Automobile active suspension control method based on adaptive inversion fast terminal sliding mode

Abstract

The present application belongs to the field of automobile active suspension control, and discloses a control method of automobile active suspension based on adaptive backstepping fast terminal sliding mode, which comprises the following steps: step one, establishing a nonlinear half-car active suspension model; step two, determining the ideal vertical and pitching trajectory of the vehicle; step three, establishing a non-singular integral sliding mode surface, and simultaneously establishing a state space model based on the selected sliding mode surface; step four, designing a virtual control force control law of the vertical motion of the vehicle based on the backstepping sliding mode control method; step five, designing an adaptive control law of the sliding mode robust term based on the adaptive control method; step six, repeating steps four-five to design a virtual control torque control law of the pitching motion of the vehicle; and step seven, calculating the output force of the left and right active suspension actuators. The present application can effectively deal with the nonlinear and uncertain problems existing in the control model, so that the vertical motion and the pitching angle motion of the vehicle body can reach a stable state in a short time.

Description

Technical Field

[0001] This invention relates to the field of active suspension control for automobiles, and particularly to an active suspension control method for automobiles based on adaptive inversion fast terminal sliding mode. Background Technology

[0002] As the connection between the car body and the wheels, the suspension system bears the weight of the vehicle and dampens vibrations transmitted from the road surface to the body, making it a key system affecting ride comfort and safety. Active suspension builds upon traditional passive suspension by installing actuators parallel to the shock absorbers between the body and wheels, such as electric motors, hydraulic actuators, or hybrid hydraulic-pneumatic actuators. Active suspension systems utilize real-time feedback signals from sensors and designed control algorithms to obtain the optimal control force output by each actuator under different driving conditions, thereby improving suspension performance. Therefore, developing excellent control algorithms has always been a hot topic in automotive active suspension research.

[0003] In recent years, researchers both domestically and internationally have studied various active suspension control methods, including full-state feedback control, optimal control, robust control, and sliding mode control. Each method has its own advantages and disadvantages. The research difficulty lies in the nonlinearity of the active suspension control model and the uncertainty of some system parameters over time. Specifically, these include uncertainties in sensor accuracy errors, nonlinearities in suspension stiffness and damper damping, and uncertainties in sprung mass and external disturbances. These factors affect the accuracy and robustness of active suspension control. Therefore, this paper proposes an active suspension control method based on adaptive inversion fast terminal sliding mode, which can effectively improve vehicle ride comfort. Summary of the Invention

[0004] The technical problem that this invention aims to solve is to design a control law for the control force of the active suspension actuator under the condition that the control model has nonlinearity and uncertainty that varies with time, so that the vertical motion and pitch motion of the vehicle body can still be well isolated from the influence of road excitation, and the system can reach a stable state in a short time.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] The active suspension control method for automobiles based on adaptive inversion fast terminal sliding mode includes the following steps:

[0007] Step 1: Establish the dynamic equations of the nonlinear half-vehicle active suspension model;

[0008] Step 2: Determine the ideal vertical and pitch motion trajectory x of the vehicle. 1d x 3d In particular, the present invention proposes that the ideal vertical acceleration and pitch angular acceleration of the vehicle are both zero;

[0009] Step 3: Establish a non-singular integral sliding surface, and at the same time transform the system state-space model based on state variables into a state-space model based on the selected sliding surface;

[0010] Step 4: Design the virtual control force control law for the vertical motion of the vehicle based on the inversion sliding mode control method;

[0011] Step 5: Design a robust adaptive control law u based on the adaptive control method. as1 Replace u in step 4 s1 Simultaneously update the virtual control force law for the vertical motion of the vehicle designed in step 4;

[0012] Step 6: Repeat steps 4-5 to design the virtual control torque law for vehicle pitch motion.

[0013] Step 7: Calculate the output forces u1 and u2 of the front and rear active suspension actuators.

