Time-varying and time-lag vibration reduction control method under complex excitation

Abstract

The invention discloses a time-varying time-lag vibration reduction control method under complex excitation, and relates to the technical field of automobile active suspension control, and the method comprises the steps: firstly constructing a 1 / 4 vehicle active suspension system dynamic differential equation and a state space equation containing variable time lag based on a Lagrangian method; then, aiming at the external excitation multi-frequency characteristic, the excitation main frequency is determined through Fourier transform, a variable time lag function expression is established, and real-time adjustment of time lag along with the excitation frequency is achieved; and finally, taking the time-delay feedback gain and the variable time-delay amount as optimization variables, solving a numerical solution of the kinetic equation in combination with an improved fine integral algorithm, and performing iterative optimization on a target function taking the vehicle body acceleration, the suspension dynamic stroke and the tire dynamic load as cores by utilizing an improved particle swarm algorithm. According to the method, the problem that traditional timing lag control and a passive suspension are poor in damping effect under complex excitation is solved, the driving comfort and the driving stability of the vehicle are remarkably improved, and a new technical scheme is provided for the design of an active suspension system.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of vehicle suspension control, and particularly relates to a time-varying time-delay vibration control method for complex excitation. BACKGROUND

[0002] With the rapid development of automobile technology, users' demand for vehicle ride comfort, safety and economy is increasing. Suspension system, as an important damping device of automobile, has an important influence on its ride comfort. Active suspension has been widely used due to its excellent damping performance, but the time delay problem is inevitably involved in its control process. Early research generally believes that time delay is not conducive to active control. However, recent research shows that reasonable introduction of time delay can not only improve the damping effect, but also has a positive effect on energy recovery. Compared with other active control methods, time delay control relies on partial state feedback, reducing the requirement for the number of sensors and simplifying the control implementation, thereby reducing the cost of the automobile. However, in the previous time delay control research, the time delay is often a fixed value. In order to further explore the damping effect of time delay control on complex excitation, the present application proposes a variable time delay control method, that is, the time delay is adjusted in real time according to the frequency of external excitation, so that the time delay active control force can dynamically adjust the system response. This method aims to further improve the damping performance of time delay control under random excitation, so that it can effectively cope with complex excitation. SUMMARY

[0003] The purpose of the present application is to propose a time-varying time-delay vibration control method for active suspension of vehicle under complex excitation, which effectively suppresses the vertical vibration of the vehicle body and realizes the dual improvement of ride comfort and driving stability, thereby providing a new theoretical support and technical scheme for the design of active suspension system.

[0004] To achieve the above purpose, the specific technical scheme of the present application is as follows:

[0005] A time-varying time-delay vibration control method under complex excitation, comprising the following steps:

[0006] 1) In actual engineering problems, the structure of the vehicle is complex and variable. Considering the universality and convenience of the vehicle suspension model, the vehicle suspension model is reasonably simplified according to the research problem, and the dynamic differential equation of the 1 / 4 vehicle suspension system containing variable time delay is obtained according to the Lagrange method:

[0007] (1)

[0008] In the formula, the mass of the vehicle body is , the stiffness coefficient and the damping coefficient of the vehicle body are , , and the vertical displacement of the vehicle body mass is ; the tire mass is , the stiffness coefficient of the tire spring and the damping coefficient of the damping element are , , the displacement of the tire mass is , the active control force of the actuator is , the external excitation is , the time-delay control force is , is a time-delay feedback gain, is a time-delay amount. If the time-delay feedback gain , and the time-delay amount is ignored, the system can be simplified as a traditional passive suspension system;

[0009] The system is analyzed by using a multi-input and multi-output state control method of a multi-degree-of-freedom vibration system:

[0010] The state variable is selected; the output is ; and the input is ;

[0011] The state space equation of the 1 / 4 vehicle suspension control system with variable time-delay feedback control is:

[0012] (2)

[0013] In the formula,

[0014]

[0015] ;

[0016] 2) A variable time-delay control method is designed, so that the time delay is adjusted in real time according to the frequency of the external excitation, and the time-delay active control force can dynamically adjust the system response;

[0017] 3) The time-delay control parameters are iteratively optimized, the time-delay feedback gain and the variable time-delay amount are taken as variables, the numerical solution of the two-degree-of-freedom variable time-delay dynamics equation is solved by using an improved fine integration algorithm, and then the objective function with the optimized variables is optimized and analyzed by using an improved particle swarm algorithm.

