A torsional vibration suppression strategy for electric drive system based on two-level model predictive control

Abstract

The invention discloses a torsional vibration suppression strategy for an electric drive system based on a double-layer model predictive control, and relates to the technical field of electric vehicle motors. The invention establishes a mathematical model of a permanent magnet synchronous motor taking into account the dynamic characteristics of the motor based on a stator voltage equation in a d-q coordinate system; based on the dynamics of a gear system, a 19-degree-of-freedom gear transmission system model is established taking into account nonlinear factors such as time-varying meshing stiffness, meshing error, and tooth side clearance; based on the model of the electric drive system, a torsional vibration suppression strategy based on a double-layer model predictive control is proposed, which suppresses the torsional vibration of an integrated electric drive system by controlling the motor target torque and reducing current harmonics and torque fluctuations, thereby enhancing the stability of the electric drive system and improving the comfort of the whole vehicle.

Description

Technical Field

[0001] The invention relates to the technical field of electric vehicle motors, and in particular to a torsional vibration suppression strategy for an electric drive system based on double-layer model predictive control. Background Art

[0002] The electric drive system is a multi-field coupled, strongly nonlinear system. The motor and reduction gear in the electric drive system are rigidly connected, so the torque fluctuation in the motor and the internal and external excitation of the gear transmission system will cause torsional vibration of the electric drive system. Torsional vibration will generate cyclic alternating stress on the transmission chain, affecting the fatigue life of the transmission chain, especially high-amplitude or high-frequency torsional vibration will cause great damage to the transmission chain.

[0003] Under some transient conditions, such as starting, braking, positive and negative torque switching and other non-smooth transitions, the electric drive system will cause torsional vibration, causing significant fluctuations in the speed and torque of the motor rotor, stimulating internal clearance collisions in the electric drive system, and causing transient torque shocks to the mechanical part. The torque shock will affect the meshing characteristics of the gear pair and aggravate the vibration and noise problems. The rapid and sudden torque changes of the electric drive system make the powertrain system bear stronger torque excitation than fuel vehicles, making the torsional vibration phenomenon more serious. Therefore, how to suppress the torsional vibration of the electric drive system has become a current research hotspot.

[0004] Active control methods of electric drive systems can reduce torsional vibration. There are three main control strategies for permanent magnet synchronous motors, namely field oriented control (FOC), direct torque control (DTC) and model predictive control (MPC). FOC control is mainly used in induction motors. Although FOC control can obtain good steady-state performance, the dynamic response still needs to be further improved. DTC control directly calculates and controls the motor flux and torque in a static coordinate system based on the mathematical model of the motor. The response speed of DTC control torque is fast, but the output stability is relatively poor. MPC has better dynamic performance and is easy to implement. Model predictive control can be divided into continuous model predictive control (CCS-MPC) and finite set model predictive control (FCS-MPC).

[0005] Currently, there are many methods for the characteristics of electric drive systems and torsional vibration suppression, but most of the research is based on a simplified electric drive system model, and rarely considers the mutual coupling relationship between the motor and the transmission system, making it difficult to effectively suppress the torsional vibration of the electric drive system. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides an electric drive system torsional vibration suppression strategy based on double-layer model predictive control. In view of the complex and changeable operating conditions of electric vehicles, the heavy nonlinear factors of the electric drive system are comprehensively considered to establish a double-layer model predictive control strategy, which can effectively reduce the torsional vibration of the integrated electric drive system, enhance the stability of the electric drive system, and improve the comfort of the whole vehicle.

[0007] The technical solution adopted by the present invention to solve the technical problem is: a torsional vibration suppression strategy of an electric drive system based on a double-layer model predictive control, comprising the following steps:

[0008] S1: Mathematical model construction: Establish the mathematical model of permanent magnet synchronous motor and the concentrated parameter model of gear transmission system;

[0009] S2: Upper-level MPC construction: dual-degree-of-freedom model predictive control (TDF-MPC) is used as the upper-level MPC; the upper-level MPC uses torque as the control variable, and the motor speed, wheel speed, motor angle, and wheel angle as state quantities to be fed back to the upper-level MPC, and calculates the state quantity and control quantity in the prediction time domain; solves the optimal solution of the quadratic programming problem according to the optimization objective, and finally outputs the optimal solution to the lower-level MPC;

[0010] S3: Lower-level MPC construction: The two-step dual-vector model predictive torque control (TSDV-MPTC) of the permanent magnet synchronous motor is used as the lower-level MPC; the lower-level MPC selects two optimal voltage vectors according to the cost function and simultaneously calculates the action time of the two optimal voltage vectors, and finally inputs the optimal voltage vector and its action time into the motor controller;

[0011] S4: Evaluation index: The longitudinal impact degree, torque fluctuation coefficient and harmonic distortion rate are used to evaluate the performance of the torsional vibration suppression strategy.