[0014] Preferably, in step 1,

[0015] The dynamic equations of the nonlinear half-vehicle active suspension model are:

[0016]

[0017] m is the sprung mass of the vehicle, Δm is the uncertain part of the sprung mass, and z c This represents the vertical displacement of the vehicle. For the second derivative, u z For the virtual control force of the vehicle's vertical motion, F kf F kr For the spring elastic force and damping force of the front active suspension, F cf F cr Let represent the spring elastic force and damping force of the rear active suspension, ΔF represent the unknown disturbance force during the vehicle's vertical motion, I represent the moment of inertia during the vehicle's pitch motion, and ΔI represent the uncertain part of the moment of inertia. The vehicle's pitch angle, ΔM is the virtual control torque for vehicle pitch motion, where a and b are the distances from the center of the front and rear active suspension to the center of the vehicle's sprung mass, respectively, and ΔM is the unknown disturbance torque for pitch motion.

[0018] And F kf F kr and F cf F cr The expression is as follows:

[0019]

[0020] Where z1 and z2 are the forward and backward displacements of the unsprung mass, For the first derivative, kf k r c represents the front and rear elastic stiffness coefficients. f c r The damping coefficients are the front and rear damping forces.

[0021] Assuming the output forces of the front and rear actuators are u1 and u2 respectively, then the virtual control force for the vertical motion of the vehicle is u. z Virtual control torque for vehicle pitch motion

[0022]

[0023] Define state variables x1, x2, x3, x4:

[0024]

[0025] The dynamic equations of the nonlinear half-vehicle active suspension model are rewritten as follows:

[0026]

[0027] in:

[0028] Variable F(x1,x2,x3,x4)=-F kf -F kr -F cf -F cr Variable M(x1,x2,x3,x4) = -a(F kf +F cf )+b(F kr +F cr ),variable variable

[0029] Preferably, in step 3:

[0030] Define the tracking error e1 = x1 - x 1d e3 = x3 - x 3d The expression for the non-singular integral sliding surface is:

[0031]

[0032] Where: s1 and s2 are sliding surfaces, parameters k1, k2, k3, k4, λ1, λ2, p1, p2, q1, q2 are sliding surface parameters, all of which are positive scalars, and they have the following properties:

[0033]

[0034] therefore:

[0035]

[0036] The state-space model based on the selected sliding surface is as follows:

[0037]

[0038] Where s1 to s6 are the state variables of the third-order state-space model based on the selected sliding surfaces s1 and s4; the expressions for the variables f1(e1,e2), g1(e2), f2(e1,e2), and g2(e4) in the state-space model based on the selected sliding surfaces are:

[0039]

[0040] Preferably, in step 4:

[0041] Define coordinate transformation:

[0042]

[0043] Where μ1 and μ2 are process virtual control variables; θ1, θ2, and θ3 are process virtual control errors;

[0044] 4.1 Design the virtual control quantity μ1(t):

[0045] Based on coordinate changes, we have Introducing Lyapunov functions If we design μ1 = -ξ1θ1, and parameter ξ1 > 0, then:

[0046]

[0047] This indicates that as long as θ2 = 0, θ1 will be asymptotically stable;

[0048] 4.2 Design the virtual control quantity μ2(t):

[0049] Based on coordinate changes, we have Introducing Lyapunov functions Given μ2(t) = -ξ2θ2 - θ1 + ξ1s2, and parameter ξ2 > 0, then:

[0050]

[0051] This indicates that as long as θ3 = 0, θ1 and θ2 will be asymptotically stable;

[0052] 4.3 Design of the virtual control law u for the vertical motion of the vehicle z (t): Introducing Lyapunov functions Then we have:

[0053]

[0054] design Among them, robustness term u s1 =mg1 -1 (e2)∫((Δ1+ε1)sign(θ3)), where sign(θ3) is the sign function of θ3, and the parameter

[0055] therefore:

[0056]

[0057] This indicates that θ1, θ2, and θ3 will converge to 0 in a finite amount of time.

