Electric drive system double-layer active torsional vibration suppression method based on electromechanical coupling characteristics

Abstract

The invention relates to an electromechanical coupling characteristic-based electric drive system double-layer active torsional vibration suppression method, which belongs to the technical field of electric automobile motors and comprises the following steps of S1, establishing a permanent magnet synchronous motor mathematical model, an electric drive system helical gear pair kinetic model and a gear transmission lumped parameter model; s2, establishing an upper-layer state feedback control method based on pole assignment, including establishing a transmission system dynamic state space equation, a state observer and a state feedback controller; and S3, establishing a lower torsional vibration suppression method based on active-disturbance-rejection control. According to the invention, voltage deviation generated by nonlinearity of the inverter is compensated, and current harmonics and torque fluctuation are reduced; according to the invention, the damping ratio at the pole corresponding to the inherent frequency which easily causes resonance is improved, the low-frequency torsional vibration is reduced, and the time for reaching the steady state is shortened; according to the invention, current harmonics and torque ripples are reduced, and high-frequency torsional vibration of an electric drive system is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric vehicle motors and relates to a double-layer active torsional vibration suppression method for an electric drive system based on electromechanical coupling characteristics. Background Art

[0002] Electric drive systems are widely used in electric vehicles due to their compact size, high power density, and fast response. Electric drive systems are complex electromechanical coupled systems with complex and variable operating conditions. Nonlinear excitation of the electromechanical system can exacerbate high- and low-frequency torsional vibrations in the electric drive system, leading to reduced reliability and vehicle comfort. Electric drive systems are highly nonlinear systems with multi-field coupling. The motor and reduction gear are rigidly connected. Torque fluctuations in the motor and internal and external excitations in the gear transmission system cause torsional vibrations in the electric drive system. Torsional vibrations generate cyclic alternating stresses in the drive train, affecting its fatigue life. High-amplitude or high-frequency torsional vibrations are particularly damaging. Transient conditions, such as starting, braking, positive-negative torque switching, and other non-stationary transitions, can induce torsional vibrations in the electric drive system. This can cause significant fluctuations in the motor rotor's speed and torque, triggering internal clearance impacts within the electric drive system and exacerbating vibration and noise issues such as rattle, clack, and shuffle. The rapid and sudden change of torque in the electric drive system causes the powertrain to be subjected to stronger torque excitation than that of fuel vehicles, making the torsional vibration phenomenon more serious.

[0003] Active torsional vibration suppression in electric drive systems relies on precise control of the system's dynamic characteristics. Traditional control methods are usually designed based on a linearized model of the motor itself. Although they can achieve basic performance requirements, they have significant limitations in terms of parameter sensitivity, nonlinear disturbance suppression, and dynamic response robustness. Modern control theory can achieve multi-objective collaborative optimization of the system's dynamic response by constructing a state-space model. For example, it can directly adjust the damping characteristics of torsional vibration suppression by configuring the closed-loop pole position; while nonlinear robust methods such as active disturbance rejection control and sliding mode control use a disturbance observation-compensation mechanism to uniformly treat internal and external system uncertainties as "total disturbances" for dynamic offset, significantly improving control adaptability under complex working conditions. These methods break through the traditional strategy's reliance on linear assumptions and precise models, and open up new technical paths for high-reliability active torsional vibration suppression.

[0004] Currently, there are many studies on motor torque fluctuations or torsional vibrations of electric drive systems. However, most of these studies are based on simplified electric drive system models and only consider low-frequency torsional vibrations or high-frequency torsional vibrations of electric drive systems. Few consider simultaneously suppressing low-frequency and high-frequency torsional vibrations of electric drive systems, and less consider the electromechanical coupling relationship between the motor and the gear transmission system. This makes it difficult to accurately evaluate the control method's effect on suppressing torsional vibrations of electric drive systems. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a double-layer active torsional vibration suppression method for an electric drive system based on electromechanical coupling characteristics, so as to optimize the reference torque and DQ axis current value of the motor, suppress torque fluctuations, and reduce voltage disturbances caused by dead zone, electrical angular velocity coupling terms and nonlinear excitation.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A double-layer active torsional vibration suppression method for an electric drive system based on electromechanical coupling characteristics comprises the following steps:

[0008] S1: Establish the mathematical model of permanent magnet synchronous motor, the dynamic model of helical gear pair of electric drive system and the lumped parameter model of gear transmission;

[0009] S2: Establish an upper-level state feedback control method based on pole placement, including establishing the transmission system dynamic state space equations, state observer, and state feedback controller. The upper-level state feedback control method uses the motor torque as the control variable and feeds the state variable obtained by the state observer into the full state feedback controller to optimize the motor reference torque and output it to the lower-level controller.

[0010] S3: Establish a lower-level torsional vibration suppression method based on ADRC, including using an Extended State Observer (ESO) to calculate new dq-axis current values based on the target voltage and current current. and And compared with the target current to compensate for the total disturbance and Reduce voltage disturbances caused by dead zone, electrical angular velocity coupling terms, and nonlinear excitation.