[0012] Further, the step S2 specifically includes the following steps: in order to simplify the upper-level MPC controller, reduce the calculation time, and improve the controller response speed, the motor and gear transmission system are simplified into a two-degree-of-freedom model;

[0013] S21: Prediction model:

[0014] The equivalent inertia of the whole vehicle in the simplified model is:

[0015] In the above formula, I1 is the moment of inertia of the input stage small gear, I2 is the moment of inertia of the input stage large gear, I3 is the moment of inertia of the output stage small gear, I4 is the moment of inertia of the output stage large gear, I g is the differential moment of inertia, I w is the wheel moment of inertia, I v is the vehicle moment of inertia, I v ' is the equivalent moment of inertia of the vehicle, i12 is the first gear reduction ratio, i 34 is the secondary gear reduction ratio;

[0016] According to the simplified model of the power transmission system, the torsional vibration differential equation is established:

[0017]

[0018] In the above formula, k v is the equivalent vehicle stiffness, c v is the equivalent vehicle damping;

[0019] Assume the state Control quantity u=T m , the disturbance is d = T L ;

[0020] The state space equation established is:

[0021] S22: Prediction output:

[0022] According to the controller sampling period T s The forward Euler method is used to discretize the state space equation and its coefficients, and the new state space equation is obtained as follows:

[0023]

[0024] In order to stabilize the system and reduce static errors, the above discrete model is changed to an incremental model:

[0025]

[0026] Among them, Δx(k)=x(k)-x(k-1), Δu(k)=u(k)-u(k-1);

[0027] Model predictive control uses the current state variables and the solved control variables to predict future results;

[0028] S23: Optimization and feedback control:

[0029] While suppressing torsional vibration, the output torque of the motor must also be able to meet the power requirements of the driver; the deviation between the output torque of the motor and the required torque must be controlled within a reasonable range. The comprehensive control objectives are as follows:

[0030]

[0031] R c (k+1)=[r(k+1)r(k+2)…r(k+N p )] T ;

[0032] In the above formula, R c is the reference sequence; Q and R are weight matrices; ||Q(YR c )|| 2 is to control the torsional vibration fluctuation to be as small as possible; ||RΔU|| 2 Motor output torque change rate;

[0033] In actual control systems, the motor output torque and torque variation are limited by the motor performance; therefore, the constraints on the control variables are as follows:

[0034] In the above formula, U min , U max They are the maximum and minimum values ​​of the motor torque respectively; ΔU min , ΔU max are the minimum and maximum values ​​of the motor torque increment respectively;

[0035] The above constrained optimization problem is transformed into a quadratic programming problem. In each iteration, the inequality constraint problem is transformed into an equality constraint problem, and the optimal solution sequence ΔU is obtained by solving it. * , add the first value of the sequence to the control amount at the previous moment to get the control amount u(k) at the current moment, and then update the MPC prediction model according to the new state variables of the system to achieve rolling optimization solution.

[0036] Further, the step S3 specifically includes the following steps:

[0037] S31: Establish a discrete mathematical model of permanent magnet synchronous motor:

[0038] In order to calculate the state quantity of the permanent magnet synchronous motor at the next moment, the forward Euler method is used to discretize the mathematical model of the permanent magnet synchronous motor, and the change rate model of the stator current is obtained as follows:

[0039]

[0040] S32: Select voltage vector:

[0041] The two-step dual-vector prediction model predictive torque control is to select the voltage vector V in the traditional model predictive torque control. opt1 Based on this, another voltage vector selection is performed to determine the second optimal voltage vector V opt2 ; Optimal voltage vector V opt2 Selected by cost function; the cost function is: In the above formula is the torque reference value;

[0042] The predicted V opt1The calculated predicted value of the torque is substituted into the above cost function, so that the voltage vector with the minimum cost function is the optimal voltage vector;

[0043] The predicted value of the DQ axis current at time k+n can be obtained by the first-order Euler discretization method:

[0044]

[0045] In the above formula, the superscript p represents the predicted value of the variable; n = 1, 2;

[0046] The two-level inverter can generate 6 effective voltages and 2 zero voltage vectors, a total of 7 voltage vectors; opt2 When selecting, the optimal voltage vector V opt1 and 7 alternative voltage vectors, and pre-allocate the action time of the two voltage vectors in each combination; then use the mathematical model of the predicted value of the DQ axis current at time k+n to predict the current, while considering the action time of the two voltage vectors; at this time, u in the above formula d and u q for:

