A Design Method of Vehicle Active Suspension Controller Based on Tire Force Estimation

Abstract

The present invention discloses a design method for a vehicle active suspension controller based on tire force estimation, belonging to the field of automotive control, and comprising the following steps: Step 1: Establish a two-degree-of-freedom nonlinear active suspension model, define state variables, and construct a state space expression of the system in combination with the concept of diffeomorphism; Step 2: Derive and design a suspension controller according to the suspension model established in Step 1. The present invention can effectively solve the conflict between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, improve the ride comfort and handling stability of the vehicle, and at the same time can estimate the force on the tire, effectively solving the adverse impact on the vehicle performance caused by the complex nonlinearity and difficulty in measuring the tire force, thereby improving the ride smoothness of the vehicle.

Description

Technical Field

[0001] The present invention relates to the field of vehicle control, and in particular to a design method for an active suspension controller of a vehicle based on tire force estimation. Background Art

[0002] When a vehicle vibrates too much during driving, it often brings many adverse effects, such as causing damage to goods and discomfort to passengers. To solve these problems, a suspension system is introduced. The performance of the suspension system can directly determine the ride comfort of the vehicle and the comfort of passengers. Suspensions can be classified into active suspensions and passive suspensions. Since the traditional passive suspension cannot freely change its stiffness and damping and cannot adapt to complex and changeable road surfaces, while the active suspension can change the performance of the suspension by adjusting the magnitude of the control force, so that the vehicle can maintain the best shock-absorbing state. Therefore, active suspensions have received extensive attention in the academic community.

[0003] An active suspension system installs a device that can generate force in the control link and uses a method of suppressing force with force to suppress the impact force of the road surface on the vehicle body and the tilting force of the vehicle body. An active suspension is a new type of suspension controlled by a computer, which has a power source that can generate acting force. The actuator can transmit this acting force and work continuously. It has a variety of sensors and centralizes relevant data to a microcomputer for operation and determination of the control method. Therefore, an active suspension combines the technical knowledge of mechanics and electronics and is a relatively complex high-tech device. The application of active suspensions has further improved various performances of the vehicle.

[0004] Tires are important factors affecting the ride performance of a vehicle. During the driving process of the vehicle, the force on the tires is affected by various factors, making it difficult to calculate the force on the tires. Since the force on the tires during the driving process of the vehicle is non-linear and difficult to measure, the active suspension often fails to achieve the expected effect in actual applications. There is a conflict between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension. While reducing the vertical acceleration of the vehicle body, the service life of the suspension should not be damaged. Therefore, for the designed active suspension, it is necessary to coordinate the relationship between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a design method for an active suspension controller of a vehicle based on tire force estimation. According to this method, an active suspension controller based on tire force can be derived and designed, effectively solving the conflict between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, overcoming the difficulty of complex non-linear tire force that is difficult to measure, accurately estimating the tire force, and then designing an active suspension controller to eliminate the adverse effects of tire force on vehicle performance, thereby improving the ride comfort of the vehicle.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is as follows: A design method for a vehicle active suspension controller based on tire force estimation, and the steps are as follows:

[0007] Step 1: Establish a two-degree-of-freedom nonlinear active suspension model, define state variables, and construct the state space expression of the system in combination with the concept of diffeomorphism;

[0008] Step 2: Derive and design a suspension controller according to the suspension model established in Step 1.

[0009] A further improvement of the technical solution of the present invention lies in that: in Step 1, the definition of the state variable specifically defines the dynamic travel of the suspension as the system state variable.

[0010] A further improvement of the technical solution of the present invention lies in that: when designing the suspension controller in Step 2, the barrier Lyapunov function is used to directly limit the dynamic travel of the suspension.

[0011] A further improvement of the technical solution of the present invention lies in that: when designing the suspension controller in Step 2, the radial basis neural network function is used to approximately replace the tire force.

[0012] A further improvement of the technical solution of the present invention lies in that: Step 1 specifically includes:

[0013] Establish a two-degree-of-freedom nonlinear active suspension model. According to Newton's second law, the differential equation of the suspension system can be established, that is

[0014]

[0015] where, m s and m u are the body mass and the wheel mass respectively, x s is the vertical displacement at the center of mass of the body, x u is the vertical displacement of the wheel, x r is the random road surface excitation of the wheel, k s and c s are the spring stiffness and damping of the suspension respectively, f is the nonlinear force of the tire, and u is the control force of the suspension controller;

[0016] Select the state variables in the suspension system model as:

[0017]

[0018] The system output is:

[0019] y = x s (3)

[0020] From the state variables, the state space expression of the system can be obtained:

[0021]

[0022] Construct its diffeomorphism form as follows:

[0023]

[0024] Differentiate the above formula and substitute formula (4) to obtain:

[0025]

[0026] Formula (6) is the two-degree-of-freedom nonlinear active suspension model.