[0018] In the step 2), the step 2) comprises:

[0019] To further explore the effect of time delay control on complex excitation, the present application proposes a variable time delay control method, that is, the time delay is adjusted in real time according to the frequency of external excitation, so that the time delay active control force can dynamically adjust the system response. The expression of variable time delay control is given as follows:

[0020] (3)

[0021] In the formula, is the time delay feedback gain, expresses the time delay value changing with time.

[0022] For the characteristic of multiple excitation frequencies, this section establishes the expression of the variable time delay function.

[0023] (4)

[0024] In the formula, is an array containing N elements, representing different time delay values; the number of N needs to be determined according to the main frequency of external excitation, which will be introduced in detail in the next section; is the time step; t is the current time; mod is the modulus operation.

[0025] To determine the number of N in formula (4) under multiple frequency excitation, we can convert the signal from time domain to frequency domain by Fourier transform, and the expression of continuous Fourier transform is

[0026] (5)

[0027] In the formula, is the amplitude, is the frequency, is a continuous periodic signal, is the time in time domain, is a complex function.

[0028] In the Fourier transform, the essence of the operation is the integration of signals with equal time intervals, which can be represented by discrete Fourier transform. Its expression is

[0029] (6)

[0030] The inverse transform formula of the above formula (6) is

[0031] (7)

[0032] In the formula, l is the number of sampling points.

[0033] Step 3) includes:

[0034] The time delay feedback gain and the variable time delay As the variable, the numerical solution of two-degree-of-freedom variable time-delay dynamic equation is solved by using the improved precise integration algorithm. Then, the objective function containing the optimization variable is optimized by the improved particle swarm algorithm. The specific method is as follows:

[0035] Let

[0036] (8)

[0037] Equation (1) can be written as a state equation

[0038] (9)

[0039] Where

[0040] (10)

[0041] The time delay term and the external excitation term in equation (9) are regarded as non-homogeneous terms, and the solution of the equation can be written as:

[0042] (11)

[0043] The numerical dispersion of equation (11) is taken as Δt=t k+1 -t k , and if the simulation time is T, the total number of steps n=T / Δt:

[0044] (12)

[0045] Equation (11) can be discretized into the following recursive form of step-by-step integration formula:

[0046] (13)

[0047] The above equation can be further written as:

[0048] (14)

[0049] In the above equation , the initial conditions of the equation are:

[0050] (15)

[0051] The above equation can be solved by transient integral method to obtain the system vibration response at each time node k, and the system vibration response in time domain can be expressed as:

[0052] (16)

[0053] The body mass at the time t, is the vibration velocity, is the tire mass at the time t, is the vibration velocity, wherein the magnitude depends on the simulation length;

[0054] Transforming equation (1) gives

[0055] (17)

[0056] Substituting the result of equation (16) , , , into equation (17) gives the body mass at the time t , the tire mass at the time t .

[0057] According to the requirements for the ride comfort of the automobile, the weighted root mean square values of the body acceleration, the suspension dynamic travel and the tire dynamic load are used as the optimization objective function to maximize the ride comfort. Since the units and orders of magnitude of the various performance indicators are different, they need to be divided by the corresponding passive suspension performance indicator values to obtain the fitness function as follows:

[0058] (18) (19)

[0059] In equation (18), RMS is the root mean square of the body acceleration, RMS is the root mean square of the suspension dynamic deflection, RMS is the root mean square of the tire dynamic load. In equation (18), , , , are weight coefficients. The parameter values are = 0.5, = 0.2, = 0.3, , , are the root mean square values of the corresponding performances of the passive suspension. is the maximum travel value of the suspension.

