A skyhook-adrc-fosmc-based active suspension control method and system

Abstract

The application belongs to the technical field of active suspension control, and particularly relates to an active suspension control method and system based on Skyhook-ADRC-FOSMC, the method obtains key parameters by establishing a 1 / 4 vehicle suspension dynamics model and constructs a state space model, on the basis, introduces active disturbance rejection control, realizes real-time estimation and compensation of vehicle body displacement and system total disturbance, combines fractional order sliding mode control, constructs a fractional order sliding mode surface by using Caputo operator, takes into account strong robustness and smoothness, suppresses the problem of traditional sliding mode chattering, and finally realizes weighted fusion of the high-frequency vibration isolation advantage of Skyhook control and the anti-disturbance ability of ADRC-FOSMC. The application solves the problems of model simplification and control distortion, and single strategy unable to consider multiple target performances in the prior art, realizes adaptive weighted switching by fusing ADRC, FOSMC and Skyhook control, effectively improves the robustness, smoothness and real-time performance of the active suspension under complex working conditions, and thus realizes the collaborative optimization of vehicle comfort and safety.

Description

Technical Field

[0001] This application belongs to the field of active suspension control technology, specifically, it relates to an active suspension control method and system based on Skyhook-ADRC-FOSMC. Background Technology

[0002] The vehicle suspension system is a crucial component connecting the vehicle body and wheels. Its core function is to isolate vibrations caused by road surface excitations and balance ride comfort and driving stability. Traditional suspension systems are divided into passive suspension and semi-active suspension: passive suspension uses a structure with fixed stiffness and damping, which can only maintain limited performance balance under specific road conditions; semi-active suspension, although its damping can be adjusted through devices such as solenoid valves, has a limited adjustment range and is difficult to cope with complex and varied road environments (such as potholes, speed bumps, and irregular undulations). With the development of automotive electronics and intelligent control technology, active suspension systems, by introducing external power sources (such as hydraulic pumps and motors), can actively output control forces, becoming the core direction for improving suspension performance. However, active suspension control faces three major challenges: first, the nonlinear characteristics of hydraulic actuators make control accuracy susceptible to interference; second, the irregularity of road excitations (such as random bumps, sinusoidal fluctuations, and convex obstacles) increases the difficulty of vibration suppression; and third, system parameter perturbations (such as changes in spring / damping coefficients) reduce control robustness.

[0003] Existing active suspension control strategies have significant drawbacks:

[0004] 1. PID control: Although simple in structure, it has poor adaptability to nonlinear and time-varying parameters and is difficult to cope with complex road surface excitation.

[0005] 2. Skyhook control: It optimizes comfort by adjusting the damping force, but its multi-axis adaptability is limited, its high-frequency vibration suppression capability is insufficient, and it cannot compensate for internal and external disturbances of the system.

[0006] 3. Active Disturbance Suppression Control (ADRC): It can estimate and compensate for the total disturbance, but it relies on a lot of computing resources and has poor real-time performance, especially under high-frequency operating conditions where estimation delays are likely to occur.

[0007] 4. Integer-order sliding mode control (SMC): It is robust and has a fast response, but it suffers from severe "chattering" and is prone to actuator wear, which affects suspension stability.

[0008] To address the bottlenecks of single control strategies, existing research has attempted to integrate ADRC with integer-order SMC, Skyhook with ADRC, etc., but has yet to simultaneously achieve synergistic optimization of "robust disturbance rejection, chattering suppression, and real-time response": ADRC + integer-order SMC improves robustness, but the chattering problem is not fundamentally solved; Skyhook + ADRC enhances high-frequency vibration isolation, but the dynamic adjustment accuracy is insufficient. Therefore, there is an urgent need for an active suspension control method that can integrate the advantages of multiple control methods and balance disturbance rejection, smoothness, and real-time performance. Summary of the Invention

[0009] To address the technical problems of existing technologies, such as poor adaptability of PID control, insufficient high-frequency vibration isolation of Skyhook control, limited real-time performance of ADRC control, and severe chattering in integer sliding mode control, this application provides an active suspension control method and system based on Skyhook-ADRC-FOSMC. By establishing a 1 / 4 vehicle suspension dynamics model, it obtains state information such as the vertical displacement and velocity of the vehicle body and tires. Combining the real-time disturbance estimation and compensation capabilities of Active Disturbance Suppression Control (ADRC), the strong robustness and dynamic smoothness of Fractional Sliding Mode Control (FOSMC), and the simple engineering implementation and high-frequency vibration isolation advantages of Skyhook control, it achieves seamless switching between multiple control strategies through continuously weighted coefficients (based on the Sigmoid function), ultimately outputting the optimal active control force to adjust suspension parameters. This invention effectively addresses core challenges such as nonlinearity of hydraulic actuators, irregular road surface excitations (e.g., random road surfaces, sinusoidal road surfaces, convex road surfaces), and system parameter perturbations, improving the comprehensive control performance of the active suspension system and contributing to the synergistic optimization of vehicle ride comfort and driving safety in the fields of intelligent vehicles and autonomous driving.

[0010] On the one hand, this application provides an active suspension control method based on Skyhook-ADRC-FOSMC, the method comprising:

[0011] Step 1: Configure the key parameters of the 1 / 4 vehicle suspension model based on the suspension system characteristics of the target vehicle, and establish a dynamic equilibrium relationship model on this basis. Then define the state variables and output variables and construct the state space model of the 1 / 4 vehicle suspension system.

[0012] Step 2: Construct an ADRC controller based on the 1 / 4 vehicle suspension model. Select the vehicle body displacement as the measurement output. Determine the controlled object channel as the channel through which the control force acts on the vehicle body acceleration based on the vehicle body motion equation. Generate the desired displacement reference and desired velocity reference through the tracking differentiator. Use the extended state observer to estimate the vehicle body displacement, vehicle body velocity, and the total system disturbance including road excitation online. Obtain the intermediate control quantity by passing the desired reference quantity and the estimated quantity through error feedback. Compensate for the estimated total disturbance based on the object channel gain and output the final control force to achieve real-time suppression of the total disturbance and equivalent linearization of the controlled object.

[0013] Step 3: Based on the position error and velocity error obtained in Step 2, construct the state error, calculate the fractional derivative of the state error using Caputo fractional calculus, and construct the sliding surface function based on the state error and its fractional derivative. Decompose the sliding control law into the equivalent control law and the switching control law, and superimpose the two to form the final fractional sliding control force, which serves as the control input for the object channel, in order to construct the fractional sliding controller.

[0014] Step 4: Construct the Skyhook control force, and construct the switching criterion between Skyhook and ADRC-FOSMC based on the vehicle speed and the relative speed between the vehicle and the tires. Obtain continuous weights by mapping with the Sigmoid function. Based on this, perform weighted fusion on the two control branches to generate the final active control force as the control input of the controlled system channel.

[0015] In the preferred implementation, step 1 further includes:

[0016] Step 1.1: Based on the suspension system characteristics of the target vehicle, determine and configure the key parameters of the 1 / 4 vehicle suspension model;

[0017] Key parameters include vehicle weight (m) s Tire mass m u Suspension spring k s Tire stiffness k t Damper c0;

[0018] Step 1.2: Based on the key parameters, establish a dynamic equilibrium model of the 1 / 4 vehicle suspension system according to Newton's second law;

[0019] The dynamic equilibrium model of a 1 / 4 vehicle suspension system includes the vehicle body motion equation and the tire unsprung mass motion equation; the vehicle body motion equation is determined by the following formula:

[0020]

[0021] The equation of motion for the unsprung mass of a tire is determined by the following formula:

[0022]

[0023] In the formula: x s x u x r These are respectively the vertical displacement of the vehicle body, the vertical displacement of the tires, and the displacement caused by road surface excitation; These are the vertical accelerations of the vehicle body and tires, respectively. These represent the speeds of the vehicle body and tires, respectively; u represents the active control force.

[0024] Step 1.3: Based on the dynamic equilibrium relationship model, define the state variables and output variables of the suspension system, and construct a 1 / 4 vehicle suspension model through the state variables and output variables;

[0025] The state variable is The output variable is

[0026] The 1 / 4 scale vehicle suspension system model is as follows:

[0027]

[0028] Y = CX + Du

[0029] In the formula: A represents the derivative of the state variable; B represents the input matrix; d represents the disturbance term; C represents the output matrix; D represents the pass-through matrix; X represents the state variable; Y represents the output variable.

[0030] In the preferred implementation, step 2 further includes:

[0031] Step 2.1: Based on the core parameters of the 1 / 4 vehicle suspension model determined in Step 1.1, determine the parameters of the second-order tracking differentiator. According to the output channel in Step 1.3, take y = x. s As input to a second-order tracking differentiator, it generates a smooth tracking trajectory and outputs a displacement reference r. a and speed reference r b ;

[0032] Step 2.2: Based on the vehicle motion equations from Step 1, rearrange them into a controlled canonical form, and determine the input gain b = 1 / m of the controlled object accordingly. s And the measurement output is taken as y = x s Based on this, an extended state observer is constructed to estimate the vehicle body displacement, vehicle body speed, and total system disturbance online;

[0033] Controlled standard form, i.e., the object channel is:

[0034]

[0035] In the formula: f(·) represents the part of the vehicle acceleration determined by the coupling term of the suspension spring and damping. ω t For the road surface displacement x r diameter k t The effects transmitted to the vehicle body and disturbances such as parameter uncertainties; Indicates the total disturbance; The input gain of the target channel;

[0036] The extended state observer is:

[0037]

[0038] In the formula: The vehicle displacement x s Vehicle speed The estimated value; The total disturbance estimate is calculated by summing up the model coupling terms and external road surface excitations; k1, k2, and k3 are the observer gains; b is the ADRC control gain. x s This represents the actual vehicle body displacement;

[0039] Step 2.3: Using the reference trajectory (r) obtained in Step 2.1 a ,r b The state and perturbation estimates output by the extended state observer in step 2.2 Calculate the intermediate control quantity u0 according to the error feedback law, and based on the vehicle channel gain b = 1 / m determined in step 1. s The estimated total disturbance is compensated to obtain the final control force u. A This is to achieve real-time suppression of total system disturbances and object linearization;

[0040] Ultimate control u A for:

[0041]

[0042] In the formula: k p The proportional and differential gain of the position loop; k d For the proportional and differential gain of the velocity loop; r a The desired vehicle body displacement; Vehicle displacement x s The estimated value; For position error; r b The desired vehicle speed; Vehicle speed The estimated value; For speed error; is the estimated value of the total disturbance; b is the vehicle channel gain.

[0043] In the preferred implementation, step 3 further includes:

[0044] Step 3.1: Construct the Caputo fractional calculus operator;

[0045] Step 3.2: The desired displacement trajectory r obtained in step 2 a , desired velocity trajectory r b and their respective real estimates and Based on this, the displacement error is used to construct the state error, and the fractional derivative of the state error is calculated using the Caputo operator in step 3.1, which is then used as the input to the sliding surface.

