PID parameter design method and system for direct drive working condition torsional vibration control and medium

Abstract

The present application relates to a kind of PID parameter design method, system and medium of direct drive working condition torsional vibration control, comprising the following steps: S1: in simulation software, the multiple-degree-of-freedom torsional vibration model of transmission system under direct drive working condition is built;S2: the second-order torsional vibration response of P1 motor under direct drive working condition is calculated, and according to the second-order torsional vibration target line under direct drive working condition of vehicle type setting;S3: the function expression of Jacobian matrix J Jac Is established;S4: the relationship formula of the first order modal damping ratio of system and Jacobian matrix J Jac Is established;S5: the optimization model with the minimum value of differential adjustment coefficient K d Is established;S6: the minimum differential adjustment coefficient K d And the damping adjustment coefficient K p Corresponding to it under different frequency are solved.The present application can achieve the engineering demand of better control steady-state speed fluctuation and quickly eliminate transient speed fluctuation.

Description

Technical Field

[0001] This invention belongs to the field of vibration and noise control technology for hybrid vehicles, specifically relating to a PID parameter design method, system, and medium for torsional vibration control under direct drive conditions. Background Technology

[0002] Currently, there are relatively mature methods for controlling torsional vibration in the transmission systems of gasoline vehicles, such as using dual-mass flywheels, centrifugal pendulums, rubber-damped torsional dampers, and flexible couplings. With the increasing popularity of new energy vehicles, hybrid models have gradually gained more favor among consumers; however, torsional vibration control for hybrid models has not received sufficient attention.

[0003] Currently, hybrid vehicles on the market operate in a direct-drive mode, where power is primarily provided by the engine, and the output torque of the drive motor is close to zero. In this direct-drive mode, the loose gears in the electric drive assembly pose a knocking risk under the engine's second-order excitation. The wide-frequency response generated by gear knocking may induce resonance in other components, and the resulting structural noise is transmitted to the passenger compartment through the suspension, leading to complaints from passengers. Considering the high operating costs of dual-mass flywheels and centrifugal pendulums, it is particularly important to utilize relatively inexpensive torque limiters and employ cost-effective PID torque control technology in the electric motor.

[0004] PID (including PI and PD) controllers have been around for nearly 70 years and are widely used in various control systems, such as circuit control, flow control, pressure control, and temperature control. They have many advantages, including simple structure, reliable operation, and good stability. Engineers have conducted extensive research on the parameter design methods for PID controllers, and these methods vary across different fields. Currently, for PID parameter design in torsional vibration control of hybrid vehicles, engineering practice often employs a trial-and-error approach. While this can solve the problem, the results are often not optimal, lack theoretical support, and are inefficient.

[0005] Therefore, it is necessary to develop a new PID parameter design method, system, and medium for torsional vibration control under direct drive conditions. Summary of the Invention

[0006] The purpose of this invention is to provide a PID parameter design method, system, and medium for torsional vibration control under direct drive conditions, so as to meet the engineering requirements of better control of steady-state speed fluctuations and rapid elimination of transient speed fluctuations.

[0007] In a first aspect, the PID parameter design method for torsional vibration control under direct drive conditions according to the present invention includes the following steps:

[0008] S1: Build a multi-degree-of-freedom torsional vibration model of the transmission system under direct drive conditions in simulation software;

[0009] S2: Calculate the second-order torsional vibration response at the P1 motor under direct drive conditions, and set the second-order torsional vibration target line under direct drive conditions according to the vehicle model;

[0010] S3: Establish the Jacobian matrix J Jac The function expression;

[0011] S4: Establish the first-order modal damping ratio and Jacobian matrix of the system J Jac Relationship;

[0012] S5: Establish a differential adjustment coefficient K d An optimization model whose objective is to optimize the minimum value;

[0013] S6: Solve for the minimum differential adjustment coefficient K at different frequencies d and the corresponding damping adjustment coefficient K p .

