Active suspension control method based on uka theory analysis dynamics model, vehicle

Abstract

The present application belongs to the field of vehicle under-actuated system control, and particularly relates to an active suspension control method based on the analytical dynamics model of the Utkin theory and a vehicle. The control method first constructs an equivalent 1 / 4 suspension model of the vehicle; then takes the roll angle, the pitch angle and the vertical displacement of the vehicle and the displacement of the non-spring mass in each wheel suspension as one degree of freedom respectively, constructs a seven-degree-of-freedom vehicle dynamics model based on the active suspension, and converts it into a matrix form; then takes the roll angle, the pitch angle and the vertical displacement following the expectation as the control target, establishes the corresponding three-dimensional error equation and the constraint equation, and converts the constraint equation into a matrix form; finally, designs the control strategy of the vehicle based on the constraint following error, calculates the servo control force and the additional control force in combination with the real-time state of the vehicle, and then obtains the active control vector; the present application can significantly improve the coupling control effect of the vehicle pitch and roll, and improve the dynamic response speed and control precision of the system.

Description

Technical Field

[0001] This invention belongs to the field of vehicle control, specifically relating to an active suspension control method based on the Udwadia-Kalaba analytical dynamics model, and the corresponding active suspension system and vehicle. Background Technology

[0002] Vehicles are prone to pitch and roll during dynamic conditions such as acceleration, braking, and cornering. Pitch and roll not only reduce ride comfort but can also lead to loss of control or rollover accidents, severely impacting driving stability, handling, ride comfort, and safety. Traditional passive suspension systems, due to their fixed structure and control methods, struggle to comprehensively balance damping performance, handling stability, and comfort. Active suspension technology, however, uses electric motors, hydraulic or electromagnetic actuators to actively apply control forces. By adjusting the suspension output force in real time according to vehicle conditions, it effectively suppresses pitch and roll, significantly improving the vehicle's dynamic response and safety.

[0003] Although there have been many research results on roll and pitch control based on active suspension, the control accuracy is limited, the algorithm response is slow, most traditional control methods are based on linear models, which are difficult to adapt to the highly nonlinear dynamic behavior under actual working conditions, and the handling of roll and pitch coupling is not perfect. There is a complex coupling relationship between roll and pitch, and existing control strategies have not fully considered this mutual influence, resulting in unreasonable control force distribution and poor suppression effect. Summary of the Invention

[0004] To address the issues of slow response and inadequate handling of roll and pitch coupling in existing active suspension control algorithms, this invention provides an active suspension control method based on an analytical dynamic model of Uka theory, along with the corresponding active suspension system and vehicle.

[0005] This invention is achieved using the following technical solution:

[0006] An active suspension control method based on an analytical dynamic model of Vucic's theory, comprising:

[0007] Construct an equivalent suspension model for the vehicle; in the equivalent suspension model, any... i Suspension force of each wheel F i Force from suspension springs f si Damping force f ci and control f di Synthesis. That is: F i = f si+ f ci + f di .in, i =1,2,3,4 represent the front left, front right, rear left, and rear right wheels of the vehicle, respectively.

[0008] The vehicle's roll angle Pitch angle and vertical displacement z s and the displacement of unsprung mass in each wheel suspension z ui Each degree of freedom is treated as a separate degree of freedom, and a seven-DOF vehicle dynamics model based on active suspension is constructed; then, according to VUCA theory, it is simplified into the following matrix form:

[0009] ;

[0010] In the above formula, M Represents the mass matrix of the vehicle; Represents generalized acceleration; N Represents the combined force vector; B Represents the control input matrix; This represents a set of control forces for each wheel. f di The active control vector can be expressed as: .

[0011] by , and z s Taking the desired outcome as the control objective, a corresponding three-dimensional error equation is established, leading to first-order and second-order constraints. Then, based on Vucic's theory, the constraint equations are transformed into matrix form:

[0012] The first-order constraint is expressed as: The second-order constraint is expressed as: .

[0013] In the above formula, A , c , b These represent the constraint matrix, the first-order constraint vector, and the second-order constraint vector, respectively. It represents generalized speed.