[0046] The state error is e = xr a ;

[0047] The fractional derivative of the state error is:

[0048]

[0049] In the formula: D 1-a Γ(a) is a fractional-order calculus operator; Γ(a) is the value of the gamma function at point a; (tx) a-1 Here, a is the integral kernel function; a⁻¹ is the fractional order. The first derivative of the state error is...

[0050] Step 3.3: Define the sliding surface based on the state error and its fractional derivative.

[0051] The sliding surface is:

[0052]

[0053] In the formula, S is the sliding surface function; λ is the positive weighting parameter; and e is the state error. This is the fractional derivative of the state error;

[0054] Step 3.4: Based on the object channel and vehicle body channel gain b = 1 / m from Step 1 s Based on the sliding mode invariance condition, a sliding mode control law is designed, and the sliding mode control law is decomposed into an equivalent control law and a switching control law;

[0055] The equivalent control law is:

[0056]

[0057] In the formula: b0 is the channel gain; λ is the weighting factor; D a e is the fractional derivative of the state error, with order a; To compress the system's vehicle displacement, vehicle speed, parameter uncertainties, and external disturbances into a single mapping function;

[0058] The switching control law is:

[0059] u sw =-k s ·sat(S / δ)

[0060] In the formula: k s δ is the switching gain; sat(·) is the saturation function; S is the sliding surface; δ is the saturation function threshold.

[0061] Step 3.5: Integrate the equivalent control law from Step 3.4 with the switching control law to construct the FOSMC final control force, and apply it to the suspension system as the control input of the object channel;

[0062] FOSMC's ultimate control is:

[0063] u F =u sw +u equ

[0064] In the formula: u sw To switch control laws; u equ This is an equivalent control law.

[0065] In the preferred implementation, step 4 further includes:

[0066] Step 4.1: Based on the principle of "skyhook damper", the estimated value of vehicle speed is used as feedback to generate damping control force, and the Skyhook control law is obtained.

[0067] Step 4.2: Construct the switching criteria between Skyhook and ADRC-FOSMC based on the vehicle speed and the relative speed between the vehicle and the tires, and map the switching criteria into continuous weights using the Sigmoid function;

[0068] Step 4.3: Combine the composite control force of Skyhook, ADRC, and FOSMC multi-control strategies to output the final active control force.

[0069] In the preferred implementation, further, in step 4.1, the Skyhook control law is:

[0070]

[0071] In the formula: u sky For Skyhook control; c sky The damping coefficient of Skyhook; This represents the vertical velocity of the vehicle body.

[0072] In the preferred implementation, further, in step 4.2, the switching criterion is:

[0073]

[0074] In the formula: This is an estimated value for the vehicle's speed. This is an estimate of the tire speed;

[0075] Map the switching signal to continuous weights β∈[0,1]:

[0076]

[0077] In the formula: β(t) is the weighting coefficient; s(t) is the handover criterion; k is the handover sensitivity coefficient.

[0078] In the preferred implementation, when s(t)>0, Skyhook high-frequency vibration isolation is activated; when s(t)<0, ADRC-FOSMC disturbance rejection and smoothing control is activated.

[0079] In a preferred implementation, step 4.3 further includes:

[0080] Step 4.3.1: Calculate the combined control force of ADRC and FOSMC;

[0081] ADRC-FOSMC composite control force u AF for:

[0082]

[0083] In the formula: u equ For equivalent control law; -k s •sat(S / δ) is the switching control law; b0 is the estimated total disturbance; b0 is the channel gain.

[0084] Step 4.3.2: Integrate the Skyhook control force with the ADRC-FOSMC composite control force to output the final active control force u:

[0085] The formula for the final active control force u is as follows:

[0086] u=β(t)·u AF +[1-β(t)]·u sky

[0087] In the formula: β(t) is the weighting coefficient of the ADRC-FOSMC fused control branch; u AF The ADRC-FOSMC composite control force; 1-β(t) is the weighting coefficient of the Skyhook control branch; u skyFor Skyhook control.

[0088] On the other hand, the present invention also provides an active suspension control system for Skyhook-ADRC-FOSMC, the system comprising:

[0089] 1 / 4 vehicle suspension dynamics modeling module: used to construct a simplified mathematical model of the suspension system, configure and load the key parameters of the target vehicle's suspension system, including vehicle body mass, tire mass, suspension stiffness, damping coefficient, tire stiffness and road input characteristics, and establish a dynamic balance relationship model between the vehicle body and tires based on the parameters, define state variables and output variables and form a state space model of the 1 / 4 vehicle suspension system;

[0090] ADRC perturbation estimation and compensation module: connected to the modeling module, used to construct an active perturbation suppression controller based on the state-space model, the module includes:

[0091] The tracking differentiator is used to generate a smooth desired displacement reference and velocity reference based on the vehicle body displacement measurement.

[0092] Extended state observer is used to estimate vehicle displacement, vehicle speed, and total system disturbance including road excitation online;

[0093] The control law unit is used to feed back the error between the desired reference quantity and the estimated quantity, generate intermediate control quantity, compensate for the estimated total disturbance based on the vehicle channel gain, and output the final control force.

[0094] The FOSMC sliding mode control module is connected to the ADRC disturbance estimation and compensation module. It is used to construct the state error based on the position error and velocity error, calculate the fractional derivative of the state error using the Caputo fractional calculus operator, construct the sliding mode surface function based on the state error and its fractional derivative, decompose the sliding mode control law into the equivalent control law and the switching control law, and superimpose the two to form the fractional sliding mode control force.

[0095] The Skyhook-ADRC-FOSMC weighted fusion module is connected to the FOSMC sliding mode control module and the ADRC disturbance estimation and compensation module. It is used to construct the Skyhook control force and construct the switching criteria between Skyhook and ADRC-FOSMC based on the vehicle speed and the relative speed between the vehicle and the tires. The switching criteria are mapped to continuous weights through the Sigmoid function. The Skyhook control force and ADRC-FOSMC control force are weighted and fused to output the final active control force as the control input of the controlled system channel.

[0096] The beneficial effects of this application are:

[0097] First, the active suspension control method based on Skyhook-ADRC-FOSMC proposed in this application effectively overcomes the problems of poor adaptability of PID control, insufficient high-frequency vibration isolation of Skyhook control, limited real-time performance of ADRC control, and chattering of integer-order sliding mode control in existing technologies. Specifically, this application utilizes the extended state observer of ADRC to achieve real-time estimation and compensation of road excitation and total system disturbance, thereby improving the system's disturbance rejection and robustness; it introduces fractional-order sliding mode control (FOSMC) to reduce chattering of traditional sliding mode control while maintaining fast response and strong robustness, ensuring actuator life and control stability; and it combines the high-frequency vibration isolation characteristics of Skyhook control with continuous weighted fusion of ADRC-FOSMC through the Sigmoid function, enabling the controller to adaptively switch between multiple strategies according to the motion state of the vehicle body and tires. Therefore, this application not only achieves efficient vibration suppression and real-time control under conditions such as complex random road surfaces, sudden convex obstacles, and sinusoidal fluctuations, but also takes into account comfort, stability, and safety, solving the technical problem in the background technology that "single control cannot simultaneously achieve robust disturbance rejection, chattering suppression, and real-time response".

[0098] Secondly, in the preferred implementation, this application constructs a 1 / 4 vehicle suspension state-space model based on the suspension characteristics of the target vehicle, accurately transforming the dynamic relationship between the vehicle body and tires into a mathematical model. This not only reduces computational complexity but also ensures the accuracy and scalability of the control design. Using this model, the Skyhook-ADRC-FOSMC control method of this application can accurately reflect the coupling characteristics of the vehicle body, suspension, and tires at the modeling level, thus providing a unified modeling foundation for subsequent disturbance estimation, fractional sliding mode convergence, and weighted fusion of multiple control strategies. Compared with existing technologies, this application avoids the control distortion problem caused by a single control strategy relying on a simplified model, improves the dynamic response accuracy, model adaptability, and control reliability under complex road surface excitation and parameter perturbation conditions, and effectively solves the problem in the background technology of "mismatch between control strategy and actual vehicle dynamics, leading to difficulty in balancing robustness and comfort."

[0099] Third, in the preferred implementation, this application constructs an extended state observer (ESO) based on a 1 / 4 vehicle suspension model. This allows for real-time estimation of vehicle speed and total system disturbance under conditions where only vehicle displacement is measured, and active compensation is achieved by combining feedback control of position and speed errors. Therefore, this application effectively solves the problems of traditional PID and Skyhook control relying on precise models and struggling to handle unknown disturbances, while avoiding the real-time performance deficiencies caused by estimation delays in ADRC under high-frequency conditions. By tightly coupling the observation and compensation links, this application not only ensures the equivalent linearization of the controlled object but also improves its adaptability to parameter perturbations and irregular road surface excitations, thereby achieving stable and reliable suspension control and higher ride comfort under complex conditions.

[0100] Fourth, in the preferred implementation, this application introduces a Caputo fractional operator on the basis of traditional sliding mode control. By constructing a sliding surface through fractional derivative calculations of the state error, and combining this with an equivalent control law and a saturation function switching control law, the severe chattering problem commonly found in integer-order sliding mode control is effectively alleviated. This design not only maintains the advantages of fast convergence and strong robustness of sliding mode control, but also enhances its adaptability to complex operating conditions and parameter uncertainties through the "memory characteristics" of the fractional operator, making the control process smoother and more stable. Compared with existing technologies, this application avoids excessive wear of the actuator caused by high-frequency chattering, improves the engineering feasibility and long-term reliability of the system, and further solves the problem of "difficulty in balancing robustness and execution smoothness" in the prior art.

[0101] Fifth, in the preferred implementation, this application introduces a switching criterion based on the relationship between vehicle body and tire speed between Skyhook control and ADRC-FOSMC control, and utilizes the Sigmoid function to achieve continuous weighted fusion, enabling the controller to automatically select the optimal control strategy under different operating conditions. When the vehicle body and tires vibrate at high speed in the same direction, Skyhook control takes priority to enhance high-frequency vibration isolation; under low-frequency or strong disturbance conditions, ADRC-FOSMC takes the lead to improve disturbance rejection and robustness. This design avoids the shortcomings of existing technologies where a single control method cannot simultaneously achieve comfort and stability, realizing dynamic coordination and smooth switching of multiple control laws, thereby ensuring ride comfort, driving safety, and real-time control under complex and changing road conditions, and solving the contradictory problem of "insufficient high-frequency vibration isolation and difficulty in suppressing low-frequency disturbances" in the background technology.

[0102] Sixth, the Skyhook-ADRC-FOSMC active suspension control system proposed in this application organically combines modeling, disturbance estimation, fractional sliding mode control, and multi-strategy weighted fusion through a modular architecture, forming a complete closed-loop control system. At the modeling level, this system ensures the accurate representation of suspension dynamics; at the control level, it utilizes ADRC to achieve real-time estimation and compensation of total disturbances; and the combination of FOSMC fractional operators enhances robustness against nonlinearity and uncertainty while avoiding the severe chattering of traditional sliding mode control. Finally, through the weighted fusion of Skyhook and ADRC-FOSMC, the system can adaptively switch control strategies to meet the different requirements of low-frequency and high-frequency operating conditions, achieving systematic optimization of comfort, stability, and real-time performance, and improving the overall performance and engineering application value of active suspension control under complex road conditions. Attached Figure Description

[0103] Figure 1 This is a flowchart illustrating the steps of the active suspension control method based on Skyhook-ADRC-FOSMC of the present invention.