[0060] Subsequently, the improved particle swarm optimization algorithm is used to optimize the parameters of the variable time delay differential equation. First, the objective function and the constraint condition are determined, and the numerical solution of the variable time delay system dynamic equation (1) is solved by using the improved precise integration algorithm. The corresponding dynamic response at each time under the initial control parameters is obtained, and the corresponding body acceleration, suspension deflection and tire dynamic load at each time are obtained according to formula (16). According to the objective function (18), the objective function value J under the optimal feedback gain and the time delay is obtained. The objective function value is compared in the group, and the time delay control parameter corresponding to the minimum objective function is selected. Then the control parameters are updated, and the equation (1) under the new control parameters is solved again to calculate the new objective function value J, and the comparison is carried out again. By constantly updating the control parameters and comparing the objective function value J, the control parameters with smaller objective function J are selected as the optimal control parameters.

[0061] The technical scheme of the present application can bring the following beneficial effects:

[0062] The simulation results under complex excitation show that, under the premise of ensuring the stability of the time delay control system, the variable time delay control is better than the fixed time delay control and the passive system in the body acceleration vibration reduction control effect. Under the complex excitation with more main frequencies, the variable time delay control method optimizes the body acceleration by 55.53% and 28.08% respectively compared with the passive suspension and the active suspension system of the fixed time delay control. The variable time delay control method designed in the present application can significantly improve the vehicle performance, and the method provides a new idea for the vibration reduction of the variable time delay control. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 The present application is a schematic diagram of a 1 / 4 vehicle suspension system with variable time delay feedback control.

[0064] Figure 2 It is a random excitation spectrum analysis diagram.

[0065] Figure 3 It is a road excitation displacement response diagram.

[0066] Figure 4 It is a body acceleration diagram under the method of the present application and the passive suspension and the fixed time delay control.

[0067] Figure 5 It is a suspension deflection diagram under the method of the present application and the passive suspension and the fixed time delay control.

[0068] Figure 6 It is a tire dynamic load diagram under the method of the present application and the passive suspension and the fixed time delay control. DETAILED DESCRIPTION ​​

[0069] The technical solutions in the embodiments of the present application will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0070] As shown in Figures 1-6 , a time-varying time-delay vibration control method under complex excitation comprises the following steps:

[0071] Step 1: establishing a dynamic model of a variable time-delay active suspension system;

[0072] In actual engineering problems, the structure of a vehicle is complex and variable. Considering the universality and the characteristics of facilitating research of a vehicle suspension model, the vehicle suspension model is reasonably simplified for the researched problem, as shown in Figure 1 According to the Lagrange method, a dynamic differential equation of a 1 / 4 vehicle suspension system containing a variable time delay is obtained:

[0073] (1)

[0074] In the formula, the body mass is , the stiffness coefficient and the damping coefficient of the body are , , the vertical displacement of the body mass is ; the tire mass is , the stiffness coefficient of the tire spring and the damping coefficient of the damping element are , , the displacement of the tire mass is , the active control force of the actuator is , the external excitation is , the time-delay control force is , is the time-delay feedback gain, is the time delay. If the time-delay feedback gain , and the time delay is ignored, the system can be simplified as a traditional passive suspension system;

[0075] The system is analyzed by using a multi-input multi-output state control method of a multi-degree-of-freedom vibration system:

[0076] The state variable is selected; the output is ; and the input is ;

[0077] The state space equation of the 1 / 4 vehicle suspension control system containing a variable time-delay feedback control is:

[0078] (2)

[0079] wherein

[0080]

[0081] ;

[0082] Step 2: a variable time delay control method is designed, so that the time delay is adjusted in real time according to the frequency of external excitation, and then the time delay active control force can dynamically adjust the system response;

[0083] In order to further explore the vibration reduction effect of time delay control on complex excitation, the present application proposes a variable time delay control method, that is, the time delay is adjusted in real time according to the frequency of external excitation, so that the time delay active control force can dynamically adjust the system response. The expression of variable time delay control is given as follows:

[0084] (3)

[0085] wherein is the time delay feedback gain, expresses the time-varying time delay value.