[0058] Preferably, in step 6:

[0059] Define the following coordinate transformations:

[0060]

[0061] The virtual control quantities in the design process are μ4(t) = -ξ4θ4(t), ξ4 > 0, and μ5(t) = -ξ5θ5(t) - θ4(t) + ξ4s5, ξ5 > 0.

[0062] Design a virtual control torque law for vehicle pitch motion. The expression is:

[0063]

[0064] Among them, the sliding mode robust adaptive control law u as2 for:

[0065]

[0066] in The adaptive control law parameter γ2 > 0.

[0067] Preferably, in step 7:

[0068] The output forces u1 and u2 of the front and rear active suspension actuators are as follows:

[0069]

[0070] Due to the adoption of the above technical solution, the beneficial effects achieved by this invention are:

[0071] This invention addresses the nonlinearity and uncertainty issues in the active suspension control model caused by factors such as sensor accuracy errors, nonlinearity of suspension stiffness and damper damping, sprung mass, and uncertainties of external disturbances during actual vehicle movement. It discloses an active suspension control method for automobiles based on adaptive inversion and fast terminal sliding mode control. This method ensures that the system remains stable and controllable even when uncertainties exist, and that the vertical and pitch movements of the vehicle body can still effectively isolate the effects of road surface excitations. Furthermore, the use of fast terminal sliding mode control ensures that the system can quickly reach stability within a finite time, significantly improving the vehicle's ride comfort and driving safety. Attached Figure Description

[0072] Figure 1 This is a flowchart of the control algorithm of the present invention;

[0073] Figure 2 This is a model diagram of the semi-vehicle active suspension established by this invention;

[0074] Figure 3 This is a simulation test result diagram of the vertical displacement of the vehicle body according to the present invention;

[0075] Figure 4 This is a simulation test result diagram of the vehicle body pitch angle of this invention. Detailed Implementation

[0076] The invention will now be further described with reference to the accompanying drawings.

[0077] An active suspension control method for automobiles based on adaptive inversion fast terminal sliding mode, such as Figure 1 As shown, it includes the following steps:

[0078] Step 1: Establish a nonlinear semi-vehicle active suspension model. The dynamic equations of the nonlinear semi-vehicle active suspension model are as follows:

[0079]

[0080] Where F kf F kr and F cf F cr These are the spring elastic force and damping force of the front and rear active suspensions, respectively, expressed as follows:

[0081]

[0082] Among them, z c This represents the vertical displacement of the vehicle. denoted as denoted as vehicle pitch angle; m as vehicle sprung mass, Δm as the uncertain part of sprung mass; I as vehicle pitch motion moment of inertia, ΔI as the uncertain part of moment of inertia; ΔF as unknown disturbance force for vehicle vertical motion, ΔM as unknown disturbance torque for pitch motion; a and b are the distances from the center of the front and rear active suspensions to the center of the vehicle sprung mass, respectively; u z Virtual control force for the vertical motion of the vehicle. Virtual control torque for vehicle pitch motion.

[0083] The virtual control force and torque are generated by front and rear actuators installed on the front and rear active suspensions. The relationship between the output forces u1 and u2 of the front and rear actuators and the virtual control force and torque is as follows:

[0084]

[0085] Define state variables:

[0086]

[0087] The dynamic equations of the nonlinear half-vehicle active suspension model can then be rewritten in the following state-space form:

[0088]

[0089] Where F(x1,x2,x3,x4)=-F kf -F kr -F cf -F cr M(x1,x2,x3,x4)=-a(F kf +F cf )+b(F kr +F cr ),

[0090] Step 2, determine the ideal vertical and pitch motion trajectory x of the vehicle. 1d x 3d Generally speaking, the ideal vertical acceleration and pitch angular acceleration of a vehicle are both zero.