[0104] Figure 2 This is a schematic diagram of a 1 / 4 scale vehicle active suspension model of the present invention;

[0105] Figure 3 This is a structural block diagram of the Skyhook-ADRC-FOSMC active suspension control system of the present invention. Detailed Implementation

[0106] To enable those skilled in the art to better understand the technical solutions of this application, the following will provide a more detailed description of this application in conjunction with the accompanying drawings and embodiments.

[0107] The directional terms such as above, below, left, right, front, and back used in this application are based on the positional relationships shown in the attached drawings. Different attached drawings may result in different positional relationships, therefore they should not be interpreted as limitations on the scope of protection.

[0108] In this application, the terms "installation," "connection," "interlocking," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, an integral connection, a mechanical connection, an electrical connection, or a connection that allows communication between components. They can also refer to a direct connection or an indirect connection through an intermediate medium. They can refer to the internal connection of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0109] This invention describes an active suspension control method and system based on Skyhook-ADRC-FOSMC. This method is not a simple superposition of existing control strategies, but rather a systematic integration of the advantages of Skyhook control, Active Disturbance Rejection Control (ADRC), and Fractional Sliding Mode Control (FOSMC) by establishing a 1 / 4 vehicle suspension dynamics model. Specifically, Skyhook control, due to its simple engineering implementation and high-frequency vibration isolation performance, is used to improve vehicle vibration suppression. ADRC enhances the system's adaptability and robustness by using an extended state observer to estimate and compensate for uncertain disturbances caused by complex road conditions and the nonlinearity of hydraulic actuators in real time. FOSMC introduces fractional operators on top of the robustness of traditional sliding mode control, giving the control process both smoothness and anti-bounce characteristics. Furthermore, this invention organically unifies the three control concepts through a continuous weighted coefficient mechanism based on the Sigmoid function, achieving dynamic balance and seamless switching between multiple control strategies. This allows for the output of optimal active control force under typical irregular road surface excitation conditions such as random, sinusoidal, and convex surfaces, comprehensively improving the vibration reduction performance and stability of the suspension system. This control framework addresses key challenges such as nonlinearity of hydraulic actuators, complexity of road excitation, and perturbation of system parameters, forming an innovative solution that coordinates comfort and safety, and is particularly suitable for active suspension systems in intelligent vehicles and autonomous driving scenarios.

[0110] It should be noted that Skyhook-ADRC-FOSMC is an abbreviation for Skyhook Active Disturbance Rejection Fractional-Order Sliding Mode Controller. In the field of control, Skyhook refers to Skyhook control, which is a typical vibration reduction control strategy in vehicle suspension systems. This method assumes that there is a virtual damper between the vehicle body and the "sky," thereby simulating the "skyhook" effect in the controller. Its core idea is to suppress vehicle body vibration through a virtual reference point, thereby improving vehicle comfort and handling stability. ADRC stands for Active Disturbance Rejection Control. It's a novel control theory that actively estimates and compensates for the total disturbance when the system model is inaccurate or strong disturbances exist. This method uses an Extended State Observer (ESO) to estimate the disturbance and dynamically compensate for external uncertainties and internal modeling errors. In active suspension control, ADRC improves the system's robustness and adaptability to complex road disturbances. FOSMC stands for Fractional-Order Sliding Mode Control. Sliding mode control is a robust control method that maintains good control performance even with varying system parameters and uncertainties. FOSMC introduces fractional-order calculus operators into traditional sliding mode control, resulting in a more flexible dynamic response and stronger anti-blowout capability. In active suspension applications, FOSMC can reduce the "blowout problem" common in traditional sliding mode control while ensuring robustness. The Skyhook-ADRC-FOSMC controller of this application combines the vibration reduction performance of Skyhook control, the strong disturbance suppression capability of ADRC, and the robustness and anti-shaking characteristics of FOSMC. This controller can improve the vibration reduction effect and stability of the vehicle's active suspension system in complex road environments.

[0111] As per the instruction manual Figure 1 This invention provides an active suspension control method based on Skyhook-ADRC-FOSMC, the method comprising:

[0112] Step 1: Configure the key parameters of the 1 / 4 vehicle suspension model based on the suspension system characteristics of the target vehicle, and establish a dynamic equilibrium relationship model on this basis. Then, define the state variables and output variables and construct the state space model of the 1 / 4 vehicle suspension system.

[0113] The purpose of step 1 is to transform the physical and dynamic characteristics of the vehicle suspension system into a mathematical expression by constructing a state-space model of a 1 / 4 vehicle suspension. This will provide a unified modeling basis for the subsequent design and implementation of the active suspension controller, ensuring that the control method can accurately reflect the dynamic coupling relationship between the vehicle body and the tires, and on this basis, achieve comprehensive optimization of comfort and safety.

[0114] It should be noted that the quarter-car suspension model is a simplified model used in vehicle dynamics research and suspension control. This model decomposes the entire vehicle along longitudinal and lateral symmetries, taking only the suspension portion corresponding to one of the four wheels (i.e., "1 / 4 of the vehicle's mass and one tire") as an independent unit of dynamics study. Since the entire vehicle suspension system contains a seven-degree-of-freedom model (vertical, pitch, roll, etc.) or a higher-dimensional model, the calculations are complex and difficult to apply in real-time control. By using symmetry analysis to decompose the entire vehicle into a quarter-car model, the computational complexity can be significantly reduced while preserving key dynamic characteristics.

[0115] The 1 / 4 vehicle suspension dynamics modeling module clarifies the force and motion relationships of the suspension system, providing a foundational model for subsequent controller design. Specifically, step 1 includes:

[0116] Step 1.1: Based on the suspension system characteristics of the target vehicle, determine and configure the key parameters of the 1 / 4 vehicle suspension model.

[0117] Before constructing a 1 / 4 scale vehicle suspension model, it is necessary to clarify the physical meaning and engineering acquisition methods of various parameters based on the suspension system characteristics of the target vehicle. These characteristics directly determine the form of the dynamic equations and the accuracy of the state-space representation. The suspension system characteristics of the target vehicle include body mass characteristics, tire unsprung mass characteristics, suspension stiffness characteristics, damping characteristics, tire stiffness characteristics, and road input characteristics. These suspension system characteristics constitute the core parameters of the 1 / 4 scale vehicle suspension model. Body mass characteristics are expressed through body mass m. s The unsprung mass characteristic of a tire is expressed through the tire mass m. u The suspension stiffness characteristics are expressed through the suspension spring k. s The damping characteristics are expressed through the damper c0, and the road surface input characteristics are expressed through the road surface excitation displacement x. r Express.

[0118] like Figure 2 As shown, Figure 2 This is a 1 / 4 scale vehicle suspension model. The core parameters of a 1 / 4 scale vehicle suspension model include the vehicle's mass (m). s (1 / 4 of the total vehicle weight), tire weight m u(Mass of a single wheel), suspension spring k s Tire stiffness k t Damper c0 and road excitation displacement x r (x r This is the road surface displacement input under a single wheel (an external disturbance) to suit the standard specifications of family cars. The vehicle mass m... s The mass representing 1 / 4 of the vehicle body determines the vehicle's inertial response under road surface excitation. A larger mass results in better low-frequency vibration isolation, but reduces suspension response speed. Tire mass m u This refers to the mass of the tire connected to the suspension, affecting the vehicle's high-frequency vibration characteristics and the stability of the tire's contact with the road surface. A smaller unsprung mass results in better tire traction, but also requires a higher level of lightweight construction. (Suspension spring k) s This represents the equivalent stiffness of the suspension springs, which determines the frequency characteristics of vehicle body vibration. Excessive stiffness reduces comfort but improves handling stability; insufficient stiffness enhances comfort but makes the vehicle body prone to large swaying. Tire stiffness k t This represents the tire's equivalent stiffness in the vertical direction, determining the level of high-frequency excitation transmitted from the road surface to the vehicle body. Higher tire stiffness results in a more pronounced road feel but reduced comfort; conversely, insufficient stiffness leads to greater tire deformation, potentially compromising handling stability. The damper c0 represents the suspension damper's damping characteristics, controlling the relative speed between the vehicle body and tires and determining the system's vibration decay rate. Excessive damping results in a stiff system response; insufficient damping leads to slow vibration decay, reducing both comfort and safety. Road excitation displacement x r The main external disturbances to the suspension system include random road surfaces (conforming to the ISO road spectrum), sinusoidal road surfaces (periodic excitation), and convex road surfaces (sudden disturbances), which directly act on the tires, causing changes in tire dynamic loads, which are then transmitted to the vehicle body. These parameters are obtained through experimental calibration or technical specifications and serve as the basic inputs for model construction.

[0119] Step 1.2: Based on the key parameters, establish a dynamic equilibrium model of the 1 / 4 vehicle suspension system according to Newton's second law.

[0120] The dynamic equilibrium model of a quarter-vehicle suspension system includes the vehicle body motion equations and the tire unsprung mass motion equations. The vehicle body motion equations are determined by the following formula:

[0121]

[0122] The equation of motion for the unsprung mass of a tire is determined by the following formula:

[0123]

[0124] In equations (1) and (2): x s xu x r These are respectively the vertical displacement of the vehicle body, the vertical displacement of the tires, and the displacement caused by road surface excitation; These are the vertical accelerations of the vehicle body and tires, respectively. These represent the speeds of the vehicle body and tires, respectively; u represents the active control force (corresponding only to a single suspension unit), which is the core control quantity that this method needs to output.

[0125] The above dynamic relationship can accurately describe the mechanical interaction mechanism between the vehicle body, tires, and road surface. In formula (1), the left-hand side term... This represents the inertial force on the vehicle body (sprung mass), i.e., the net force acting on the vehicle body. -k s (x s -x u ) represents the spring force term, which occurs when the vehicle body moves upward relative to the tire (x). s >x u When the suspension spring is compressed, it generates a downward restoring force on the vehicle body; when the vehicle body moves downward relative to the tire, the spring is stretched, generating an upward restoring force on the vehicle body; this item reflects the adjustment function of the suspension spring on the relative displacement between the vehicle body and the tire. The damping force term is represented by the damper, which generates a reverse resistance when the vehicle body and tire speeds are inconsistent, suppressing the relative speed. For example, when the vehicle body sinks faster than the tires, the damper generates an upward damping force to slow down the vehicle body sinking. This term is mainly used to dissipate energy and improve the comfort of vehicle body vibration. +u represents the active control force, which is an external force provided by the active suspension actuator (hydraulic or electric motor). It can be dynamically adjusted according to the control algorithm, which is the key difference between active suspension and traditional passive suspension. Formula (1) describes the vertical motion balance of the vehicle body under the combined action of springs, dampers and active control forces.

