Active suspension control method and system based on Skyhook-ADRC-FFORC

Abstract

The invention belongs to the technical field of active suspension control, and particularly relates to an active suspension control method and system based on Skhook-ADRC-FFORC. According to the method, key parameters are obtained by establishing a 1 / 4 vehicle suspension dynamical model, a state space model is constructed, active disturbance suppression control is introduced on the basis, and the stability of the vehicle suspension is improved. Real-time estimation and compensation of vehicle body displacement and total disturbance of a system are realized, fractional order sliding mode control is combined, a fractional order sliding mode surface is constructed by using a Caputo operator, high robustness and smoothness are considered, the buffeting problem of a traditional sliding mode is suppressed, and finally, the high-frequency vibration isolation advantage of Skyhook control and the anti-interference capability of ADRC-FFORC are subjected to weighted fusion. The problems that in the prior art, model simplification and control distortion are caused, and a single strategy cannot give consideration to multi-target performance are solved, and by fusing ADRC, FOSMC and Skyhook control and realizing adaptive weighted switching, the robustness, smoothness and real-time performance of the active suspension under complex working conditions are effectively improved, so that collaborative optimization of vehicle comfort and safety is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of active suspension control, and in particular, relates to an active suspension control method and system based on Skyhook-ADRC-FOSMC. BACKGROUND

[0002] A vehicle suspension system is a key component connecting a vehicle body and wheels, and its core function is to isolate vibrations caused by road excitation and balance ride comfort and driving stability. Traditional suspension systems are divided into passive suspension and semi-active suspension: passive suspension adopts a fixed stiffness and damping structure, and can only maintain a limited performance balance under specific road conditions; although the semi-active suspension can adjust the damping through electromagnetic valves and other devices, the adjustment range is limited, and it is difficult to cope with complex and variable road conditions (such as potholes, speed bumps, and irregular undulating roads). With the development of automobile electronics and intelligent control technology, active suspension systems can actively output control force by introducing external power sources (such as hydraulic pumps and motors), and have become the core direction of improving suspension performance. However, active suspension control faces three key challenges: first, the non-linear characteristics of hydraulic actuators can easily affect control accuracy; second, the irregularity of road excitation (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 obvious defects:

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

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

[0006] 3. Active disturbance rejection control (ADRC): can estimate and compensate for total disturbances, but relies on a large amount of computing resources, has poor real-time performance, and is prone to estimation delays, especially in high-frequency conditions;

[0007] 4. Integer order sliding mode control (SMC): strong robustness and fast response, but has a serious "chattering" phenomenon, which can easily cause actuator wear and affect suspension stability.

[0008] To solve the bottleneck of single control strategy, existing researches attempt to fuse ADRC with integer order SMC, Skyhook with ADRC, etc., but still fail to achieve the collaborative optimization of "robust anti-disturbance-chattering suppression-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 regulation accuracy is insufficient. Therefore, an active suspension control method is urgently needed, which can integrate the advantages of multiple controls, and take into account the anti-disturbance, smoothness and real-time performance. SUMMARY

[0009] In view of the technical problems in the prior art that PID control has poor adaptability, Skyhook control has insufficient high-frequency vibration isolation, ADRC control has limited real-time performance, and integer order sliding mode control has serious chattering, the present application provides an active suspension control method and system based on Skyhook-ADRC-FOSMC, which establishes a 1 / 4 vehicle suspension dynamics model to obtain state information such as vertical displacement and speed of the vehicle body and tires, combines the real-time disturbance estimation and compensation capability of active disturbance rejection control (ADRC), the strong robustness and dynamic smoothness of fractional order sliding mode control (FOSMC), and the simple engineering implementation and high-frequency vibration isolation advantages of Skyhook control, realizes seamless switching of multiple control strategies through continuous weighting coefficients (based on Sigmoid function), and finally outputs the optimal active control force to adjust the suspension parameters. The present application can effectively cope with core challenges such as nonlinear hydraulic actuators, irregular road excitation (such as random road, sinusoidal road, convex road), and system parameter perturbation, improve the comprehensive control performance of the active suspension system, and help to optimize the vehicle ride comfort and driving safety in the field of intelligent vehicles and autonomous driving.

[0010] In one aspect, the present application provides an active suspension control method based on Skyhook-ADRC-FOSMC, which comprises:

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

[0012] Step 2: Based on the 1 / 4 vehicle suspension model, the ADRC controller is constructed, the body displacement is selected as the measurement output, the controlled object channel is determined as the channel of the control force acting on the body acceleration according to the body motion equation, the expected displacement reference and the expected speed reference are generated through the tracking differentiator, the body displacement, the body speed and the total disturbance including the road excitation are estimated online by the extended state observer, the expected reference quantity and the estimated quantity are fed back through the error to obtain the intermediate control quantity, and the estimated total disturbance is compensated based on the object channel gain to output the final control force, so as to realize the real-time suppression of the total disturbance and the equivalent linearization of the controlled object;

[0013] Step 3: Based on the position error and the speed error obtained in step 2, the state error is constructed, the fractional order derivative of the state error is calculated by Caputo fractional calculus, and the sliding mode surface function is constructed based on the state error and the fractional order derivative, the sliding mode control law is decomposed into an equivalent control law and a switching control law, and the two are superimposed to form the final fractional order sliding mode control force as the control input of the object channel, so as to construct the fractional order sliding mode controller;

[0014] Step 4: The Skyhook control force is constructed, and the body speed and the relative speed between the body and the tire are used to construct the switching criterion of the Skyhook and the ADRC-FOSMC and to map the continuous weight through the Sigmoid function, so as to weight and fuse 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, further, step 1 specifically includes:

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

[0017] The key parameters include the body mass m s , the tire mass m u , the suspension spring k s , the tire stiffness k t , and the damper c0.

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

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

[0020]

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

[0022]

[0023] wherein x s , x u , x r are the body vertical displacement, tire vertical displacement, road excitation displacement, respectively; are the body, tire vertical acceleration, respectively; are the body, tire velocity, respectively; u is the active control force;

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

[0025] The state variables are The output variables are

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

[0027]

[0028] Y=CX+Du

[0029] wherein: denotes the derivative of the state variable; A denotes the system matrix; B denotes the input matrix; d denotes the disturbance term; C denotes the output matrix; D denotes the straight-through matrix; X denotes the state variable; Y denotes the output variable;

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

[0031] Step 2.1: Based on the core parameters of the 1 / 4 vehicle suspension model determined in step 1.1, the parameters of the second-order tracking differentiator are determined, and according to the output channel of step 1.3, y=x s is taken as the input of the second-order tracking differentiator and a smooth tracking trajectory is generated, and the displacement reference r a and the velocity reference r b are output;

[0032] Step 2.2: Based on the body motion equation of step 1, it is arranged into a controlled standard form, according to which the input gain b=1 / m s of the controlled object is determined, and the measurement output is taken as y=x s , and on this basis, an extended state observer is constructed to estimate the body displacement, body velocity and total disturbance of the system online;

[0033] The 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; For 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, further, step 3 specifically comprises:

[0044] Step 3.1: Constructing Caputo fractional calculus operator;

[0045] Step 3.2: Taking displacement error to construct state error based on the expected displacement trajectory r a , the expected velocity trajectory r b and their respective real-time estimations and respectively obtained in step 2, and using the Caputo operator in step 3.1 to calculate the fractional derivative of the state error as the input of the sliding mode surface;

[0046] The state error is e = x - r a ;

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

[0048]

[0049] In the formula: D 1-a is the fractional calculus operator; Γ(a) is the value of the gamma function at a; (t - x) a-1 is the integral kernel function; a - 1 is the fractional order; is the first derivative of the state error, i.e.