[0014] Optionally, in step S1, the vibration equation of the multi-degree-of-freedom torsional vibration model is:

[0015]

[0016] Where: n represents the number of degrees of freedom in the multi-degree-of-freedom torsional vibration model of the transmission system, θ n×1 Represents an n-dimensional column vector of angular displacements. Represents an n-dimensional column vector of angular velocities. J represents an n-dimensional column vector of angular accelerations. n×n Represents the nth-order rotational moment of inertia matrix, C n×n Denotes the nth-order torsional damping coefficient matrix, K n×n Represents the nth-order torsional stiffness matrix, T n×1 This represents an n-dimensional column vector of excitation torques.

[0017] Optionally, step S3 specifically includes:

[0018] Introduce an auxiliary equation:

[0019]

[0020] Combining formula (2) with formula (1), we get:

[0021]

[0022] make but Then the free state equation of formula (3) is expressed as:

[0023]

[0024] in:

[0025]

[0026] Let X be the magnitude column vector, λ be the eigenvalue, and t be time, then x = X·e λt ,but Formula (4) is transformed into:

[0027] (A·λ+B)X=0 (6)

[0028] Let I 2n×2n Given a 2n×2n identity matrix, multiply A on the left of formula (6). -1 get:

[0029] [λI 2n×2n -(-A -1 B)]X=0 (7)

[0030] At this point, solving for the eigenvalues ​​of the free state equations has been transformed into solving for matrix -A. -1 Eigenvalues ​​of B, -A -1 B is the Jacobian matrix of the free state equations with respect to the state variable x, defined as J. Jac Then formula (7) can be expressed as:

[0031] [λI 2n×2n -J Jac X = 0 (8)

[0032] Let I n×n It is an n×n identity matrix. For J n×n The inverse matrix of J, then J Jac Represented as:

[0033]

[0034] Optionally, step S4 specifically includes:

[0035] Since the free state equations have non-zero solutions, the determinant of the coefficient matrix is ​​zero.

[0036] |λI 2n×2n -J Jac |=0 (10)

[0037] The eigenvalues ​​of the equation are n pairs of conjugate complex numbers, namely σ1±jω. d1 σ2±jω d2 、…、σ n ±jω dn , where σ i The damping factor representing the i-th mode, with the imaginary part ω. di Let ζ represent the free vibration frequency of the i-th mode, i = 1, 2, ..., n; iLet ω be the damping ratio of the i-th mode. i Let be the natural frequency of the i-th mode, then the i-th eigenvalue s i Represented as:

[0038]

[0039] Then ζ i The formula for calculation is:

[0040]

[0041] Optionally, step S5 specifically includes:

[0042] A PID controller module is added at the P1 motor position in the multi-degree-of-freedom model. For any frequency within the direct-drive operating frequency range, the differential adjustment coefficient K is used. d With damping adjustment coefficient K p To optimize the variables, the differential adjustment coefficient K is used. d Minimize as the optimization objective, with the second-order torsional vibration response |Θ2(k)| of motor P1 being lower than the second-order torsional vibration target line Θ. T With the constraint that the first-order modal damping ratio ζ1 equals 1, an optimization model is established:

[0043]

[0044] In the formula, F(K) d ,K p ) represents the differential adjustment coefficient K d ζ1=1、|Θ2(k)|≤Θ T As a constraint, the solution is obtained in the optimization solver to obtain the required minimum differential adjustment coefficient K. d and the corresponding damping adjustment coefficient K p .

[0045] Optionally, step S6 specifically includes:

[0046] Equal-interval frequency interpolation is performed within the frequency range of the direct drive operating condition, for a total of N frequencies, ω1, ω2, ..., ω... N Calculate the minimum differential adjustment coefficient K at each frequency. d With the corresponding damping adjustment coefficient K p .

[0047] Secondly, the PID parameter design system for torsional vibration control under direct drive conditions according to the present invention includes a memory and a controller. The memory stores a computer-readable program, which, when called by the controller, can execute the steps of the PID parameter design method for torsional vibration control under direct drive conditions as described in the present invention.

[0048] Thirdly, the present invention provides a medium storing a computer-readable program, which, when invoked by a controller, can execute the steps of the PID parameter design method for direct-drive torsional vibration control as described in the present invention.