[0047] u q (n) = t opt1_n u q_opt1_n +(T s -t opt1_n ) qj_n ;

[0048] u q (n) = t opt1 (n)u d_opt1 (n)+(T s -t opt1 (n))u dj (n);

[0049] In the above formula, t opt1 is the optimal voltage vector V opt1 The action time of u d_opt1 and u q_opt1 They are the optimal voltage vector V opt1 DQ axis component of stator voltage; u dj 、u qj The jth voltage vector V j The corresponding DQ axis voltage components, where j = 1, 2, ... 7;

[0050] S33: Distribution of voltage vector action time:

[0051] The q-axis deadbeat is used to allocate two voltage vectors V in one sampling period. opt1 and V j The action time must meet the following requirements:

[0052] According to the above formula, V opt1 The action time is:

[0053]

[0054] In the above formula,

[0055]

[0056]

[0057]

[0058] In (k+n)T s The predicted value of electromagnetic torque at time can be obtained by the following formula:

[0059]

[0060] Furthermore, the two-step dual-vector model predictive torque control strategy control method is as follows:

[0061] a. Select the optimal voltage vector V according to the value function opt1 , then by the V opt1 The action time formula allocates the time for each of the two voltage vectors in one sampling cycle to the seven voltage vector combinations;

[0062] b. Based on the discrete mathematical model of the permanent magnet synchronous motor, the predicted value formula of the DQ axis current at time k+n in step 32 and the predicted value formula at (k+n)T in step 33 are combined. s The prediction value formula of electromagnetic torque at the moment calculates the torque value under the 7 voltage vector combinations, and then brings it into the cost function in step 32 to calculate the corresponding cost function value;

[0063] c. Compare 7 g i value, choose the cost function g i The minimum voltage vector is taken as the second optimal voltage vector;

[0064] d. Repeat the above steps (a)-(c) to perform the second step prediction; opt1 (k+2), V opt2 (k+2) and the corresponding action time are output to the motor controller.

[0065] Beneficial effects of the present invention:

[0066] 1. Compared with the dual-vector model predictive torque control strategy, the present invention can correct the motor reference torque command according to state quantities such as the actual vehicle speed and the actual motor speed.

[0067] 2. The present invention reduces the influence of control delay, can select voltage vector more accurately, further reduces torque fluctuation, reduces current harmonics, and improves system stability.

[0068] 3. Compared with the dual-vector model predictive torque control strategy, it can reduce the torque fluctuation rate of the electric drive system and the impact of the vehicle, weaken the torsional vibration of the electric drive system, and show excellent performance in both dynamic and steady states. It enhances the reliability of the electric drive system and improves vehicle comfort. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 The present invention is a flow chart of a torsional vibration suppression strategy for an electric drive system based on double-layer model predictive control.

[0070] Figure 2 The present invention discloses a two-step dual-vector model predictive torque control strategy flow chart of an electric drive system torsional vibration suppression strategy based on a double-layer model predictive control.

[0071] Figure 3 The present invention discloses a double-degree-of-freedom model predictive control strategy flow chart of a torsional vibration suppression strategy of an electric drive system based on a double-layer model predictive control.

[0072] Figure 4 The present invention discloses a double-layer model predictive control strategy flow chart of a torsional vibration suppression strategy of an electric drive system based on double-layer model predictive control.

[0073] Figure 5 It is a schematic diagram of a 19-DOF dynamic model of a motor in an electric drive system torsional vibration suppression strategy based on double-layer model predictive control according to the present invention.

[0074] Figure 6 It is a simplified model schematic diagram of an integrated electric drive system in a torsional vibration suppression strategy of an electric drive system based on double-layer model predictive control of the present invention.

[0075] Figure 7 The present invention discloses a two-level three-phase voltage source inverter topology diagram for a vehicle with an electric drive system torsional vibration suppression strategy based on a double-layer model predictive control.

[0076] Figure 8 It is a comparison chart of experimental results between the torsional vibration suppression strategy of the electric drive system based on the double-layer model predictive control and the traditional dual-vector model predictive torque motor control strategy. DETAILED DESCRIPTION

[0077] The present invention is further described in detail below with reference to the accompanying drawings.

[0078] In view of the complex and changeable working conditions of electric vehicles, the present invention considers the nonlinear factors in the electric drive system and establishes a double-layer model predictive control strategy to reduce the torsional vibration of the electric drive system. The specific technical solutions are as follows.