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

[0051] The sliding mode surface is:

[0052]

[0053] In the formula, S is the sliding mode surface function; λ is a positive weight parameter; e is the state error; is the fractional derivative of the state error;

[0054] Step 3.4: Based on the object channel gain b = 1 / m s and the sliding mode invariance condition in step 1, designing the sliding mode control law, and decomposing the sliding mode control law 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 weight factor; D a e is the fractional derivative of the state error, and the order is a; To compress the body displacement, body speed, parameter uncertainty, external disturbance, etc. of the system into a mapping function;

[0058] The switching control law is:

[0059] u sw = -k s ·sat(S / δ)

[0060] In the formula: k s 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 of step 3.4 and the switching control law to build the FOSMC final control force, and apply it to the suspension system as the control input of the object channel;

[0062] The FOSMC final control force is:

[0063] u F = u sw + u equ

[0064] In the formula: u sw is the switching control law; u equ is the equivalent control law.

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

[0066] Step 4.1: Based on the "skyhook damper" principle, generate a damping control force with the estimated value of the body speed as the feedback, and obtain the Skyhook control law;

[0067] Step 4.2: Construct the switching criterion of Skyhook and ADRC-FOSMC with the body speed and the relative speed of the body and the tire, and map the switching criterion to a continuous weight through the Sigmoid function;

[0068] Step 4.3: Combine the composite control force of Skyhook, ADRC, and FOSMC multiple 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 is the Skyhook control force; c sky is the Skyhook damping coefficient; is the body vertical speed.

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

[0073]

[0074] wherein: is the vehicle body speed estimation value; is the tire speed estimation value;

[0075] The switching signal is mapped to a continuous weight β∈[0,1]:

[0076]

[0077] wherein: β(t) is the weighting coefficient; s(t) is the switching criterion; k is the switching sensitivity coefficient.

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

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

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

[0081] ADRC-FOSMC compound control force u AF is:

[0082]

[0083] wherein: u equ is the equivalent control law; -k s ·sat(S / δ) is the switching control law; is the total disturbance estimation value; b0 is the channel gain;

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

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

[0086] u = β(t)·u AF + [1-β(t)]·u sky

[0087] wherein: β(t) is the weight coefficient of the ADRC-FOSMC fusion control branch; u AF is the ADRC-FOSMC compound control force; 1-β(t) is the weight coefficient of the Skyhook control branch; u skyFor Skyhook control force.

[0088] In another aspect, the application also provides a Skyhook-ADRC-FOSMC active suspension control system, the system comprising:

[0089] 1 / 4 vehicle suspension dynamics modeling module: for building a simplified suspension system mathematical model, configuring and loading the key parameters of the suspension system of the target vehicle, including the body mass, tire mass, suspension stiffness, damping coefficient, tire stiffness and road input characteristics, and establishing a dynamic equilibrium relationship model of the body and the tire based on the parameters, defining the state variables and output variables and forming a state space model of the 1 / 4 vehicle suspension system;

[0090] ADRC disturbance estimation and compensation module: connected with the modeling module, for building an active disturbance rejection controller based on the state space model, the module comprising:

[0091] tracking differentiator, for generating smooth expected displacement reference and speed reference according to body displacement measurement;

[0092] extended state observer, for online estimation of body displacement, body speed and total disturbance of the system including road excitation;

[0093] control law unit, for error feedback of expected reference and estimated quantity, generating intermediate control quantity, and compensating estimated total disturbance based on body channel gain, outputting final control force;

[0094] FOSMC sliding mode control module: connected with the ADRC disturbance estimation and compensation module, for building state error based on position error and speed error, calculating fractional order derivative of state error using Caputo fractional calculus operator, and building sliding mode function based on state error and its fractional order derivative, decomposing sliding mode control law into equivalent control law and switching control law, and superimposing the two to form fractional order sliding mode control force;

[0095] Skyhook-ADRC-FOSMC weighted fusion module: connected with the FOSMC sliding mode control module and ADRC disturbance estimation and compensation module, for building Skyhook control force, and constructing switching criterion of Skyhook and ADRC-FOSMC based on body speed and relative speed of body and tire, mapping the switching criterion to continuous weight through Sigmoid function, weighting Skyhook control force and ADRC-FOSMC control force, and outputting final active control force as control input of the controlled system channel.

[0096] The beneficial effects of the present application are:

[0097] Firstly, the Skyhook-ADRC-FOSMC-based active suspension control method of the 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 the prior art. Specifically, the application uses the extended state observer of ADRC to realize real-time estimation and compensation of road excitation and system total disturbance, improving the disturbance rejection and robustness of the system; introduces fractional order sliding mode control (FOSMC), which weakens the chattering phenomenon of traditional sliding mode control while maintaining fast response and strong robustness, ensuring the service life and control stability of the actuator; combines the high-frequency vibration isolation characteristics of Skyhook control, and realizes continuous weighted fusion with ADRC-FOSMC through Sigmoid function, so that the controller can realize multi-strategy adaptive switching according to the motion state of the vehicle body and the tire. Therefore, the application not only realizes efficient vibration suppression and real-time control under complex random road conditions, sudden convex obstacles and sinusoidal fluctuations, but also takes into account comfort, stability and safety, solving the technical problem of "single control difficult to realize robust disturbance rejection, chattering suppression and real-time response" in the background technology.

[0098] Secondly, in the preferred implementation, the application accurately converts the dynamic relationship between the vehicle body and the tire into a mathematical model by constructing a 1 / 4 vehicle suspension state space model based on the target vehicle suspension characteristics, not only reducing the computational complexity, but also ensuring the accuracy and scalability of the control design. With the help of the model, the Skyhook-ADRC-FOSMC control method of the application can accurately reflect the coupling characteristics of the vehicle body, suspension and tire at the modeling level, thereby providing a unified modeling basis for subsequent disturbance estimation, fractional order sliding mode convergence and multi-control strategy weighted fusion. Compared with the prior art, the application avoids the control distortion problem caused by the dependence of a single control strategy on a simplified model, improves the dynamic response accuracy, model adaptability and control reliability under complex road excitation and parameter perturbation conditions, and effectively solves the problem of "mismatch between control strategy and actual vehicle dynamics, leading to difficulty in balancing robustness and comfort" in the background technology.

[0099] Third, in the preferred implementation, the application can estimate the vehicle body speed and total disturbance in real time under the condition of only measuring the vehicle body displacement by constructing an extended state observer (ESO) based on a 1 / 4 vehicle suspension model, and realize active compensation by combining position error and speed error feedback control. Thus, the application effectively solves the problem of relying on accurate models and difficulty in handling unknown disturbances for traditional PID and Skyhook control, while avoiding the real-time deficiency caused by estimation delay of ADRC in high-frequency working conditions. By tightly coupling the observation and compensation links, the application not only ensures the equivalent linearization of the control object, but also improves the adaptability to parameter perturbation and irregular road excitation, thereby realizing stable and reliable suspension control and higher ride comfort in complex working conditions.

[0100] Fourth, in the preferred implementation, the application introduces Caputo fractional operator based on traditional sliding mode control, constructs a sliding mode surface by performing fractional derivative operation on state error, and combines equivalent control law and saturated function switching control law, effectively alleviating the severe chattering problem commonly existing in integer order sliding mode control. This design not only maintains the advantages of fast convergence and strong robustness of sliding mode control, but also improves the adaptability to complex working conditions and parameter uncertainty through the "memory feature" of fractional operator, making the control process smoother and more stable. Compared with the prior art, the 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 smooth execution" in the background technology.