[0011] Furthermore, the mathematical model of the permanent magnet synchronous motor is established as follows:

[0012] The PMSM stator voltage equation in the synchronous rotating coordinate system is:

[0013]

[0014]

[0015] Where u d / q 、,i d / q , ψ d / q and L d / q are the dq axis stator voltage, current, flux linkage and inductance respectively, R s is the stator resistance, ω e is the motor electrical angular velocity, ψ f is the permanent magnet flux;

[0016] The electromagnetic torque of the permanent magnet synchronous motor is:

[0017] T e =1.5P n i q [i d (L d -L q )+ψ f ]

[0018] Where P n is the number of magnetic pole pairs, the motor electrical angular velocity ω e and mechanical angular velocity ω m The relationship is:

[0019] ω e =P n ω m .

[0020] Furthermore, the dynamic model of the helical gear pair of the electric drive system is established as follows:

[0021] Considering the axial and radial translation vibration of the bearing, the bearing support stiffness is k jx 、k jy 、k jz , j=1,2,3,4, support damping is c jx 、c jy 、c jz , the meshing error is e i , i=1,2; assuming that the first-stage driving gear rotates clockwise and right-handed, and the second-stage driving gear rotates counterclockwise and right-handed, the relative displacements of the first and second-stage gears in the x, y, and z directions are:

[0022]

[0023]

[0024] Where x j 、y j 、z j are the displacements of the gears in the directions of the three coordinate axes, R j is the base circle radius of the gear, θ j is the angular displacement of the gear, is the angle between the meshing surface of the i-th helical gear and the y-axis; the relative displacement of the first and second gears on the meshing line is:

[0025]

[0026]

[0027] The meshing force of the first and second gears and their components in the x, y, and z directions are:

[0028]

[0029]

[0030] Where, F mi is the meshing force of the i-th gear, F xi 、F yi and F zi is the component force of the meshing force of the i-th gear in the x, y, and z directions, β bi is the base circle helix angle, k mi is the meshing stiffness of the gear, c mi For meshing damping.

[0031] Furthermore, the gear transmission concentrated parameter model is established as follows:

[0032] Considering the time-varying meshing stiffness, meshing error, tooth side clearance, and bearing stiffness, and further considering the half-axles, wheels, and body in the transmission system, the transmission system dynamics model is constructed using the lumped parameter method. The motor rotor, wheels, and body are treated as equivalent to rotational inertia elements, the mass of the shaft is ignored, and the shaft is equivalent to a stiffness-damping element. The system characteristics during steering are not considered. The lumped parameter model of the gear transmission is constructed as follows:

[0033]

[0034] Where m j is the gear mass, I j is the moment of inertia of the gear around the z axis, θ j is the angular displacement of the gear, θ m ,θ w ,θ v are the motor rotor angular displacement, wheel angular displacement and vehicle equivalent angular displacement, respectively, T m is the electromagnetic torque, T l is the driving resistance torque;

[0035] In order to prevent the gears from getting stuck due to heat expansion caused by friction between each other, a gap is left on the tooth profile, and its expression is:

[0036]

[0037] Where b m is the tooth side clearance of the meshing tooth pair, and x is the relative displacement between the gears.

[0038] Furthermore, the establishment of the transmission system dynamic state space equation in step S2 includes:

[0039] Perform pole placement on the transmission system transfer function and transform the transmission system dynamics equation into a state space equation to obtain:

[0040]

[0041] In the formula, the state variable C is the damping matrix;

[0042] Given input u = T m , disturbance d = T l , output get:

[0043]

[0044] B=[1 / I m 0 0 0 0 0 0 0 0 0 0 0 0 0]

[0045] C=[1 0 0 0 0 0 0 0 0 0 0 0 0 0]

[0046] D=0

[0047] E=[0 0 0 0 0 0-1 / I v 0 0 0 0 0 0 0]

[0048] According to the state observability criterion, the observability matrix of the system must be full rank, and we get:

[0049] O=[CCACA 2 …CA n-1 ] T

[0050] Where Rank(O)=n, n is a constant;

[0051] According to the system controllability criterion, the controllability matrix is obtained:

[0052] C o =[BABA 2 B…A n-1 B]

[0053] In the formula, Rank(C o )=n;

[0054] With ζ=1 as the goal, the poles of the transfer function are placed on the real axis of the left half of the complex plane.

[0055] Furthermore, the step S2 of establishing a state observer includes:

[0056] Using the Romberg observer, it is expressed as:

[0057]

[0058] Where, is the state variable value estimated by the observer, is the output calculated based on the estimated state variable value, L is the gain matrix, y is the output that can be directly observed, and the observation error is obtained based on this

[0059]

[0060] When the real parts of the eigenvalues of the matrix (A-LC) are all negative, the observation error increases with time. It approaches 0, so it is necessary to find a suitable L. The pole selection of the observer is 2 to 5 times faster than the expected pole of the system, so that the observation error decays faster than the system response.

