ-axis.

[0118] When a permanent magnet synchronous motor operates in steady state, the differential values ​​of all variables are zero, allowing the steady-state values ​​of each parameter to be solved. By applying a small-signal disturbance to the system under steady-state conditions, each variable will fluctuate above its steady-state value. These state fluctuations in the state equations are then expressed as linear increments, assuming... This yields a linear model for small-signal analysis.

[0119] First, equation (10) is processed using a small-signal model, and its expression is as follows:

[0120]

[0121] Where p is the differential operator, Δi d Let Δi be the d-axis current disturbance. q Let Δu be the q-axis current disturbance. d Let Δu be the d-axis voltage disturbance. q Let Δω be the q-axis voltage disturbance. r The rotor angular velocity disturbance, ΔT L This represents the load torque disturbance.

[0122]

[0123]

[0124]

[0125]

[0126] Where, ψ f For permanent magnet flux linkage, R s L is the stator resistance.d For the d-axis inductance, L q Let P be the q-axis inductance, P be the number of pole pairs of the motor, J be the moment of inertia, and i be the q-axis inductance. d0 Let i be the steady-state value of the d-axis current. q0 Let ω be the steady-state value of the q-axis current. r0 ω is the steady-state value of the rotor angular velocity. e0 This represents the steady-state value of the electric angular velocity.

[0127] Under small perturbation signals, the angle estimation error is no longer zero, but is considered to be infinitesimal. Therefore, the voltage and current of the two coordinate axes are as follows:

[0128]

[0129] Where, Δi γ Let Δi be the γ-axis current disturbance. δ Let Δu be the delta-axis current disturbance. d Let Δu be the d-axis voltage disturbance. q This represents the q-axis voltage disturbance. This is the given value for the γ-axis voltage disturbance. Δi is the given value of the δ-axis voltage disturbance. d Let Δi be the d-axis current disturbance. q This represents the q-axis current disturbance. The given value of the δ-axis steady-state voltage. Given the γ-axis voltage, i d0 Let i be the steady-state value of the d-axis current. q0 Let Δθ be the steady-state value of the q-axis current. r The angle between the d-axis and the γ-axis.

[0130] Substituting equation (19) into equations (11) to (16), and rearranging them into matrix form, we obtain the state variable equations as follows:

[0131]

[0132] Where p is the differential operator, Δw1 is the disturbance of the integral value of the input error of the speed PI controller, Δw2 is the disturbance of the integral value of the input error of the d-axis current PI controller, Δw3 is the disturbance of the integral value of the input error of the q-axis current PI controller, and Δw4 is the disturbance of the integral value of the input error of the position observer. To estimate the disturbance of angular velocity, This is the given value for the d-axis current disturbance. Δθ is the given value of the rotor angular velocity disturbance. r Let Δx be the angle between the d-axis and the γ-axis. s As shown in equation (18),

[0133]

[0134]

[0135]

[0136] Among them, K pe K is the scaling factor for the position observer. ie K represents the integral coefficient of the position observer. pd K is the proportional coefficient of the d-axis current PI controller. id K represents the integral coefficient of the d-axis current PI controller. ps K is the proportional coefficient of the speed PI controller. is ω is the integral coefficient of the speed PI controller. c This is the filter cutoff frequency. To estimate the steady-state value of the angular velocity, i d0 Let i be the steady-state value of the d-axis current. q0 i is the steady-state value of the q-axis current. δ0 This represents the steady-state value of the delta-axis current. Set the value for the q-axis inductance. The given value is the stator resistance.

[0137] The system input Δu s It can also be represented in state variable form, as follows:

[0138] Δu s =F w Δw+F x Δx s +F r Δr (21)

[0139] Where, Δx s and Δu s As shown in equation (18), Δw and Δr are as shown in equation (20).

[0140]

[0141]

[0142]

[0143] Among them, K pq K is the proportional coefficient of the q-axis current PI controller. iq K represents the integral coefficient of the q-axis current PI controller. pd K is the proportional coefficient of the d-axis current PI controller. id K represents the integral coefficient of the d-axis current PI controller. ps K is the proportional coefficient of the speed PI controller. is i is the integral coefficient of the speed PI controller.d0 Let i be the steady-state value of the d-axis current. q0 This represents the steady-state value of the q-axis current. This is the given value of the steady-state voltage along the γ-axis.

