Active suspension practical specified time control method based on period lag sliding mode

Abstract

The invention discloses an active suspension practical specified time control method based on a period lag sliding mode, and belongs to the field of automobile active suspension control. The control method comprises the following steps: 1, establishing a half-vehicle active suspension model with system uncertainty; 2, separating uncertain items of the system, and constructing a tracking error control model of the height and the attitude of the vehicle body; and 3, based on a periodic lag sliding mode control method, respectively designing a vehicle body displacement control law and a vehicle body attitude control law. The method is applied to automobile active suspension control.

Description

Technical Field

[0001] This invention belongs to the field of automotive suspension control technology, specifically relating to a practical time-specified control method for active suspension based on periodic hysteresis sliding mode control. Background Technology

[0002] The suspension system is a crucial component of a vehicle chassis, and its performance directly impacts key dynamic performance indicators such as ride comfort, handling stability, and driving safety. With the rapid development of automotive technology, people are placing increasingly higher demands on vehicle comfort and stability. In recent years, active suspension technology has gradually gained widespread attention from academia and industry due to its advantage of simultaneously improving and comprehensively optimizing multiple performance indicators. Currently, conventional model-free control methods (such as PID control) typically face the problems of complex parameter tuning and a large amount of debugging work. Meanwhile, existing model-based control methods (such as model predictive control and backstepping control) mainly rely on accurate system models, lacking effective compensation and processing mechanisms for nonlinear uncertainties in parameters such as sprung mass, spring stiffness coefficient, and damping coefficient, making it difficult to guarantee the robustness of the control system under actual operating conditions.

[0003] Furthermore, for active suspension control systems, dynamic response characteristics greatly determine vehicle comfort. Existing control methods typically only achieve asymptotic stability, meaning that theoretically, the time required for the system state to fully converge to the equilibrium point is infinitely long, making it difficult to meet the stringent response time requirements in real-world operating conditions. To address this issue, finite-time control and fixed-time control methods have been proposed. While these methods can ensure that the system state reaches stability within a finite time, the upper bound of their convergence time is often determined by multiple factors such as the initial state and controller parameters, resulting in complex forms that are difficult to design precisely. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing active suspension control methods, such as insufficient robustness to nonlinear parameter uncertainties and external disturbances, long system state convergence times, and difficulty in precise pre-setting. This invention provides a practical, time-specified control method for active suspension based on periodic lag sliding mode control. This method effectively handles various uncertainties and disturbances in vehicle suspension, ensuring system robustness while guaranteeing that the state error of the closed-loop control system converges rapidly and accurately to the equilibrium point within a preset finite time, thereby significantly improving vehicle ride comfort and handling stability.

[0005] A practical time-specified control method for active suspension based on periodic hysteresis sliding mode includes the following steps:

[0006] Step 1: Establish a semi-vehicle active suspension model with system uncertainties;

[0007] Step 2: Separate the uncertainties in the system and construct a tracking error control model for vehicle height and attitude;

[0008] Step 3: Based on the periodic lag sliding mode control method, design the vehicle displacement and vehicle attitude control laws respectively.

[0009] Furthermore, the specific process of establishing a semi-vehicle active suspension model with system uncertainties in step one is as follows: when only considering the vehicle height and pitch angle attitude, the suspension model is simplified to a four-degree-of-freedom semi-vehicle suspension model, and the semi-vehicle suspension dynamic equation is established; during the actual vehicle operation, the range of variation of sprung mass parameters and suspension parameters is set.