[0049] This invention offers the following advantages: Directly applying torsional vibration control methods from gasoline vehicles to hybrid vehicles suffers from drawbacks such as high cost, slow power response, high energy consumption, and ineffective control of transient response, resulting in a severe lack of market competitiveness for hybrid vehicles. This invention proposes a method using a torque limiter in conjunction with PID control of torsional vibration, which is inexpensive, has high power response sensitivity, and effectively controls energy consumption, meeting the engineering requirements of better controlling steady-state speed fluctuations and quickly eliminating transient speed fluctuations. Attached Figure Description

[0050] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a flowchart of the PID parameter design method for torsional vibration control under direct drive conditions in this embodiment.

[0052] Figure 2 This is a schematic diagram of the single-degree-of-freedom torsional vibration system in this embodiment.

[0053] Figure 3 This diagram illustrates the effect of rotational inertia and torsional stiffness on the torsional vibration response in the inertia control region in this embodiment.

[0054] Figure 4 This diagram illustrates the effect of damping on the transient response in this embodiment.

[0055] Figure 5 This diagram illustrates the effect of damping on the torsional vibration response in the inertia control region in this embodiment.

[0056] Figure 6 This is a schematic diagram of the PID parameter design system for torsional vibration control under direct drive conditions in this embodiment. Detailed Implementation

[0057] Embodiments of this application will now be described in more detail with reference to the accompanying drawings. While some embodiments of this application are shown in the drawings, it should be understood that this application can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this application. It should be understood that the accompanying drawings and embodiments are for illustrative purposes only and are not intended to limit the scope of protection of this application.

[0058] The theoretical principle used in this embodiment is as follows:

[0059] like Figure 2 As shown, in a single-degree-of-freedom torsional vibration system, J1, K1, and C1 represent the equivalent moment of inertia, equivalent torsional stiffness, and equivalent torsional damping coefficient at motor P1 in the direct-drive condition, respectively. θ1 represents the second-order angular displacement of the transmission system, T1·sin(2ωt) represents the second-order sinusoidal excitation applied to the system, T1 represents the second-order torque amplitude, ω represents the angular frequency, t represents time, and T... p (t) represents the torque provided by the PID controller. Let... Indicates second-order angular velocity. Let denot the second-order angular acceleration, then the vibration equation of the system is:

[0060]

[0061] In PID control, T p (t) can be represented as:

[0062]

[0063] Where: K p K is the proportional adjustment coefficient. i K is the integral adjustment coefficient. d Let be the differential adjustment coefficient, and e(t) be the control error term. Taking the second-order speed fluctuation Δrpm of the motor as zero as the error term, we can obtain the following based on the proportional relationship:

[0064]

[0065] Substituting equation (3) into equation (2), we get:

[0066]

[0067] Substituting equation (4) into equation (1), we get:

[0068]

[0069] As can be seen from the above formula, proportional control is equivalent to increasing the torsional damping coefficient of the system, integral control is equivalent to increasing the torsional stiffness of the system, and derivative control is equivalent to increasing the moment of inertia of the system.

[0070] To simplify the calculation, the following relationship is established:

[0071]

[0072] Then formula (5) can be transformed into:

[0073]

[0074] Let the second-order angular amplitude of the transmission system be Θ1, and its magnitude can be expressed as:

[0075]

[0076] Under normal circumstances, the torsional natural frequency of hybrid vehicles in direct-drive mode is relatively low, while the second-order frequency of the engine speed in direct-drive mode is much higher than the system's torsional natural frequency. Therefore, no torsional resonance occurs in direct-drive mode. Assuming there is no PID control (K... p K i With K d (both are zero), J' = 0.1 kg·m 2 K' = 888.3 Nm / rad (natural frequency 15 Hz), C' = 1.9 Nm·s / rad (damping ratio 0.1), T1 = 10 Nm. If the engine speed in direct-drive operation is 1500–1800 rpm (second-order frequency 50–60 Hz), torsional vibration within this frequency range falls within the inertia-controlled region. Increasing the moment of inertia can significantly reduce torsional vibration, while decreasing the torsional stiffness has little effect on it. Figure 3 As shown. Therefore, from the perspective of minimizing energy consumption, the control method for the steady-state response in the inertia control region should primarily focus on increasing inertia.