[0101] Fifth, in the preferred implementation, the application introduces a switching criterion based on the relationship between the vehicle body and tire speed between Skyhook control and ADRC-FOSMC control, and realizes continuous weighted fusion using Sigmoid function, so that the controller can automatically select the optimal control strategy under different working conditions. In the case of high-speed vibration of the vehicle body and the tire in the same direction, Skyhook control is given priority to enhance high-frequency vibration isolation; in the case of low-frequency or strong disturbance, ADRC-FOSMC is dominant to improve disturbance rejection and robustness. This design avoids the shortcomings of single control mode in the prior art that cannot balance comfort and stability, realizes dynamic coordination and smooth switching of multiple control laws, and thus ensures ride comfort, driving safety and control real-time performance under complex and variable road conditions, solving the contradictory problem of "insufficient high-frequency vibration isolation and difficult to suppress low-frequency disturbance" in the background technology.

[0102] Sixth, the Skyhook-ADRC-FOSMC active suspension control system proposed in the application combines modeling, disturbance estimation, fractional order sliding mode control and multi-strategy weighted fusion organically through a modular architecture, forming a complete closed-loop control system. The system ensures accurate expression of the suspension dynamics characteristics at the modeling level, and realizes real-time estimation and compensation of the total disturbance using ADRC at the control level, which strengthens the robustness to nonlinearity and uncertainty through the FOSMC fractional operator, while avoiding the severe chattering of traditional sliding mode; finally, through the weighted fusion of Skyhook and ADRC-FOSMC, the system can adaptively switch control strategies to cope with the different needs of low-frequency and high-frequency working conditions, realizing the 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. BRIEF DESCRIPTION OF DRAWINGS

[0103] Figure 1 The step flow chart of the active suspension control method based on Skyhook-ADRC-FOSMC of the application is shown in the figure.

[0104] Figure 2 The schematic diagram of the 1 / 4 vehicle active suspension model of the application is shown in the figure.

[0105] Figure 3 The structure block diagram of the Skyhook-ADRC-FOSMC active suspension control system of the application is shown in the figure. DETAILED DESCRIPTION

[0106] In order to make those skilled in the art better understand the technical solutions of the present application, the present application will be further described in detail below with reference to the accompanying drawings and examples.

[0107] The up, down, left, right, front and back orientation terms in the present application are established based on the positional relationship shown in the drawings. If the drawings are different, the corresponding positional relationship may also change accordingly, so it cannot be understood as a limitation on the scope of protection.

[0108] In the present application, the terms "mounting", "connection", "interface", "connection", "fixing" and the like should be understood broadly, for example, it can be fixed connection, it can also be detachable connection, it can also be integrally connected, it can also be mechanical connection, it can also be electrical connection or can communicate with each other, it can also be direct connection, it can also be indirect connection through an intermediate medium, it can be the interconnection of two components, or it can be the interaction relationship between two components. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0109] The application discloses a Skyhook-ADRC-FOSMC-based active suspension control method and system, which is not a simple superposition of existing control strategies, but systematically integrates the advantages of Skyhook control, active disturbance rejection control (ADRC) and fractional order sliding mode control (FOSMC) by establishing a 1 / 4 vehicle suspension dynamics model. Specifically, the Skyhook control is used to improve the body vibration suppression effect due to its simple engineering implementation and high-frequency vibration isolation performance; the ADRC estimates and compensates the uncertain disturbance caused by complex road conditions and nonlinear hydraulic actuators in real time through an extended state observer, thereby enhancing the adaptive and robust capabilities of the system; the FOSMC introduces a fractional order operator on the basis of the robustness of traditional sliding mode control, so that the control process has both smoothness and anti-chattering characteristics. On this basis, the application organically unifies the three types of control ideas through a continuous weighting coefficient mechanism based on a Sigmoid function, realizes the dynamic balance and seamless switching of multiple control strategies, and outputs optimal active control force under typical irregular road excitation conditions such as random, sinusoidal and convex, thereby comprehensively improving the damping performance and stability of the suspension system. The control framework forms an innovative solution that coordinates comfort and safety in view of key challenges such as nonlinear hydraulic actuators, complex road excitation and system parameter perturbation, and is particularly suitable for active suspension systems in intelligent vehicle and autonomous driving scenarios.

[0110] It should be noted that Skyhook-ADRC-FOSMC is the abbreviation of Skyhook Active Disturbance Rejection Fractional-Order Sliding Mode Controller, wherein Skyhook is the abbreviation of Skyhook control in the control field, and the Skyhook control is a typical damping control strategy in the vehicle suspension system, which assumes that there is a virtual damper between the vehicle body and the "sky", thereby simulating the "skyhook" effect in the controller, and the core idea is to suppress the body vibration through a virtual reference point to improve the comfort and handling stability of the vehicle. ADRC is the abbreviation of Active Disturbance Rejection Control, and the active disturbance rejection control is a new type of control theory, which can actively estimate and compensate the "total disturbance" in the case of inaccurate system model or strong disturbance, and the method realizes disturbance estimation through the introduction of an extended state observer (ESO, Extended State Observer) and dynamically compensates external uncertainty and internal modeling error. In the active suspension control, the ADRC can improve the robustness and adaptability to complex road disturbances of the system. FOSMC is the abbreviation of Fractional-Order Sliding Mode Control, and the sliding mode control is a robust control method that can maintain good control performance in the case of system parameter variation and uncertainty. The fractional-order sliding mode control introduces a fractional-order calculus operator on the basis of the traditional sliding mode control, so that the control law has more flexible dynamic response and stronger anti-chattering ability. In the application of active suspension, the FOSMC can reduce the "chattering problem" commonly seen in traditional sliding mode control while ensuring robustness. The Skyhook-ADRC-FOSMC controller of the application combines the damping performance of the Skyhook control, the strong disturbance suppression capability of the ADRC, and the robustness and anti-chattering characteristics of the FOSMC. The controller can improve the damping effect and stability of the vehicle active suspension system in complex road environments.

[0111] As shown in the accompanying drawings Figure 1 The application provides an active suspension control method based on Skyhook-ADRC-FOSMC, which comprises the following steps:

[0112] Step 1: configuring key parameters of a 1 / 4 vehicle suspension model based on the characteristics of a target vehicle suspension system, and establishing a dynamic equilibrium relationship model on this basis, and then defining state variables and output variables and constructing a 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 corresponding to a single wheel), suspension spring k s , tire stiffness k t , damper c0 and road excitation displacement x r (x r is the road displacement input under a single wheel, which is an external disturbance), to adapt to the regular specifications of a family sedan. Among them, the body mass m s represents the mass of 1 / 4 of the body, which determines the inertial response of the vehicle under road excitation. The greater the mass, the better the low-frequency vibration isolation performance, but the suspension response speed is reduced. The tire mass m u represents the mass of the tire connected to the suspension, which affects the high-frequency vibration characteristics of the vehicle and the stability of the tire in contact with the road. The smaller the unsprung mass, the better the tire followability, but the requirement for structural lightweighting is higher. The suspension spring k s represents the equivalent stiffness of the suspension spring, which determines the frequency characteristics of the body vibration. If the stiffness is too large, the comfort is reduced but the handling stability is improved; if the stiffness is too small, the comfort is enhanced but the body is prone to large swing. The tire stiffness k t represents the equivalent stiffness of the tire in the vertical direction, which determines the degree of high-frequency excitation transmitted from the road to the body. The greater the tire stiffness, the more obvious the road feel, and the comfort is reduced; if the stiffness is too small, the tire deformation is large, which easily damages the handling stability. The damper c0 represents the damping characteristics of the suspension damper, which controls the relative speed of the body and the tire, and determines the vibration decay speed of the system. If the damping is too large, the system response is stiff; if the damping is too small, the vibration decay is slow, and the comfort and safety are reduced. The road excitation displacement x r represents the main external disturbance source of the suspension system, including random road (consistent with ISO road spectrum), sinusoidal road (periodic excitation) and convex road (sudden disturbance), which directly acts on the tire end to form tire dynamic load changes, and then is transmitted to the body. These parameters are obtained through experiments or technical specifications and are used as the basis for model construction.