[0014] The vehicle control strategy is designed based on the constraint following error. The servo control force is calculated using the following formula, taking into account the real-time state of the vehicle. and additional control And ultimately obtain the active control vector containing the control forces of each wheel in the vehicle suspension. :

[0015] ;

[0016] In the above formula, S This represents a preset value used for generation. The adjustment vector, ; I Represents the identity matrix; This represents the constraint deviation vector, which can be regarded as a direct measure of system performance. This represents a preset value used for generation. The regulation constant, ; This represents the Moore–Penrose generalized inverse operation. When the constraint matrix A is not full rank or the system is underactuated, the generalized inverse operation is used to obtain the acceleration and control force solutions that hold in the least squares sense of the constraints.

[0017] As a further improvement of the present invention, the expression for the equivalent suspension model of the vehicle is as follows:

[0018] ;

[0019] In the above formula, Δ z si Indicates the first i The suspension at each wheel z Change in displacement; k s Indicates the spring stiffness of the suspension; z ui and They represent the first i Displacement and velocity of unsprung mass in the suspension at each wheel; Indicates the first i The suspension at each wheel z Towards velocity; k c This represents the damping coefficient of the damper.

[0020] As a further improvement to the present invention, the suspension at the left front, right front, left rear, and right rear positions... z directional displacement change Δ z s1 Δ z s2 Δ z s3 Δ z s4 The calculation formula is as follows:

[0021] ;

[0022] In the above formula, l f and l r These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. t f and t r These are the front wheel track and the rear wheel track of the vehicle, respectively.

[0023] As a further improvement to this invention, the expression for the seven-degree-of-freedom vehicle dynamics model is as follows:

[0024] ;

[0025] In the above formula, m s Indicates the sprung mass of the entire vehicle; h r Indicates the height of the vehicle's center of gravity; a y This indicates the vehicle's lateral acceleration; g Represents gravitational acceleration; I x and I y These represent the moments of inertia of the vehicle about the X-axis and Y-axis, respectively. F 1, F 2, F 3, F 4 represents the suspension force of the vehicle's left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; f ti Indicates the first i Dynamic load on each wheel; m ui Indicates the first i The unsprung mass of the suspension in each wheel; , , and They represent , , z s and z ui The second derivative of .

[0026] As a further improvement to the present invention, any third i Dynamic load of each wheel f ti The calculation formula is:

[0027] ;

[0028] In the above formula, k t Indicates tire stiffness;z ri Indicates the first i Road surface excitation at each wheel.

[0029] As a further improvement to the present invention, in the matrix form of the seven-degree-of-freedom vehicle dynamics model, M , , N , B and They are as follows:

[0030] ,

[0031] ,

[0032] ;

[0033] ;

[0034] In the above formula, m u1 , m u2 , m u3 , m u4 These represent the unsprung masses of the suspension in the left front, right front, left rear, and right rear wheels of the vehicle, respectively. , , and These represent the unsprung masses in the suspension of the vehicle's left front, right front, left rear, and right rear wheels, respectively. z Towards acceleration; f s1 , f s2 , f s3 , f s4 These represent the suspension spring forces in the left front, right front, left rear, and right rear wheels of the vehicle, respectively. f c1 , f c2 , f c3 , f c4 These represent the damping forces of the suspension in the left front, right front, left rear, and right rear wheels of the vehicle, respectively. f t1 , f t2 , f t3 , f t4These represent the dynamic loads of the vehicle's left front, right front, left rear, and right rear wheels, respectively. f d1 , f d2 , f d3 , f d4 These represent the control forces of the suspension in the left front, right front, left rear, and right rear wheels of the vehicle, respectively.

[0035] As a further improvement to this invention, the three-dimensional error equations characterizing the vehicle's pitch angle error, roll angle error, and vertical displacement error are constructed as follows:

[0036]

[0037] In the above formula, e Represents the error vector. e 1, e 2, e 3 represents pitch angle error, roll angle error, and vertical displacement error, respectively; , , z sd These are the desired pitch angle, desired roll angle, and desired vertical displacement, respectively.

[0038] The expressions for the first-order and second-order constraints of vehicle attitude control, based on the three-dimensional error equation, are as follows:

[0039] ;

[0040] In the above formula, j This represents the dimension of the error equation. j When =1,2,3, they correspond to respectively , and z s Three dimensions of control objectives; l j1 , l j2 and l j3 All are constants greater than zero; e j Indicates the first j The tracking error of the control target relative to the expected value; and They represent e j The first and second derivatives.

[0041] As a further improvement of the present invention, servo control force The solution method is as follows:

[0042] (1) Let and The seven-degree-of-freedom vehicle dynamics model is then expressed as:

[0043] .