[0010] Furthermore, the specific process of separating the system uncertainties in step two and constructing a tracking error control model for vehicle height and pitch angle attitude is as follows:

[0011] Step 2.1: Define the system state;

[0012] Step 2.2: Introduce a reference trajectory, establish a tracking error control model, and analyze uncertainties;

[0013] Step 2.3: Establish the constraint range of the parameters based on the uncertainty of the system parameters in Step 1;

[0014] Furthermore, step three, based on the periodic lag sliding mode control method, involves designing the control laws for vehicle displacement and vehicle attitude, as follows:

[0015] Step 3.1: Define the specified time and design the sliding mode variables;

[0016] Step 3.2: Design the vehicle body displacement control law;

[0017] Step 3.3: Design sliding mode variables;

[0018] Step 3.4: Design the vehicle body pitch angle control law.

[0019] The advantages of this invention compared to the prior art are:

[0020] The method proposed in this invention overcomes the problems of complex parameter tuning and slow dynamic response in traditional active suspension control methods, and has the advantages of simple parameter structure and ease of engineering implementation. Furthermore, this invention can effectively achieve rapid and accurate convergence of the system state within any specified time, significantly improving the dynamic response performance of the active suspension and making it more suitable for practical engineering applications.

[0021] Meanwhile, this invention fully considers the uncertainty of model parameters in active suspension. By clearly separating the uncertainties of the system from the nominal model, it estimates the upper bound of the range of parameter uncertainty variation, effectively reducing the control performance degradation caused by parameter changes and significantly improving the robustness of the control system. Furthermore, addressing the significant chattering defect in traditional sliding mode control, this invention designs an improved sliding mode switching function, significantly suppressing chattering and improving the applicability and control performance of the sliding mode control method in practical engineering.

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments: Attached Figure Description

[0023] Figure 1 This is a model of a semi-vehicle active suspension.

[0024] Figure 2 This is a time-domain comparison of the vertical acceleration and pitch acceleration of the vehicle body under passive suspension and the method of this invention;

[0025] Figure 3 This is a time-domain comparison of the vehicle's vertical displacement and pitch angle under passive suspension and the method of this invention;

[0026] Figure 4 This is a frequency domain comparison of the vehicle's vertical acceleration and pitch acceleration under passive suspension and the method of this invention. Detailed Implementation

[0027] Specific Implementation Method 1: A practical time-specified control method for active suspension based on periodic hysteresis sliding mode, comprising the following steps:

[0028] Step 1: Establish a semi-vehicle active suspension model with system uncertainties;

[0029] Step 2: Separate the uncertainties in the system and construct a tracking error control model for vehicle height and attitude;

[0030] Step 3: Based on the periodic lag sliding mode control method, design control laws for vehicle displacement and vehicle attitude respectively.

[0031] This implementation plan aims to achieve rapid and precise adjustment of vehicle height and posture, and effectively improve vehicle driving comfort and overall stability.

[0032] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the specific process of establishing the semi-vehicle active suspension model with system uncertainties in step one is as follows:

[0033] When only considering vehicle height and pitch angle, the car suspension model is simplified to a four-degree-of-freedom half-vehicle suspension model, and the model dynamics are as follows: Figure 1 As shown. The dynamic equation of the half-vehicle suspension is:

[0034]

[0035] Among them, z b Let θ be the vertical displacement of the vehicle's center of mass. b Let be the vehicle's pitch angle, and a and b be the horizontal distances from the center of gravity to the front and rear suspensions, respectively, in meters. b and I p These represent the vehicle body mass and pitch moment of inertia, respectively, in meters. wf and m wr These represent the front and rear unsprung masses, respectively; the vertical displacements of the front and rear wheels are respectively determined by z. wf and z wr Given that the disturbance displacements of the road surface acting on the front and rear wheels are denoted as z, respectively. df and z dr Suspension forces include the spring forces F of the front and rear suspensions. sf and F sr And the damping force F of the front and rear suspensions df and F dr The active actuator control forces of the front and rear suspensions are denoted as U, respectively. af and U ar The elastic force generated by the front and rear tires is expressed as F. tf F tr The damping forces generated by the front and rear tires are respectively expressed as F. bf F br The expressions for each force are as follows:

[0036]

[0037] Where, k i i = f1,nf1,r1,nr1,f2,r2 and b j j = e1, e2, c1, c2, f2, r2 represent the elastic coefficient and damping coefficient, respectively, and Δy f and Δy r These represent the compression amounts of the front and rear suspensions, respectively. and These represent the compression speeds of the front and rear suspensions, respectively, both of which can be measured in real time by sensors.