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

[0120] The dynamic balance relationship model of the 1 / 4 vehicle suspension system includes the body motion equation and the tire unsprung mass motion equation. The body motion equation is determined by the following formula:

[0121]

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

[0123]

[0124] In formula (1), (2): x s , xu , x r are the body vertical displacement, tire vertical displacement, road excitation displacement, respectively; are the body, tire vertical acceleration, respectively; are the body, tire velocity, respectively; u is the active control force (only corresponding to a single suspension unit), which is the core control quantity that the method needs to output.

[0125] Through the above dynamics, the mechanical action mechanism between the body, tire and road can be accurately described. In formula (1), the left side term represents the inertial force of the body (sprung mass), that is, the net force acting on the body. -k s (x s -x u ) represents the spring force term. When the body moves upward relative to the tire (x s >x u ), the suspension spring is compressed, generating a downward restoring force on the body; when the body moves downward relative to the tire, the spring is stretched, generating an upward restoring force on the body; this term embodies the adjustment effect of the suspension spring on the relative displacement between the body and the tire. represents the damping force term. When the body and tire velocities are inconsistent, the damper generates a reverse resistance to inhibit the relative velocity; for example, when the body sinks faster than the tire, the damper will generate an upward damping force to slow down the body sinking; this term is mainly used to dissipate energy and improve the comfort of body vibration. +u represents the active control force, which is provided by the active suspension actuator (hydraulic or motor) and 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 body under the joint action of the spring, damper and active control force.

[0126] In formula (2), the left side term represents the inertial force of the tire and the non-sprung mass part. +k s (x s -x u ) represents the spring force from the body, which causes the suspension spring to generate a restoring force due to the relative displacement between the body and the tire; for the tire, this force is in the opposite direction of the spring force in the body equation, embodying the "action and reaction". represents the damping force from the body, which is related to the relative velocity and is in the opposite direction of the corresponding term in the body equation, embodying the symmetry of the damping interaction between the body and the tire. -kt(x u -x r ) represents the tire's own elastic force, reflecting the tire's response to road irregularities as an elastic body. When the road is convex (x u <x r), the tire is compressed, generating an upward restoring force; when the road surface is concave, the tire is stretched, generating a downward restoring force, which embodies the "supporting property" of the tire interacting with the road surface. -u represents the active control force, opposite to the +u direction in the body equation, indicating that the control force not only acts directly on the vehicle body, but also acts on the tire system, ensuring the overall momentum conservation. Equation (2) describes the vertical motion of the tire mass under the action of the suspension spring force, damping force, tire stiffness force, and active control force.

[0127] Step 1.2: Equation (1) describes the dynamic response of the body comfort (riding experience), and equation (2) describes the tire's following ability and grip ability (driving safety) to road excitation. The two equations are coupled through the suspension spring and damper, and are jointly controlled by the active suspension actuator output u, and the road input x r The active control force u is realized by "applying to the body and reacting to the tire" to achieve compensation and optimization.

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

[0129] It should be noted that the state variable is a minimum variable set used to completely describe the dynamic characteristics of the system. In the vehicle suspension system, the state variables usually include position and velocity, because through these two types of variables, the kinematics and dynamics of the system can be reconstructed. The output variable is a key performance indicator derived from the state variable, which directly reflects 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, which links the evolution of the state variable to the input and output.

[0130] Since the road excitation x r It is difficult to measure directly, it is regarded as an external disturbance, the state variables and outputs are defined, and it is converted into a standard state space form:

[0131] The state variables include body displacement, body velocity, tire displacement, and tire velocity, which are the core state variables of the system control:

[0132]

[0133] The system output corresponds to the associated variables of the body vibration, suspension dynamic deflection, and tire dynamic load:

[0134]

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

[0136]

[0137] Y = CX + Du (6)

[0138] In formulas (5), (6): denotes the derivative of state variable, describing the trend of state change over time; A denotes the system matrix, embodying the coupling relationship within the suspension system (such as the vibration transmission characteristics between the vehicle body and the tire); B denotes the input matrix, describing the path of the control input u (active suspension output force) on the system state; d denotes the disturbance term, reflecting the influence of road excitation displacement x r on the system; C denotes the output matrix, linearly mapping the state variable to the system output; D denotes the direct-through matrix, describing the direct influence of the input on the output (usually zero or minimal in this model); X denotes the state variable (formula 3), describing the internal "true state" of the system; Y denotes the output variable, representing the system performance indicators (comfort, safety, stability).

[0139] It should be noted that formulas (3) and (4) are X and Y in physical sense, respectively, and the state variable X is directly taken from the physical quantity of the system, which has a clear physical meaning, describing the motion state of the vehicle body and the tire. The output variable Y is a set of performance indicators which are directly reflected in engineering as indicators of comfort, safety, and stability. The state space equations (5), (6) are the mathematical expressions of formulas (3) and (4), formula (5) organizes formula (3) into a state vector through matrices A, B, d, for linear algebra and matrix operations, and formula (6) organizes formula (4) into an output vector through matrices C, D, d, to convert complex dynamics into a standardized mathematical model, facilitating the application of control theory tools (such as pole placement, optimal control, robust control, etc.). The state space equations built by the present application establish a unified mathematical framework between state, input, and output, which is the core tool for the control method design of the present application.

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

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

[0142]

[0143] From the above matrix A, B, C, D, d:

[0144] Matrix A embodies the vibration coupling mechanism of the vehicle body and the tire, and describes the natural dynamic behavior of the suspension system under the action of stiffness, damping and mass without active control force input. Matrix A has four rows, among which, the first row: [0, 1, 0, 0] represents that the derivative of the body displacement is the body speed, which belongs to the kinematic relationship. The second row: -k s / m s represents the restoring force of the suspension stiffness on the vehicle body, when the vehicle body displacement x s increases, the suspension spring produces a downward restoring force to inhibit the vehicle body displacement; -c0 / m s represents the inhibitory effect of the damper on the vehicle body speed, when the vehicle body speed is large, the damper produces damping force to slow down the motion; +k s / m s represents the coupling effect of the tire unsprung mass displacement x u on the vehicle body, when the tire jumps up, it will "push the vehicle body" through the spring action, forming a positive effect. +c0 / m s represents the coupling effect of the tire speed on the vehicle body through the damper, the tire motion will be transmitted to the vehicle body through the damper, causing the vehicle body to change the corresponding speed. The third row: [0, 0, 0, 1] represents that the derivative of the tire displacement is the tire speed. The fourth row: +k s / m u represents the effect of the vehicle body displacement x s on the tire through the suspension spring, the vehicle body depression will stretch the suspension spring, and then exert a downward force on the tire. +c0 / m u represents the effect of the vehicle body speed on the tire through the damper, the vehicle body motion will make the damper produce damping force, and then affect the tire speed; -(k s +k t ) / m u represents the inhibitory effect of the suspension stiffness and the tire stiffness on the tire displacement x u , when the tire deviates from the equilibrium position, the stiffness force of the suspension spring and the tire itself will pull it back; -c0 / m u represents the inhibitory effect of the damper on the tire speed , the more intense the tire vibration, the greater the damping force, thereby attenuating the motion.