[0061] Furthermore, the state feedback controller in step S2 is established as follows:

[0062] The state feedback controller is a full state feedback controller, let:

[0063] u=-Gx

[0064] Where, G=[g1g2g3g4g5g6g7g8g9g 10 g 11 g 12 g 13 g 14 ];

[0065] The state variables are fully fed back into the original system to form a closed-loop system, and we get:

[0066]

[0067] Where, (A-BG) is the state matrix of the closed-loop control system;

[0068] Let |(A-BG)-λI|=0, and find the eigenvalue λ of the state matrix; configure the values in the matrix G so that the eigenvalue λ is a real number less than 0. The eigenvalues of the state matrix correspond to the poles of the transfer function, thereby configuring the poles of the transfer function of the original state space equation to the real axis; combine the state feedback controller with the state observer, and use the estimated value As the feedback signal instead of x, that is:

[0069]

[0070] Substitute the above formula into the Lumberg observer matrix, where L and G are set separately and do not affect each other, but it is necessary to ensure that the convergence speed of the observer is faster than that of the controller.

[0071] Furthermore, the lower layer torsional vibration suppression method based on active disturbance rejection control in step S3 specifically includes:

[0072] According to the voltage equation of the permanent magnet synchronous motor, the voltage disturbance caused by the inverter nonlinearity is set to Δu d and Δu q , the new voltage equation is:

[0073]

[0074] The formula contains ω e The current decoupling error caused by the coupling term and the voltage deviation caused by the inverter nonlinearity are both regarded as disturbances, that is:

[0075]

[0076] The extended state observer expands the total disturbance into a new state variable of the system, reconstructs the original state variable and disturbance value through the input and output of the system, and then performs feedback compensation to eliminate the influence of inverter nonlinearity and decoupling error. For a first-order single-input single-output system, the form of its first-order extended state observer is:

[0077]

[0078] Where u and y are the input and output of the system, and are the estimated values of the output variable and the total disturbance, β1 and β2 are the gains of the output error, and b0 is the compensation factor. The fal function is a piecewise nonlinear function that uses different gains in different intervals to achieve the purpose of rapid adjustment. Its expression is as follows:

[0079]

[0080] Where, α i is the tracking factor, δ is the filtering factor, sign is the sign function, and e is the error between the estimated value and the actual value of the output variable;

[0081] Rewrite the voltage equation as:

[0082]

[0083] Where, fd =(Δu d +ω e L q i q -R s i d ) / L d , f q =(Δu q -ω e (L d i d +ψ f )-R s i q ) / L q , the voltage equation is first order, so the extended state observer of the dq axis voltage is designed as:

[0084]

[0085]

[0086] Where i d and i q is the dq axis current value output by the motor, and is the dq axis voltage value of the input motor, and is the dq axis current value estimated by the extended state observer.

[0087] The beneficial effects of the present invention are:

[0088] (1) The present invention compensates for the voltage deviation caused by the nonlinearity of the inverter and reduces the current harmonics and torque fluctuations through the extended state observer in the active disturbance rejection control.

[0089] (2) Compared with traditional control methods, the pole configuration and anti-disturbance control method proposed in the present invention improves the damping ratio at the pole corresponding to the natural frequency that is prone to cause resonance, reduces low-frequency torsional vibration, and shortens the time to reach steady state.

[0090] (3) Compared with the traditional control method, the present invention can timely and real-time correct the motor torque according to the electric drive output torque, reduce current harmonics and torque fluctuations, and reduce the high-frequency torsional vibration of the electric drive system.

[0091] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0093] Figure 1 Schematic diagram of the model of the double-layer active torsional vibration suppression method for the electric drive system based on electromechanical coupling characteristics;

[0094] Figure 2 It is the dynamic model of the first-stage helical gear pair;

[0095] Figure 3 It is the torsional dynamics model of the gear transmission system;

[0096] Figure 4 is the zero-pole distribution diagram of the transfer function based on the state space equation of the original system;

[0097] Figure 5 It is the control block diagram of the state observer;

[0098] Figure 6 It is the block diagram of the state feedback controller;

[0099] Figure 7 This is the state space diagram of the combination of observer and feedback controller;

[0100] Figure 8 This is a block diagram of the harmonic suppression strategy based on active disturbance rejection control;

[0101] Figure 9 Comparison of half-shaft torque fluctuations under steady-state conditions using the traditional method, pole placement, and active disturbance rejection control methods;

[0102] Figure 10 This is a comparison chart of the maximum acceleration under transient conditions using the traditional method, pole configuration, and active disturbance rejection control methods. DETAILED DESCRIPTION

[0103] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0104] It should be noted that the illustrations provided in the following embodiments are merely schematic illustrations of the basic concept of the present invention. Therefore, the illustrations only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0105] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it will be apparent to those skilled in the art that the embodiments of the present invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring the embodiments of the present invention.