[0038] During actual vehicle operation, due to changes in occupant load, important system parameters such as vehicle mass, pitch moment of inertia, and center of gravity position will experience significant fluctuations that cannot be accurately measured in real time. Therefore, this embodiment, following the principle of explicitly separating parameter uncertainty from nominal terms, sets the range of variation for the sprung mass parameter:

[0039]

[0040] in, and It is a known nominal value, Δm b ΔI p Δ(ab) is the upper bound of the known parameter's range of variation, and λ i ∈[-1,1], i=m b I p Furthermore, factors such as environmental humidity, temperature changes, and component aging also lead to certain uncertainties in the suspension spring stiffness and damping coefficient, and these uncertainties are difficult to measure accurately in real time. Setting the suspension parameter variation range:

[0041]

[0042] in and Given the nominal value, Δk i and Δb j It is the upper bound of the known parameter variation range.

[0043] Specific Implementation Method Three: This implementation method further specifies that step two is specifically as follows:

[0044] Step 2.1: Define the system state as follows The control input is u1 = U af u2=U ar The state-space expression for the semi-vehicle active suspension can then be expressed as:

[0045]

[0046] as well as

[0047]

[0048] Among them, u b =u1+u2、u θ =au1-bu2. The state-space equation (5) is the system to be controlled in this embodiment, while the state-space equation (6) is its corresponding zero-dynamic system.

[0049] Step 2.2: Introduce a reference trajectory, establish a tracking error control model, and analyze uncertainties. This embodiment introduces a reference trajectory x. 1ref and x 3ref This reference trajectory should be adjusted in real time according to changes in road conditions. Therefore, the tracking error is defined as... The following tracking error control model is obtained by separating the system uncertainties:

[0050]

[0051] Where g1(t)=1 / m b g2(t)=1 / I p ,and

[0052]

[0053] in, F i This represents the actual suspension force, while This represents the nominal suspension force calculated from the nominal parameters.

[0054] Step 2.3: From the uncertainty of system parameters in Step 1, we know that d1(t), d2(t), g1(t), and g2(t) have the following constraint ranges:

[0055]

[0056] in

[0057]

[0058] Specific Implementation Method Four: This implementation method further specifies that step three is specifically as follows:

[0059] Step 3.1: Define a specified time T and design the sliding mode variable s1(t).

[0060] s1=σ2+a1σ1+K1(t)σ1(th) (9)

[0061] Where σ1(th) = ∈1(th), t∈[0,h] is a bounded function, and K1(t) is defined as

[0062]

[0063] in It is a function with a period of 2 hours, defined as follows:

[0064]

[0065] in

[0066]

[0067] Where a1 is a constant greater than zero, and h = T / 4.

[0068] Step 3.2: Design the vehicle body displacement control law u b

[0069]

[0070] in

[0071]

[0072] Where ε1 and ε2 are positive constants, s1(t) = ε2(t), t∈[-h,0] is a bounded function, and 1 / 2 < τ1 < 1.

[0073] Step 3.3: Design the sliding mode variable s2(t) as follows

[0074] s2=σ4+a2σ3+K2(t)σ3(th) (18)

[0075] Where σ3(th)=∈3(th),t∈[0,h] is a bounded function, and K2(t) is similar to the definition of K1(t) in step 3.1, a2 is a constant greater than zero, and h=T / 4.

[0076] Step 3.4: Design the vehicle body pitch angle control law u θ

[0077]

[0078] in

[0079]

[0080] Where ε3 and ε4 are positive constants, s2(t) = ε4(t), t ∈ [-h, 0] is a bounded function, and 1 / 2 < τ2 < 1.