[0027] 7. A further improvement of the technical solution of the present invention lies in that: Step two specifically includes:

[0028] The non-linear force of the tire is a function of z 3 Using Lagrange transformation, the following relationship is obtained:

[0029]

[0030] Wherein, is between the interval [0, x 3 .

[0031] A first-order filter is introduced and its form is as follows:

[0032]

[0033] Wherein, η i is a positive constant, α if is the output of the first-order filter, α i is the virtual control law, let y i =α if -α i , which is the error value between the filter output and the virtual control law;

[0034] Use the radial basis neural network function to approximately replace the tire force, and the specific form is as follows:

[0035]

[0036] Wherein, is the neural network basis function, ε i (X i ) is the neural network estimation error and satisfies is an unknown positive constant,

[0037] For the active suspension system, the following coordinate transformation is introduced

[0038] ξ1 = z 1 -z d , ξ 2 = z 2 -α 1f , ξ 3 = z 3 -α 2f , ξ 4 = z 4 -α 3f 。

[0039] Among them, z d is the expected output of the system.

[0040] For the first-order subsystem, construct a Lyapunov function in the following form:

[0041]

[0042] Take the derivative of the above Lyapunov function to get

[0043]

[0044] By Young's inequality, the following inequality holds:

[0045]

[0046] Among them,

[0047] Design a virtual controller

[0048]

[0049] Among them, ρ i is a positive constant.

[0050] Substitute (12) and (13) into (11) to get

[0051]

[0052] Construct the Lyapunov function of the second-order subsystem as follows:

[0053]

[0054] Among them, is the estimator of and is the unknown parameter of the neural network.

[0055] Take the derivative of the above Lyapunov function to get

[0056]

[0057] Substitute Equation (9) into Equation (16), we get

[0058]

[0059] By Young's inequality, the following inequality holds:

[0060]

[0061] where λ 1 , γ 1 , μ 1 are positive constants, is the upper bound of g, and define [g] = -|g|, and [g] ≤ [ g ] .

[0062] Design the controller and adaptive control law as follows

[0063]

[0064]

[0065] where β i is a positive constant.

[0066] Substitute (18), (19) and (20) into (17), we get

[0067]

[0068] where

[0069] Construct the Lyapunov function of the third-order subsystem as follows:

[0070]

[0071] where k is a positive constant.

[0072] Take the derivative of the above Lyapunov function, we get

[0073]

[0074] where

[0075] By Young's inequality, the following inequality holds:

[0076]

[0077] Design the virtual control law as follows:

[0078]

[0079] Substituting (24) and (25) into (23), we get

[0080]

[0081] where

[0082] Construct the Lyapunov function of the fourth - order subsystem as follows:

[0083]

[0084] Taking the derivative of the above Lyapunov function, we get

[0085]

[0086] Using the radial basis neural network function to approximate the unknown non - linear function, we get

[0087]

[0088] where

[0089] By Young's inequality, the following inequality holds:

[0090]

[0091] The suspension controller and the suspension adaptive control law are as follows:

[0092]

[0093]

[0094] Substituting (30), (31) and (32) into (29), we get

[0095]

[0096] where

[0097] Due to the above technical solution, the technical progress achieved by the present invention is as follows: By using a neural network function to approximately substitute the tire force and combining with an adaptive control algorithm, the above controller can still maintain a good control effect when the tire force changes, improving the ride comfort of the vehicle. By taking the dynamic stroke of the suspension as the state variable of the system and using the barrier Lyapunov function to limit it, making it stable within a predetermined range, the service life of the suspension is guaranteed. On this premise, the performance of the controller is optimized, thus coordinating the relationship between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension. Effectively improving the ride comfort and handling stability of the vehicle. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings;

[0099] Figure 1 is a two-degree-of-freedom 1 / 4 vehicle suspension system model;

[0100] Figure 2 is a comparison curve graph of the displacement of the vehicle body mass center;

[0101] Figure 3 is a comparison curve graph of the acceleration of the vehicle body mass center;

[0102] Figure 4 is a curve graph of the suspension stroke;

[0103] Figure 5 is a comparison curve graph of the static and dynamic load ratio of the tire. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0104] A design method for a vehicle active suspension controller based on tire force estimation is as follows:

[0105] Step 1: Establish a two-degree-of-freedom nonlinear active suspension model, define state variables, and construct a state space expression of the system in combination with the concept of diffeomorphism;

[0106] Step 2: Derive and design a suspension controller according to the suspension model established in Step 1.