[0106] Example 1:

[0107] Reference Figure 1 As shown, the present invention provides a double-layer active torsional vibration suppression method for an electric drive system based on electromechanical coupling characteristics, comprising the following steps:

[0108] S1: Mathematical model construction: Establish an electromechanical coupling model of the electric drive system.

[0109] The basic parameters of the permanent magnet synchronous motor selected in this embodiment are maximum power 160kW, maximum torque 320Nm, maximum speed 16000Rpm, DC voltage 354V, pole pair number 8, permanent magnet flux linkage 0.05Wb, direct-axis inductance 0.1mH, quadrature-axis inductance 0.3mH, and stator resistance 11.66mΩ.

[0110] The PMSM stator voltage equation in the synchronous rotating coordinate system is:

[0111]

[0112]

[0113] Where u d / q 、,i d / q , ψ d / q and L d / q are the dq axis stator voltage, current, flux linkage and inductance respectively, R s is the stator resistance, ω e is the motor electrical angular velocity, ψ f is the permanent magnet flux.

[0114] The electromagnetic torque of the permanent magnet synchronous motor is:

[0115] T e =1.5P n i q [i d(L d -L q )+ψ f ]

[0116] Where P n is the number of magnetic pole pairs, the motor electrical angular velocity ω e and mechanical angular velocity ω m The relationship is:

[0117] ω e =P n ω m

[0118] Considering the axial and radial translation vibration of the bearing, the dynamic model of the helical gear pair is as follows: Figure 2 As shown, the bearing support stiffness is k jx 、k jy 、k jz (j=1, 2, 3, 4), support damping is c jx 、c jy 、c jz (j=1, 2, 3, 4), the meshing error is e i (i=1, 2), assuming that the first-stage driving gear rotates clockwise and the second-stage driving gear rotates counterclockwise, then the relative displacements of the first and second-stage gears in the x, y, and z directions are:

[0119]

[0120]

[0121] Where x j 、y j 、z j (j=1, 2, 3, 4) are the displacements of the gear in the directions of the three coordinate axes, R j (j=1, 2, 3, 4) is the base circle radius of the gear, θ j (j=1, 2, 3, 4) is the angular displacement of the gear, is the angle between the meshing surface of the i-th helical gear and the y-axis. The relative displacement of the first and second gears on the meshing line is:

[0122]

[0123]

[0124] The meshing force of the first and second gears and their components in the x, y, and z directions are:

[0125]

[0126]

[0127] Where, F mi (i=1, 2) is the meshing force of the i-th gear, F xi 、F yi and F zi (i=1, 2) is the component force of the meshing force of the i-th gear in the x, y, and z directions, β bi (i=1, 2) is the base circle helix angle, k mi (i=1, 2) is the meshing stiffness of the gear, c mi (i=1, 2) is the meshing damping.

[0128] After establishing the dynamic model of the helical gear pair, the time-varying meshing stiffness, meshing error, tooth side clearance, and bearing stiffness are considered. Furthermore, factors such as the half-axles, wheels, and body in the transmission system are considered. The transmission system dynamic model is constructed using the lumped parameter method, as shown below. The motor rotor, wheels, and body are treated as rotational inertia elements, the mass of the shaft is not considered, the shaft is treated as a stiffness-damping element, and the system characteristics during steering are not considered. The structure is as follows: Figure 3 shown.

[0129]

[0130] Where m j (j=1, 2, 3, 4) is the gear mass, I j (j=1, 2, 3, 4) is the moment of inertia of the gear around the z axis, θ j (j=1, 2, 3, 4) is the angular displacement of the gear, θ m ,θ w ,θ v are the motor rotor angular displacement, wheel angular displacement and vehicle equivalent angular displacement, respectively, T m is the electromagnetic torque, T l is the driving resistance torque.

[0131] In order to prevent the gears from getting stuck due to heat expansion caused by friction between each other, a gap is usually left in the tooth profile. The expression is:

[0132]

[0133] Where b m is the tooth side clearance of the meshing tooth pair, and x is the relative displacement between the gears.

[0134] S2: Establishing a state feedback control method based on pole placement

[0135] S21: Establishing the state-space equations of the transmission system dynamics

[0136] Perform pole placement on the transmission system transfer function and transform the transmission system dynamics equation into a state space equation to obtain:

[0137]

[0138] In the formula, the state variable C is the damping matrix.

[0139] Given input u = T m , disturbance d = T l , output Can get

[0140]

[0141] B=[1 / I m 0 0 0 0 0 0 0 0 0 0 0 0 0]

[0142] C=[1 0 0 0 0 0 0 0 0 0 0 0 0 0]

[0143] D=0

[0144] E=[0 0 0 0 0 0-1 / I v 0 0 0 0 0 0 0]

[0145] According to the state observability criterion, the observable matrix of the system needs to be full rank, which can be obtained:

[0146] O=[CCACA 2 …CA n-1 ] T

[0147] Where, Rank(O)=n, n=14. After testing and judgment, the system is observable.