[0126] In formula (2), the left-hand side term This represents the inertial force of the tire and its unsprung mass. +k s (x s -x u The force () represents the spring force from the vehicle body. The relative displacement between the vehicle body and the tires causes the suspension springs to generate a restoring force. For the tires, this force is opposite in direction to the spring force in the vehicle body equation, reflecting the "action and reaction". This represents the damping force from the vehicle body, which is related to the relative velocity of the vehicle body. Its direction is opposite to the corresponding term in the vehicle body equation, reflecting the symmetry of the damping interaction between the vehicle body and the tires. -kt(x u -x r (x) represents the tire's own elastic force, reflecting the tire's response as an elastic body to road unevenness. When there is a convexity on the road surface... u <x rWhen the tire is compressed, it generates an upward restoring force; when the road surface is concave, the tire is stretched, generating a downward restoring force. This term reflects the "supporting characteristic" of the interaction between the tire and the road surface. -u represents the active control force, which is opposite in direction to +u in the vehicle equation. This indicates that the control force not only acts directly on the vehicle body but also on the tire system, ensuring the overall momentum is conserved. Formula (2) describes the vertical motion law of the tire mass under the action of suspension spring force, damping force, tire stiffness force and active control force.

[0127] Step 1.2 The vehicle body equation (1) characterizes the dynamic response of vehicle comfort (ride experience), and the tire equation (2) characterizes the tire's following ability and grip (driving safety) in response to road surface excitation. The two equations are coupled through the suspension springs and dampers and are jointly controlled by the output u of the active suspension actuator and the road surface input x. r The effect of tire stiffness is transmitted to the vehicle body, while the active control force u is compensated and optimized by "applying to the vehicle body and reacting to the tires".

[0128] Step 1.3: Based on the dynamic equilibrium relationship model, define the state variables and output variables of the suspension system, and construct a 1 / 4 vehicle suspension model through the state variables and output variables.

[0129] It's important to note that state variables are the smallest set of variables used to fully describe the dynamic characteristics of a system. In a vehicle suspension system, state variables typically include position and velocity, as these two types of variables allow for the reconstruction of the system's kinematic and dynamic characteristics. Output variables are key performance indicators derived from the state variables; they directly reflect the control objectives of the vehicle suspension system, such as comfort, stability, and safety. The state-space equation is a dynamic system model expressed in matrix form, linking the evolution of state variables with the inputs and outputs.

[0130] Due to road surface excitation x r Since it is difficult to measure directly, we treat it as an external disturbance, define the system state variables and output, and transform it into standard state-space form:

[0131] The state variables include four core states: vehicle displacement, vehicle speed, tire displacement, and tire speed, which serve as the core state variables for system control.

[0132]

[0133] The system outputs the correlation variables corresponding to vehicle body vibration, suspension dynamic deflection, and tire dynamic load:

[0134]

[0135] The 1 / 4 vehicle suspension system model is represented by the following state-space equations:

[0136]

[0137] Y = CX + Du(6)

[0138] In formulas (5) and (6): A represents the derivative of the state variable, describing the trend of state change over time; B represents the system matrix, reflecting the coupling relationship within the suspension system (such as the vibration transmission characteristics between the vehicle body and tires); C represents the input matrix, describing the path of the control input u (active suspension output force) on the system state; D represents the disturbance term, reflecting the road excitation displacement x. r The impact on the system; C represents the output matrix, which linearly maps the state variables to the system output; D represents the pass-through matrix, which describes the direct impact of the input on the output (usually zero or minimal in this model); X represents the state variable (Formula 3), which describes the "true state" inside the system; Y represents the output variable, which characterizes the system performance indicators (comfort, safety, stability).

[0139] It should be noted that formulas (3) and (4) are X and Y in the physical sense, respectively, and the state variable X is directly taken from the physical quantity of the system. They have clear physical meanings, describing the motion of the vehicle body and tires. The output variable Y is a set of performance indicators. These are indicators that directly reflect comfort, safety, and stability in engineering. State-space equations (5) and (6) transform equations (3) and (4) into mathematical expressions. Equation (5) organizes equation (3) into a state vector using matrices A, B, and d, which is used for linear algebra and matrix operations. Equation (6) organizes equation (4) into an output vector using matrices C, D, and d, transforming complex dynamic problems into standardized mathematical models, which facilitates the application of control theory tools (such as pole placement, optimal control, and robust control). This application establishes a unified mathematical framework between state, input, and output through state-space equations, which is the core tool for the design of the control method in this application.

[0140] Matrices A, B, C, and D are derived from suspension parameters, and the external disturbance term d represents the road surface excitation displacement x. r Impact on the system. This state-space model not only facilitates the subsequent mathematical modeling and design of the controller, but also provides a standardized computational framework for system simulation verification.

[0141] In formulas (5) and (6), matrices A, B, C, and D are expressed by the following formulas:

[0142]

[0143] From the matrices A, B, C, D, and d above, we can see that:

[0144] Matrix A illustrates the vibration coupling mechanism between the vehicle body and tires, describing the natural dynamic behavior of the suspension system under the influence of stiffness, damping, and mass when no active control force is input. Matrix A consists of four rows. The first row, [0,1,0,0], represents the derivative of the vehicle displacement, which is the vehicle velocity, belonging to a kinematic relationship. The second row contains -k... s / m s This represents the restoring force of the suspension stiffness on the vehicle body when the vehicle body displacement is x. s When the pressure increases, the suspension springs generate a downward restoring force to suppress vehicle displacement; -c0 / m s This indicates the damper's effect on suppressing vehicle speed; when the vehicle speed... When the value is large, the damper generates a damping force to slow down the motion; +k s / m s The unsprung mass displacement of the tire is represented by x. u The coupling effect on the vehicle body is such that when the tires bounce, the springs "push" the vehicle body, creating a positive impact. +c0 / m s Indicates tire speed Through the coupling effect of the damper on the vehicle body, the tire motion is transmitted to the vehicle body via the damper, causing a corresponding change in the vehicle body's speed. The third line: [0,0,0,1] indicates that the derivative of the tire displacement is the tire speed. The fourth line: +k s / m u Indicates vehicle displacement x s The suspension springs exert a downward force on the tires as the vehicle body compresses, stretching the springs and thus applying a downward force to the tires. +c0 / m u Indicates vehicle speed The action transmitted to the tires through the damper causes the vehicle's movement to generate a damping force in the damper, thus affecting the tire speed; -(k s +k t ) / m u This indicates that the suspension stiffness and tire stiffness together affect the tire displacement x. u The restraining effect is that when the tire deviates from its balance position, the stiffness force of the suspension spring and the tire itself will pull it back; -c0 / m u Indicates the damper's effect on tire speed The damping effect is that the more intense the tire vibration, the greater the damping force, thus damping the motion.

[0145] Matrix B determines the path of the active suspension control force, indicating that the control force affects both the vehicle body and tires simultaneously, but in opposite directions, demonstrating the bidirectional action characteristic of the suspension actuator. In matrix B, the first row: 0 corresponds to the state variable x. s=Equation for vehicle speed. The system input u does not directly affect the vehicle's displacement or velocity, but rather indirectly through acceleration; therefore, it is zero here. Second line: 1 / m s Corresponding vehicle acceleration The dynamic equations indicate that the control force u acts directly on the vehicle body mass m. s It affects the vehicle body in the form of acceleration, with a coefficient of 1 / m. s This reflects that the greater the vehicle's mass, the smaller the impact of control force on the vehicle's acceleration. The third line: 0 corresponds to the state variable. The equation states that the control force does not directly change the tire's displacement or velocity, but is indirectly reflected through tire acceleration; therefore, it is zero here. Fourth line: -1 / m u Corresponding tire acceleration The dynamic equation represents the reaction force of the active suspension control force acting on the unsprung mass m of the tire. u The symbol above, with a negative sign, reflects the "action-reaction" principle. When the actuator applies an upward force to the vehicle body, the tire experiences an equal and opposite downward force. Matrix B shows that the displacement of the vehicle body and tires is not directly affected by the control force, while the vehicle body acceleration and tire acceleration are the direct objects of the control force, and their directions are opposite.

[0146] Matrix C will These are converted into output variables Y, which are core indicators used to evaluate vehicle performance (comfort, safety, suspension performance). In matrix C, the first row corresponds to the vehicle body acceleration output, i.e. It is caused by differences in suspension stiffness and damping, and is a direct indicator of ride comfort. When the road surface or tires are disturbed, the magnitude of the vehicle's acceleration determines the passenger's sense of bumpiness. The second line corresponds to the suspension travel (the difference between vehicle displacement and tire displacement), with "1" indicating that the output directly takes the vehicle displacement x. s "-1" means to subtract the tire displacement x u , that is, x s -x u "0" indicates that vehicle speed and tire speed do not contribute to this output. The second line reflects the suspension's damping capacity; if the deflection is too large, the suspension may "lock up" or "compress to its limit." (The last part, "x," appears to be an unrelated instruction and is left untranslated.) s -x u Ensure the suspension operates within reasonable limits to avoid mechanical damage. The third line corresponds to the displacement x of the unsprung mass of the tire. u The mathematical expression is Directly selecting tire displacement from the state variables reflects the impact of road surface unevenness on tire position and is a key indicator for measuring tire-road contact status and vehicle driving safety.

[0147] Matrix D illustrates the immediate improvement in vehicle acceleration caused by the active suspension control force; changes in control force can instantly alter ride comfort. In Matrix D, the first row contains: 1 / m s The corresponding output is the vehicle acceleration. The dynamic equations show that the control force u acts directly on the vehicle mass m. s And instantly change the vehicle's acceleration, with a coefficient of 1 / m s This indicates that the greater the vehicle's mass, the smaller the effect of control force on vehicle acceleration. The second line: 0 corresponds to the suspension dynamic travel x in the output. s -x u The control force *u* does not directly change the relative displacement of the suspension, but rather indirectly affects it through the dynamic coupling of the system (the effect of matrices A and B). The third line: 0 corresponds to the tire dynamic load (x) in the output. u -x r (or tire dynamic performance indicators) The control force does not have an immediate direct effect on this output, but rather indirectly transmits its influence by changing tire acceleration and displacement.

[0148] The disturbance term d describes how road surface unevenness affects the tires and is subsequently transmitted to the vehicle body; it is an external excitation that the active suspension system must handle. In the disturbance term d matrix, the first row: 0 corresponds to the state variables... The equation states that road surface input does not directly affect vehicle displacement or speed, but rather indirectly through the tire-suspension transmission, hence the value is zero. The second line: 0 corresponds to vehicle acceleration. Road surface input has no direct effect on vehicle acceleration; the vehicle's acceleration mainly comes from suspension forces and control forces, therefore this line is also zero. Third line: 0 corresponds to the state variable. The equation states that the road surface input has no direct effect on tire speed; instead, it affects tire acceleration through the elastic effect of tire stiffness. Therefore, the value here is also zero. Fourth line: Corresponding tire acceleration The equation represents the road surface excitation displacement x. r Through tire stiffness k t Transmitted unsprung mass m to the tire u This directly affects tire acceleration, thus becoming an external disturbance to the system. (Coefficient) This reflects the tire stiffness k t The larger the road surface roughness, the more significant its impact on tire acceleration. (The unsprung mass of the tire, m...) u The larger the value, the weaker the impact of road surface disturbance on its acceleration.