[0077] To eliminate transient speed fluctuations caused by vehicle acceleration and deceleration in the shortest possible time, the PID control model should be designed as a critically damped system, i.e., the damping ratio ζ' equals 1. The control effect of different damping ratios on the transient response of the system is as follows: Figure 4 As shown. Critical damping can not only effectively suppress the transient response of the system, but also reduce the steady-state response in the inertia control region to a certain extent, such as... Figure 5 As shown.

[0078] In formula (8), for any frequency within the direct drive operating frequency range, J' and C' are used as optimization variables, J' is minimized as the optimization objective, and the second-order torsional vibration response of motor P1 is lower than the target line and ζ' is equal to 1 as constraints. An optimization model is established: minF(J',C'). By solving the optimization solver, the minimum inertia J' and the corresponding damping coefficient C' required at any frequency can be obtained. Among them, minF(J',C') represents the objective function.

[0079] The above describes the parameter design principle of the PID controller in this invention, which can take into account both the steady-state and transient responses of the torsional vibration system.

[0080] like Figure 1 As shown in this embodiment, a PID parameter design method for torsional vibration control under direct drive conditions includes the following steps:

[0081] S1: Build a multi-degree-of-freedom torsional vibration model of the transmission system under direct drive conditions in simulation software. The vibration equation of this multi-degree-of-freedom torsional vibration model is:

[0082]

[0083] Where: n represents the number of degrees of freedom in the multi-degree-of-freedom torsional vibration model of the transmission system, θ n×1 Represents an n-dimensional column vector of angular displacements. Represents an n-dimensional column vector of angular velocities. J represents an n-dimensional column vector of angular accelerations. n×n Represents the nth-order rotational moment of inertia matrix, C n×n Denotes the nth-order torsional damping coefficient matrix, K n×n Represents the nth-order torsional stiffness matrix, T n×1 This represents an n-dimensional column vector of excitation torques.

[0084] S2: Calculate the second-order torsional vibration response of the P1 motor (referring to the ISG motor, which is responsible for generating electricity) under direct drive conditions according to formula (9), and set the second-order torsional vibration target line of the P1 motor under direct drive conditions according to the vehicle model.

[0085] The excitation torque in formula (9) is composed of the superposition of torques at multiple frequencies. Since the second-order torque is dominant, only the second-order torque needs to be considered. Let the column vector of the second-order torque amplitude be T2, the column vector of the second-order angular amplitude be Θ2, and j be the unit imaginary number. Then the magnitude of Θ2 can be expressed as:

[0086] |Θ2|=|[-J n×n (2ω) 2 +K n×n +jC n×n 2ω] -1 ·T2| (10)

[0087] Here, each component of |Θ2| represents the second-order torsional vibration response of each degree of freedom. If the lumped inertia represented by motor P1 is the k-th degree of freedom of the torsional vibration model, then the k-th component of |Θ2| is the second-order torsional vibration response at motor P1, which can be expressed as |Θ2(k)|.

[0088] The target line for the second-order torsional vibration at motor P1 was set subjectively. The second-order torsional vibration response at motor P1 under direct-drive conditions was tested using a torsional vibration sensor on the road. The magnitude of the second-order torsional vibration was controlled using a PID strategy. When PID control was not engaged, a large torsional vibration caused a knocking sound in the gears. As the degree of PID control engagement increased (K...), the vibration decreased. p With K d The knocking sound gradually decreases. The magnitude of the second-order torsional vibration at which no knocking sound occurs is multiplied by a safety factor and used as the target value for second-order torsional vibration control. T .