[0086] For the characteristics of multiple frequencies of external excitation, the expression of variable time delay function is established in this section.

[0087] (4)

[0088] wherein is an array containing N elements, representing different time delay values; wherein the number of N needs to be determined according to the main frequency of external excitation, which will be introduced in detail in the next section; is the time step; t is the current time; mod is the modulus operation.

[0089] In order to determine the number of N in formula (4) under multiple frequency excitation, we can convert the signal from time domain to frequency domain by Fourier transform, and the expression of continuous Fourier transform is

[0090] (5)

[0091] wherein is the amplitude, is the frequency, is a continuous periodic signal, is the time in time domain, is a complex function;

[0092] In Fourier transform, the essence of the operation is the integration of signals with equal time intervals, which can be expressed by using discrete Fourier transform. The expression is

[0093] (6)

[0094] The inverse transform formula of the above formula (6) is

[0095] (7)

[0096] In the formula is the number of sampling points.

[0097] Step 3: Iterative optimization of time delay control parameters, time delay feedback gain and variable time delay As a variable, the improved fine integral algorithm is used to solve the numerical solution of the two-degree-of-freedom variable time delay dynamic equation, and then the improved particle swarm algorithm is used to optimize the objective function containing the optimization variable.

[0098] Time delay feedback gain and variable time delay As a variable, the improved fine integral algorithm is used to solve the numerical solution of the two-degree-of-freedom variable time delay dynamic equation. Then, through the improved particle swarm algorithm, the objective function containing the optimization variable is optimized. The specific method is as follows:

[0099] Let

[0100] (8)

[0101] Equation (1) can be written in the form of state equation

[0102] (9)

[0103] Where

[0104] (10)

[0105] The time delay term and the external excitation term in equation (9) are regarded as non-homogeneous terms, and the solution of the equation can be written as

[0106] (11)

[0107] Numerically disperse equation (11) and take the time step as Δt=t k+1 -t k If the simulation time is T, the total number of steps n=T / Δt:

[0108] (12)

[0109] Equation (11) can then be discretized into the following stepwise integral formula in recursive form:

[0110] (13)

[0111] The above equation can be further written as:

[0112] (14)

[0113] In the above formula The initial conditions of the equation are:

[0114] (15)

[0115] By solving the above equations using the transient integration method, the system vibration response at each time node k can be obtained. The system vibration response in the time domain can then be expressed as:

[0116] (16)

[0117] For vehicle body quality exist Vibration displacement at time, For vibration velocity, For tire quality In Vibration displacement at time, Let be the vibration velocity, where The size depends on the simulation duration;

[0118] Transforming equation (1) yields

[0119] (17)

[0120] The result of equation (16) , , , The vehicle body mass can be obtained by substituting into equation (17). exist Vibration acceleration at time t Tire quality In Vibration acceleration at time t .

[0121] Based on vehicle ride comfort requirements, the root mean square values ​​of vehicle acceleration, suspension travel, and tire dynamic load are weighted and used as the optimization objective function to maximize ride comfort. Since the units and orders of magnitude of each performance index are different, they need to be divided by the corresponding passive suspension performance index value, resulting in the following fitness function:

[0122] (18) (19)

[0123] where is the root mean square of body acceleration, is the root mean square of suspension deflection, is the root mean square of tire dynamic load. Where , , is the weight coefficient. The parameter values are = 0.5, = 0.2, = 0.3, , , is the root mean square value of the corresponding performance of the passive suspension. is the maximum suspension travel value.