[0148] According to the system controllability criterion, the controllability matrix can be obtained:

[0149] C o =[BABA 2 B…A n-1 B]

[0150] In the formula, Rank(C o )=n, n=14, after inspection and judgment, the system is observable.

[0151] When the real part of all the poles of the transmission system's transfer function is less than 0, the system output eventually stabilizes. However, if the poles contain imaginary parts, the system may oscillate but this does not affect its stability. Furthermore, when the transmission system's damping ratio ζ = 1, the system is in a critical damping state, at which point the system converges more quickly. The present invention targets ζ = 1 and places the poles of the transfer function on the real axis of the left half of the complex plane.

[0152] The present invention is aimed at the underdamped electric drive system. From the analysis of its inherent characteristics, it can be seen that the zero-order point distribution diagram of the transfer function can be obtained, such as Figure 4 The first and second order natural frequencies of the electric drive system have a greater impact on low-frequency torsional vibration. The poles corresponding to the first and second order natural frequencies both contain imaginary parts. To reduce the low-frequency torsional vibration of the electric drive system, the present invention mainly makes the poles corresponding to the first and second order natural frequencies fall on the real axis.

[0153] S22: Establishing a state observer

[0154] In actual situations, the dynamic characteristics of electric drive systems are difficult to obtain, and an observer is needed to estimate other state variables based on easily accessible state variables. The present invention sets the motor speed as the state variable to be obtained, but open-loop observation is prone to cumulative errors. In order to correct the observer's estimated value in real time, the difference between the observable output value and the estimated output value is used for feedback to reduce the error between the estimated value and the observed value, forming a closed loop. The present invention uses the Lumberg observer, which is expressed as follows:

[0155]

[0156] Where, is the state variable value estimated by the observer, is the output calculated based on the estimated state variable value, L is the gain matrix, y is the output that can be directly observed, and the observation error can be obtained based on this

[0157]

[0158] When the real parts of the eigenvalues of the matrix (A-LC) are all negative, the observation error increases with time. Approaching 0, therefore, it is necessary to find a suitable L. In order to make the estimated value of the observer quickly approach the actual observable value, the pole selection of the general observer is 2 to 5 times faster than the expected pole of the system, which makes the observation error decay faster than the system response. The state space equation frame of the observer and the original system is limited by the size of the gain matrix L. Figure 5 shown.

[0159] S23: Design of State Feedback Controller

[0160] The feedback controller used in the present invention is a full-state feedback controller, where:

[0161] u=-Gx

[0162] In the above formula, G=[g1g2g3g4g5g6g7g8g9g 10 g 11 g 12g 13 g 14 ].

[0163] By fully feeding the state variables back into the original system to form a closed-loop system, we can obtain:

[0164]

[0165] Where (A-BG) is the state matrix of the closed-loop control system.

[0166] Let |(A-BG)-λI|=0, and the eigenvalue λ of the state matrix can be obtained. By configuring the values in the matrix G, the eigenvalue λ is a real number less than 0. The eigenvalues of the state matrix correspond to the poles of the transfer function, and thus the poles of the transfer function of the original state space equation can be configured on the real axis. Since most of the state variables in the original system cannot be directly observed, it is necessary to combine the state feedback controller with the state observer and use the estimated value As the feedback signal instead of x, that is:

[0167]

[0168] Substituting the above formula into the Lumberg observer matrix, we can get the state space diagram of the combination of observer and feedback controller as follows: Figure 6 As shown in the figure, L and G can be set separately without affecting each other. However, in order to make the estimated value used by the controller more accurate, it is necessary to ensure that the convergence speed of the observer is faster than that of the controller. In this paper, the poles corresponding to the original 1st and 2nd order natural frequencies are configured as -126 and -33.4, and the corresponding matrix G = [9.8 46.2 11.2 -179.5 8.6 -0.07 3×10 -4 -3×10 -3 -7×10 -3 -4×10 -4 5×10 -3 -7×10 -4 7×10 -4 2×10 -6 ], matrix L = [-0.08 46.2 11.2-179.5 8.6 -0.07 3×10 -4 -3×10 -3 -7×10 -3 -4×10 -4 5×10 -3 -7×10 -4 7×10 -4 2×10 -6 ] T , from which the zero-pole distribution after feedback control can be obtained as Figure 7As shown in the figure, the damping ratio at the poles corresponding to the 1st and 2nd order natural frequencies is 1, which achieves the design goal. In addition, the poles do not contain imaginary parts, but only negative real parts.

[0169] S3: Establish a lower-level torsional vibration suppression method based on active disturbance rejection control to reduce current harmonics and motor torque fluctuations, while reducing high-frequency and low-frequency torsional vibrations of the electric drive system and enhancing the reliability of the electric drive system.