[0149] Step 2: Construct an ADRC controller based on the 1 / 4 vehicle suspension model. Select vehicle displacement as the measurement output. Determine the controlled object channel as the channel through which the control force acts on the vehicle acceleration according to the vehicle motion equation. Generate desired displacement reference and desired velocity reference through a tracking differentiator. Use an extended state observer to estimate the vehicle displacement, vehicle velocity, and total system disturbance including road excitation online. Obtain intermediate control quantity by passing the desired reference quantity and the estimated quantity through error feedback. Compensate for the estimated total disturbance based on the object channel gain and output the final control force to achieve real-time suppression of the total disturbance and equivalent linearization of the controlled object.

[0150] The purpose of step 2 is to estimate and compensate the total disturbance of the 1 / 4 vehicle suspension in real time through the ADRC disturbance estimation and compensation module, simplify the control difficulty, achieve smooth tracking of vehicle displacement and speed and acceleration suppression, thereby improving comfort and road adhesion retention.

[0151] It's important to note that ADRC (Active Disturbance Rejection Control) is a method of robust control that does not rely on an accurate model of the controlled object. It achieves robust control by estimating and compensating for the "total disturbance" online. It treats all uncertainties—parameter variations, unmodeled dynamics, external disturbances (such as road surface undulations), and even some nonlinearities—as the "total disturbance," estimating and then compensating for them. An ADRC controller consists of a TD (Tracking Differentiator), an ESO (Extended State Observer), and a control law / NLSEF (Nonlinear State Error Feedback). The TD transforms the desired signal into a smooth trajectory and provides its derivative, avoiding the amplification of noise through direct numerical differentiation, and outputs reference displacement and reference velocity. The ESO estimates the system's critical states (such as position and velocity) and an extended state, which is the estimate of the "total disturbance," given only the output measurement. The control law generates a "nominal control quantity" using the state error and then uses the disturbance estimate from the ESO for feedforward compensation.

[0152] Specifically, step 2 includes:

[0153] Step 2.1: Based on the core parameters of the 1 / 4 vehicle suspension model determined in Step 1.1, determine the parameters of the second-order tracking differentiator (TD). According to the output channel in Step 1.3, take y = x. s As input to a second-order tracking differentiator, it generates a smooth tracking trajectory and outputs a displacement reference r. a and speed reference r b .

[0154] It should be noted that the reference signal is the desired vehicle body displacement signal given by the upper-level control or setting module.

[0155] According to step 1.1, the core parameters of the 1 / 4 vehicle suspension model are known to be {m}. s ,m u ,k s ,kt,c0}, where m s ,k s c0 determines the frequency and decay of the first-order mode of the vehicle body, m u The high-frequency response of the tire-unsprung channel, which is dominated by kt, provides physical constraints for TD parameter tuning. According to the vehicle dynamics formula (1) in step 1.2, the vehicle acceleration is determined by x. s and Determined in conjunction with control force, but directly measured x s Contains noise, Since reliable access is difficult, a smoothing reference needs to be generated via TD. This is for subsequent observation and control. The set of output variables defined in step 1.3. Includes vehicle body displacement x s Directly related to its differential Therefore, in step 2.1, y = x is selected from this set. s As the input to TD, the output is a smooth displacement trajectory r. a Velocity trajectory r b It maintains consistency with the system output structure and reduces noise propagation.

[0156] The second-order tracking differentiator (TD) in the continuous domain is expressed as follows:

[0157]

[0158] In the formula: r a This is the smooth position reference output by TD, corresponding to the reference trajectory of the vehicle body displacement; r b R is the smoothed speed reference for the TD output, corresponding to the desired vehicle speed; R is the tracking speed factor, which determines the convergence speed and anti-interference capability of the TD, R > 0; sgn(·) is the sign function; r a r b The dimensions of x are respectively s , Consistent with the vehicle motion equation in step 1.2 or the output y = x in step 1.3. s docking; For the desired vehicle speed r b The rate of change of r, i.e., the expected acceleration; a -x sThe position error is the difference between the position estimated by TD and the actual measured reference position. For the speed-dependent nonlinear "braking term", when r b When moving quickly toward the target, The project "pushed back" the "switching surface" in advance to avoid overdoing it.

[0159] The only parameter R that can be adjusted simultaneously affects both the upper limit of acceleration in formula (8) and the response speed in formula (7). Increasing R results in faster convergence but greater sensitivity to noise; decreasing R leads to smoother, better noise immunity but slower tracking. Therefore, the selection of R must match the physical characteristics given in step 1.1. First, determine the angular frequency ω of the vehicle's main mode. b And the angular frequency ω ω The main modal angular frequency ω of the vehicle body b By m s ,k s Dominant, m s The smaller or k s The larger ω is b The higher the angular frequency ω, the better. ω By m u KT is the dominant force, and M is the dominant force. u The smaller or the larger kt is, the better ω ω The higher the value, the greater the effective bandwidth ω of TD. r Take at ω r ∈[0.6,1]·ω b , and ω r ≤0.35ω ω ω r ∈[0.6,1]·ω b Used to ensure keeping up with the vehicle's main mode, ω r ≤0.35ω ω This is used to provide sufficient margin for isolation from high-frequency wheel jumps. Therefore, R = ω r 2 .

[0160] When the damping c0 is too small (vehicle vibration decays slowly), ω is lowered to suppress noise and overshoot. r When the damping is too high (response stiff) and the equivalent reduction of R is 10–30%, ω can be slightly increased. r To avoid tracking lag. When the excitation x is random / rough or convex abrupt road surface... r When the high-frequency components are stronger, for ω r Set to conservative settings, ω r On the basis of lowering the damping c0 due to its small size, further reduce it by 10-30%. The force path of the active suspension actuator (hydraulic or electric) on the vehicle body is supplied by type (1). The control force acts directly on the vehicle body and has a reaction effect on the tires; the corresponding gain of the vehicle body acceleration channel is 1 / m. sTherefore, the reference "acceleration intensity" caused by TD should not drive u beyond the control force capability: R≤R max R max It is calculated from the control force of the active suspension actuator, the rate of change of the control force of the active suspension actuator, and the comfort (vehicle acceleration) limit.

[0161] For example: if ω is estimated b ≈12rad / s, ω ω ≈60rad / s, then ω r =min(0.8×12,0.35×60)=9.6rad / s. R=92(m / s 2 If the road surface is rough and the damping is small, choose R≈0.8×92≈74R.

[0162] Formulas (7) and (8) are two simultaneous equations of the same second-order TD, respectively governing the "kinematic relationship" and "acceleration control". Together, they form an acceleration-constrained second-order tracking differentiator, used to control the position trajectory r. a Smoothly follow x s In formula (7), the position trajectory r of TD a The derivative is the velocity trajectory r. b Formula (8) is used to determine the velocity trajectory r. b A switch acceleration of magnitude R, according to the switch function The symbol is used to determine the direction, which is equivalent to "pushing the state towards the goal as quickly as possible". When hour, Decelerate or accelerate downwards; when hour, Upward acceleration; state (r) a ,r b First, reach the switching surface with a constant acceleration ±R. (i.e., a parabola in the phase plane, the error and velocity curve), then slides along this plane, eventually reaching (r) a =x s ,r b =0).

[0163] Step 2.2: Based on the vehicle motion equations from Step 1, rearrange them into a controlled canonical form, and determine the input gain b = 1 / m of the controlled object accordingly. s And the measurement output is taken as y = x s Based on this, an extended state observer (ESO) is constructed to estimate the vehicle body displacement, vehicle body speed, and total system disturbance online.

[0164] In step 1, the equation of motion for the vehicle body is: Organize it into a controlled standard form (i.e., object channel):

[0165]

[0166] In the formula: f(·) represents the part of the vehicle acceleration determined by the coupling term of the suspension spring and damping. ω t For the road surface displacement x r diameter k t The effects transmitted to the vehicle body and disturbances such as parameter uncertainties; Indicates the total disturbance; The input gain of the target channel.

[0167] The extended state observer (ESO) in this application adopts a third-order linear structure:

[0168]

[0169] In the formula: The vehicle displacement x s Vehicle speed The estimated value; The total disturbance estimate is obtained by summing up the model coupling terms and external road excitations; k1, k2, and k3 are the observer gains, determined by the pole placement method to ensure the convergence of the estimate; b is the ADRC control gain, associated with the parameters of 1 / 4 of the vehicle model; x s The actual vehicle body displacement is collected by a displacement sensor.

[0170] The process of online estimation of vehicle displacement, vehicle velocity, and total system disturbance by the extended state observer includes: In formula (10), the input y = x s The control force u is output in real time by the Extended State Observer (ESO). (Vehicle displacement estimation) (Vehicle speed estimation) (Estimation of total system disturbance).

[0171] The observation results from step 2.2 are used for the control law calculation in step 2.3.

[0172] Step 2.3: Using the reference trajectory (r) obtained in Step 2.1 a ,r b The state and perturbation estimates output by the extended state observer in step 2.2 Calculate the intermediate control quantity u0 according to the error feedback law, and based on the vehicle channel gain b = 1 / m determined in step 1. s The estimated total disturbance is compensated to obtain the final control force u. A This is to achieve real-time suppression of total system disturbances and object linearization.

[0173] Based on steps 2.1 and 2.2, define the position error e1 and the velocity error e2:

[0174]

[0175] Determine the intermediate control quantity u0:

[0176] u0 = k p e1+k d e2(13)

[0177] Where, k p For the proportional and differential gain of the position loop, k p =ω c 2 ;k d For the proportional and differential gain of the velocity loop, k d =2ζω c ;ω c ω is the dominant frequency that the closed loop is expected to reach. c ≈TD equivalent bandwidth ω r (See step 2.1); ζ is the damping coefficient of the desired second-order closed loop; ζ∈[0.7,0.9].

[0178] Furthermore, determine the ultimate control force u A :

[0179]

[0180] First use offset object pair The "total disturbance" effect is then used to map the "expected nominal acceleration" u0 into the force that the actuator needs to apply, thereby achieving object equivalent linearization and real-time disturbance rejection.

[0181] Step 2 achieves smooth tracking and disturbance observation compensation by constructing ADRC. A second-order TD generates a smooth trajectory for the reference signal, suppressing noise and input abrupt changes; a linear ESO estimates the vehicle displacement, velocity, and total disturbance online; then, disturbance compensation is used to form a control law, effectively eliminating unknown internal and external disturbances and parameter uncertainties. This results in smoother tracking, faster response, improved robustness and stability, more effective suppression of strong disturbances such as road surface excitation, and improved overall ride comfort and control accuracy.