[0079] Reference Figures 1 to 8 , a torsional vibration suppression strategy for an electric drive system based on a two-layer model predictive control includes the following steps:

[0080] S1: Mathematical model construction: Establish the mathematical model of permanent magnet synchronous motor and the concentrated parameter model of gear transmission system.

[0081] Step S1 is specifically as follows:

[0082] S11: Establishing a mathematical model of a permanent magnet synchronous motor. 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 4, stator flux 0.0255Wb, and stator inductance 0.05mH.

[0083] In the synchronous rotating coordinate system, the voltage equation of the permanent magnet synchronous motor is:

[0084]

[0085] In the above formula, u d 、u q and i d 、i q are the stator DQ axis voltage and current respectively; R is the stator resistance; L d , L q are the DQ axis inductance respectively; f is the permanent magnet flux; ω e is the rotor electrical angular frequency.

[0086] S12: Establish a concentrated parameter model of the gear transmission system.

[0087] The permanent magnet synchronous motor, gears, wheels and body are equivalent to a concentrated mass block with rotational inertia. The power transmission shaft is equivalent to an elastic shaft when stiffness and damping are considered. In the process of gear meshing, time-varying meshing stiffness, meshing error, meshing damping and tooth side clearance are important nonlinear excitations that cause torsional vibration of the electric drive system. A 19-degree-of-freedom concentrated parameter model of the gear transmission system considering nonlinear excitations such as time-varying meshing stiffness, meshing error, meshing damping and tooth side clearance is established as shown in formula (2). Figure 5 shown.

[0088]

[0089] In the above formula, θ m, θ1, θ2, θ3, θ4, θ w and θ v They are the motor shaft angle, input stage pinion angle, input stage gear angle, output stage pinion angle, output stage gear angle, wheel angle and vehicle body equivalent angle. m , T L They represent the driving torque and load torque respectively, I1 represents the moment of inertia of the input stage pinion, I2 represents the moment of inertia of the input stage gear, I3 represents the moment of inertia of the output stage pinion, I4 represents the moment of inertia of the output stage gear, and I g represents the differential moment of inertia, k s1 Indicates the torsional stiffness of the power input shaft, k m1 It represents the normal meshing stiffness per unit length of the first-stage gear pair, k s2 Indicates the torsional stiffness of the power output shaft, k a represents the half-shaft torsional stiffness, k w represents the wheel torsional stiffness, c s1 Indicates the torsional damping ratio of the power input shaft, c m1 and c m2 Respectively represent the meshing damping of the first and second gears, c s2 Indicates the output shaft torsional damping ratio, c a Represents the half-shaft torsional damping, R a represents the semi-axis radius, c w represents wheel torsional damping, m represents vehicle mass, i 12 Indicates the first gear reduction ratio, i 34 represents the secondary gear reduction ratio, r represents the wheel radius, f represents the rolling resistance coefficient, C d represents the air resistance coefficient, and A represents the frontal area.

[0090] The resistance load of the car when it is working can be expressed as:

[0091] In order to prevent the gear teeth from expanding and getting stuck due to heat generated by friction between each other, a gap is usually left between the tooth profiles. The tooth side gap can be expressed as:

[0092] In the above formula, b is half of the tooth side clearance, and x is the relative displacement of the gear meshing point.

[0093] The contact line length of a single pair of gear teeth first increases and then decreases as the driving gear rotates during the meshing process. The angle state of the driving gear can be used to represent the time-varying meshing stiffness of the helical gear. The gear pair has a damping effect when transmitting power, which can be expressed as:

[0094] In the above formula, ξ mrepresents the meshing damping ratio, and its value range is 0.03~0.17. According to engineering experience, ξ m =0.15; m i Represents the mass of gear i.

[0095] The meshing displacement of the gear along the meshing line is: y =R1θ1-R2θ2-e (6);

[0096] In the above formula, θ1 is the angular displacement of gear 1; θ2 is the angular displacement of driven gear 2; R1 is the radius of gear 1; R2 is the radius of gear 2; and e is the meshing error.

[0097] The normal elastic deformation of the gear along the contact line is: i =δ y cosβ b (7);

[0098] In the above formula, β b is the base circle helix angle.

[0099] The meshing force of a gear pair can be expressed as:

[0100]

[0101] In the above formula, c m is the gear meshing damping, k m is the gear mesh stiffness.