[0107] Step 1 is specifically as follows:

[0108] Establish a two-degree-of-freedom nonlinear active suspension model, as Figure 1 shown. Among them, m s and m u are the vehicle body mass and the wheel mass respectively, and x sis the vertical displacement at the vehicle body's center of mass, x u is the vertical displacement of the wheel, x r is the random road excitation of the wheel, k s and c s are the spring stiffness and damping of the suspension respectively, f is the non - linear force of the tire, and u is the control force of the suspension controller.

[0109] According to Newton's second law, the differential equation of the suspension system can be established, that is

[0110]

[0111] In order to take into account both the ride comfort of the vehicle and the problem of limited suspension dynamic stroke, it is necessary to construct a state - space equation that contains both the vehicle body displacement and the suspension dynamic stroke as two state variables. The state variables selected in the suspension system model are

[0112]

[0113] where, x 1 represents the first state variable, x 2 represents the second state variable, x 3 represents the third state variable, x 4 represents the fourth state variable.

[0114] The system output is

[0115] y = x s (3)

[0116] From the state variables, the state - space expression of the system can be obtained

[0117]

[0118] In the iterative process of the backstepping method, since both the vehicle body displacement and the suspension dynamic stroke appear as state variables, only the desired output and the constraint function need to be set to achieve the purpose of taking both into account. However, because the actual control quantity appears in the above - mentioned expression during the iterative process and the backstepping method cannot be directly applied, its diffeomorphic form is used to transform the expression. The diffeomorphic form is as follows:

[0119]

[0120] Taking the derivative of the above formula and substituting formula (4) into it, the two - degree - of - freedom active suspension mathematical model is obtained:

[0121]

[0122] Step two is specifically as follows:

[0123] The transformed system is a non-strict feedback system, and the backstepping method cannot be directly used to design the system control strategy. Given that the non-linear force on the tire is a function of z 3 , the following relationship is obtained using the Lagrangian transformation:

[0124]

[0125] where, is within the interval [0, x 3 .

[0126] To solve the "differential explosion" problem that occurs during the design process of the backstepping method, a first-order filter is introduced to avoid this problem, and its form is as follows:

[0127]

[0128] where η i is a positive constant, α if is the output of the first-order filter, and α i is the virtual control law. Let y i = α if - α i , which is the error value between the filter output and the virtual control law.

[0129] Define the dynamic surface function y i = α if - α i , and we can obtain:

[0130]

[0131]

[0132] where,

[0133] Aiming at the problem that the force on the tire is non-linear and difficult to calculate during vehicle driving, a method of approximately replacing the tire force with a radial basis neural network function is given, which reduces the adverse impact of linear substitution on the actual control effect, enabling the designed controller to further improve the ride comfort of the vehicle in practical applications. The specific form is as follows:

[0134]

[0135] where, is the neural network basis function, ε i (X i ) is the neural network estimation error and satisfies is an unknown positive constant,

[0136] Design a controller according to the above mathematical model to reduce the vertical acceleration of the vehicle body, stabilize the dynamic travel of the suspension within a safe range, and reduce the dynamic-static load ratio on the basis of meeting the conditions.

[0137] Let ξ 1 = z 1 - z d , ξ 2 = z 2 - α 1f , ξ 3 = z 3 - α 2f , ξ 4 = z 4 - α 3f

[0138] where ξ 1 = z 1 - z d is the tracking error, ξ 2 = z 2 - α 1f , ξ 3 = z 3 - α 2f , ξ 4 = z 4 - α 3f is the state error, where α 1f is a stable virtual control function and z d is the desired output of the system.