[0044] In the above formula, Represents the inertial decoupling mapping vector of the combined forces;

[0045] The second-order constraint is expressed as:

[0046] .

[0047] in, The inertial decoupling mapping matrix representing the constraint. .

[0048] (2) Let the equivalent constraint acceleration requirement for: and ,but , and Satisfy the following equation:

[0049] .

[0050] In the above formula, This represents the inertial decoupling mapping matrix for the control force input.

[0051] (3) Based on the given , and There is at least one servo control force. If and only if This makes the seven-degree-of-freedom vehicle dynamics model For constraints It is servo-controlled. At this time, the servo control force... Satisfy the following formula:

[0052] .

[0053] As a further improvement to the present invention, additional control force The solution method is as follows:

[0054] (1) Considering that the first-order constraints under the initial conditions are not always absolutely satisfied, we define the constraint deviation vector. as follows:

[0055] .

[0056] (2) Let D for MThe inverse matrix, i.e. Then the constraint deviation input projection Satisfy the following formula:

[0057] .

[0058] (3) Through additional control To correct Then we have:

[0059] .

[0060] The present invention also includes an active suspension system comprising active suspension applied to each wheel of a vehicle, and a suspension controller. The suspension controller acquires the real-time operating state of the vehicle and, using the aforementioned active suspension control method based on the Uka theory analytical dynamics model, generates an active control vector for the vehicle suspension system in conjunction with the vehicle's real-time state. Then according to Dynamically adjust the suspension control force of each wheel. f di This is to suppress the pitch and roll phenomena of the vehicle.

[0061] The invention also includes a vehicle that employs the active suspension system described above.

[0062] The technical solution provided by this invention has the following beneficial effects:

[0063] Based on the constructed equivalent suspension model and seven-degree-of-freedom vehicle dynamics model, this invention uses the constrained following UCA control method to solve for the control forces of each wheel suspension that can meet attitude control requirements. This enables dynamic adjustment of vehicle attitude, such as roll angle, pitch angle, and vertical acceleration, according to the real-time state of the vehicle. It effectively suppresses fluctuations in the vehicle's roll angle, pitch angle, and vertical acceleration, thereby improving the stability, safety, and comfort of the vehicle during driving.

[0064] The present invention achieves integrated control of vehicle attitude parameters such as roll angle, pitch angle, and vertical acceleration, improving response time and accuracy while reducing the time cost of decoupled control. In this solution, the control force output by the controller for regulation is within the actuation range of the vehicle's actuators, thus meeting practical needs and applicable to existing active suspension systems, avoiding insufficient control force from the actuators and reducing actuator costs. Attached Figure Description

[0065] Figure 1 This is a flowchart of the steps of the active suspension control method based on the analytical dynamic model of Uka theory provided in Embodiment 1 of the present invention.

[0066] Figure 2 This is a schematic diagram of the 1 / 4 equivalent suspension model used in Embodiment 1 of the present invention.

[0067] Figure 3 Parts (a) and (b) are force diagrams of the constructed seven-degree-of-freedom vehicle dynamics model in the yz and xz planes, respectively.

[0068] Figure 4 This is a road surface excitation diagram simulating a vehicle passing over a speed bump in a simulation experiment.

[0069] Figure 5 The curves show the change of vehicle roll angle over time for the present invention and the control group schemes in the simulation experiment.

[0070] Figure 6 The curves show the change of vehicle pitch angle over time for the present invention and the control group schemes in the simulation experiment.

[0071] Figure 7 The figures show the curves of the vertical displacement of the vehicle over time for the present invention and the control group in the simulation experiment.

[0072] Figure 8 The curves show the change of vertical acceleration of each wheel of the vehicle over time in the simulation experiment.

[0073] Figure 9 The curve of the control force actively output by the present invention changing over time in the simulation experiment is shown. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0075] Example 1

[0076] To address the issues of slow response and inadequate coupling handling of roll and pitch control algorithms in current active suspension systems, this embodiment provides an active suspension control method based on an analytical dynamic model using Ucca theory. This method constructs a seven-DOF analytical dynamic model of the active suspension and proposes an integrated control method based on constraint following to achieve real-time control of pitch angle, roll angle, and vehicle displacement. This effectively suppresses changes in vehicle attitude while maintaining fast control response, thereby improving the stability and comfort of the vehicle during driving.