[0144] By integrating equations (18), (20), and (21), we can obtain the linear state model of the system:

[0145]

[0146] Among them, A s A x A w B s B r B T F x F w F r All are parameter matrices. Let be the state transition matrix. According to Lyapunov's second linear system theory, the distribution of the eigenvalues ​​of the state transition matrix determines whether the system is stable. By changing the parameters within the matrix, the trajectory of the system's eigenvalues ​​can be plotted, thereby analyzing the influence of the parameters on the system's stability.

[0147] Based on the relationship between damping ratio, natural frequency, and sensorless proportional-integral parameters, and the influence of damping ratio and natural frequency on the steady-state error of the system, all eigenvalues ​​of the natural frequency of the state transition matrix in the linear state model of the system can be determined. The conjugate eigenvalues ​​are taken as the dominant eigenvalues, and the natural frequency of the state transition matrix is ​​changed to obtain the trajectory diagram of the dominant eigenvalues.

[0148] When the damping ratio is 1, the sensorless PI parameters are as follows:

[0149]

[0150] Among them, K pe K is the scaling factor for the position observer. ie ω is the integral coefficient of the position observer. n It is the natural frequency.

[0151] Determine the given d-axis current i d In the vector control method with 0 = 0, the current loop closed-loop bandwidth is set to 1000Hz, the speed loop closed-loop bandwidth is set to 10Hz, and the speed loop filter is set to 300Hz. The steady-state operating point is selected as a motor speed of 45000 r / min and a load torque of 6 N·m. During stable operation, the dq-axis current is consistent with the estimated γ-δ-axis current, and the estimated angle error Δθ is... r As is an infinitesimal quantity, it can be seen from equation (23) that for each given natural frequency ω nThere are 8 eigenvalue solutions, 6 of which are negative real roots. There is only one pair of conjugate eigenvalues, and only this single pair of conjugate eigenvalues ​​affects the stability of the entire system. Taking one of the conjugate eigenvalue loci as the dominant eigenvalue, a dominant eigenvalue locus diagram with varying natural frequencies can be plotted.

[0152] Based on the dominant eigenvalue locus plot, determine the first range of natural frequencies when all dominant eigenvalues ​​are located in the left half-plane.

[0153] like Figure 6 The diagram shows the eigenvalue locus of the system with varying natural frequencies. As the natural frequency increases, the dominant eigenvalues ​​of the system initially move away from the imaginary axis, then reach an inflection point and move closer to the imaginary axis, finally shifting to the right half of the imaginary axis plane. The inflection point is ω marked in the diagram. n At ω = 115 rad / s, when ω n When the eigenvalue is greater than 450 rad / s, the characteristic roots shift to the right half-plane; when all system poles are distributed in the left half-plane of the imaginary axis, the system can return to stability after being subjected to small-signal disturbances, therefore the first range of the natural frequency is 0 < ω. n ≤450rad / s.

[0154] Based on the preset actual needs, determine the second range of natural frequencies, find the intersection of the first and second ranges, and obtain the final range of natural frequencies.

[0155] Given a given speed on a ramp, there exists a fixed angle error. This steady-state error is related to the given speed slope R and the natural frequency, with the maximum angle error being e. exp Under these conditions, the second range of natural frequencies

[0156] Given a system input speed increase slope of 10000 r / min / s, and considering engineering application requirements, the angle error range is controlled within 15° electrical angle. The second range of values ​​for the natural frequency ω is obtained. n ≥63.55rad / s.

[0157] Combining the first and second value ranges of the natural frequency, the final selection range of the natural frequency can be determined as 63.55 rad / s ≤ ω. n ≤450rad / s.

[0158] The above method achieves control parameter tuning, avoiding cumbersome parameter adjustments in practical applications and significantly improving the control performance of motors based on sensorless technology. Furthermore, by determining the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters, as well as the influence of the damping ratio and natural frequency on the system's steady-state error, the method effectively avoids system oscillations. The method employs small-signal model stability analysis for system stability analysis, i.e., locally linearizing the nonlinear system and applying small disturbance signals during steady-state operation. This reduces the difficulty of sensorless control parameter tuning under harsh conditions, decreases the complexity of parameter adjustments in practical applications, and enhances system robustness and practicality.

[0159] Based on the same technical solution, the present invention also discloses a software device for the above method, a sensorless control parameter tuning device, comprising:

[0160] The local transfer function module, based on the voltage model of the permanent magnet synchronous motor in the rotating coordinate system, solves the extended back EMF in the rotating coordinate system for the sensorless system and establishes the local transfer function for the sensorless system.