[0139] For the first-order subsystem, construct a Lyapunov function in the following form:

[0140]

[0141] Take the derivative of the above Lyapunov function to get

[0142]

[0143] By Young's inequality, the following inequality holds:

[0144]

[0145] where

[0146] Design a virtual controller

[0147]

[0148] where ρ i is a positive constant.

[0149] Substituting (14) and (15) into (13) gives

[0150]

[0151] Construct the Lyapunov function of the second - order subsystem as follows:

[0152]

[0153] where, is the estimator of and the unknown parameters of the neural network are

[0154] Differentiating the above Lyapunov function gives

[0155]

[0156] Substituting equation (11) into equation (18) gives

[0157]

[0158] By Young's inequality, the following inequality holds:

[0159]

[0160] where, λ 1 γ 1 μ 1 are positive constants, is the upper bound of g, and define [g]= -|g|, and it satisfies [g]≤ [ g ] .

[0161] Design the controller and adaptive control law as follows

[0162]

[0163]

[0164] where, β i is a positive constant.

[0165] Substituting (20), (21) and (22) into (19) gives

[0166]

[0167] where,

[0168] Construct the Lyapunov function of the third - order subsystem as follows:

[0169]

[0170] where \(k\) is a positive constant.

[0171] Taking the derivative of the above Lyapunov function, we get

[0172]

[0173] where

[0174] By Young's inequality, the following inequality holds:

[0175]

[0176] Design the virtual control law as follows:

[0177]

[0178] Substituting (26) and (27) into (25), we get

[0179]

[0180] where

[0181] Construct the Lyapunov function of the fourth-order subsystem as follows:

[0182]

[0183] Taking the derivative of the above Lyapunov function, we get

[0184]

[0185] Using the radial basis neural network function to approximate the unknown nonlinear function, we get

[0186]

[0187] where

[0188] By Young's inequality, the following inequality holds:

[0189]

[0190] Design the system controller and the adaptive control law as follows:

[0191]

[0192]

[0193] Substituting (32), (33), and (34) into (31), we get

[0194]

[0195] where

[0196] So far, the design of the controller has been completed. Next, we will prove the stability of the system and the boundedness of the controller.

[0197] From the above process, we can obtain

[0198]

[0199] Obviously, when |ξ 3 | < k, the following formula is satisfied:

[0200]

[0201] Substituting (37) into (36), we can get

[0202]

[0203] From (35) and (38), we can get

[0204]

[0205] where

[0206] According to Lyapunov's bounded stability theorem, the system is stable.

[0207] Since the system is stable, the dynamic controllers (14), (21), (27), (33) designed in the above process and the adaptive control laws (22), (34) are all bounded and stable, which indicates the effectiveness of the designed controller and also limits the dynamic stroke of the suspension within the preset range, achieving effective suppression of vehicle system vibration.

[0208] Based on the above process, the system controller designed in the present invention gives a solution to the problem that it is difficult to calculate the tire force and improves the ride performance of the vehicle on the premise of ensuring that the dynamic stroke of the suspension can be stably within the limited range.

[0209] The following further elaborates on the present invention with reference to embodiments:

[0210] Embodiment 1: Controller parameter adjustment and comparison of simulation results

[0211] Simulation verification

[0212] The parameters of the suspension system are shown in Table 1

[0213] Parameter Value Parameter Value <![CDATA[m s > 340 kg <![CDATA[m t > 40 kg <![CDATA[k s > 8500 N / m <![CDATA[k t > 22000 N / m <![CDATA[c s > 2000 N·s / m <![CDATA[c t > 300 N·s / m <![CDATA[ρ 1 > 5.5 <![CDATA[ρ 2 > -2 <![CDATA[ρ 3 > 2 <![CDATA[ρ 4 > -30 <![CDATA[η 1 > 100000 <![CDATA[η 2 > 1000000 <![CDATA[η 3 > 1000 <![CDATA[λ 1 > 0.0001 <![CDATA[γ 1 > 0.01 <![CDATA[μ 1 > 0.01 <![CDATA[σ 1 > 1 <![CDATA[β 1 > 0.1 <![CDATA[β 2 > 0.1 κ 0.15

[0214] Table 1

[0215] Considering that the road surface excitation should be universal, a form of superposition of three groups of sine functions with different frequencies is adopted as the road surface excitation, and the form is as follows:

[0216] x r = 0.01sin(2πt) + 0.01sin(3πt) + 0.01sin(5πt)