[0077] Specifically, such as Figure 1As shown, the active suspension control method based on the analytical dynamics model of Uka theory provided in this embodiment includes the following process:

[0078] I. Constructing an equivalent suspension model for the vehicle

[0079] In this embodiment, taking a conventional vehicle with four-wheel independent suspension as an example, the 1 / 4 equivalent suspension model of the suspension installed at each wheel of the vehicle is as follows: Figure 2 As shown, in the equivalent suspension model, any first... i Suspension force of each wheel F i Force from suspension springs f si Damping force f ci and control f di Synthesis. That is:

[0080] .

[0081] in, i =1,2,3,4 represent the front left, front right, rear left, and rear right wheels of the vehicle, respectively.

[0082] In this implementation, control force f di This is the force actively output to adjust the vehicle's attitude through the suspension, and it is also the final adjustment parameter in this embodiment. The suspension spring force... f si and damping force f ci This is determined by the suspension itself and affected by changes in the suspension's shape. Specifically, during vehicle operation, due to the roll angle... and pitch angle The existence of four suspensions z Displacement z si Changes will occur; based on this, the various wheel positions in the vehicle's active suspension system will change. f si and f ci The values ​​of these values ​​satisfy the following equations:

[0083] ;

[0084] In the above formula, z s Indicates the vertical displacement of the vehicle; k s Indicates the spring stiffness of the suspension; z si Indicates the first i The suspension at each wheelz Displacement; Indicates the first i The suspension at each wheel z Towards velocity; z ui and They represent the first i Unsprung mass in the suspension at each wheel z Displacement and velocity; k c Δ represents the damping coefficient of the damper. z si Indicates the first i The suspension at each wheel z The change in displacement, including the suspension at the left front, right front, left rear, and right rear wheels. z directional displacement change Δ z s1 Δ z s2 Δ z s3 Δ z s4 The calculation formulas are as follows:

[0085] ;

[0086] In the above formula, l f and l r These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. t f and t r These are the front wheel track and the rear wheel track of the vehicle, respectively.

[0087] II. Constructing a seven-DOF vehicle dynamics model based on active suspension

[0088] In this embodiment, the vehicle's direction of travel in the horizontal plane is taken as the X-axis, the direction perpendicular to the X-axis in the horizontal plane is taken as the Y-axis, and the direction perpendicular to the horizontal plane is taken as the Z-axis. The vehicle's roll angle is then defined. Pitch angle and vertical displacement z s and the displacement of unsprung mass in each wheel suspension z ui Each is treated as a degree of freedom, and the following structures are constructed: Figure 3 The image shows a seven-DOF vehicle dynamics model based on active suspension. The expression for this seven-DOF vehicle dynamics model is:

[0089] ;

[0090] In the above formula, , , and They represent , , z s and z ui The second derivative; m s Indicates the sprung mass of the entire vehicle; h r Indicates the height of the vehicle's center of gravity; a y This indicates the vehicle's lateral acceleration; g Represents gravitational acceleration; I x and I y These represent the moments of inertia of the vehicle about the X-axis and Y-axis, respectively. F 1, F 2, F 3, F 4 represents the suspension force of the vehicle's left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; f ti Indicates the first i Dynamic load on each wheel; m ui Indicates the first i The unsprung mass of the suspension in each wheel.

[0091] Figure 3 middle, Indicates the lateral speed of the vehicle; express The first derivative; F l This indicates the force on the left side of the vehicle's suspension. F l = F 1+ F 3; F r This indicates the force on the right side of the vehicle's suspension. F l = F 2+ F 4; F f This indicates the front wheel suspension force of the vehicle. F f = F 1+ F 2; F b This indicates the rear wheel suspension force of the vehicle. F l =F 3+ F 4.

[0092] Based on VUCA's theory, the above seven-degree-of-freedom vehicle dynamics model can be simplified into the following matrix form:

[0093] ;

[0094] In the above formula, M Represents the mass matrix of the vehicle; Represents the generalized acceleration vector; N Represents the combined force vector; B This represents the control input matrix. This represents a set of control forces for each wheel. f di The active control vector, in this embodiment, can be represented as: ;in, f d1 , f d2 , f d3 , f d4 These represent the control forces of the suspension in the left front, right front, left rear, and right rear wheels of the vehicle, respectively.

[0095] In this embodiment, the vehicle's mass matrix M It is a diagonal matrix, and its expression is:

[0096] ;

[0097] In the above formula, m u1 , m u2 , m u3 , m u4 These represent the unsprung masses of the suspension in the left front, right front, left rear, and right rear wheels of the vehicle, respectively.