[0145] Matrix B determines the action path of the active suspension control force, which shows that the control force affects the vehicle body and the tire at the same time, but in opposite directions, which embodies the bidirectional action characteristics of the suspension actuator. In matrix B, the first row: 0 corresponds to the state variable x s= equation of body velocity, system input u does not directly act on body displacement or velocity, but indirectly through acceleration, hence zero here. Row 2: 1 / m s corresponding to body acceleration , equation of dynamics, control force u directly acts on body mass m s to influence body in acceleration form, coefficient 1 / m s reflects that the larger the body mass, the smaller the influence of control force on body acceleration. Row 3: 0 corresponding to equation of state variable , control force does not directly change tire displacement or velocity, but indirectly through tire acceleration, hence zero here. Row 4: -1 / m u corresponding to tire acceleration , equation of dynamics, active suspension control force acts on tire unsprung mass m u , sign is negative, reflecting the principle of “action-reaction”, when the actuator exerts an upward force on the body, the tire receives an equal and opposite downward force. As can be seen from matrix B, body and tire displacement are not directly affected by control force, while body acceleration and tire acceleration are directly affected by control force, and the directions are opposite.

[0146] Matrix C converts into output variables Y, which are the core indicators for evaluating vehicle performance (comfort, safety, suspension performance). In matrix C, the first row corresponds to body acceleration output, i.e. , which is caused by suspension stiffness difference and damping difference, and is a direct evaluation indicator of ride comfort, when the road or tire is disturbed, the size of the body acceleration determines the passenger's jolt. The second row corresponds to suspension travel (the difference between body displacement and tire displacement), “1” means that the output directly takes the body displacement x s , “-1” means that the tire displacement x u is to be subtracted, i.e. x s -x u , “0” means that the body velocity and tire velocity do not contribute to this output, the second row reflects the suspension cushioning capacity, if the deflection is too large, the suspension may be “dead top” or “compressed to the limit”, through x s -x u to ensure that the suspension works within a reasonable range and avoids mechanical damage. The third row corresponds to the displacement x u of the tire unsprung mass, the mathematical expression is , which directly selects the tire displacement in the state variable, reflecting the influence of road unevenness on tire position, and is a key indicator for measuring tire contact with the road and vehicle driving safety.

[0147] The matrix D indicates the immediate effect of the active suspension control force on the body acceleration, and the change of the control force can immediately change the ride comfort. In the matrix D, the first row: 1 / m s The body acceleration in the corresponding output The dynamics equation of the body acceleration, indicates that the control force u will directly act on the body mass m s , and immediately change the body acceleration, the coefficient 1 / m s represents that the greater the body mass, the smaller the effect of the control force on the body acceleration. The second row: 0 corresponds to the suspension dynamic displacement x s -x u , the control force u will not directly change the relative displacement of the suspension, but indirectly affect through the dynamics coupling of the system (the effect of the matrix A, B). The third row: 0 corresponds to the tire dynamic load (x u -x r ) or the tire dynamic performance index, the control force has no immediate direct effect on the output, but indirectly transmits the influence by changing the tire acceleration and displacement.

[0148] The disturbance term d describes how the road unevenness affects the tire and then transmits to the body, which is the external excitation that the active suspension system must deal with. In the matrix of the disturbance term d, the first row: 0 corresponds to the equation of the state variable , the road input will not directly affect the body displacement or speed, but indirectly affect through the tire-suspension transmission, so it is zero. The second row: 0 corresponds to the body acceleration The road input has no direct effect on the body acceleration, and the acceleration of the body is mainly derived from the transmission of the suspension force and the control force, so this row is also zero. The third row: 0 corresponds to the equation of the state variable , the road input has no direct effect on the tire speed, but affects the acceleration of the tire through the elastic effect of the tire stiffness, so it is also zero. The fourth row: corresponds to the equation of the tire acceleration , which indicates that the road excitation displacement x r is transmitted to the tire unsprung mass m t through the tire stiffness k u , directly affecting the tire acceleration, thereby becoming the external disturbance of the system. The coefficient embodies that the greater the tire stiffness k t , the more significant the effect of the road unevenness on the tire acceleration, and the greater the tire unsprung mass m u , the weaker the effect of the road disturbance on its acceleration.

[0149] Step 2: Construct the ADRC controller based on the 1 / 4 vehicle suspension model, select the body displacement as the measurement output, determine the controlled object channel as the channel of the control force acting on the body acceleration according to the body motion equation, generate the expected displacement reference and the expected speed reference through the tracking differentiator, estimate the body displacement, the body speed and the total disturbance including the road excitation online using the extended state observer, obtain the intermediate control quantity through error feedback of the expected reference quantity and the estimated quantity, and output the final control force based on the object channel gain to compensate for the estimated total disturbance, so as to realize the real-time suppression of the total disturbance and the 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, realize the smooth tracking of the body displacement and speed and the acceleration suppression, and thus improve the comfort and road adhesion retention capability.

[0151] It should be noted that the ADRC controller (Active Disturbance Rejection Control) is a kind of method that does not depend on the accurate model of the controlled object, estimates and offsets the "total disturbance" online to realize robust control. It unifies all uncertain items, such as parameter changes, unmodeled dynamics, external disturbances (such as road fluctuations), and even part of the nonlinearities, as "total disturbance", estimates and compensates them. The ADRC controller is composed of TD (Tracking Differentiator), ESO (Extended State Observer) and control law / NLSEF (Nonlinear State Error Feedback). TD is used to change the expected signal into a smooth trajectory and give its derivative, avoiding direct numerical differentiation to amplify noise, and outputting the reference displacement and the reference speed. ESO estimates the key states of the system (such as position and speed) and an extended state under the condition of only measuring the output. The extended state is the estimated value of the "total disturbance". The control law generates a "nominal control quantity" using the state error, and then compensates for the disturbance estimation given by ESO.

[0152] Specifically, step 2 includes:

[0153] Step 2.1: Determine the parameters of the second-order tracking differentiator (TD) based on the core parameters of the 1 / 4 vehicle suspension model determined in step 1.1, and take y=x s as the input of the second-order tracking differentiator and generate a smooth tracking trajectory, output the displacement reference r a and the speed reference r b .

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

[0155] According to step 1.1, the core parameters of the 1 / 4 vehicle suspension model are known as {m s ,m u ,k s ,kt,c0}, wherein m s ,k s ,c0 determine the frequency and attenuation of the first-order modal of the vehicle body, m u ,kt dominate the high-frequency response of the tire-unsprung channel, and these parameters collectively provide physical constraints for TD tuning. According to the body dynamics formula (1) of step 1.2, the body acceleration is determined by x s and together with the control force, but the directly measured x s contains noise, and is difficult to obtain reliably, so a smooth reference is needed to be generated by TD for subsequent observation and control. The output variable set defined in step 1.3 contains the body displacement x s and its differential directly related to Therefore, in step 2.1, y=x s is selected as the TD input from the set, and the output gets a smooth displacement trajectory r a , a speed trajectory r b , and a consistent system output structure that reduces noise propagation.