[0102] S2: Upper-level MPC construction: dual-degree-of-freedom model predictive control (TDF-MPC) is used as the upper-level MPC; the upper-level MPC takes torque as the control quantity, and the motor speed, wheel speed, motor angle, and wheel angle are fed back to the upper-level MPC as state quantities to calculate the state quantities and control quantities in the prediction time domain; considering the computing power and calculation accuracy of the controller, the prediction time domain Np=30 and the control time domain Nc=10 are taken, and the optimal solution of the quadratic programming problem is solved according to the optimization objective, and finally the optimal solution is output to the lower-level MPC.

[0103] Step S2 specifically includes the following steps:

[0104] In order to simplify the upper-level MPC controller, reduce the calculation time and improve the controller response speed, the electric drive system is simplified to a two-degree-of-freedom model.

[0105] S21: Prediction model.

[0106] The equivalent inertia of the whole vehicle in the simplified model is:

[0107] In the above formula, I1 is the moment of inertia of the input stage small gear, I2 is the moment of inertia of the input stage large gear, I3 is the moment of inertia of the output stage small gear, I4 is the moment of inertia of the output stage large gear, I g is the differential moment of inertia, I w is the wheel moment of inertia, I v is the vehicle moment of inertia, I v ' is the equivalent moment of inertia of the vehicle, i 12 is the first gear reduction ratio, i 34 It is a two-stage gear reduction ratio.

[0108] According to the simplified model of the electric drive system, the torsional vibration differential equation is established as follows:

[0109]

[0110] In the above formula, k v is the equivalent vehicle stiffness, c v is the equivalent vehicle damping.

[0111] Assume the state Control quantity u=T m , the disturbance is d = T L The state space equation established is:

[0112] The coefficient matrix in the above formula is:

[0113]

[0114]

[0115] S22: Prediction output.

[0116] The system state is discretized according to the controller sampling period T s The forward Euler method is used to discretize the state equation and its coefficients, and the new state space equation is obtained as follows:

[0117]

[0118] The coefficient matrix in the above formula is: A f =A c T s +I;B f =B cu T s ; C f =C c

[0119] In the above formula, I is a 4th-order unit matrix. Considering the computing power and calculation accuracy of the controller, T is taken. s =0.001 is the sampling cycle time.

[0120] In order to stabilize the system and reduce static errors, the above discrete model is changed to an incremental model:

[0121]

[0122] Among them, Δx(k)=x(k)-x(k-1), Δu(k)=u(k)-u(k-1).

[0123] Model predictive control uses the current state variables and the solved control variables to predict future results. Assuming that the current sampling time is k (k>0),

[0124]

[0125] Among them, Δx(k+i|k) represents the state prediction of the system at time point k after time point i.

[0126] The predicted output of the system is:

[0127]

[0128] S23: Optimization and feedback control.

[0129] While suppressing torsional vibration, the output torque of the motor must also be able to meet the driver's power requirements. The output torque of the motor should not deviate too much from the required torque, that is, ΔU(k) ​​should not be too large. Therefore, the comprehensive control objectives are as follows:

[0130]

[0131] R c (k+1)=[r(k+1) r(k+2) … r(k+N p )] T (17);

[0132] In the above formula, R c is the reference sequence; Q and R are weight matrices; ||Q(YR c )|| 2 is to control the torsional vibration fluctuation to be as small as possible; ||RΔU|| 2 The rate of change of motor output torque.

[0133] In actual control systems, the motor output torque and torque variation are limited by the motor performance. Therefore, the constraints on the control variables are as follows:

[0134] In the above formula, U min , U max They are the maximum and minimum values ​​of the motor torque respectively; ΔU min , ΔUmax They are the minimum and maximum values ​​of the motor torque increment respectively.

[0135] Coefficient matrix A k for:

[0136]

[0137] The above constrained optimization problem is transformed into a quadratic programming problem (QP), and the inequality constraint problem is transformed into an equality constraint problem in each iteration, and the optimal solution sequence ΔU is obtained by solving it. * , add the first value of the sequence to the control amount at the previous moment to get the control amount u(k) at the current moment, and then update the MPC prediction model according to the new state variables of the system to achieve rolling optimization solution. The quadratic programming problem above can be solved using quadprog in Matlab.

[0138]

[0139] S3: Construction of lower-level MPC: The two-step dual-vector model predictive torque control (TSDV-MPTC) of permanent magnet synchronous motor is used as the lower-level MPC; the lower-level MPC selects two optimal voltage vectors according to the cost function and simultaneously calculates the action time of the two optimal voltage vectors, and finally inputs the optimal voltage vector and its action time into the motor controller.