[0098] Generalized acceleration It is a column vector, and its expression is:

[0099] ;

[0100] In the above formula, , , and These represent the unsprung masses in the suspension of the vehicle's left front, right front, left rear, and right rear wheels, respectively. z Towards acceleration.

[0101] Combined force vectorN It is a column vector, and its expression is:

[0102] ;

[0103] In the above formula, f s1 , f s2 , f s3 , f s4 These represent the suspension spring forces in the left front, right front, left rear, and right rear wheels of the vehicle, respectively. f c1 , f c2 , f c3 , f c4 These represent the damping forces of the suspension in the left front, right front, left rear, and right rear wheels of the vehicle, respectively. f t1 , f t2 , f t3 , f t4 These represent the dynamic loads of the vehicle's left front, right front, left rear, and right rear wheels, respectively.

[0104] Control input matrix B The expression is:

[0105] .

[0106] III. Establish error equations and constraint equations based on control objectives.

[0107] In this embodiment, regarding the problem of vehicle attitude control based on an active suspension system, the vehicle's roll angle is... Pitch angle and vertical displacement z s As the core control state, the control objective is to make all three follow the desired outcome. Pitch angle and vertical displacement z s The value and the desired pitch angle Desired roll angle and desired vertical displacement z sd Since the values ​​are equal, the errors of the three factors approach zero. Based on this, the corresponding three-dimensional error equation is established as follows:

[0108]

[0109] in, Q d Let the desired vector be a vector that satisfies:

[0110]

[0111] e Represents the error vector. e 1, e 2, e 3 represents the pitch angle error, roll angle error, and vertical displacement error, respectively. Error vector e It should tend to 0 as t→0, therefore the following first-order constraint can be given:

[0112] ,

[0113] in, j This represents the dimension of the error equation. j When =1,2,3, they correspond to respectively , and z s Three dimensions of control objectives; e j Indicates the first j The dimension control objective is the following error relative to the desired outcome. In this embodiment, the complete expression for the first-order constraint is:

[0114] .

[0115] The second-order constraint is:

[0116] .

[0117] In the above two formulas, l j1 , l j2 and l j3 All are constants greater than zero. In this embodiment, the complete expression for the second-order constraint is:

[0118] .

[0119] In the above formula, and They represent e j The first and second derivatives.

[0120] Next, based on Vucic's theory, the constraint equations are transformed into matrix form. Specifically, the first-order constraints can be expressed as:

[0121] ,

[0122] Second-order constraints can be expressed as:

[0123] .

[0124] In the above formula, A , c , b These represent the constraint matrix, the first-order constraint vector, and the second-order constraint vector, respectively. It represents generalized speed.

[0125] IV. Design a vehicle control strategy based on constraint following error, and generate an active control vector according to the real-time state of the vehicle.

[0126] In this embodiment, the control force of each suspension in the active control vector f di It consists of two parts: one part is the servo control quantity designed using the constraint tracking method, and the other part is the additional control quantity designed to overcome initial condition deviations. Specifically, in this embodiment, the servo control force is calculated using the following formula based on the real-time state of the vehicle. and additional control And ultimately includes active control vectors for the suspension control forces of each wheel. :

[0127] ;

[0128] In the above formula, S This represents a preset value used for generation. The adjustment vector, ; I Represents the identity matrix; The constraint deviation vector represents the constraint deviation vector, which in this embodiment can be regarded as a direct measure of system performance. This represents a preset value used for generation. The regulation constant, ; This represents the Moore–Penrose Pseudoinverse. When the constraint matrix A is not full rank or the system is underactuated, the Moore–Penrose Pseudoinverse is used to obtain the acceleration and control force solutions that hold in the least squares sense of the constraints.

[0129] In detail, in the scheme of this embodiment, the servo control force The solution method is as follows:

[0130] (1) Let and The seven-degree-of-freedom vehicle dynamics model is then expressed as:

[0131] .

[0132] In the above formula, Represents the inertial decoupling mapping vector of the combined forces;

[0133] The second-order constraint is expressed as:

[0134] .

[0135] in, The inertial decoupling mapping matrix representing the constraint. .

[0136] (2) Let the equivalent constraint acceleration requirement for: and ,but , and Satisfy the following equation:

[0137] .

[0138] In the above formula, This represents the inertial decoupling mapping matrix for the control force input.