[0161] The analysis module determines the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters, as well as the impact of the damping ratio and natural frequency on the system's steady-state error, based on the sensorless local transfer function.

[0162] The system linear state model module uses the small-signal model stability analysis method to perform system stability analysis and obtain the system linear state model.

[0163] The eigenvalue trajectory module obtains the dominant eigenvalue trajectory of the natural frequency of the state transition matrix in the linear state model of the system based on the relationship between the damping ratio, natural frequency, and sensorless proportional-integral parameters, as well as the influence of the damping ratio and natural frequency on the steady-state error of the system.

[0164] The tuning module determines the tuning values ​​of the sensorless control parameters based on the dominant characteristic root locus diagram and the preset actual requirements.

[0165] The data processing flow and methods of each module in the above device are consistent, and are described again here.

[0166] Based on the above method, a method for obtaining the rotor angle of a permanent magnet synchronous motor can be further constructed, including: using the above-mentioned sensorless control parameter tuning method to tune the parameters in the sensorless control algorithm (d-axis EEMF algorithm based on traditional PI); and using the tuned sensorless control algorithm to obtain the rotor angle of the permanent magnet synchronous motor.

[0167] Based on the same technical solution, the present invention also discloses a computer-readable storage medium storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform a sensorless control parameter tuning method.

[0168] Based on the same technical solution, the present invention also discloses a computing device, including one or more processors, one or more memories, and one or more programs, wherein the one or more programs are stored in the one or more memories and configured to be executed by the one or more processors, and the one or more programs include instructions for performing a sensorless control parameter tuning method.

[0169] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0170] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0171] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0172] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0173] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of the claims of the present invention pending approval.

Claims

1. A position sensorless control parameter tuning method, characterized by, The position sensorless control parameter is a natural frequency, and the method comprises the following steps: According to the voltage model of the permanent magnet synchronous motor in the system in the rotating coordinate system, the extended back electromotive force of the position sensorless in the rotating coordinate system is solved, and the local transfer function of the position sensorless is established; According to the local transfer function of the position sensorless, the relationship among the damping ratio, the natural frequency and the position sensorless proportional integral parameter is determined, and the influence of the damping ratio and the natural frequency on the steady-state error of the system is determined; The small signal model stability analysis method is used for system stability analysis, and a linear state model of the system is obtained; According to the relationship among the damping ratio, the natural frequency and the position sensorless proportional integral parameter, and the influence of the damping ratio and the natural frequency on the steady-state error of the system, all characteristic roots of the state transition matrix natural frequency in the linear state model of the system are determined; the conjugate characteristic root is taken as a dominant characteristic root, the natural frequency of the state transition matrix is changed, and a dominant characteristic root trajectory diagram is obtained; According to the dominant characteristic root trajectory diagram, when all the dominant characteristic roots are located in the left half plane, a first value range of the natural frequency is determined; according to the actual demand, a second value range of the natural frequency is determined; and the first value range and the second value range are intersected to obtain an ultimate range of the natural frequency.

2. A method of setting control parameters without position sensor according to claim 1, characterized in that, According to the voltage model of the permanent magnet synchronous motor in the system in the rotating coordinate system, the extended back electromotive force of the position sensorless in the rotating coordinate system is solved, and the local transfer function of the position sensorless is established, comprising: According to the voltage model of the permanent magnet synchronous motor in the system in the rotating coordinate system, the extended back electromotive force of the position sensorless in the rotating coordinate system is solved, and the relationship between the γ-axis back electromotive force and the angle error information is obtained; According to the relationship between the γ-axis back electromotive force and the angle error information, the local transfer function of the position sensorless is established.

3. A method of setting a control parameter without position sensor according to claim 1 or 2, characterized in that, The local transfer function of the position sensorless comprises an open loop transfer function and a closed loop transfer function; wherein the open loop transfer function is a relational expression about the position sensorless proportional integral parameter, and the closed loop transfer function is a relational expression about the damping ratio and the natural frequency.