[0140] Step S3 specifically includes the following steps:

[0141] Description of the working status of the inverter's three-way inverter bridge. Figure 7 This is the topology diagram of the two-level three-phase voltage source inverter for vehicles. DC Represents the DC bus voltage, supplied by the battery. a 、s b 、s c 、s a ′、s b ′ and s c ' respectively represent the states of the six power switching elements of the inverter.

[0142] When the switch value is 1, the corresponding switch element is in the on state. The upper and lower switch elements on the same bridge arm cannot be closed at the same time, that is, s a and a ′、s b and b ′、s c and c ' cannot be 1 at the same time.

[0143] The inverter has three inverter bridges with a total of 2 3 -1 different basic voltage vector space quantities (two zero vectors), which can be expressed as:

[0144] Therefore, the phase voltage U obtained by the motor A , U B with U C It presents a functional relationship with each switch state quantity:

[0145]

[0146] S31: Establish a discrete mathematical model of permanent magnet synchronous motor.

[0147] In order to calculate the state quantity of the permanent magnet synchronous motor at the next moment, the present invention discretizes the mathematical model of the permanent magnet synchronous motor using the forward Euler method, and the rate of change model of the stator current is:

[0148]

[0149] S32: Select voltage vector.

[0150] The two-step dual-vector model predictive torque control strategy is to select the voltage vector V in the traditional dual-vector model predictive torque control strategy. opt1 Based on this, another voltage vector selection is performed to determine the second optimal voltage vector V opt2 . When performing the optimal voltage vector V opt2 The cost function shown in the following formula 23 is used when selecting. The predicted value of the torque can be calculated by the mathematical model of the permanent magnet synchronous motor, that is, formula 22. The cost function selected by the present invention is:

[0151] In the above formula is the torque reference value.

[0152] The two-level inverter can generate 6 effective voltages and 2 zero voltage vectors, a total of 7 voltage vectors. opt1 The calculated torque is substituted into the cost function, and the voltage vector that minimizes the cost function is the optimal voltage vector.

[0153] The predicted value of the DQ axis current at time k+n can be obtained by the first-order Euler discretization method:

[0154]

[0155] The superscript p represents the predicted value of the variable, n=1,2.

[0156] In progress opt2 When selecting, the optimal voltage vector V opt1and 7 alternative voltage vectors, and pre-allocate the action time of the two voltage vectors in each combination. Then use equation 24 to predict the current, taking into account the action time of the two voltage vectors. d and u q for:

[0157] u q (n) = t opt1_n u q_opt1_n +(T s -t opt1_n ) qj_n (25);

[0158] u q (n) = t opt1 (n)u d_opt1 (n)+(T s -t opt1 (n))u dj (n) (26);

[0159] In the above formula, t opt1 is the optimal voltage vector V opt1 The action time of u d_opt1 and u q_opt1 They are the optimal voltage vector V opt1 DQ axis component of the stator voltage. dj 、u qj The jth voltage vector V j Corresponding DQ axis voltage components (j=1, 2,…7).

[0160] S33: Distribution of voltage vector action time.

[0161] The present invention uses q-axis deadbeat to allocate two voltage vectors V in one sampling period. opt1 and V j The action time must meet the following requirements:

[0162] According to the above formula, V opt1 The action time is:

[0163]

[0164] In the above formula,

[0165]

[0166]

[0167]

[0168] In (k+n)T sThe predicted value of electromagnetic torque at time can be obtained by the following formula:

[0169]

[0170] The control method of the two-step dual-vector model predictive torque control strategy is as follows:

[0171] a. Select the optimal voltage vector V according to the value function opt1 , and then equation 28 is used to allocate the time for each of the two voltage vectors in one sampling cycle among the seven voltage vector combinations.

[0172] b. According to the IPMSM discrete mathematical model, the torque values ​​under the seven voltage vector combinations are calculated by combining equations 24 and 29. Substitute into equation 23 to calculate the corresponding cost function value.

[0173] c. Compare 7 g i value, choose the cost function g i The minimum voltage vector is taken as the second optimal voltage vector.

[0174] d. Repeat the above steps (a)-(c) to perform the second step prediction. opt1 (k+2), V opt2 (k+2) and the corresponding action time are output to the motor controller.

[0175] S4: Evaluation index: The longitudinal impact degree, torque fluctuation coefficient and harmonic distortion rate are used to evaluate the performance of the torsional vibration suppression strategy.