[0139] (3) Based on the given , and There is at least one servo control force. If and only if This makes the seven-degree-of-freedom vehicle dynamics model For constraints It is servo-controlled. At this time, the servo control force... Satisfy the following formula:

[0140] .

[0141] Furthermore, the vehicle under consideration may not satisfy the second-order constraints under the initial conditions. or To achieve the control objective, an additional control force needs to be added. To handle possible deviations in initial conditions. In this embodiment, additional control force The solution method is as follows:

[0142] (1) Considering that the first-order constraints under the initial conditions are not always absolutely satisfied, we define the constraint deviation vector. as follows:

[0143] .

[0144] (2) LetD for M The inverse matrix, i.e. Then the constraint deviation input projection Satisfy the following formula:

[0145] .

[0146] (3) Through additional control To correct Then we have:

[0147] .

[0148] Finally, in the control strategy provided in this embodiment, the vehicle control Ultimately, it can be expressed as:

[0149] .

[0150] Example 2

[0151] The active suspension control method based on the analytical dynamic model of Uca theory provided in Example 1 is essentially a data processing method. It is used to generate dynamic control commands according to the real-time state of the vehicle and issue the control commands to the suspension of each wheel to dynamically adjust the suspension control force of each wheel, thereby controlling the attitude of the vehicle to suppress the pitch and roll phenomena of the vehicle.

[0152] To implement the solution of Embodiment 1, this embodiment further provides an active suspension system and a corresponding vehicle.

[0153] The active suspension system provided in this embodiment includes active suspension applied to each wheel of the vehicle, and a suspension controller. The suspension controller acquires the real-time operating state of the vehicle and uses the active suspension control method based on the Uka theory analytical dynamics model as described in Embodiment 1 to generate the active control vector of the vehicle suspension system in conjunction with the real-time state of the vehicle. Then according to Dynamically adjust the suspension control force of each wheel. f di This is to suppress the pitch and roll phenomena of the vehicle.

[0154] The vehicle uses the aforementioned active suspension system.

[0155] Simulation Experiment

[0156] To verify the performance of the active suspension control method based on the analytical dynamic model of Uka theory provided by this invention, the technicians simulated the relevant scheme and tested the control effect of the relevant scheme on vehicle pitch and roll in a seven-degree-of-freedom underactuated vehicle system including active suspension.

[0157] 1. Simulation conditions

[0158] This experiment uses Simulink to simulate and test the relevant schemes. The parameters of the experimental vehicle under the simulation conditions are as follows:

[0159] Table 1: Vehicle Parameters in Simulation Experiment

[0160]

[0161] The initial simulation experiment state parameters are selected as follows:

[0162] .

[0163] 2. Stability control effect

[0164] This experiment first took place in... Figure 4 Under the road surface excitation conditions shown, the simulation of a vehicle with a lateral acceleration of 0.1 m / s² during steering was performed. 2 The vehicle was driven at a speed of 10 m / s over an uneven road surface, and the changes in vehicle roll angle, pitch angle, and vertical displacement were tested under the condition that the active suspension control method of this invention was applied with control force. In addition, to visually demonstrate the control effect of this invention, a control group without applied control force was also included in the experiment. The curves showing the changes in vehicle roll angle, pitch angle, and vertical displacement for both the invention and the control group are shown below. Figures 5-7 As shown.

[0165] analyze Figure 5 The roll angle variation curve reveals that, compared to the roll angle of a vehicle without applied control force, the peak roll angle under the control scheme of this invention is reduced by 60%, and the roll angle approaches zero in approximately 3.5 seconds. Furthermore, during driving, the roll angle of the vehicle under the scheme of this invention remains essentially constant. Within a very small range, this indicates that the control method of the present invention can effectively suppress vehicle roll by applying the control force of the active suspension.

[0166] analyze Figure 6 The pitch angle variation curve shows that, compared with the vehicle pitch angle without applied control force, the peak value of the vehicle pitch angle under the control scheme of the present invention is reduced by 30%, and the pitch angle approaches zero in about 3 seconds, which is one second less than the reduction without applied control force. This indicates that the control method of the present invention can effectively suppress vehicle pitch by applying the control force of the active suspension.