[0182] Step 3: Based on the position error and velocity error obtained in Step 2, construct the state error, calculate the fractional derivative of the state error using Caputo fractional calculus, and construct the sliding surface function based on the state error and its fractional derivative. Decompose the sliding control law into the equivalent control law and the switching control law, and superimpose the two to form the final fractional sliding control force, which serves as the control input for the object channel, in order to construct the fractional sliding mode controller (FOSMC).

[0183] The purpose of step 3 is to introduce fractional calculus operators through the FOSMC sliding mode control module, and to introduce fractional operators into the control law through the definition of Caputo fractional derivatives, so as to balance robustness and smoothness and avoid the severe chattering phenomenon commonly found in traditional sliding mode control.

[0184] The specific steps are as follows:

[0185] Step 3.1: Construct the Caputo fractional calculus operator.

[0186] The Caputo fractional calculus operator is employed to unify the computational logic of fractional derivatives and integrals, providing a computational tool for subsequent fractional derivative calculations of state errors. The formula for the Caputo fractional calculus operator is as follows:

[0187]

[0188] In the formula: D is a fractional calculus operator, representing the a-th order differentiation of f(t); 'a' is the fractional order (which can be determined in engineering through simulation or optimization, taking into account both robustness and smoothness); -(m-a) It is a fractional integral operator with an integral order of ma, which is related to the integer differential. Combined together, they form the Caputo definition; m is the smallest integer satisfying m-1<a≤m, used to decompose the a-th order differential; f(t) is the input function to be operated on; Γ(ma) is the value of the gamma function at ma; These are the normalization coefficients; This is a convolutional memory integral, which weights and accumulates information within the time interval x∈[a,t] to the current time t. α is the lower limit (initial time), reflecting the start time of memory, and is often taken as the start time of system simulation or sampling, α=t0; (m (x) is the m-th integer derivative of f with respect to time x; (tx) m-a-1 The kernel function determines the weight distribution of historical samples.

[0189] Step 3.2: The desired displacement trajectory r obtained in step 2 a , desired velocity trajectory r b and their respective real estimates and Based on this, the displacement error is used to construct the state error, and the fractional derivative of the state error is calculated using the Caputo operator in step 3.1, which is then used as the input to the sliding surface.

[0190] Based on step 2, the expected displacement trajectory r output by TD a , desired velocity trajectory r b ESO provides online vehicle displacement estimates Vehicle speed estimation Based on this, the displacement error e is obtained. p and speed error e v :

[0191]

[0192] It should be noted that formulas (16) and (17) in step 3.2 and formulas (11) and (12) in step 2.3 represent the same pair of errors, but they are expressed by different parameter symbols for different users. Step 2.3 uses them to calculate the intermediate control quantity u0 for error feedback in ADRC. Step 3.2 emphasizes the physical meaning of position error and velocity error by changing the symbol markings, which is used for fractional-order calculations and sliding surface design in FOSMC.

[0193] If the measured quantity is used directly, then formulas (16) and (17) are written as e. p =xr a ,

[0194] To construct a fractional-order sliding surface, since the control output has been determined in step 2 as the vehicle body displacement y = x s Based on this, TD and ESO are designed. Therefore, the displacement error is kept consistent with step 2. The displacement error is taken as the state error and the displacement error is the main variable. Then, the velocity information is introduced by the Caputo fractional derivative to improve robustness and adjustability.

[0195] State error is determined by the following formula:

[0196] e = xr a (18)

[0197] According to formula (18), the rate of change (first derivative) of the state error is:

[0198]

[0199] Using the Caputo operator from step 3.1, we perform a fractional derivative of the state error. Substituting equations (18) and (19) into equation (15), the order is 1-a. When 0 < a < 1, m = 1. Thus, we obtain the fractional derivative of the state error:

[0200]

[0201] In the formula: The first derivative of the state error is... a is the fractional order; Γ(a) is the gamma function, used to normalize the integral kernel function; (tx) a-1 This is the integral kernel function.

[0202] The fractional derivative D of the aforementioned state error 1-a e(t) and e=xr a Used for the construction of the sliding surface in step 3.3.

[0203] Step 3.3: Define the sliding surface based on the state error and its fractional derivative.

[0204] The sliding surface is:

[0205]

[0206] In the formula, S is the sliding surface function, which is used to characterize the convergence target of the system state. Setting S = 0 means that the system state has converged to the desired state; λ is a positive weighting parameter, which is used to adjust the relative contribution ratio of the error term and the fractional derivative term in the sliding surface. λ > 0; e is the state error, which represents the difference between the actual displacement and the desired displacement. It is the fractional derivative of the state error, used to improve the dynamic performance of the sliding surface.

[0207] Formula (21) represents the controlled object of the 1 / 4 vehicle suspension (vertical channel of the vehicle body, input gain b = 1 / m). s The convergence objective is to bring the system state to and maintain S=0 within a finite time.

[0208] Step 3.4: Based on the object channel and vehicle body channel gain b = 1 / m from Step 1 s Based on the sliding mode invariance condition, a sliding mode control law is designed, and the sliding mode control law is decomposed into an equivalent control law and a switching control law.

[0209] Based on the sliding surface in step 3.3 Find its time derivative

[0210]

[0211] As can be seen from formula (19), It's the vehicle speed, r b It is the expected velocity trajectory. This corresponds to the vehicle speed error, from which we can know This corresponds to the vehicle body acceleration error. Furthermore, the formula (9) for the "vehicle body vertical channel" of the controlled object is... Substitution In the middle, using formula (20)D 1-a e(t) represents the sliding surface derivative Represented as a linear combination of known terms and control input u:

[0212]

[0213]

[0214] To satisfy the sliding mode invariance condition, an invariance condition is adopted on the sliding surface. The equivalent control law can then be obtained:

[0215]

[0216] Apply fractional integral operator I to both sides of equation (24) a Using the identity under zero initial value: I a D 1-a g = g, and put As the total disturbance and known terms in the ESO estimate Merging equals We can obtain:

[0217]

[0218] It should be noted that, For specific physical quantities, It compresses complex physical variables into a general functional form, where y = x s That is, the vehicle body displacement x s Represented by the generalized output y; That is, the vehicle speed x s With generalized output This indicates that u, as a set of parameters, encompasses... We introduce t to represent the changes in system dynamics and external excitation over time.

[0219] By replacing the sign function with a saturation function, chattering is reduced, resulting in the switching control law:

[0220] u sw =-k s ·sat(S / δ) (26)

[0221] In the formula: k s To switch the gain, k s >0, the larger the value, the faster the arrival speed and the stronger the robustness to disturbances, but chattering may be aggravated. The smaller the value, the opposite, ensuring that the state quickly approaches the sliding surface; sat(·) is the saturation function, used to replace the sign function to weaken chattering; S is the sliding surface; δ is the saturation function threshold, δ>0, the smaller the value, the higher the accuracy of approaching, and it is necessary to balance the chattering suppression effect.

[0222] Step 3.5: Integrate the equivalent control law from Step 3.4 with the switching control law to construct the FOSMC final control force, and apply it to the suspension system as the control input of the object channel.

[0223] FOSMC's ultimate control is:

[0224] u F =u sw +u equ (27)

[0225] The resulting FOSMC final control force possesses dynamic smoothness and strong robustness.

[0226] Step 4: Construct the Skyhook control force, and construct the switching criterion between Skyhook and ADRC-FOSMC based on the vehicle speed and the relative speed between the vehicle and the tires. Obtain continuous weights by mapping with the Sigmoid function. Based on this, perform weighted fusion on the two control branches to generate the final active control force as the control input of the controlled system channel.

[0227] It should be noted that Skyhook (skylight damping) constrains the vehicle body as if it were a "damper connected to the sky / inertial frame," using the vehicle's absolute speed feedback to inject equivalent damping into the suspension to suppress vehicle vibration. ADRC-FOSMC (fusion of active disturbance rejection and fractional sliding mode) combines ADRC's "online estimation and cancellation of total disturbance" (ESO) with FOSMC's "fractional sliding mode robust convergence," achieving both disturbance rejection and strong robustness.

[0228] The purpose of step 4 is to leverage the high-frequency vibration isolation advantage of Skyhook through the Skyhook-ADRC-FOSMC weighted fusion module, combined with continuous weighting coefficients, to achieve seamless switching between multiple strategies and output the final active control force.

[0229] The specific steps are as follows:

[0230] Step 4.1: Based on the principle of "skyhook damper", the estimated value of the vehicle speed is used as the feedback quantity to generate the damping control force, and the Skyhook control law is obtained.

[0231] It should be noted that a skyhook damper refers to a damper that, under ideal conditions, is connected between the vehicle body and a "fixed point in the sky" (inertial reference frame). The damping force is generated by the absolute velocity of the vehicle body. By suppressing the absolute velocity of the vehicle body, high-frequency vibration isolation is optimized, thereby directly suppressing the acceleration of the vehicle body.

[0232] The ideal Skyhook damper is to connect one end of a damper to the vehicle body x s The other end is connected to a stationary inertial frame (velocity 0). The damping control force is:

[0233]

[0234] The active suspension actuator exerts a pair of forces on the vehicle body and tires, thus directly affecting the F... sky It can be used as a control target force:

[0235]

[0236] Among them, u sky For Skyhook control; c sky The Skyhook damping coefficient has a larger value under high-frequency conditions to enhance vibration isolation. The vertical velocity of the vehicle body is estimated by ESO.

[0237] The Skyhook control law is to apply the concept of "dampers ideally connected to the inertial frame" to the active suspension. Its design is based on the principles of absolute velocity feedback damping and acceleration suppression. In the "high-frequency scenario" where the vehicle body and tires vibrate at high speed in the same direction, it improves vibration isolation and reduces shaking.

[0238] Step 4.2: Construct the switching criteria between Skyhook and ADRC-FOSMC based on the vehicle speed and the relative speed between the vehicle and the tires, and map the switching criteria into continuous weights using the Sigmoid function.

[0239] Estimation of vehicle speed based on ESO input from step 2 Tire speed estimation Constructing switching criteria:

[0240]

[0241] Map the switching signal to continuous weights β∈[0,1]:

[0242]

[0243] In the formula: β(t) is the weighting coefficient, which is a continuous weight obtained from the switching signal s(t) through the Sigmoid function; s(t) is the switching criterion; k is the switching sensitivity coefficient, k>0, to ensure that β(t) transitions quickly when the switching condition s(t) changes.

[0244] When s(t) > 0 (vehicle and tire speeds are in the same direction, high-frequency vibration scenario), Skyhook high-frequency vibration isolation is activated; when s(t) < 0 (low-frequency vibration scenario), ADRC-FOSMC disturbance rejection and smoothing control is activated. The closer β(t) is to 1, the more it is dominated by the side where s(t) > 0; the closer it is to 0, the more it is dominated by the side where s(t) < 0. As s(t) increases, β(t) increases; when s(t) = 0, β(t) = 0.5.