[0170] S31: Establish a torsional vibration suppression method based on active disturbance rejection control

[0171] According to the voltage equation of the permanent magnet synchronous motor, the voltage disturbance caused by the inverter nonlinearity is set to Δu d and Δu q , the new voltage equation is:

[0172]

[0173] The above formula contains ω e As the speed increases, the proportion of the coupling term will become larger and larger, which will also reduce the accuracy of motor and vehicle control. Therefore, in order to reduce the impact of the coupling term, the current decoupling error caused by the coupling term and the voltage deviation caused by the inverter nonlinearity are both regarded as disturbances, that is:

[0174]

[0175] The extended state observer expands the total disturbance into a new state variable of the system, reconstructs the original state variable and disturbance value through the input and output of the system, and then performs feedback compensation to eliminate the influence of inverter nonlinearity and decoupling error. For a first-order single-input single-output system, the form of its first-order extended state observer is:

[0176]

[0177] Where u and y are the input and output of the system, and are the estimated values of the output variable and the total disturbance, β1 and β2 are the gains of the output error, and b0 is the compensation factor. The fal function is a piecewise nonlinear function that uses different gains in different intervals to achieve the purpose of rapid adjustment. Its expression is as follows:

[0178]

[0179] Where, α i is the tracking factor, δ is the filtering factor, sign is the sign function, and e is the error between the estimated value and the actual value of the output variable.

[0180] Rewrite the voltage equation as:

[0181]

[0182] Where, f d =(Δu d +ω e L q i q -R s i d ) / L q , f q =(Δu q -ω e (L d i d +ψ f )-R s i q ) / L q , the voltage equation is first order, so the extended state observer of the dq axis voltage can be designed as:

[0183]

[0184]

[0185] Where i d and i q is the dq axis current value output by the motor, and is the dq axis voltage value of the input motor, and is the dq axis current value estimated by the extended state observer. According to the constructed extended state observer, the control block diagram of the permanent magnet synchronous motor with ESO feedback control is as follows Figure 8 As shown in the figure, compared with the previous motor control, the current decoupling link is removed and the ESO observation value feedback is used instead to compensate for the voltage deviation caused by the interference.

[0186] S32: Establish an active double-layer torsional vibration suppression method based on pole placement and active disturbance rejection control

[0187] A two-layer active torsional vibration suppression method is established based on the pole placement method and the self-disturbance rejection control method. The upper-layer state feedback control method uses the motor torque as the control variable and feeds back the motor speed, motor angle, vehicle speed and other state variables obtained by the state observer to the full-state feedback device to optimize the motor reference torque and output it to the lower-layer controller. The ESO in the lower-layer torsional vibration suppression algorithm calculates the new dq axis current value based on the target voltage and current current. and And compared with the target current to compensate for the total disturbance and To reduce the voltage disturbance caused by dead zone, electrical angular velocity coupling term and nonlinear excitation.

[0188] To further verify the effectiveness of the torsional vibration suppression strategy proposed in the present invention, the present invention built an electric drive system torsional vibration test platform for experimental verification. The control program was written using Matlab, compiled by Speedgoat, and then sent torque commands to the motor controller via USB-CAN. The voltage, current, speed, acceleration, temperature, and torque signals were transmitted back to the computer through a power analyzer. In the experiment, the sampling frequency of the current and voltage signals was 2MHz / s, the sampling frequency of the acceleration, speed, and torque was 50kHz / s, and the sampling frequency of the temperature signal was 100Hz / s. Compared with traditional methods, the pole configuration and active disturbance rejection control method proposed in the present invention compensates for the voltage deviation caused by the nonlinearity of the inverter through the extended state observer in the active disturbance rejection control, reduces current harmonics and torque fluctuations. Based on the principle of pole configuration, the motor reference torque is optimized, the damping ratio at the pole that has a greater impact on the low-frequency torsional vibration of the transmission system is increased, the low-frequency torsional vibration of the electric drive system is reduced, and the stability of the electric drive system is improved. Simulation and test results show that compared with the traditional control method, the present invention can reduce the torque fluctuation rate of the electric drive system under different steady-state conditions by about 20%. Figure 9 As shown in Figure 2, the maximum acceleration is reduced by about 80% under the torque mutation condition, and the time it takes for the electric drive system to reach stability is significantly shortened. Figure 10 As shown in the figure, it also reduces the high-frequency and low-frequency torsional vibrations of the electric drive system, enhances the stability of the electric drive system, and improves the smoothness of the vehicle.

[0189] Example 2:

[0190] An electronic device comprising a memory and a processor;

[0191] The memory is used to store computer programs;

[0192] The processor is configured to implement the method described in Example 1 when executing the computer program.

[0193] Example 3:

[0194] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method described in Example 1 is implemented.

[0195] Example 4:

[0196] A computer program product includes a computer program, which implements the method described in embodiment 1 when executed by a processor.

[0197] In the above embodiments, references to "this embodiment" in the specification indicate that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple occurrences of "this embodiment" do not necessarily refer to the same embodiment.

[0198] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of these embodiments will be apparent to those skilled in the art based on the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the present invention are intended to encompass all such alternatives, modifications, and variations that fall within the broad scope of the appended claims.