[0167] analyze Figure 7 The vertical displacement variation curves reveal that, compared to the vehicle's vertical displacement without applied control force, the peak value under the present invention's control scheme is reduced by 50%, and the vehicle's vertical displacement approaches zero in approximately 3.5 seconds. The data in the figure also demonstrates that the control method of the present invention can consistently keep the vehicle displacement below 0.01m under a road surface excitation of 0.3m, exhibiting excellent control performance.

[0168] 3. Comfort assessment

[0169] The magnitude of vertical acceleration during vehicle operation can be used as an indicator to assess the comfort of vehicle occupants. Generally speaking, the smoother the vertical acceleration and the smaller the peak value, the higher the comfort level. Conversely, the more drastic the changes in vertical acceleration and the higher the peak value during driving, the lower the occupant comfort level.

[0170] This experiment further collected the vertical acceleration of the vehicle during the test and plotted it as follows: Figure 8 The curve showing the change in vertical acceleration is shown. Analysis. Figure 8 The experimental data shows that the control method of the present invention can effectively suppress the magnitude of the vehicle's vertical acceleration. Compared with the scheme without applied control force, the peak vertical acceleration of the vehicle in the present invention is reduced by 50%, thus improving ride comfort.

[0171] 4. Feasibility assessment

[0172] This experiment further plotted the curves of control force input changes transmitted to each suspension actuator of the vehicle during the test, and the results are as follows: Figure 9 As shown in the figure, the analysis of the data shows that the peak value of the control force applied to each wheel by the solution of the present invention does not exceed 1500N, which is within the executable range of the automobile actuator. This verifies the feasibility of the solution of the present invention.

[0173] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An active suspension control method based on analytical dynamics model of Utkin theory, characterized by, It comprises: constructing an equivalent suspension model of the vehicle; the suspension force of any wheel i F i by the suspension spring force f si , the damping force f ci and the control force f di are synthesized; i = 1, 2, 3, 4 respectively represent the front left, front right, rear left, and rear right wheels of the vehicle​ the roll angle of the vehicle the pitch angle the vertical displacement z s and the displacement of the unsprung mass in each wheel suspension z ui A seven-degree-of-freedom vehicle dynamics model based on active suspension is constructed with the roll angle, the pitch angle, the vertical displacement, the displacement of the unsprung mass in each wheel suspension, respectively as one degree of freedom, and is simplified into a matrix form according to the Utkin theory: ； In the above formula, M denotes a mass matrix of the vehicle; denotes a generalized acceleration; N denotes a resultant force vector; B denotes a control input matrix; denotes an active control vector containing the control forces of the individual wheels; In , and z s Following the desired control target, the corresponding three-dimensional error equation is established, and then the first-order constraint and the second-order constraint are obtained; according to the Uka theory, the constraint equation is converted into a matrix form, the first-order constraint is , and the second-order constraint is: , wherein A , c , b respectively represent the constraint matrix, the first-order constraint vector and the second-order constraint vector; represents the generalized velocity; The control strategy of the vehicle is designed based on the constraint following error, and the servo control force is calculated by the following formula in combination with the real-time state of the vehicle and the additional control force , and finally : ； In the above formula, S denotes a preset adjustment vector for generating , ; I denotes an identity matrix; denotes a constraint deviation vector; denotes a preset control constant for generating , ; denotes a Moore-Penrose generalized inverse operation.

2. The active suspension control method based on the analytical dynamics model of the ukat theory according to claim 1, wherein, The expression of the equivalent suspension model is: ； In the above formula, Δ z si denotes a change in displacement of the suspension at the jth wheel; i z denotes a change in displacement of the suspension at the jth wheel; k s denotes a spring rate of the suspension; z ui and denote a displacement and a velocity, respectively, of the unsprung mass in the suspension at the jth wheel; i denote a change in velocity of the suspension at the jth wheel; denote a change in velocity of the suspension at the jth wheel; i denote a change in velocity of the suspension at the jth wheel; z denote a change in velocity of the suspension at the jth wheel; k c denotes a damping coefficient of the damper.​ 3. The active suspension control method based on the analytical dynamics model of the ukat theory according to claim 2, wherein, Suspensions at the front left, front right, rear left, and rear right wheels z The displacement variation Δ z s1 The displacement variation Δ z s2 The displacement variation Δ z s3 The displacement variation Δ z s4 The calculation formula is as follows: ； In the above formulae, l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively; t f and t r are the front and rear wheel track of the vehicle, respectively.