[0245] Ultimately, this is used to perform weighted fusion of the two control branches (Skyhook and ADRC-FOSMC). Which branch corresponds to β or 1-β depends on the given weighting formula. For example, if u = βu is used... sky +(1-β)uAF A larger β indicates a stronger bias towards Skyhook; conversely, the opposite meaning applies if the order is reversed. Where u AF It is the ADRC-FOSMC fusion control force, which combines the "virtual control" given by fractional sliding mode control with the disturbance compensation of ADRC, and then calculates the actuator force in reverse according to the object input gain (see step 4.3).

[0246] Step 4.3: Combine the composite control force of Skyhook, ADRC, and FOSMC multi-control strategies to output the final active control force.

[0247] Step 4.3 includes:

[0248] Step 4.3.1: Calculate the combined control force of ADRC and FOSMC.

[0249] will u F As the intermediate control variable u0 of ADRC, further compensation of disturbances yields the ADRC-FOSMC composite control force u. AF The formula is as follows:

[0250]

[0251] Step 4.3.2: Integrate the Skyhook control force with the ADRC-FOSMC composite control force to output the final active control force u.

[0252] The formula for the final active control force u is as follows:

[0253] u=β(t)·u AF +[1-β(t)]·u sky (33)

[0254] In the formula: u is the final active control force (unit: N), which is executed by the electro-hydraulic actuator to adjust the suspension parameters in real time.

[0255] Example

[0256] Taking a mid-sized family sedan as the target vehicle, the Skyhook-ADRC-FOSMC active suspension control method proposed in this invention is implemented as follows:

[0257] Vehicle parameter settings:

[0258] Based on the suspension system characteristics of this vehicle model, the core parameters of the 1 / 4 vehicle suspension model are determined as follows:

[0259] Spring mass m s = 320kg (total vehicle weight approximately 1280kg, take 1 / 4); unsprung mass m u =45kg; Suspension stiffness k s=16000N / m; tire stiffness kt=190000N / m; damping coefficient c0=1200Ns / m; road excitation input x r Take a sinusoidal disturbance: x r =0.015sin(8t)m.

[0260] Based on this, a dynamic equilibrium model of the vehicle suspension is established, where the body equation and tire equation are as follows:

[0261]

[0262] State-space model construction:

[0263] Define the state variable as The output variable is

[0264] The system state-space equations are obtained as follows: Y = CX + Du.

[0265] in:

[0266]

[0267]

[0268] The disturbance term d is:

[0269]

[0270] ADRC controller design:

[0271] Tracking differentiator parameters: principal mode frequency ω b ≈√(k s / m s )=√(16000 / 320)≈7.07rad / s; ω_wheel jump frequency ω ≈√(kt / m u )=√(190000 / 45)≈65rad / s. Let ω r =0.8×7.07=5.65rad / s, R=ωr2=32(m / s2).

[0272] ESO (Extended State Observer) pole configuration: Set the poles at -20 to obtain the observer gains k1, k2, and k3.

[0273] Control law parameter: k p =ω c 2 = (5.65) 2 ≈32,k d =2ζω c=2×0.8×5.65≈9.04.

[0274] Final ADRC control force:

[0275] When the displacement error e1 increases by 1m, the controller outputs an adjustment force of approximately 10240N; when the velocity error e2 increases by 1m / s, it outputs an adjustment force of approximately 2893N; the ESO estimates the disturbance. For every 1 m / s increase 2 Output force correction -320N.

[0276] FOSMC fractional sliding mode controller:

[0277] Sliding surface Where, e = xr a ,

[0278] Equivalent control law This embodiment takes λ is set to 10, and a is set to 0.8. For practical applications, f(·) is estimated using the "total perturbation" of ESO. Therefore, we get:

[0279]

[0280] in, Provided in real time by ESO.

[0281] Switching control laws

[0282] Where sat(·) is the saturation function; δ is taken as 0.01; k s Take 500.

[0283] FOSMC Ultimate Control

[0284] Select the Skyhook damping coefficient c sky =2000 Ns / m, control force

[0285] Fusion control strategy:

[0286] Switching criteria Sigmoid weighting function (with sensitivity coefficient k = 0.5):

[0287] ADRC-FOSMC fusion control force is

[0288] The final active control force is obtained as: u = β(t)·u AF +[1-β(t)]·usky .

[0289] Through the above steps, simulation results show that the peak vehicle acceleration is reduced by more than 30%, significantly improving ride comfort; suspension deflection is controlled within 50mm, avoiding mechanical limit impacts; tire dynamic load fluctuations are reduced, and road surface adhesion is improved. This embodiment, through Skyhook-ADRC-FOSMC fusion control, can achieve adaptive switching between low-frequency large-amplitude vibrations and high-frequency road surface excitations, balancing comfort and safety.

[0290] like Figure 3 As shown, this invention also provides an active suspension control system based on Skyhook-ADRC-FOSMC. Through a 1 / 4 vehicle suspension dynamics modeling module, the force and motion relationships of the suspension system are clearly defined, providing a basic model for subsequent controller design. The system includes:

[0291] 1 / 4 vehicle suspension dynamics modeling module: used to construct a simplified mathematical model of the suspension system, configure and load the key parameters of the target vehicle's suspension system, including vehicle body mass, tire mass, suspension stiffness, damping coefficient, tire stiffness and road input characteristics, and establish a dynamic balance relationship model between the vehicle body and tires based on the parameters, define state variables and output variables and form a state space model of the 1 / 4 vehicle suspension system;

[0292] ADRC perturbation estimation and compensation module: connected to the modeling module, used to construct an active perturbation suppression controller based on the state-space model, the module includes:

[0293] The tracking differentiator is used to generate a smooth desired displacement reference and velocity reference based on the vehicle body displacement measurement.

[0294] Extended state observer is used to estimate vehicle displacement, vehicle speed, and total system disturbance including road excitation online;

[0295] The control law unit is used to feed back the error between the desired reference quantity and the estimated quantity, generate intermediate control quantity, compensate for the estimated total disturbance based on the vehicle channel gain, and output the final control force.

[0296] The FOSMC sliding mode control module is connected to the ADRC disturbance estimation and compensation module. It is used to construct the state error based on the position error and velocity error, calculate the fractional derivative of the state error using the Caputo fractional calculus operator, construct the sliding mode surface function based on the state error and its fractional derivative, decompose the sliding mode control law into the equivalent control law and the switching control law, and superimpose the two to form the fractional sliding mode control force.

[0297] The Skyhook-ADRC-FOSMC weighted fusion module is connected to the FOSMC sliding mode control module and the ADRC disturbance estimation and compensation module. It is used to construct the Skyhook control force and construct the switching criteria between Skyhook and ADRC-FOSMC based on the vehicle speed and the relative speed between the vehicle and the tires. The switching criteria are mapped to continuous weights through the Sigmoid function. The Skyhook control force and ADRC-FOSMC control force are weighted and fused to output the final active control force as the control input of the controlled system channel.

[0298] Finally, the fusion module weights the Skyhook control force and the ADRC-FOSMC control force based on the Sigmoid continuous weight. The resulting active control force is applied between the two mass blocks of the suspension via an actuator, thereby achieving effective suppression of vehicle body vibration and coordinated satisfaction of suspension / tire performance constraints under complex road excitation and parameter uncertainty conditions.

[0299] Figure 3 In this active suspension control system based on Skyhook-ADRC-FOSMC, the observer ESO-MIMO in ADRC (Active Disturbance Rejection Control) estimates the system state and "total disturbance". Two sets of control laws are prepared: Skyhook and FOSMC (Fractional Sliding Mode Control). The Switch selects or merges the two sets of control laws according to the strategy to obtain the final control force u. The control u is applied to the 1 / 4 active suspension model. Another ESO-MIMO on the right side continues to estimate the wheel-side state to complete the feedback.

[0300] The quarter vehicle active suspension model is a 1 / 4 vehicle active suspension model. Its input is the output u of the fusion unit, and its output is x. s As the controlled object, its output is fed to the observer and the fractional-order sliding mode controller. The red dashed box represents ADRC, and the two ESO-MIMOs are extended state observers-multiple-input multiple-output (MIMOs). The input signal of the left ESO-MIMO (the observer of ADRC) is the system's measurable output and control quantity related information, and the output signal is the estimated total disturbance. Estimate the vehicle side state and "total disturbance" to provide more complete feedback and disturbance compensation for the controller; the input signal of the ESO-MIMO (wheel-side observer) on the right is x u The output signal is related to the model output quantity. This supplements the estimation of the unsprung mass of the wheels, improves system condition observation, and facilitates subsequent control or monitoring. Different parts of the same suspension system are observed collaboratively using two ESO-MIMO systems.

[0301] TD is a tracking differentiator; the input of TD is the road surface excitation displacement x. r The output of TD is the tracking signal r a r b The Skyhook Controller is a crane controller whose input is the output of the ESO-MIMO on the left side (the estimated state on the vehicle side). Its output is u sky FOSMC is a fractional-order sliding mode controller, and its input is... r a r b The output is u AF FOSMC is a robust control system based on fractional sliding mode. To compensate and improve anti-interference capabilities, use r a r b Trace reference. A switch is a switcher or fusion device whose input is u. AF u sky The output is u, which is weighted between the two control laws according to a strategy (such as operating conditions, performance indicators, or criteria) to obtain the actual actuator force. The final control force u acts on... Figure 2 The switcher or fusion unit (located in the sprung mass block m of the vehicle body) s With tire mass m u (The components marked with circular arrows in between), ultimately, the Switch weights the Skyhook control force and the ADRC-FOSMC control force based on Sigmoid continuous weights, and the resulting active control force is applied between the two suspension mass blocks (the sprung mass blocks of the vehicle body m) via actuators. s With tire mass m u (between), thereby achieving effective suppression of vehicle body vibration and coordinated satisfaction of suspension and tire performance constraints under complex road surface excitation and parameter uncertainty conditions.

[0302] The active suspension control method and system based on Skyhook-ADRC-FOSMC of this invention overcomes the bottlenecks of existing technologies, achieving synergistic optimization of robust disturbance rejection, smooth response, and real-time control under complex and variable road conditions. By introducing the disturbance observation and compensation mechanism of ADRC, it effectively suppresses uncertain disturbances caused by random bumps, sinusoidal fluctuations, and sudden convex obstacles; combined with fractional-order sliding mode control (FOSMC), it weakens the chattering problem of traditional sliding mode while maintaining fast response and strong robustness, extending actuator life; furthermore, through the high-frequency vibration isolation characteristics of Skyhook control, it enhances the vehicle's acceleration suppression capability and improves ride comfort. Ultimately, this application achieves a comprehensive improvement in comfort, stability, and safety, ensuring that the vehicle maintains excellent vibration isolation and driving stability performance under both low-frequency and high-frequency conditions, while balancing real-time performance and engineering feasibility.