[0081] This embodiment provides a control method for nonlinear systems that effectively suppresses the interference of uncertainties between model parameters and actual operating conditions, further improving the control performance. The convergence time of this method can be explicitly specified and is not affected by the initial values ​​of the system and the controller parameters, which has significant theoretical and engineering value.

[0082] Example

[0083] Considering the road surface on which the car travels is a convex hull, the road excitation input for the front and rear wheels is defined as follows:

[0084]

[0085] Where t r =t f +(a+b) / V, setting t f =0.6s is the moment the front wheel contacts the convex bump, the vehicle speed V = 80km / h, the height of the road convex bump is A = 0.1m, and the length of the convex bump is L = 0.25m. Set the desired reference trajectory x. 1ref =x 3ref=0, the initial state is x1=x3=x5=x7=0. The practical specified time control law parameters are set as T=1s, h=T / 4, a1=a2=40, τ1=τ2=0.75, ε i =0.001, i = 1, 2, 3, 4.

[0086] Figure 2 Time-domain comparison curves of the passive suspension and the proposed method on the vertical acceleration and pitch acceleration of the vehicle body are presented. The results show that the proposed method can effectively reduce the vertical and pitch acceleration response of the vehicle body. Figure 3 The time-domain response of the vehicle's vertical displacement and pitch angle under the action of passive suspension and the method of the present invention is shown. As can be seen from the figure, the proposed method can effectively track the vehicle's vertical displacement and pitch angle to the predetermined reference trajectory within a specified time T. Figure 4 Furthermore, a comparison of the frequency domain characteristics of the vehicle's vertical acceleration and pitch acceleration under passive suspension and the method of this invention is presented. It can be seen that this method significantly reduces the power spectral density (PSD) of vibration energy, demonstrating excellent vibration suppression performance. In summary, the active suspension control method proposed in this paper can effectively regulate the vehicle's vertical motion and attitude changes, thereby significantly improving the vehicle's driving comfort and handling stability.

[0087] This application has been disclosed above with preferred embodiments, but it is not intended to limit this application. Any person skilled in the art can make some changes or modifications to the above-disclosed structure and technical content to create equivalent embodiments without departing from the scope of the technical solution of this application, and all such modifications and modifications are within the scope of the technical solution of this application.

Claims

1. A practical time-specified control method for active suspension based on periodic hysteresis sliding mode, characterized in that: Includes the following steps: Step 1: Establish a semi-vehicle active suspension model with system uncertainties; Step 2: Separate the uncertainties in the system and construct a tracking error control model for vehicle height and pitch angle attitude; Step 3: Based on the periodic lag sliding mode control method, design the vehicle displacement and vehicle attitude control laws respectively.

2. The practical time-specified control method for active suspension based on periodic hysteresis sliding mode according to claim 1, characterized in that: Step 1, establishing a semi-vehicle active suspension model with system uncertainties, involves the following steps: When only vehicle height and pitch angle are considered, the suspension model is simplified to a four-degree-of-freedom semi-vehicle suspension model. The semi-vehicle suspension dynamics equations are as follows: Where: z b Let θ be the vertical displacement of the vehicle's center of mass. b Let be the vehicle's pitch angle, and a and b be the horizontal distances from the center of gravity to the front and rear suspensions, respectively, in meters. b and I p These represent the vehicle body mass and pitch moment of inertia, respectively, in meters. wf and m wr These represent the front and rear unsprung masses, respectively; the vertical displacements of the front and rear wheels are respectively determined by z. wf and z wr Given that the disturbance displacements of the road surface acting on the front and rear wheels are denoted as z, respectively. df and z dr Suspension forces include the spring forces F of the front and rear suspensions. sf and F sr And the damping force F of the front and rear suspensions df and F dr The active actuator control forces of the front and rear suspensions are denoted as U, respectively. af and U ar The elastic force generated by the front and rear tires is expressed as F. tf F tr The damping forces generated by the front and rear tires are respectively expressed as F. bf F br The expressions for each force are as follows: In the formula, k i i = f1,nf1,r1,nr1,f2,r2 and b j j = e1, e2, c1, c2, f2, r2 represent the elastic coefficient and damping coefficient, respectively, and Δy f and Δy r These represent the compression amounts of the front and rear suspensions, respectively. and These represent the compression speeds of the front and rear suspensions, respectively. During actual vehicle operation, the range of variation for the sprung mass parameter is set as follows: d ab =Δ(ab)λ ab (3) in, and It is a known nominal value, Δm b , ΔI p Δ(ab) is the upper bound of the known parameter's range of variation, and λ i ∈[-1,1], i=m b , I p ab; Set the range of suspension parameter variations: in, and Given the nominal value, Δk i and Δb j It is the upper bound of the known parameter variation range.