4. The active suspension control method based on the analytical dynamics model of the ukat theory according to claim 3, characterized in that: The expression of the seven-degree-of-freedom vehicle dynamics model is: ； In the above formulae, m s denotes the sprung mass of the vehicle; h r denotes the height of the center of mass of the vehicle; a y denotes the lateral acceleration of the vehicle; g g represents the gravitational acceleration; I x and I y Ix and Iy represent the rotational inertia of the vehicle about the X and Y axes, respectively; F 1, F 2, F 3, F 4 represent the suspension forces of the front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; f ti m represents the dynamic load of the i th wheel; m ui m represents the unsprung mass of the suspension in the i th wheel; , , and represent the second derivatives of , , z s and z ui , respectively; and / or, the dynamic load of any of the i wheels f ti The formula for calculating the dynamic load is: ； in the above formulae, k t denotes the tire stiffness; z ri denotes the road excitation at the i wheel.

5. The active suspension control method based on the analytical dynamics model of the ukat theory according to claim 4, characterized in that: In the matrix form of the seven-degree-of-freedom vehicle dynamics model, M , , N , B and are as follows, respectively: ， ， ； ； In the above formulae, m u1 , m u2 , m u3 , m u4 respectively represent unsprung masses of suspensions in the front left, front right, rear left, and rear right wheels of the vehicle; , , and respectively represent non-sprung masses of suspensions in the front left, front right, rear left, and rear right wheels of the vehicle z toward acceleration; f s1 , f s2 , f s3 , f s4 respectively represent suspension spring forces of suspensions in the front left, front right, rear left, and rear right wheels of the vehicle; f c1 , f c2 , f c3 , f c4 respectively represent damping forces of suspensions in the front left, front right, rear left, and rear right wheels of the vehicle; f t1 , f t2 , f t3 , f t4 respectively represent dynamic loads of the front left, front right, rear left, and rear right wheels of the vehicle; f d1 , f d2 , f d3 , f d4 respectively represent control forces of suspensions in the front left, front right, rear left, and rear right wheels of the vehicle.

6. The active suspension control method based on the analytical dynamics model of the ukat theory according to claim 5, characterized in that: The three-dimensional error equation is as follows: ； In the above formulae, e denotes the error vector, e 1, e 2, e 3 respectively denote the pitch angle error, the roll angle error and the vertical displacement error; , , z sd are respectively the desired pitch angle, the desired roll angle and the desired vertical displacement; The expression of the first-order constraint and the second-order constraint is as follows: ； In the above formula, j denotes the dimension of the error equation, j =1,2,3 respectively correspond to , and z s three-dimensional control target; l j1 , l j2 and l j3 are constants greater than zero; e j denotes the first j dimensional control target relative to the expected following error; and respectively denote e j the first and second derivatives.

7. The active suspension control method based on the analytical dynamics model of the ukat theory according to claim 6, characterized in that: The servo control force The solution method is as follows: (1) Let and The seven-degree-of-freedom vehicle dynamics model is represented as: ； In the above formula, represents the inertial decoupling mapping vector of the comprehensive force; The second-order constraint is expressed as: ； wherein denotes the constrained inertial decoupling mapping matrix, ; (2) Let the equivalent constraint acceleration demand be: and then , and satisfy the following equation: ； In the above formula, denotes the inertia decoupling mapping matrix of the control force input; (3) Based on the given , and , there exists at least one servo control force if and only if , so that the seven-degree-of-freedom whole vehicle dynamics model is servo-controllable for the constraint ; at this time, the servo control force satisfies the following formula: 。 8. The active suspension control method based on the analytical dynamics model of the ukat theory according to claim 7, characterized in that: The additional control force The solution method is as follows: (1) Considering that the first-order constraints are not always satisfied absolutely under the initial conditions, define the constraint deviation vector as follows: ； (2) Let D be the inverse matrix of M , i.e. , then the constraint bias input projection satisfies the following equation: ； (3) by an additional control force to correct then there is: 。 9. An active suspension system characterized by: It includes an active suspension applied to each wheel of the vehicle, and a suspension controller; the suspension controller is used to obtain the real-time running state of the vehicle, and uses the active suspension control method based on the analytical dynamic model of the Uka theory as claimed in any one of claims 1-8, combined with the real-time state of the vehicle to generate an active control vector of the vehicle suspension system ; and then dynamically adjusts the suspension control force of each wheel f di to achieve the suppression of the pitch and roll phenomenon of the vehicle.​ 10. A vehicle characterized by: It adopts the active suspension system as claimed in claim 9.

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