[0124] Subsequently, the variable time delay differential equation parameters are optimized based on the improved particle swarm optimization algorithm. First, the objective function and constraint conditions are determined, and the numerical solution of the variable time delay system dynamic equation (1) is solved by the improved precise integration algorithm. The dynamic response corresponding to each time under the initial control parameters can be obtained. According to equation (16), the body acceleration, suspension deflection and tire dynamic load corresponding to each time can be obtained. According to the objective function (18), the objective function value J under the optimal feedback gain and time delay can be obtained. The objective function values are compared in the group, and the time delay control parameters corresponding to the minimum objective function are selected. Then the control parameters are updated, and equation (1) under the new control parameters is solved again to calculate the new objective function value J, and comparison is made again. By constantly updating the control parameters and comparing the objective function value J, the control parameters with smaller objective function J are selected as the optimal control parameters.

[0125] The specific parameter settings are as follows: the initial particle number is set to 80, and the maximum iteration number is 200. During this process, the global optimal control parameters are constantly updated and determined at the end of the calculation. After the calculation is completed, the global optimal time delay control parameters are obtained, the time delay control parameter feedback gain is , , and the variable time delay control parameter feedback gain is ,

[0126] .

[0127] Simulation analysis:

[0128] Table 1 Basic parameters used in numerical simulation:

[0129] Vehicle parameters Values Vehicle parameters Values / kg 40.5 / (N / m) 190000 / kg 345 / (N·s·m -1 )]]> ​ 1500 / (N / m) 16000 —— ——

[0130] Under random excitation, the performance of the variable time delay control method is better than that of the fixed time delay control method and the passive system. 2 Under complex excitation, when the fixed time delay control method is used, the root mean square value of the vertical acceleration of the vehicle body is 6.5416 m / s ; the tire dynamic load is 2869.8 N. When the variable time delay control method designed in the application is used, the root mean square value of the vertical acceleration of the vehicle body is 4.7049 m / s², compared with the passive suspension and the active suspension system using the fixed time delay control method, the vehicle body acceleration is optimized by 55.53% and 28.08% respectively, which greatly improves the comfort of automobile riding; the tire dynamic load is 2057.0 N, which is lower than that of the passive suspension and the fixed time delay suspension system, ensuring the safety of vehicle driving. Through comparison, it can be seen that compared with the fixed time delay feedback control method, the variable time delay control method designed in the application can significantly improve the vehicle performance, verifying the effectiveness and superiority of the method proposed in the application.

[0131] It is apparent to those skilled in the art that the application is not limited to the details of the foregoing exemplary embodiments, and that the application can be implemented in other particular forms without departing from the spirit or essential characteristics of the application. Therefore, the embodiments should be considered in all respects as illustrative and not restrictive, the scope of the application being defined by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

[0132] In addition, it should be understood that although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment have been properly combined to form other embodiments easily understood by those skilled in the art.

Claims

1. A time-varying, time-delay vibration reduction control method under complex excitation, characterized in that, Includes the following steps: Step 1: Establish a dynamic model of the variable time-delay active suspension system, and obtain the dynamic differential equations of the 1 / 4 vehicle suspension system containing variable time delay using the Lagrange method: （1） The mass of the vehicle body in the formula is The stiffness coefficient and damping coefficient of the car body are , The vertical displacement of the vehicle body mass is The tire mass is The stiffness coefficient of the tire spring and the damping coefficient of the damping element are... , The displacement of the tire mass is The active control force of the actuator is External incentives The time-delay control force is , For time-delay feedback gain, For time delay, if the time delay feedback gain And ignore time delay In this case, it is simplified to a traditional passive suspension system; The system is analyzed using the multi-input multi-output state control method for multi-degree-of-freedom vibration systems: Selecting state variables Output Input quantity is ; The state-space equation of a 1 / 4 vehicle suspension control system including variable time-delay feedback control is: (2) In the formula ； Step 2: Design a variable time delay control method so that the time delay is adjusted in real time according to the frequency of external excitation, thereby enabling the time delay active control force to dynamically adjust the system response. Step 3: Iteratively optimize the time-delay control parameters, including the time-delay feedback gain and the variable time-delay value. As variables, the numerical solution of the two-degree-of-freedom variable time-delay dynamic equation is solved using an improved fine integration algorithm, and then the objective function containing optimization variables is optimized and analyzed using an improved particle swarm optimization algorithm.