[0199] Regarding the computer-readable storage medium in this embodiment, those skilled in the art will appreciate that all or part of the steps in the aforementioned method embodiments can be implemented using hardware associated with the computer program. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps in the aforementioned method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0200] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication with each other. The memory is used to store computer programs, the communication interface is used for communication, and the processor and the transceiver are used to run computer programs so that the electronic terminal executes the various steps of the above method.

[0201] In this embodiment, the memory may include a random access memory (RAM), and may also include a non-volatile memory (non-volatile memory), such as at least one disk storage.

[0202] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, and discrete hardware components.

[0203] The present invention can be used in a wide variety of general-purpose or special-purpose computing system environments or configurations, such as personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments that include any of the above.

[0204] The present invention may be described in the general context of computer-executable instructions, such as program modules, executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, and the like that perform specific tasks or implement specific abstract data types. The present invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media, including storage devices.

[0205] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A double-layer active torsional vibration suppression method for an electric drive system based on electromechanical coupling characteristics, characterized by: The following steps are involved: S1: Establish the mathematical model of permanent magnet synchronous motor, the dynamic model of helical gear pair of electric drive system and the lumped parameter model of gear transmission; S2: Establish an upper-level state feedback control method based on pole placement, including establishing the transmission system dynamic state space equations, state observer, and state feedback controller. The upper-level state feedback control method uses the motor torque as the control variable and feeds the state variable obtained by the state observer into the full state feedback controller to optimize the motor reference torque and output it to the lower-level controller. S3: Establish a lower-level torsional vibration suppression method based on active disturbance rejection control, including using the extended state observer (ESO) to calculate the new dq axis current value based on the target voltage and current current. and And compared with the target current to compensate for the total disturbance and Reduce voltage disturbances caused by dead zone, electrical angular velocity coupling terms, and nonlinear excitation.

2. The method for suppressing double-layer active torsional vibration of an electric drive system based on electromechanical coupling characteristics according to claim 1 is characterized in that: The mathematical model of the permanent magnet synchronous motor is established as follows: The PMSM stator voltage equation in the synchronous rotating coordinate system is: Where u d / q 、,i d / q , ψ d / q and L d / q are the dq axis stator voltage, current, flux linkage and inductance respectively, R s is the stator resistance, ω e is the motor electrical angular velocity, ψ f is the permanent magnet flux; The electromagnetic torque of the permanent magnet synchronous motor is: T e =1.5P n i q [i d (L d -L q )+ψ f ] Where P n is the number of magnetic pole pairs, the motor electrical angular velocity ω e and mechanical angular velocity ω m The relationship is: oh e =P n oh m 。 3. The method for suppressing double-layer active torsional vibration of an electric drive system based on electromechanical coupling characteristics according to claim 1 is characterized in that: The dynamic model of the helical gear pair of the electric drive system is established as follows: Considering the axial and radial translation vibration of the bearing, the bearing support stiffness is k jx 、k jy 、k jz , j=1,2,3,4, support damping is c jx 、c jy 、c jz , the meshing error is e i , i=1,2; assuming that the first-stage driving gear rotates clockwise and right-handed, and the second-stage driving gear rotates counterclockwise and right-handed, the relative displacements of the first and second-stage gears in the x, y, and z directions are: Where x j 、y j 、z j are the displacements of the gears in the directions of the three coordinate axes, R j is the base circle radius of the gear, θ j is the angular displacement of the gear, is the angle between the meshing surface of the i-th helical gear and the y-axis; the relative displacement of the first and second gears on the meshing line is: The meshing force of the first and second gears and their components in the x, y, and z directions are: Where, F mi is the meshing force of the i-th gear, F xi 、F yi and F zi is the component force of the meshing force of the i-th gear in the x, y, and z directions, β bi is the base circle helix angle, k mi is the meshing stiffness of the gear, c mi For meshing damping.

4. The method for suppressing double-layer active torsional vibration of an electric drive system based on electromechanical coupling characteristics according to claim 1 is characterized in that: The gear transmission concentrated parameter model is established as follows: Considering the time-varying meshing stiffness, meshing error, tooth side clearance, and bearing stiffness, and further considering the half-axles, wheels, and body in the transmission system, the transmission system dynamics model is constructed using the lumped parameter method. The motor rotor, wheels, and body are treated as equivalent to rotational inertia elements, the mass of the shaft is ignored, and the shaft is equivalent to a stiffness-damping element. The system characteristics during steering are not considered. The lumped parameter model of the gear transmission is constructed as follows: Where m j is the gear mass, I j is the moment of inertia of the gear around the z axis, θ j is the angular displacement of the gear, θ m ,θ w ,θ v are the motor rotor angular displacement, wheel angular displacement and vehicle equivalent angular displacement, respectively, T m is the electromagnetic torque, T l is the driving resistance torque; In order to prevent the gears from getting stuck due to heat expansion caused by friction between each other, a gap is left on the tooth profile, and its expression is: Where b m is the tooth side clearance of the meshing tooth pair, and x is the relative displacement between the gears.