3. The practical time-specified control method for active suspension based on periodic hysteresis sliding mode according to claim 2, characterized in that: Step two, separating the system uncertainties and constructing a tracking error control model for vehicle height and pitch angle attitude, involves the following steps: Step 2.1: Define the system state as x1 = z b , x3=θ b , x5=z wf , x7=z wr , The control input is u1 = U af u2=U ar The state-space expression for the half-vehicle active suspension is then expressed as: as well as Among them, u b =u1+u2、u θ =au1-bu2, the state-space equation (5) is the controlled part, while the state-space equation (6) is the corresponding zero-dynamic system; Step 2.2: Introduce a reference trajectory, establish a tracking error control model and analyze uncertainties, introducing the reference trajectory x. 1ref and x 3ref The reference trajectory should be adjusted in real time according to changes in road conditions, and the tracking error is defined as σ1 = x1 - x 1ref , σ3=x3-x 3ref , The following tracking error control model is obtained by separating the system uncertainties: Where g1(t)=1 / m b g2(t)=1 / I p ,and in, i = sf, df, sr, dr, F i This represents the actual suspension force, while This represents the nominal suspension force calculated from the nominal parameters; Step 2.3: From the uncertainty of system parameters in Step 1, we know that d1(t), d2(t), g1(t), and g2(t) have the following constraint ranges: in -Δ g1 ≤δ g1 ≤Δ g1 ,g2(t)=g 20 (t)(1+δ g2 ),-Δ g2 ≤δ g2 ≤Δ g2 , 4. The practical time-specified control method for active suspension based on periodic hysteresis sliding mode according to claim 3, characterized in that: Step 3, based on the periodic lag sliding mode control method, involves designing the control laws for vehicle displacement and vehicle attitude, as follows: Step 3.1: Define a specified time T and design the sliding mode variable s1(t); s1=σ2+a1σ1+K1(t)σ1(th) (9) Where σ1(th) = ∈1(th), t∈[0,h] is a bounded function, and K1(t) is defined as in, It is a function with a period of 2 hours, defined as follows: in Where a1 is a constant greater than zero, and h = T / 4; Step 3.2: Design the vehicle body displacement control law u b in Where ε1 and ε2 are positive constants, s1(t) = ε2(t), t∈[-h,0] is a bounded function, and 1 / 2 < τ1 < 1; Step 3.3: Design the sliding mode variable s2(t) s2=σ4+a2σ3+K2(t)σ3(th) (18) Where σ3(th)=∈3(th),t∈[0,h] is a bounded function, and K2(t) is similar to the definition of K1(t) in step 3.1, a2 is a constant greater than zero, and h=T / 4; Step 3.4: Design the vehicle body pitch angle control law u θ in Where ε3 and ε4 are positive constants, s2(t) = ε4(t), t ∈ [-h, 0] is a bounded function, and 1 / 2 < τ2 < 1.

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