[0091] Step 3: Establish a non-singular integral sliding surface, and at the same time transform the system state-space model based on state variables into a state-space model based on the selected sliding surface;

[0092] Define the tracking error e1 = x1 - x 1d e3 = x3 - x 3d The expression for the non-singular integral sliding surface is as follows:

[0093]

[0094] Where k1, k2, k3, k4, λ1, λ2, p1, p2, q1, q2 are controller parameters, all of which are positive scalars and satisfy the following conditions:

[0095]

[0096] therefore

[0097]

[0098] The state-space model based on the selected sliding surface is as follows:

[0099]

[0100] in

[0101]

[0102] Step 4: Design the virtual control force law for the vertical motion of the vehicle based on the inversion sliding mode control method;

[0103] Define the following coordinate transformations:

[0104]

[0105] Where μ1(t) and μ2(t) are virtual control variables of the process.

[0106] 4.1 Design the virtual control quantity μ1(t):

[0107] Based on the coordinate changes, we have Introducing Lyapunov functions Given the given μ1(t) = -ξ1θ1(t) and ξ1 > 0, then:

[0108]

[0109] This indicates that as long as θ2 = 0, θ1 will be asymptotically stable;

[0110] 4.2 Design the virtual control quantity μ2(t):

[0111] Based on the coordinate changes, we have Introducing Lyapunov functions Given the given μ2(t) = -ξ2θ2(t) - θ1(t) + ξ1s2, ξ2 > 0, then:

[0112]

[0113] This indicates that as long as θ3 = 0, θ1 and θ2 will be asymptotically stable;

[0114] 4.3 Design of the virtual control force u for vehicle vertical motion z (t):

[0115] Introducing Lyapunov functions but:

[0116]

[0117] The design described Among them, robustness term u s1 =mg1 -1 (e2)∫((Δ1+ε1)sign(θ3)), and

[0118] therefore:

[0119]

[0120] This indicates that θ1, θ2, and θ3 will converge to 0 in a finite amount of time.

[0121] Step 5: Design a robust adaptive control law u based on the adaptive control method. as1 Replace u in step 4 s1 Simultaneously update the virtual control force law for the vertical motion of the vehicle designed in step 4;

[0122] Define estimation error in To provide an approximate estimate of Δ1, the Lyapunov function is introduced. γ1>0, the robust adaptive control law is designed as follows:

[0123]

[0124] in

[0125] but:

[0126]

[0127] This indicates that θ1, θ2, and θ3 will converge to 0 in a finite amount of time.

[0128] Step 6: Repeat steps 4-5 to design the virtual control torque law for vehicle pitch motion.

[0129] Similarly, the following coordinate transformations are defined:

[0130]

[0131] The virtual control quantities in the design process are μ4(t) = -ξ4θ4(t) (ξ4 > 0) and μ5(t) = -ξ5θ5(t) - θ4(t) + ξ4s5 (ξ5 > 0).

[0132] The virtual control torque law for the vehicle's pitch motion is designed. The expression is:

[0133]

[0134] Among them, the sliding mode robust adaptive control law u as2 for:

[0135]

[0136] in

[0137] Step 7, calculate the output forces u1 and u2 of the front and rear active suspension actuators:

[0138]

[0139] To verify the feasibility and effectiveness of this method, a joint simulation experiment was conducted using the CarSim and Simulink platforms. Four step road surface excitations were set up, and the simulation results of active suspension control using the method of this invention were compared with the simulation results without control. Figure 3 The results of the test on the vertical displacement of the vehicle body are shown below. Figure 4 The results of the vehicle pitch angle test show that the active suspension control method disclosed in this invention effectively stabilizes the vehicle's vertical and pitch motion.