5. The method for suppressing double-layer active torsional vibration of an electric drive system based on electromechanical coupling characteristics according to claim 1 is characterized in that: The step S2 of establishing the transmission system dynamic state space equation includes: Perform pole placement on the transmission system transfer function and transform the transmission system dynamics equation into a state space equation to obtain: In the formula, the state variable C is the damping matrix; Given input u = T m , disturbance d = T l , output get: B=[1 / I m 0 0 0 0 0 0 0 0 0 0 0 0 0] C＝[1 0 0 0 0 0 0 0 0 0 0 0 0 0] D＝0 E=[0 0 0 0 0 0 -1 / I v 0 0 0 0 0 0 0] According to the state observability criterion, the observability matrix of the system must be full rank, and we get: O=[C CA CA 2 …CA n-1 ] T Where Rank(O)=n, n is a constant; According to the system controllability criterion, the controllability matrix is obtained: C o =[B AB A 2 B … A n-1 B] In the formula, Rank(C o )=n; With ζ=1 as the goal, the poles of the transfer function are placed on the real axis of the left half of the complex plane.

6. The method for suppressing double-layer active torsional vibration of an electric drive system based on electromechanical coupling characteristics according to claim 1 is characterized in that: The step S2 of establishing a state observer includes: Using the Romberg observer, it is expressed as: Where, is the state variable value estimated by the observer, is the output calculated based on the estimated state variable value, L is the gain matrix, y is the output that can be directly observed, and the observation error is obtained based on this When the real parts of the eigenvalues of the matrix (A-LC) are all negative, the observation error increases with time. It approaches 0, so it is necessary to find a suitable L. The pole selection of the observer is 2 to 5 times faster than the expected pole of the system, so that the observation error decays faster than the system response.

7. The method for suppressing double-layer active torsional vibration of an electric drive system based on electromechanical coupling characteristics according to claim 1 is characterized in that: The state feedback controller in step S2 is established as follows: The state feedback controller is a full state feedback controller, let: u=-Gx In the formula, G=[g1 g2 g3 g4 g5 g6 g7 g8 g9 g 10 g 11 g 12 g 13 g 14 ]; The state variables are fully fed back into the original system to form a closed-loop system, and we get: Where, (A-BG) is the state matrix of the closed-loop control system; Let |(A-BG)-λI|=0, and find the eigenvalue λ of the state matrix; configure the values in the matrix G so that the eigenvalue λ is a real number less than 0. The eigenvalues of the state matrix correspond to the poles of the transfer function, thereby configuring the poles of the transfer function of the original state space equation to the real axis; combine the state feedback controller with the state observer, and use the estimated value As the feedback signal instead of x, that is: Substitute the above formula into the Lumberg observer matrix, where L and G are set separately and do not affect each other, but it is necessary to ensure that the convergence speed of the observer is faster than that of the controller.

8. The method for suppressing double-layer active torsional vibration of an electric drive system based on electromechanical coupling characteristics according to claim 1 is characterized in that: The lower layer torsional vibration suppression method based on active disturbance rejection control in step S3 specifically includes: According to the voltage equation of the permanent magnet synchronous motor, the voltage disturbance caused by the inverter nonlinearity is set to Δu d and Δu q , the new voltage equation is: The formula contains ω e The current decoupling error caused by the coupling term and the voltage deviation caused by the inverter nonlinearity are both regarded as disturbances, that is: The extended state observer expands the total disturbance into a new state variable of the system, reconstructs the original state variable and disturbance value through the input and output of the system, and then performs feedback compensation to eliminate the influence of inverter nonlinearity and decoupling error. For a first-order single-input single-output system, the form of its first-order extended state observer is: Where u and y are the input and output of the system, and are the estimated values of the output variable and the total disturbance, β1 and β2 are the gains of the output error, and b0 is the compensation factor. The fal function is a piecewise nonlinear function that uses different gains in different intervals to achieve the purpose of rapid adjustment. Its expression is as follows: Where, α i is the tracking factor, δ is the filtering factor, sign is the sign function, and e is the error between the estimated value and the actual value of the output variable; Rewrite the voltage equation as: Where, f d =(Δu d +ω e L q i q -R s i d ) / L d , f q =(Δu q -ω e (L d i d +ψ f )-R s i q ) / L q , the voltage equation is first order, so the extended state observer of the dq axis voltage is designed as: Where i d and i q is the dq axis current value output by the motor, and is the dq axis voltage value of the input motor, and is the dq axis current value estimated by the extended state observer.

9. An electronic device, characterized in that: including memory and processor; The memory is used to store computer programs; The processor is configured to implement the double-layer active torsional vibration suppression method for an electric drive system based on electromechanical coupling characteristics as described in any one of claims 1 to 8 when executing the computer program.

10. A computer-readable storage medium, characterized in that The storage medium stores a computer program, and when the computer program is executed by the processor, the method for suppressing double-layer active torsional vibration of an electric drive system based on electromechanical coupling characteristics according to any one of claims 1 to 8 is implemented.

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