[0176] Step S4 is as follows: The purpose of designing the power transmission system control strategy is to reduce the torsional vibration of the transmission system and have better dynamic response characteristics while meeting comfort requirements. In order to evaluate the performance of the torsional vibration suppression strategy, the present invention adopts the following performance evaluation indicators:

[0177] 1) Longitudinal impact strength:

[0178]

[0179] During the Tip in / out process, the torsional vibration of the powertrain generates oscillation of the entire vehicle, which is described by the longitudinal shock degree Jerk.

[0180] 2) Torque fluctuation coefficient:

[0181]

[0182] In the above formula, T max is the maximum torque, T min is the minimum torque.

[0183] 3) Harmonic distortion rate:

[0184] Harmonic distortion is the ratio of the amplitude of all harmonic content to the amplitude of the fundamental wave.

[0185]

[0186] In the above formula, P1 is the fundamental amplitude, P n is the amplitude of each harmonic.

[0187] To further verify the effectiveness of the torsional vibration suppression strategy proposed in the present invention, the present invention builds an electric drive system torsional test platform for experimental verification, uses Matlab to write a control program, and sends a torque command to the motor controller through USB-CAN after being compiled by Speedgoat. The voltage, current, speed, acceleration, temperature and torque signals are transmitted back to the computer through the power analyzer. In the experiment, the sampling frequency of the current and voltage signals is 2MHz / s, the sampling frequency of the acceleration, speed and torque is 50kHz / s, and the sampling frequency of the temperature signal is 100Hz / s.

[0188] Compared with the traditional dual vector model predictive torque control, the present invention can correct the motor reference torque command according to the state quantities such as the actual vehicle speed and the actual motor speed, reduce the influence of control delay, and can more accurately select the voltage vector, further reduce the torque fluctuation, reduce the current harmonics, and improve the system stability. Compared with the traditional control method, the present invention can reduce the torque fluctuation rate and vehicle impact, weaken the torsional vibration of the motor, and show excellent performance in both dynamic and steady state. It enhances the reliability of the motor and improves the comfort of the vehicle.