[0089] S3: Transform n second-order differential equations into 2n first-order differential equations, and establish the Jacobian matrix (coefficient matrix) J. Jac The function expression is as follows:

[0090] Introduce an auxiliary equation:

[0091]

[0092] Combining equations (11) and (9), we get:

[0093]

[0094] make but Then the free state equation of formula (12) can be expressed as:

[0095]

[0096] in:

[0097]

[0098] Let X be the magnitude column vector and λ be the eigenvalue, then x = X·e λt ,but Equation (13) can be transformed into:

[0099] (A·λ+B)X=0 (15)

[0100] Let I 2n×2n Given a 2n×2n identity matrix, equation (15) is multiplied by A on the left. -1 We can obtain:

[0101] [λI 2n×2n -(-A -1 B)]X=0 (16)

[0102] At this point, solving for the eigenvalues ​​of equation (13) has been transformed into solving for matrix -A. -1 Eigenvalues ​​of B, -A -1B is the Jacobian matrix of equation (13) with respect to the state variable x, defined as J Jac Then equation (16) can be expressed as:

[0103] [λI 2n×2n -J Jac X = 0 (17)

[0104] Let I n×n It is an n×n identity matrix. For J n×n The inverse matrix of J, then J Jac It can be represented as:

[0105]

[0106] S4: Establish the damping ratio and Jacobian matrix J of the first-order mode of the system (frequency between 10Hz and 20Hz, with larger amplitude at motor P1 in the mode shape). Jac The relation is as follows:

[0107] Since equation (17) has a non-zero solution, the determinant of the coefficient matrix is ​​zero:

[0108] |λI 2n×2n -J Jac |=0 (19)

[0109] The eigenvalues ​​of the equation are n pairs of conjugate complex numbers, namely σ1±jω. d1 σ2±jω d2 、…、σ n ±jω dn , where σ i The damping factor representing the i-th mode, with the imaginary part ω. di Let ζ represent the free vibration frequency of the i-th mode, where i = 1, 2, ..., n. i Let ω be the damping ratio of the i-th mode. i Let be the natural frequency of the i-th mode, then the i-th eigenvalue s i It can be represented as:

[0110]

[0111] Then ζ i The formula for calculation is:

[0112]

[0113] S5: Establish a differential adjustment coefficient K d The optimization model with the minimum value as the optimization objective is:

[0114] A PID controller module is added at the P1 motor position in the multi-degree-of-freedom model. For any frequency within the direct-drive operating frequency range, the differential adjustment coefficient K is used. d With damping adjustment coefficient K p To optimize the variables, the differential adjustment coefficient K is used. d With minimization as the optimization objective, and constrained by the second-order torsional vibration response of motor P1 being lower than the second-order torsional vibration target line and the first-order modal damping ratio ζ1 being equal to 1, an optimization model is established:

[0115]

[0116] In the formula, F(K) d ,K p ) represents the differential adjustment coefficient K d ζ1=1、|Θ2(j)|≤Θ T As a constraint, the solution is obtained in the optimization solver, yielding the required minimum differential adjustment coefficient K. d and the corresponding damping adjustment coefficient K p .

[0117] S6: Solve for the minimum differential adjustment coefficient K at different frequencies d and the corresponding damping adjustment coefficient K p Specifically:

[0118] Equal-interval frequency interpolation is performed within the frequency range of the direct drive operating condition, for a total of N frequencies, ω1, ω2, ..., ω... N Calculate the minimum differential adjustment coefficient K at each frequency. d With the corresponding damping adjustment coefficient K p Under direct drive conditions, the engine operates at approximately 90% load, so there is no need to calculate the model under different loads; only the frequency variation needs to be considered.

[0119] like Figure 6 As shown in this embodiment, a PID parameter design system for torsional vibration control under direct drive conditions includes a memory and a controller. The memory stores a computer-readable program, which, when called by the controller, can execute the steps of the PID parameter design method for torsional vibration control under direct drive conditions as described in this embodiment.

[0120] In this embodiment, a medium stores a computer-readable program, which, when invoked by a controller, can execute the steps of the PID parameter design method for direct-drive torsional vibration control as described in this embodiment.