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

[0157]

[0158] In the formula: r a is the smooth position reference output by TD, corresponding to the reference trajectory of the body displacement; r b is the smooth speed reference output by TD, corresponding to the expected body speed; R is the tracking speed factor, which determines the convergence speed and anti-interference ability of TD, R>0; sgn(·) is the sign function; the dimensions of r a and r b are consistent with x s and respectively, facilitating the connection with the body motion equation of step 1.2 or the output y=x s of step 1.3; is the rate of change of the expected body speed r b , i.e., the expected acceleration; r a -x sthe position error, i.e. the difference between the estimated position of TD and the true measured reference; a velocity-dependent nonlinear "braking term" when r b when moving fast towards the target, the term pushes the "switching surface" back in time, avoiding overshooting.

[0159] The only tuning parameter R affects both the acceleration upper limit of formula (8) and the response speed of formula (7). When R is increased, the convergence is faster, but it is more sensitive to noise. When R is reduced, it is smoother and better at resisting noise, but the tracking is slower. Therefore, when R is selected, it needs to match the physical characteristics given in step 1.1. First, determine the body main modal angular frequency ω b and the wheel hop angular frequency ω ω The body main modal angular frequency ω b is dominated by m s , k s , the smaller m s or the larger k s , the higher ω b . The wheel hop angular frequency ω ω is dominated by m u , kt, the smaller m u or the larger kt, the higher ω ω . Let the equivalent bandwidth ω r of TD be taken as ω r ∈ [0.6, 1]· ω b , and ω r ≤ 0.35 ω ω , ω r ∈ [0.6, 1]· ω b is used to ensure that the body main modal is followed, and ω r ≤ 0.35 ω ω is used to leave enough margin for isolation from the high frequency of wheel hop. Accordingly, R = ω r 2 .

[0160] When the damping c0 is small (the body vibration decays slowly), to suppress noise and overshoot, ω r is reduced by 10-30% (equivalent to reducing R), and when the damping is large (the response is stiff), ω r may be slightly increased to avoid tracking lag. When the random / rough or convex mutation road excitation x r has a stronger high frequency component, ω r is set conservatively, and ω r is reduced by 10-30% based on the reduction of damping c0. The force path of the active suspension actuator (hydraulic or motor) to the body is given by formula (1) , the control force directly acts on the body and is in reaction to the tire; the corresponding body acceleration channel gain 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 we estimate ω 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] where f(·) is the part of the body acceleration determined by the suspension spring and damping coupling terms, ω t is the road displacement x r and the influence of the vehicle body dynamics is transferred to the body and the disturbances such as parameter uncertainties, etc. t denotes the total disturbance; is the input gain of the object channel.

[0167] The extended state observer (ESO) of the present application adopts a third-order linear structure:

[0168]

[0169] where: are the estimated values of the body displacement x s and the body speed ; and is the total disturbance estimate after the model coupling terms and external road excitation are summarized; k1, k2, k3 are observer gains determined by pole placement method to ensure the convergence of the estimate; b is the ADRC control gain associated with the 1 / 4 vehicle model parameters; x s is the actual body displacement collected by the displacement sensor.

[0170] The process of the extended state observer online estimating the body displacement, the body speed and the total disturbance of the system includes: in formula (10), the input y = x s and the control force u are output in real time by the extended state observer (ESO) (body displacement estimate), (body speed estimate), (total disturbance estimate of the system).

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

[0172] Step 2.3: the reference trajectory (r a , r b ) obtained in step 2.1 and the state and disturbance estimates output by the extended state observer in step 2.2 are used to calculate the intermediate control amount u0 according to the error feedback law, and the body channel gain b = 1 / m s determined in step 1 is used to compensate for the estimated total disturbance to obtain the final control force u A to realize the real-time suppression of the total disturbance of the system and the linearization of the object.

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

[0174]

[0175] Determine the intermediate control amount u0:

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

[0177] where k p is the proportional and derivative gain of the position loop, k p = ω c 2 ; k d is the proportional and derivative gain of the velocity loop, k d = 2ζω c ; ω c is the desired dominant frequency of the closed loop, ω 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] Further, determine the final control force u A :

[0179]

[0180] First, use to offset the "total disturbance" effect of the object on , and then use b to map the "desired nominal acceleration" u0 to the force that the actuator needs to apply, achieving object equivalent linearization and real-time disturbance rejection.

[0181] Step 2 achieves smooth tracking and disturbance observation compensation by constructing an ADRC. The second-order TD generates a smooth trajectory for the reference signal, suppresses noise and input mutations; the linear ESO estimates the total disturbance and the displacement and velocity of the vehicle body online; and then the disturbance compensation forms the control law, so that unknown internal and external disturbances and parameter uncertainties are equivalent to be eliminated. This makes the tracking smoother, the response faster, the robustness and stability improved, the suppression of strong disturbances such as road excitation more effective, and the overall ride comfort and control accuracy improved.

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

[0183] The purpose of step 3 is to introduce a fractional calculus operator through the FOSMC sliding mode control module, introduce a fractional operator in the control law through the Caputo fractional derivative definition, and consider robustness and smoothness to avoid the common phenomenon of severe chattering 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 used to unify the calculation logic of fractional differentiation and integration, providing an operation tool for subsequent fractional derivative calculation of state error. The Caputo fractional calculus operator formula is as follows:

[0187]

[0188] In the formula: is the fractional calculus operator, indicating a-order differentiation of f(t); a is the fractional order (which can be determined by simulation or optimization in engineering, considering robustness and smoothness); D -(m-a) is the fractional integral operator, and the integral order is m-a, which is combined with the integer-order derivative to form the Caputo definition; m is the minimum integer, satisfying m-1 is the normalization coefficient; is a convolution-type memory integral that weights and accumulates information in the time period x∈[a,t] to the current time t, and α is the lower limit (initial time), reflecting the start time of memory, which is usually taken as the system simulation or sampling start time α=t0; f (m )(x) is the m-order integer derivative of f, taken at time x; (t-x) m-a-1 is the kernel function, which determines the weight distribution of historical samples.

[0189] Step 3.2: Based on the expected displacement trajectory r a , the expected speed trajectory r b and their respective real-time estimates and obtained in step 2, take the displacement error to construct the state error, and use the Caputo operator in step 3.1 to calculate the fractional derivative of the state error as the sliding mode surface input.

[0190] Based on the expected displacement trajectory r a , the expected speed trajectory r b output by TD in step 2, and the vehicle body displacement estimate Vehicle body speed estimation Accordingly, displacement error e is obtained p and speed error e v :

[0191]

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

[0193] If the measured quantity is used directly, the formulas (16), (17) are written as e p = x - r a ,

[0194] In order to construct the fractional order sliding mode surface, since the control output is taken as the vehicle body displacement y = x s in step 2, and the TD and ESO are designed according to it, therefore, the displacement error is taken as the state error to keep consistency with step 2, and the displacement error is taken as the main variable, and then the Caputo fractional order derivative is used to introduce the speed information, so as to improve the robustness and adjustability.

[0195] The state error is determined by the following formula:

[0196] e = x - r a (18)

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

[0198]

[0199] The Caputo operator in step 3.1 is used to do fractional order differentiation on the state error, and the formulas (18), (19) are substituted into formula (15), the order is 1-a, 0

[0200]

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

[0202] Fractional derivative of state error D 1-a e(t) and e = x - r a Sliding surface construction for step 3.3.

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

[0204] Sliding surface is:

[0205]

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

[0207] The convergence objective of 1 / 4 vehicle suspension controlled object (vehicle body vertical channel, input gain b = 1 / m s ) is embodied by formula (21): the system state reaches and remains at S = 0 in a finite time.