[0303] The above descriptions are merely embodiments of this application, and common knowledge regarding specific structures and characteristics in the solutions is not described in detail here. It will be apparent to those skilled in the art that this application is not limited to the details of the above exemplary embodiments, and that this application can be implemented in other specific forms without departing from the spirit or essential characteristics of this application. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of this application is defined by the appended claims rather than the foregoing description. Therefore, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within this application. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. An active suspension control method based on Skyhook-ADRC-FOSMC, characterized in that, The method includes: Step 1: Configure the key parameters of the 1 / 4 vehicle suspension model based on the suspension system characteristics of the target vehicle, and establish a dynamic equilibrium relationship model on this basis. Then define the state variables and output variables and construct the state space model of the 1 / 4 vehicle suspension system. Step 2: Construct an ADRC controller based on the 1 / 4 vehicle suspension model. Select the vehicle body displacement as the measurement output. Determine the controlled object channel as the channel through which the control force acts on the vehicle body acceleration based on the vehicle body motion equation. Generate the desired displacement reference and desired velocity reference through the tracking differentiator. Use the extended state observer to estimate the vehicle body displacement, vehicle body velocity, and the total system disturbance including road excitation online. Obtain the intermediate control quantity by passing the desired reference quantity and the estimated quantity through error feedback. Compensate for the estimated total disturbance based on the object channel gain and output the final control force to achieve real-time suppression of the total disturbance and equivalent linearization of the controlled object. Step 3: Based on the position error and velocity error obtained in Step 2, construct the state error, calculate the fractional derivative of the state error using Caputo fractional calculus, and construct the sliding surface function based on the state error and its fractional derivative. Decompose the sliding control law into the equivalent control law and the switching control law, and superimpose the two to form the final fractional sliding control force, which serves as the control input for the object channel, in order to construct the fractional sliding controller. Step 4: Construct the Skyhook control force, and construct the switching criteria between Skyhook and ADRC-FOSMC based on the vehicle speed and the relative speed between the vehicle and the tires. Obtain continuous weights by mapping with the Sigmoid function. Based on this, perform weighted fusion on the two control branches to generate the final active control force as the control input of the controlled system channel.

2. The active suspension control method based on Skyhook-ADRC-FOSMC according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Based on the suspension system characteristics of the target vehicle, determine and configure the key parameters of the 1 / 4 vehicle suspension model; Key parameters include vehicle weight Tire quality Suspension springs Tire stiffness Dampers ; Step 1.2: Based on the key parameters, establish a dynamic equilibrium model of the 1 / 4 vehicle suspension system according to Newton's second law; The dynamic equilibrium model of a 1 / 4 vehicle suspension system includes the vehicle body motion equation and the tire unsprung mass motion equation; the vehicle body motion equation is determined by the following formula: ； The equation of motion for the unsprung mass of a tire is determined by the following formula: ； In the formula: x s x u , These are respectively the vertical displacement of the vehicle body, the vertical displacement of the tires, and the displacement caused by road surface excitation; These are the vertical accelerations of the vehicle body and tires, respectively. These represent the speeds of the vehicle body and tires, respectively; u represents the active control force. Step 1.3: Based on the dynamic equilibrium relationship model, define the state variables and output variables of the suspension system, and construct a 1 / 4 vehicle suspension model through the state variables and output variables; The state variable is The output variable is ; The 1 / 4 scale vehicle suspension system model is as follows: ； CX+You; In the formula: A represents the derivative of the state variable; B represents the input matrix; d represents the disturbance term; C represents the output matrix; D represents the pass-through matrix; X represents the state variable; Y represents the output variable.

3. The active suspension control method based on Skyhook-ADRC-FOSMC according to claim 2, characterized in that, Step 2 specifically includes: Step 2.1: Based on the core parameters of the 1 / 4 vehicle suspension model determined in Step 1.1, determine the parameters of the second-order tracking differentiator. According to the output channel in Step 1.3, take y = As input to a second-order tracking differentiator, it generates a smooth tracking trajectory and outputs a displacement reference. and speed reference ; Step 2.2: Based on the vehicle motion equations from Step 1, rearrange them into a controlled canonical form, and determine the input gain b = 1 / And the measured output is taken as y= Based on this, an extended state observer is constructed to estimate the vehicle body displacement, vehicle body speed, and total system disturbance online; Controlled standard form, i.e., the object channel is: ； In the formula: The portion of the vehicle body acceleration determined by the coupling term of the suspension springs and damping is considered. ; For road surface displacement path The effects transmitted to the vehicle body and parameter uncertainty disturbances; Indicates the total disturbance; The input gain of the target channel; The extended state observer is: ； In the formula: , Vehicle displacement Vehicle speed The estimated value; The total disturbance estimate is obtained by summing up the model coupling terms and external road surface excitations. , , b is the observer gain; b is the ADRC control gain, b= ; This represents the actual vehicle body displacement; Step 2.3: Use the reference trajectory obtained in Step 2.1 The state and perturbation estimates output by the extended state observer in step 2.2 Calculate intermediate control quantities according to error feedback law And based on the vehicle channel gain b=1 / determined in step 1 The final control force is obtained by compensating for the estimated total disturbance. This is to achieve real-time suppression of total system disturbances and object linearization; Ultimate control for: ； In the formula: The proportional and differential gain of the position loop; The proportional and differential gain of the velocity loop; The desired vehicle body displacement; For vehicle body displacement The estimated value; This refers to the positional error; The desired vehicle speed; Vehicle speed The estimated value; For speed error; is the estimated value of the total disturbance; b is the vehicle channel gain.

4. The active suspension control method based on Skyhook-ADRC-FOSMC according to claim 3, characterized in that, Step 3 specifically includes: Step 3.1: Construct the Caputo fractional calculus operator; Step 3.2: The desired displacement trajectory obtained in step 2 Expected velocity trajectory and their respective real estimates and Based on this, the displacement error is used to construct the state error, and the fractional derivative of the state error is calculated using the Caputo operator in step 3.1, which is then used as the input to the sliding surface. State error is ; The fractional derivative of the state error is: ； In the formula: It is a fractional calculus operator; The value of the gamma function at point a; Here, a is the integral kernel function; a⁻¹ is the fractional order. The first derivative of the state error is... ; Step 3.3: Define the sliding surface based on the state error and its fractional derivative; The sliding surface is: ； In the formula, For sliding surface functions; These are positive weighting parameters; This refers to the state error; This is the fractional derivative of the state error; Step 3.4: Based on the object channel and vehicle body channel gain from Step 1, b = 1 / Based on the sliding mode invariance condition, a sliding mode control law is designed, and the sliding mode control law is decomposed into an equivalent control law and a switching control law; The equivalent control law is: ； In the formula: Channel gain; As a weighting factor; Let be the fractional derivative of the state error, with order 'a'; To compress the system's vehicle displacement, vehicle speed, parameter uncertainties, and external disturbances into a single mapping function; The switching control law is: ； In the formula: To switch the gain; S is a saturation function; S is a sliding surface; The threshold for the saturation function; Step 3.5: Integrate the equivalent control law from Step 3.4 with the switching control law to construct the FOSMC final control force, and apply it to the suspension system as the control input of the object channel; FOSMC's ultimate control is: ； In the formula: To switch control laws; This is an equivalent control law.

5. The active suspension control method based on Skyhook-ADRC-FOSMC according to claim 4, characterized in that, Step 4 specifically includes: Step 4.1: Based on the principle of "skyhook damper", the estimated value of the vehicle speed is used as the feedback quantity to generate the damping control force, and the Skyhook control law is obtained. Step 4.2: Construct the switching criteria between Skyhook and ADRC-FOSMC based on the vehicle speed and the relative speed between the vehicle and the tires, and map the switching criteria into continuous weights using the Sigmoid function; Step 4.3: Combine the composite control force of Skyhook, ADRC, and FOSMC multi-control strategies to output the final active control force.

6. The active suspension control method based on Skyhook-ADRC-FOSMC according to claim 5, characterized in that, In step 4.1, the Skyhook control law is: ； In the formula: u sky For Skyhook control; c sky The damping coefficient of Skyhook; This represents the vertical velocity of the vehicle body.

7. The active suspension control method based on Skyhook-ADRC-FOSMC according to claim 6, characterized in that, In step 4.2, the switching criterion is: ； In the formula: This is an estimated value for the vehicle's speed. This is an estimate of the tire speed; Map the switching signal to continuous weights : ； In the formula: is the weighting coefficient; s(t) is the handover criterion; k is the handover sensitivity coefficient.

8. The active suspension control method based on Skyhook-ADRC-FOSMC according to claim 7, characterized in that, When s(t) > 0, Skyhook high-frequency vibration isolation is activated; when s(t) < 0, ADRC-FOSMC disturbance rejection and smoothing control is activated.

9. The active suspension control method based on Skyhook-ADRC-FOSMC according to claim 5, characterized in that, Step 4.3 includes: Step 4.3.1: Calculate the combined control force of ADRC and FOSMC; ADRC-FOSMC composite control force u AF for: ； In the formula: This is an equivalent control law; To switch control laws; This is the estimated total disturbance. Channel gain; Step 4.3.2: Integrate the Skyhook control force with the ADRC-FOSMC composite control force to output the final active control force u: The formula for the final active control force u is as follows: ； In the formula: For the weighting coefficients of the ADRC-FOSMC fused control branch; ADRC-FOSMC composite control force; The weighting coefficients for the Skyhook control branches; For Skyhook control.

10. A Skyhook-ADRC-FOSMC active suspension control system, characterized in that, The system includes: 1 / 4 vehicle suspension dynamics modeling module: used to construct a simplified mathematical model of the suspension system, configure and load the key parameters of the target vehicle's suspension system, including vehicle body mass, tire mass, suspension stiffness, damping coefficient, tire stiffness and road input characteristics, and establish a dynamic balance relationship model between the vehicle body and tires based on the parameters, define state variables and output variables and form a state space model of the 1 / 4 vehicle suspension system; ADRC perturbation estimation and compensation module: connected to the modeling module, used to construct an active perturbation suppression controller based on the state-space model, the module includes: The tracking differentiator is used to generate a smooth desired displacement reference and velocity reference based on the vehicle body displacement measurement. Extended state observer is used to estimate vehicle displacement, vehicle speed, and total system disturbance including road excitation online; The control law unit is used to feed back the error between the desired reference quantity and the estimated quantity, generate intermediate control quantity, compensate for the estimated total disturbance based on the vehicle channel gain, and output the final control force. The FOSMC sliding mode control module is connected to the ADRC disturbance estimation and compensation module. It is used to construct the state error based on the position error and velocity error, calculate the fractional derivative of the state error using the Caputo fractional calculus operator, construct the sliding mode surface function based on the state error and its fractional derivative, decompose the sliding mode control law into the equivalent control law and the switching control law, and superimpose the two to form the fractional sliding mode control force. The Skyhook-ADRC-FOSMC weighted fusion module is connected to the FOSMC sliding mode control module and the ADRC disturbance estimation and compensation module. It is used to construct the Skyhook control force and construct the switching criteria between Skyhook and ADRC-FOSMC based on the vehicle speed and the relative speed between the vehicle and the tires. The switching criteria are mapped to continuous weights through the Sigmoid function, and the Skyhook control force and ADRC-FOSMC control force are weighted and fused to output the final active control force as the control input of the controlled system channel.

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