[0121] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A PID parameter design method for torsional vibration control under direct drive conditions, characterized in that, Includes the following steps: S1: Build a multi-degree-of-freedom torsional vibration model of the transmission system under direct drive conditions in simulation software. The vibration equation of the multi-degree-of-freedom torsional vibration model is: （1） Where: n represents the number of degrees of freedom in the multi-degree-of-freedom torsional vibration model of the transmission system, θ n×1 Represents an n-dimensional column vector of angular displacements. Represents an n-dimensional column vector of angular velocities. Represents an n-dimensional column vector of angular accelerations. Represents an nth-order rotational moment of inertia matrix. Represents the nth-order torsional damping coefficient matrix. Represents the nth order torsional stiffness matrix, Represents an n-dimensional column vector of excitation torques; S2: Calculate the second-order torsional vibration response at motor P1 under direct drive conditions. Based on the vehicle model, set the second-order torsional vibration target line under direct drive conditions. ; S3: Construct the Jacobian matrix The function expression; S4: Establish the first-order modal damping ratio and Jacobian matrix of the system. Relationship; S5: Establish a differential adjustment coefficient The optimization model with the minimum value as the optimization objective is: （13） In the formula, Describing the differential adjustment coefficient , , As a constraint; where, let Let be the damping ratio of the i-th mode; （12）； in, The damping factor representing the i-th mode, with its imaginary part. The frequency of free vibration of the i-th mode is represented by i = 1, 2, ..., n; S6: Solve for the minimum differential adjustment coefficient at different frequencies and the corresponding damping adjustment coefficient .

2. The PID parameter design method for torsional vibration control under direct drive conditions according to claim 1, characterized in that: Step S3 specifically involves: Introduce an auxiliary equation: （2） Combining formula (2) with formula (1), we get: （3） make ,but Then the free state equation of formula (3) is expressed as: （4） in: （5） Let X be the magnitude column vector, λ be the eigenvalues, and t be time, then we have ,but Formula (4) is transformed into: （6） make Given a 2n×2n identity matrix, multiply the left side of formula (6) get: （7） At this point, solving for the eigenvalues ​​of the free state equations has been transformed into solving the matrix. eigenvalues, That is, the Jacobian matrix of the free state equation with respect to the state variable x, defined as follows: Then formula (7) can be expressed as: （8） make It is an n×n identity matrix. for The inverse matrix, then Represented as: （9）。 3. The PID parameter design method for torsional vibration control under direct drive conditions according to claim 2, characterized in that: Step S4 specifically involves: Since the free state equations have non-zero solutions, the determinant of the coefficient matrix is ​​zero. （10） The eigenvalues ​​of the equation are n pairs of conjugate complex numbers, respectively , … ,set up Let be the natural frequency of the i-th mode, then the i-th eigenvalue... Represented as: （11） 。 4. The PID parameter design method for torsional vibration control under direct drive conditions according to claim 3, characterized in that: Step S5 specifically involves: A PID controller module is added at the P1 motor position in the multi-degree-of-freedom model. For any frequency within the direct-drive operating frequency range, the differential adjustment coefficient is used. With damping adjustment coefficient To optimize variables, the differential adjustment coefficient is used. Minimize the second-order torsional vibration response of motor P1 as the optimization objective. Below the second-order torsional vibration target line First-order modal damping ratio An optimization model is established with the constraint that the coefficient equals 1; the model is then solved in the optimization solver to obtain the required minimum differential adjustment coefficient. and the corresponding damping adjustment coefficient .

5. The PID parameter design method for torsional vibration control under direct drive conditions according to claim 4, characterized in that: Step S6 specifically involves: Equal-interval frequency interpolation is performed within the frequency range of the direct drive operating condition, for a total of N frequencies, ω1, ω2, ..., ω... N Calculate the minimum differential adjustment coefficient K at each frequency. d With the corresponding damping adjustment coefficient K p .

6. A PID parameter design system for torsional vibration control under direct drive conditions, characterized in that: It includes a memory and a controller, wherein the memory stores a computer-readable program, which, when invoked by the controller, can execute the steps of the PID parameter design method for direct-drive torsional vibration control as described in any one of claims 1 to 5.

7. A medium, characterized in that: It contains a computer-readable program that, when invoked by the controller, can execute the steps of the PID parameter design method for direct-drive torsional vibration control as described in any one of claims 1 to 5.

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