4. The method of claim 3, wherein, According to the local transfer function of the position sensorless, the relationship among the damping ratio, the natural frequency and the position sensorless proportional integral parameter is determined, and the influence of the damping ratio and the natural frequency on the steady-state error of the system is determined, comprising: According to the open loop transfer function and the closed loop transfer function, the relationship among the damping ratio, the natural frequency and the position sensorless proportional integral parameter is determined; According to the relationship among the damping ratio, the natural frequency and the position sensorless proportional integral parameter, the influence of the damping ratio and the natural frequency on the steady-state error of the system is determined.

5. A method of setting a control parameter without a position sensor according to claim 4, characterized in that, The relationship among the damping ratio, the natural frequency and the position sensorless proportional integral parameter is: wherein K pe is a proportional coefficient for the position sensorless, K ie is an integral coefficient for the position sensorless, ζ is a damping ratio, ω n is a natural frequency, E ex is an extended back EMF of the permanent magnet synchronous motor d-axis; The influence of the damping ratio and the natural frequency on the steady-state error of the system is that, in the case that the damping ratio is 1, the greater the natural frequency, the smaller the steady-state error of the system.

6. The method of parameter tuning for sensorless control as claimed in claim 1, wherein, The linear state model of the system is: where p is a differential operator, Δx s and Δw is an output vector, Δx s = [Δi d Δi q Δω r ] T , Δi d is a d-axis current disturbance, Δi q is a q-axis current disturbance, Δω r is a rotor angular velocity disturbance, is an estimated angular velocity disturbance, Δw1 is a speed PI controller input error integral value disturbance, Δw2 is a d-axis current PI controller input error integral value disturbance, Δw3 is a q-axis current PI controller input error integral value disturbance, Δw4 is a position sensorless input error integral value disturbance, Δθ r is a d-axis and γ-axis included angle, is a state transition matrix, A s , A x , A w , B s , B r , B T , F x , F w , F r are parameter matrices, K pd is a d-axis current PI controller proportional coefficient, K pq is a q-axis current PI controller proportional coefficient, K id is a d-axis current PI controller integral coefficient, K is is a speed PI controller integral coefficient, K ps is a speed PI controller proportional coefficient, K iq is a q-axis current PI controller integral coefficient, i d0 is a d-axis current steady state value, i q0 is a q-axis current steady state value, is a γ-axis steady state voltage given value, is a stator resistance given value, ω c is a filter cutoff frequency, L d is a d-axis inductance, L q is a q-axis inductance, P is a motor pole pair number, J is a rotational inertia, K pe is a position sensorless proportional coefficient, is a q-axis inductance given value, to estimate the steady state value of the angular velocity, ω r0 is the steady state value of the rotor angular velocity, ω e0 is the steady state value of the electrical angular velocity, ψ f is the permanent magnet flux linkage, R s is the stator resistance, parameter , parameter , i δ0 is the steady state value of the δ-axis current, K ie is the integral coefficient for sensorless, is the given value of the d-axis current disturbance, is the given value of the rotor angular velocity disturbance, ΔT L is the load torque disturbance.

7. A sensorless control parameter tuning device, characterized in that, The position sensorless control parameter is a natural frequency, and the device comprises: A local transfer function module, which, according to the voltage model of the permanent magnet synchronous motor in the system in the rotating coordinate system, solves the extended back electromotive force of the position sensorless in the rotating coordinate system, and establishes the local transfer function of the position sensorless; The analysis module determines the relationship among the damping ratio, the natural frequency and the proportional integral parameters of the position sensorless, and the influence of the damping ratio and the natural frequency on the steady-state error of the system according to the local transfer function of the position sensorless; The system linear state model module performs system stability analysis by using a small signal model stability analysis method, and obtains a linear state model of the system; The eigenvalue locus diagram module determines all eigenvalues of the state transition matrix of the linear state model of the system according to the relationship among the damping ratio, the natural frequency and the proportional integral parameters of the position sensorless, and the influence of the damping ratio and the natural frequency on the steady-state error of the system; takes the conjugate eigenvalues as dominant eigenvalues, changes the natural frequency of the state transition matrix, and obtains a dominant eigenvalue locus diagram; The tuning module determines a first value range of the natural frequency when all the dominant eigenvalues are located in the left half plane according to the dominant eigenvalue locus diagram; determines a second value range of the natural frequency according to a preset actual requirement; and obtains a final range of the natural frequency by intersecting the first value range and the second value range.

8. A computer-readable storage medium storing one or more programs, the one or more programs comprising instructions that when executed by a computer cause the computer to perform a method of any of claims 1-7. The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform the method of any one of claims 1-6.

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