[0208] Step 3.4: Based on the object channel and vehicle body channel gain b = 1 / m s of step 1, design a sliding mode control law, and decompose the sliding mode control law into an equivalent control law and a switching control law.

[0209] Sliding surface according to step 3.3 Take its time derivative

[0210]

[0211] As can be seen from formula (19), is the vehicle body speed, r b is the desired speed trajectory, corresponding to the vehicle body speed error, so corresponds to the vehicle body acceleration error. Further, the "vehicle body vertical channel" of the controlled object formula (9) is substituted into , and formula (20) D 1-a e(t) is used to write the derivative of the sliding surface as a linear combination of known terms and control input u:

[0212]

[0213]

[0214] To satisfy the sliding mode invariance condition, the invariance condition is taken on the sliding surface The equivalent control law can be solved as:

[0215]

[0216] The fractional order integral operator I is applied to both sides of equation (24) a Using the identity under zero initial condition: I a D 1-a g = g, And the total disturbance and known items estimated by ESO are combined as The following can be obtained:

[0217]

[0218] It should be noted that is a specific physical quantity, is to compress complex physical variables into a general function form, where y = x s , that is, the body displacement x s is expressed by the generalized output y; that is, the body speed x s is expressed by the generalized output ; u is a parameter set, which covers t is introduced to represent the time-varying of system dynamics and external excitation.

[0219] The switching control law is obtained by replacing the sign function with a saturation function to weaken chattering:

[0220] u sw = -k s ·sat(S / δ) (26)

[0221] Where: k s is the switching gain, k s > 0, the larger the value, the faster the reaching speed and the stronger the robustness to disturbance, but the chattering may be intensified, and vice versa, to ensure that the state quickly approaches the sliding surface; sat(·) is a 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 approaching accuracy, and the effect of chattering suppression needs to be balanced.

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

[0223] The final control force of FOSMC is:

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

[0225] The final control force of the FOSMC obtained has dynamic smoothness and strong robustness.

[0226] Step 4: The Skyhook control force is constructed, and the switching criterion of the Skyhook and the ADRC-FOSMC is constructed with the vehicle body speed and the relative speed of the vehicle body and the tire, and a continuous weight is obtained by mapping through the Sigmoid function, according to which the two control branches are weighted and fused to generate the final active control force as the control input of the controlled system channel.

[0227] It should be noted that the Skyhook (skyhook damper) is to constrain the vehicle body as if it is connected to a damper in the sky / inertial system, and to inject equivalent damping into the suspension to suppress the vibration of the vehicle body by using the absolute speed feedback of the vehicle body. The ADRC-FOSMC (fusion of active disturbance rejection and fractional order sliding mode) combines the "online estimation and cancellation of total disturbance" (ESO) of ADRC and the "fractional order sliding mode robust convergence" of FOSMC, which is both anti-disturbance and strong robustness.

[0228] The purpose of step 4 is to use the high-frequency vibration isolation advantage of Skyhook through the Skyhook-ADRC-FOSMC weighted fusion module, to realize multi-strategy seamless switching by combining the continuous weighting coefficient, and to 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 body speed is used as the feedback to generate the damping control force, and the Skyhook control law is obtained.

[0231] It should be noted that the Skyhook damper (Skyhook damper) is to connect a damper between the vehicle body and a "fixed point in the sky" (inertial reference frame) in an ideal case, and to use the absolute speed of the vehicle body to generate a damping force, and to optimize high-frequency vibration isolation by suppressing the absolute speed of the vehicle body to directly suppress the vehicle body acceleration.

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

[0233]

[0234] The active suspension actuator is a pair of forces acting on the vehicle body and the tire, so the F sky is directly taken as the control target force.

[0235]

[0236] where, u sky is the Skyhook control force; c sky is the Skyhook damping coefficient, which is larger in high-frequency working conditions to enhance the vibration isolation effect; is the vertical velocity of the vehicle body, which is estimated by the ESO.

[0237] The Skyhook control law is to "equivalent the damper connected to the inertial system" to the active suspension, and its design is based on the principle of absolute velocity feedback damping and acceleration suppression. In the "high-frequency scene" where the vehicle body and the tire vibrate in the same direction at high speed, the vibration isolation and the reduction of jitter are improved.

[0238] Step 4.2: Construct the switching criterion of Skyhook and ADRC-FOSMC with the vehicle body speed and the relative speed of the vehicle body and the tire, and map the switching criterion to a continuous weight through the Sigmoid function.

[0239] Vehicle body speed estimation based on ESO input in step 2 Tire speed estimation Construct the switching criterion:

[0240]

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

[0242]

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

[0244] When s(t)>0 (the vehicle body and the tire speed are in the same direction, high-frequency vibration scene), activate the Skyhook high-frequency vibration isolation; when s(t)<0 (low-frequency vibration scene), activate the ADRC-FOSMC anti-disturbance and smooth control. 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; s(t)=0, β(t)=0.5.

[0245] Finally, it is used to weight and fuse the two control branches (Skyhook and ADRC-FOSMC), and which branch corresponds to β or 1-β depends on the given weighting formula. For example: if u=βu sky +(1-β)uAF The greater the value of β, the more biased towards Skyhook, and vice versa if the order is reversed. Wherein, u AF is the ADRC-FOSMC fusion control force, which combines the "virtual control" given by the fractional order sliding mode control and the disturbance compensation of the ADRC, and then calculates the actuator force 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 strategy, and output the final active control force.

[0247] Step 4.3 includes:

[0248] Step 4.3.1: Calculate the ADRC-FOSMC fusion control force.

[0249] Take u F as the intermediate control amount u0 of ADRC, and further compensate the disturbance to obtain the ADRC-FOSMC composite control force u AF , which is as follows:

[0250]

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

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

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

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

[0255] Embodiment

[0256] A medium-sized family car is taken as the target vehicle, and the Skyhook-ADRC-FOSMC active suspension control method proposed by the present application is adopted, and the specific implementation process is as follows:

[0257] Vehicle parameter setting:

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

[0259] Sprung mass m s = 320 kg (the total vehicle mass is about 1280 kg, and 1 / 4 is taken); unsprung mass m u = 45 kg; suspension stiffness k s= 16000 N / m; tire stiffness kt= 190000 N / m; damping coefficient c0= 1200 Ns / m; road excitation input x r Take sinusoidal disturbance: x r = 0.015 sin(8t) m.

[0260] On this basis, the dynamic balance relationship model of the vehicle suspension is established, in which the body equation and the tire equation are respectively:

[0261]

[0262] State space model construction:

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

[0264] Get the system state space equation: Y = CX + Du.

[0265] Wherein:

[0266]

[0267]

[0268] The disturbance term d is:

[0269]

[0270] ADRC controller design:

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

[0272] ESO (extended state observer) pole configuration: take the pole at -20, get the observer gains k1, k2, k3.

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

[0274] Final ADRC control force:

[0275] When displacement error el increases by 1 m, the controller outputs about 10240 N of adjustment force; when speed error e2 increases by 1 m / s, it outputs about 2893 N of adjustment force; ESO estimates disturbance increases by 1 m / s 2 , the output force is corrected by -320 N.

[0276] FOSMC fractional order sliding mode controller:

[0277] Sliding surface Where e = x - r a ,

[0278] Equivalent control law This embodiment takes λ takes 10, a takes 0.8. For practical application, f(·) is estimated by the "total disturbance" of ESO Thus we get:

[0279]

[0280] Where, Given by ESO in real time.