[0140] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A method for active suspension control of automobiles based on adaptive inversion fast terminal sliding mode, characterized in that, Includes the following steps: Step 1: Establish the dynamic equations of the nonlinear half-vehicle active suspension model; Define state variables ; This represents the vertical displacement of the vehicle. The vehicle's pitch angle; Step 2: Determine the ideal vertical and pitch motion trajectory of the vehicle. , ; Step 3: Establish a non-singular integral sliding surface, and simultaneously transform the system state-space model based on state variables into a state-space model based on the selected sliding surface; In step 3: Define tracking error , The expression for the non-singular integral sliding surface is: in: and For sliding surface, parameters , ; These are the parameters of the sliding surface, all of which are positive scalars; The variables in the state-space model based on the selected sliding surface The expression is: ； Step 4: Design the virtual control law for the vehicle's vertical motion based on the inversion sliding mode control method, and design the virtual control law for the vehicle's vertical motion using the robust term, where the robust term is... , for The sign function, For process virtual control error, The sprung mass of the vehicle; Step 5: Design a robust adaptive control law based on the adaptive control method. Replace the robust term in step 4 Simultaneously update the virtual control force law for the vertical motion of the vehicle designed in step 4; Step 6: Repeat steps 4-5 to design the virtual control torque law for vehicle pitch motion. ; Step 7: Calculate the output force of the front and rear active suspension actuators. , .

2. The active suspension control method for automobiles based on adaptive inversion fast terminal sliding mode as described in claim 1, characterized in that, In step 1, The dynamic equations of the nonlinear half-vehicle active suspension model are: For the uncertain part of the sprung mass, For the second derivative, Virtual control force for the vertical motion of the vehicle. , The spring elastic force and damping force of the front active suspension. , For the spring elastic force and damping force of the rear active suspension, For the unknown disturbance force on the vertical motion of the vehicle. Let the moment of inertia be the vehicle's pitch motion. For the uncertain part of the moment of inertia, For the virtual control torque of vehicle pitch motion, , These are the distances from the center of the front and rear active suspension to the center of the vehicle's sprung mass, respectively. For unknown disturbance torque during pitch motion; and , and , The expression is as follows: in, , The forward and backward displacements of the unsprung mass. For the first derivative, , These are the front and rear elastic stiffness coefficients. , The damping coefficients are the front and rear damping forces. Assume the output forces of the front and rear actuators are respectively , Then there is a virtual control force for the vertical motion of the vehicle. Virtual control torque for vehicle pitch motion : The dynamic equations of the nonlinear half-vehicle active suspension model are rewritten as follows: Where: variables ,variable ,variable ,variable .

3. The active suspension control method for automobiles based on adaptive inversion fast terminal sliding mode as described in claim 2, characterized in that, In step 3: And there are: therefore: Based on the selected sliding surface and Construct a third-order state-space model, whose state variables include , , , , , , where: s2 and Sliding surfaces The first and second derivatives, and Sliding surfaces The first and second derivatives of the third-order state-space model give the differential equation as follows: 。 4. The active suspension control method for automobiles based on adaptive inversion fast terminal sliding mode as described in claim 3, characterized in that, In step 4: Define coordinate transformation: in , For process virtual control variables; For process virtual control error; Step 4.1: Design virtual control variables : Based on coordinate changes, we have Introducing the first sub-Lyapunov function ,design ,parameter ,but: This indicates that as long as , It will be asymptotically stable; Step 4.2: Design virtual control variables : Based on coordinate changes, we have Introducing a second sub-Lyapunov function ,design ,parameter ,but: This indicates that as long as , and It will be asymptotically stable; Step 4.3: Design the virtual control law for the vertical motion of the vehicle. Introducing a third-child Lyapunov function Then we have: design Among them, robust items And parameters , ; therefore: This indicates , and It will converge to 0 within a finite amount of time.

5. The active suspension control method for automobiles based on adaptive inversion fast terminal sliding mode as described in claim 4, characterized in that, In step 6: Define the following coordinate transformations: Among them, virtual control quantities in the design process , ; Design a virtual control torque law for vehicle pitch motion. The expression is: Among them, the sliding mode robust term adaptive control law for: in Adaptive control law parameters .

6. The active suspension control method for automobiles based on adaptive inversion fast terminal sliding mode as described in claim 5, characterized in that, In step 7: Front and rear active suspension actuator output force , as follows: 。

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