2. The time-varying and time-delay vibration reduction control method under complex excitation according to claim 1, characterized in that, The expression for the variable time-delay control method in step 2 is: (3) In the formula For time-delay feedback gain, Express the time delay value as it changes over time; (4) In the formula It is an array containing N elements, representing different time delay values; the size of N needs to be determined based on the frequency of the external stimulus. t is the time step; t is the current time; mod is the modulo operation; To determine the number of N in equation (4) under multi-frequency excitation, the signal is transformed from the time domain to the frequency domain using Fourier transform, where the expression for the continuous Fourier transform is: (5) In the formula For amplitude, For frequency, It is a continuous periodic signal. For time in the time domain, It is a complex function; In the Fourier transform, the operation is the integration of signals with equal time intervals, which can be represented using the Discrete Fourier Transform, and its expression is: (6) The inverse transformation formula of equation (6) above is: (7) In the formula The number of sampling points.

3. The time-varying and time-delay vibration reduction control method under complex excitation according to claim 2, characterized in that, Step 3 specifically involves: Step 3.1, in formula (1) (8) Equation (1) can be written in the form of a state equation. (9) in (10) If we consider both the time delay term and the external excitation term in equation (9) as non-homogeneous terms, then the solution to the equation is: (11) Numerical discretization is performed on equation (11), and the time step is taken as Δt=t. k+1 -t k If the simulation duration is T, then the total number of steps is... : (12) Equation (11) is then discretized into the following stepwise integral formula in recursive form: (13) The above equation can be further written as: (14) In the above formula The initial conditions of the equation are: (15) Solving the above equations using the transient integration method yields the system vibration response at each time node k. The system vibration response in the time domain is then expressed as: (16) in, For vehicle body quality exist Vibration displacement at time, For vibration velocity, For tire quality In Vibration displacement at time, Let be the vibration velocity, where The size depends on the simulation duration; Transforming equation (1) yields (17) The result of equation (16) , , , Substituting into equation (17) yields the vehicle body mass. exist Vibration acceleration at time t Tire quality In Vibration acceleration at time t ; Step 3.2: Based on the vehicle ride comfort requirements, the root mean square values ​​of vehicle acceleration, suspension dynamic travel, and tire dynamic load are weighted and used as the optimization objective function, with the goal of maximizing ride comfort. The resulting fitness function is as follows: (18) (19) In the formula The root mean square of the vehicle body acceleration, For the root mean square of suspension dynamic deflection, The root mean square of the tire dynamic load is given by , where , , The weighting coefficients have values ​​of [value 1]. =0.5, =0.2, =0.3, , , This represents the root mean square value of the passive suspension's corresponding performance. This represents the maximum travel value of the suspension. Step 3.3: Optimize and analyze the parameters of the variable time-delay differential equation based on the improved particle swarm optimization algorithm.

4. The time-varying and time-delay vibration reduction control method under complex excitation according to claim 3, characterized in that, Specifically, step 3.3 involves: first, determining the objective function and constraints, then using an improved refined integration algorithm to solve the numerical solution of the dynamic equation (1) of the variable time-delay system, thereby obtaining the numerical solution at each time step under the initial control parameters. The corresponding dynamic response is obtained at each moment according to equation (16). The corresponding vehicle body acceleration, suspension dynamic deflection and tire dynamic load are obtained according to the objective function (18) to obtain the objective function value J under the optimal feedback gain and time delay. The objective function values ​​are compared within the group, and the time delay control parameter corresponding to the minimum objective function is selected. Then the control parameters are updated, and the equation (1) under the action of the new control parameters is solved again to calculate the new objective function value J. The comparison is performed again. By continuously updating the control parameters and comparing the objective function value J, the control parameter with the smaller objective function J is selected as the optimal control parameter.

5. The time-varying and time-delay vibration reduction control method under complex excitation according to claim 1, characterized in that, In step 3, the improved particle swarm algorithm has an initial particle count of 80 and a maximum iteration count of 200.

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