[0281] Switching control law

[0282] Where sat(·) is a saturation function; δ takes 0.01; k s takes 500.

[0283] FOSMC final control force

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

[0285] Fusion control strategy:

[0286] Switching criterion is Sigmoid weight function (take sensitivity coefficient k = 0.5):

[0287] ADRC-FOSMC fusion control force is

[0288] Get the final active control force: u = β(t) · u AF + [1-β(t)]·usky .

[0289] Through the above steps, the simulation results show that the body acceleration peak is reduced by more than 30%, the ride comfort is obviously improved, the suspension deflection is controlled within 50mm, the mechanical limit impact is avoided, and the tire dynamic load fluctuation is reduced and the road adhesion is improved. The Skyhook-ADRC-FOSMC fusion control in the embodiment can realize adaptive switching between low-frequency large vibration and high-frequency road excitation, and can take into account comfort and safety.

[0290] As shown in Figure 3 , the application also provides a Skyhook-ADRC-FOSMC-based active suspension control system, which defines the force and motion relationship of the suspension system through a 1 / 4 vehicle suspension dynamics modeling module, and provides a basic model for subsequent controller design. The system comprises:

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

[0292] ADRC disturbance estimation and compensation module: connected with the modeling module, used to build an active disturbance suppression controller based on the state space model, the module comprises:

[0293] tracking differentiator, used to generate smooth expected displacement reference and speed reference according to body displacement measurement;

[0294] extended state observer, used to estimate the body displacement, body speed and total disturbance of the system including road excitation online;

[0295] control law unit, used to perform error feedback on the expected reference and the estimated quantity, generate an intermediate control quantity, and compensate for the estimated total disturbance based on the body channel gain, and output the final control force;

[0296] FOSMC sliding mode control module: connected with the ADRC disturbance estimation and compensation module, used to build a state error based on the position error and speed error, calculate the fractional order derivative of the state error using Caputo fractional calculus operator, and build a sliding mode function based on the state error and its fractional order derivative, decompose the sliding mode control law into equivalent control law and switching control law, and superimpose the two to form a fractional order sliding mode control force;

[0297] The Skyhook-ADRC-FOSMC weighted fusion module is connected with the FOSMC sliding mode control module and the ADRC disturbance estimation and compensation module, and is used for constructing a Skyhook control force, and constructing a switching criterion of the Skyhook and the ADRC-FOSMC based on the vehicle body speed and the relative speed of the vehicle body and the tire, mapping the switching criterion into a continuous weight through a Sigmoid function, weighting the Skyhook control force and the ADRC-FOSMC control force, and outputting a final active control force as a control input of a 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, and the obtained active control force is applied to the suspension two mass blocks through an actuator, so that the effective suppression of the vehicle body vibration and the cooperative satisfaction of the suspension / tire performance constraints are realized under the conditions of complex road excitation and parameter uncertainty.

[0299] Figure 3 In the embodiment, the Skyhook-ADRC-FOSMC-based active suspension control system estimates the system state and the total disturbance through an observer ESO-MIMO in ADRC (active disturbance rejection control); two sets of control laws, namely, a Skyhook and a FOSMC (fractional order sliding mode), are prepared; a switch selects or fuses the two sets of control laws according to a strategy to obtain a final control force u; the control force u is applied to a 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 active suspension model, the input of which is the output u of the fusion device, and the output of which is x s , which is a controlled object, and the output of which is given to the observer and the fractional order sliding mode controller. The red dashed box represents the ADRC, and the two ESO-MIMOs are extended state observers-multi-input multi-output. The input signal of the ESO-MIMO on the left side (the observer of the ADRC) is the system measurable output and the control quantity related information, and the output signal is the estimated total disturbance , which estimates the vehicle body side state and the total disturbance, and provides more complete feedback and disturbance compensation for the controller. The input signal of the ESO-MIMO on the right side (the wheel side observer) is x u , and the output signal is , which is used to supplement the state estimation of the wheel unsprung mass, improve the system state observation, and facilitate subsequent control or monitoring. The two ESO-MIMOs cooperatively observe different parts of the same suspension system.

[0301] TD is a tracking differentiator, the input of TD is road excitation displacement x r , the output of TD is tracking signal r a , r b Skyhook Controller is a skyhook controller, the input of Skyhook Controller is the output of left ESO-MIMO (estimated state of vehicle body ), the output of Skyhook Controller is u sky FOSMC is a fractional order sliding mode controller, the input of FOSMC is r a , r b , the output of FOSMC is u AF , FOSMC is based on strong robust control of fractional order sliding mode, compensates with , improves anti-interference ability, and tracks reference with r a , r b Switch is a switch or a fusion device, the input of Switch is u AF , u sky , the output of Switch is u, according to a strategy (such as a working condition, a performance index or a criterion), the actual actuator force is obtained by weighting between two control laws. Figure 2 The final control force u acts on the Switch switch or fusion device of s (the element with a circular arrow mark between the sprung mass block m u and the tire mass m u ), finally, the Switch based on Sigmoid continuous weight weights the skyhook control force and the ADRC-FOSMC control force, and the obtained active control force is applied to the suspension between the two mass blocks (the sprung mass block m s and the tire mass m u ), so that the effective suppression of the vehicle body vibration and the cooperative satisfaction of the suspension and tire performance constraints are realized under the conditions of complex road excitation and parameter uncertainty.

[0302] The active suspension control method and system based on Skyhook-ADRC-FOSMC of the application break through the bottleneck of the prior art, and can realize the cooperative optimization of robust anti-interference, smooth response and real-time control under complex and changeable road working conditions. By introducing the disturbance observation and compensation mechanism of ADRC, the uncertain disturbance caused by random jolting, sinusoidal fluctuation and sudden convex obstacle is effectively suppressed; in combination with fractional order sliding mode control (FOSMC), the chattering problem of traditional sliding mode is weakened while the rapid response and strong robustness are maintained, and the service life of the actuator is prolonged; and through the high-frequency vibration isolation characteristic of Skyhook control, the vehicle body acceleration suppression ability is enhanced, and the ride comfort is improved. Finally, the application realizes the comprehensive improvement of comfort, stability and safety, ensures that the vehicle can maintain excellent vibration isolation and driving stability performance under low-frequency and high-frequency working conditions, and takes into account real-time performance and engineering realizability.

[0303] The foregoing is merely illustrative of the embodiments of this application, and various modifications can be made by those skilled in the art without departing from the spirit or scope of the application. Therefore, the scope of the application is not intended to be limited to the details of the above described embodiments but can be practiced with variations within the scope and spirit of the appended claims. Any reference citations herein are incorporated by reference in their entirety. No reference is cited with any particular citation number to limit 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 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.

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 (m) s Tire mass m u Suspension springs k s Tire stiffness k t Damper c0; 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 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. 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: Y = CX + Du 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 = 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 ; 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; Controlled standard form, i.e., the object channel is: 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; The extended state observer is: 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; 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; Ultimate control u A for: 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.

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 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. The state error is e = xr a ; The fractional derivative of the state error is: 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... Step 3.3: Define the sliding surface based on the state error and its fractional derivative. The sliding surface is: 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; 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; The equivalent control law is: 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; The switching control law is: you sw =-k s ·sat(S / d) 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. 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 F =in sw +in equ In the formula: u sw To switch control laws; u equ 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 β∈[0,1]: In the formula: β(t) 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: 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. 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: u=β(t)·u AF +[1-β(t)]·u sky 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 sky 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 smooth desired displacement and velocity references based on vehicle body displacement measurements. 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. 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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