[0189] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for suppressing torsional vibration of an electric drive system based on a double-layer model predictive control, characterized in that: The following steps are involved: S1: Mathematical model construction: Establish the mathematical model of permanent magnet synchronous motor and the concentrated parameter model of gear transmission system; S2: Upper-level MPC construction: dual-degree-of-freedom model predictive control (TDF-MPC) is used as the upper-level MPC; the upper-level MPC uses torque as the control variable, and the motor speed, wheel speed, motor angle, and wheel angle as state quantities to be fed back to the upper-level MPC, and calculates the state quantity and control quantity in the prediction time domain; solves the optimal solution of the quadratic programming problem according to the optimization objective, and finally outputs the optimal solution to the lower-level MPC; S3: Lower-level MPC construction: two-step dual-vector model predictive torque control (TSDV-MPTC) of permanent magnet synchronous motor as the lower-level MPC; The lower MPC selects two optimal voltage vectors according to the cost function and calculates the action time of the two optimal voltage vectors at the same time, and finally inputs the optimal voltage vectors and their action time into the motor controller; S4: Evaluation index: longitudinal impact degree, torque fluctuation coefficient and harmonic distortion rate are used to evaluate the performance of torsional vibration suppression strategy; The step S2 specifically includes the following steps: in order to simplify the upper-level MPC controller, reduce the calculation time, and improve the controller response speed, the motor and gear transmission system are simplified into a two-degree-of-freedom model; S21: Prediction model: The equivalent inertia of the whole vehicle in the simplified model is: In the above formula, I1 is the moment of inertia of the input stage small gear, I2 is the moment of inertia of the input stage large gear, I3 is the moment of inertia of the output stage small gear, I4 is the moment of inertia of the output stage large gear, I g is the differential moment of inertia, I w is the wheel moment of inertia, I v is the vehicle moment of inertia, I v ' is the equivalent moment of inertia of the vehicle, i 12 is the first gear reduction ratio, i 34 is the secondary gear reduction ratio; According to the simplified model of the power transmission system, the torsional vibration differential equation is established: In the above formula, k v is the equivalent vehicle stiffness, c v is the equivalent vehicle damping, θ m is the motor shaft angle, θ v Equivalent turning angle of the vehicle body, T m is the driving torque; T L is the load torque; I m is the motor shaft moment of inertia; I v 'Equivalent moment of inertia of the whole vehicle; Assume the state Control quantity u=T m , the disturbance is d = T L ; The state space equation established is: S22: Prediction output: According to the controller sampling period T s The forward Euler method is used to discretize the state space equation and its coefficients, and the new state space equation is obtained as follows: In order to stabilize the system and reduce static errors, the above discrete model is changed to an incremental model: Among them, Δx(k)=x(k)-x(k-1), Δu(k)=u(k)-u(k-1); Model predictive control uses the current state variables and the solved control variables to predict future results; S23: Optimization and feedback control: While suppressing torsional vibration, the output torque of the motor must also be able to meet the power requirements of the driver; the deviation between the output torque of the motor and the required torque must be controlled within a reasonable range. The comprehensive control objectives are as follows: R c (k+1)=[r(k+1) r(k+2) … r(k+N p )] T ; In the above formula, R c is the reference sequence; Q and R are weight matrices; ||Q(YR c )|| 2 is to control the torsional vibration fluctuation to be as small as possible; ||RΔU|| 2 Motor output torque change rate; In actual control systems, the motor output torque and torque variation are limited by the motor performance; therefore, the constraints on the control variables are as follows: In the above formula, U min , U max They are the maximum and minimum values ​​of the motor torque respectively; ΔU min , ΔU max They are the minimum and maximum values ​​of the motor torque increment respectively; ΔU represents the motor torque increment; U t represents the motor torque at time t; Coefficient matrix A k for: The above constrained optimization problem is transformed into a quadratic programming problem. In each iteration, the inequality constraint problem is transformed into an equality constraint problem, and the optimal solution sequence ΔU is obtained by solving it. * , add the first value of the sequence to the control amount at the previous moment to get the control amount u(k) at the current moment, and then update the MPC prediction model according to the new state variables of the system to achieve rolling optimization solution; The step S3 specifically comprises the following steps: S31: Establish a discrete mathematical model of permanent magnet synchronous motor: In order to calculate the state quantity of the permanent magnet synchronous motor at the next moment, the forward Euler method is used to discretize the mathematical model of the permanent magnet synchronous motor, and the change rate model of the stator current is obtained as follows: S32: Select voltage vector: The two-step dual-vector prediction model predictive torque control is to select the voltage vector V in the traditional model predictive torque control. opt1 Based on this, another voltage vector selection is performed to determine the second optimal voltage vector V opt2 ; Optimal voltage vector V opt2 Selected by cost function; the cost function is: In the above formula is the torque reference value; The predicted V opt1 The calculated predicted value of the torque is substituted into the above cost function, so that the voltage vector with the minimum cost function is the optimal voltage vector; The predicted value of the DQ axis current at time k+n can be obtained by the first-order Euler discretization method: In the above formula, the superscript p represents the predicted value of the variable; n = 1, 2; The two-level inverter can generate 6 effective voltages and 2 zero voltage vectors, a total of 7 voltage vectors; opt2 When selecting, the optimal voltage vector V opt1 and 7 alternative voltage vectors, and pre-allocate the action time of the two voltage vectors in each combination; then use the mathematical model of the predicted value of the DQ axis current at time k+n to predict the current, while considering the action time of the two voltage vectors; at this time, u in the above formula d and u q for: u q (n)=t opt1_n u q_opt1_n +(T s -t opt1_n )u qj_n ; u q (n)=t opt1 (n)u d_opt1 (n)+(T s -t opt1 (n))u dj (n); In the above formula, t opt1 is the optimal voltage vector V opt1 The action time of u d_opt1 and u q_opt1 They are the optimal voltage vector V opt1 DQ axis component of stator voltage; u dj 、u qj The jth voltage vector V j The corresponding DQ axis voltage components, where j = 1, 2, ... 7; S33: Distribution of voltage vector action time: The q-axis deadbeat is used to allocate two voltage vectors V in one sampling period. opt1 and V j The action time must meet the following requirements: According to the above formula, V opt1 The action time is: In the above formula, In (k+n)T s The predicted value of electromagnetic torque at time can be obtained by the following formula: The control method of the two-step dual-vector model predictive torque control strategy is as follows: a. Select the optimal voltage vector V according to the value function opt1 , then by the V opt1 The action time formula allocates the time for each of the two voltage vectors in one sampling cycle to the seven voltage vector combinations; b. Based on the discrete mathematical model of the permanent magnet synchronous motor, the predicted value formula of the DQ axis current at time k+n in step 32 and the predicted value formula at (k+n)T in step 33 are combined. s The prediction value formula of electromagnetic torque at the moment calculates the torque value under the 7 voltage vector combinations, and then brings it into the cost function in step 32 to calculate the corresponding cost function value; c. Compare 7 g i value, choose the cost function g i The minimum voltage vector is taken as the second optimal voltage vector; d. Repeat the above steps (a)-(c) to perform the second step prediction; opt1 (k+2), V opt2 (k+2) and the corresponding action time are output to the motor controller.

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