[0217] The control effect of the controller is further illustrated by the following graphical comparison. The curves of the vehicle's centroid displacement and centroid acceleration are as Figure 2 and Figure 3 shown. By comparing with the passive suspension, it can be seen that the backstepping adaptive controller given in this paper has obvious improvement effects in terms of centroid displacement and acceleration, and to a certain extent, improves the ride smoothness and ride comfort of the vehicle; the dynamic stroke curve of the suspension is as Figure 4 shown. It can be seen that after introducing the state limit condition into the controller, the dynamic stroke of the system suspension is well constrained within the predetermined range; the curve of the static and dynamic load ratio of the tire is as Figure 5 shown. The controller given in this paper also has a good effect in improving the static and dynamic load ratio of the tire, thus improving the driving safety of the vehicle.

[0218] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A design method for a vehicle active suspension controller based on tire force estimation, characterized in that, the steps are as follows: Step 1: Establish a two-degree-of-freedom non-linear active suspension model, define state variables, and construct the state space expression of the system in combination with the concept of diffeomorphism; specifically define the state variables as the dynamic stroke of the suspension being defined as the system state variable, specifically: Establish a two-degree-of-freedom non-linear active suspension model, and according to Newton's second law, the differential equation of the suspension system can be established, that is where m s and m u are the vehicle body mass and the wheel mass respectively, x s is the vertical displacement at the vehicle body centroid, x u is the wheel vertical displacement, x r is the random road excitation of the wheel, k s and c s are the spring stiffness and damping of the suspension respectively, f is the non-linear force of the tire, and u is the control force of the suspension controller; Select the state variables in the suspension system model as: The system output is: y = x s (3) The state space expression of the system can be obtained from the state variables: Construct its diffeomorphism form as follows: Take the derivative of the above formula and substitute formula (4) to get: Formula (6) is the two-degree-of-freedom non-linear active suspension model; Step 2: Derive and design a suspension controller based on the suspension model established in Step 1. When designing the suspension controller, use the barrier Lyapunov function to directly limit the dynamic travel of the suspension, and use the radial basis neural network function to approximately replace the tire force. Specifically: The non-linear force on the tire is a function of z 3 , and the following relationship is obtained using the Lagrangian transformation: Among them, between [0, x 3 interval; Introduce a first-order filter with the following form: where, η i is a positive constant, α if is the output of a first-order filter, and α i is the virtual control law. Let y i = α if - α i , which is the error value between the filter output and the virtual control law; Use the radial basis neural network function to approximately replace the tire force, and the specific form is as follows: Among them, is the neural network basis function, ε i (X i ) is the neural network estimation error and satisfies is an unknown positive constant, For the active suspension system, the following coordinate transformation ξ is introduced 1 = z 1 - z d , ξ 2 = z 2 - α 1f , ξ 3 = z 3 - α 2f , ξ 4 = z 4 - α 3f ; where z d is the system expected output; For the first-order subsystem, construct a Lyapunov function in the following form: Take the derivative of the above Lyapunov function to get By Young's inequality, the following inequality holds: Among them, Design a virtual controller where ρ i is a positive constant; Substitute (12) and (13) into (11) to get Construct the Lyapunov function of the second-order subsystem as follows: Among them, is the estimator of θ i , and θ i is the unknown parameter of the neural network; Take the derivative of the above Lyapunov function to get Substitute formula (9) into formula (16) to get By Young's inequality, the following inequality holds: Among them, λ 1 , γ 1 , μ 1 are positive constants, is the upper bound of g, and [g] = -|g| is defined, and [g] ≤ [g] ; Design the controller and the adaptive control law as follows where β i is a positive constant; Substitute (18), (19) and (20) into (17) to get Among them, Construct the Lyapunov function of the third-order subsystem as follows: where k is a positive constant; Take the derivative of the above Lyapunov function to get Among them, By Young's inequality, the following inequality holds: Design the virtual control law as follows: Substitute (24) and (25) into (23) to get Among them, Construct the Lyapunov function of the fourth-order subsystem as follows: Take the derivative of the above Lyapunov function to get Use the radial basis neural network function to approximate the unknown non-linear function to get Among them, By Young's inequality, the following inequality holds: The suspension controller and the suspension adaptive control rate are as follows: wherein, is the parameter estimation value of θ i , β i is the adaptive law design parameter and is a positive constant; substituting (30), (31) and (32) into (29), we get Among them,

Images