An active air suspension adaptive sliding mode control method based on disturbance observer

Abstract

The present application relates to a kind of active air suspension adaptive sliding mode control method based on disturbance observer.It includes the following steps, S1, based on thermodynamics and fluid mechanics theory, the nonlinear modeling of each component of additional air chamber air spring is carried out;S2, linearization is handled to air spring model, the equivalent stiffness and equivalent damping of system are obtained;S3, the characteristic parameters of system are determined and active suspension model is established;S4, on the basis of suspension model, the influence brought by parameter uncertainty is considered;S5, disturbance observer is designed to observe parameter uncertainty disturbance change;S6, adaptive sliding mode control method is designed based on disturbance observer.The present application provides a kind of adaptive sliding mode control method based on disturbance observer on the basis of additional air chamber air suspension model, and disturbance observer can estimate the parameter uncertainty of system and disturbance change, and the control effect of active suspension control is improved by considering the adaptive sliding mode controller of disturbance.

Description

Technical Field

[0001] This invention belongs to the field of active control of vehicle air spring suspension, and in particular, it relates to an active air suspension adaptive sliding mode control method based on a disturbance observer that addresses parameter uncertainties and external disturbances. Applying this method to the active control of actual vehicle air spring suspension can help improve the ride comfort and safety of the vehicle. Background Technology

[0002] As a crucial component connecting the vehicle body and tires, the suspension system significantly impacts a vehicle's ride smoothness, comfort, and safety. Vehicles equipped with air suspension systems achieve lower natural vibration frequencies, exhibiting minimal frequency shifts in body vibration under varying loads and maintaining a relatively constant vehicle height, resulting in superior ride smoothness and safety.

[0003] Due to structural limitations, it is difficult to further improve the performance of traditional air suspension. In order to cope with the complex application environment and various technical requirements, active air suspension design with additional air chambers has been gradually adopted in engineering practice.

[0004] While active air suspension with additional air chambers offers significant advantages, several complex issues remain to be addressed. Automotive active suspension systems are affected by factors such as strong nonlinearity, external disturbances, and parameter uncertainties. Therefore, complex dynamic models are needed to accurately evaluate the suspension system. Furthermore, conventional control algorithms struggle to meet the ever-increasing performance requirements of suspension systems. Summary of the Invention

[0005] This invention addresses technical problems in prior art by providing an adaptive sliding mode control method for active air suspension based on a disturbance observer. It utilizes an air spring with an additional air chamber as the primary actuator of the air suspension while considering the uncertainties in air spring parameters and the impact of external disturbances on suspension performance. A disturbance observer is used to offset mismatch uncertainties in the system. By designing a new sliding surface based on disturbance estimation, even in the presence of mismatched disturbances, the system state is asymptotically driven to the desired equilibrium through sliding motion along the sliding surface. Furthermore, a discontinuous control law with high-frequency switching gain is designed to force the initial state to reach the designed sliding surface, thereby ensuring better suspension ride comfort and safety.

[0006] The technical solution adopted by this invention to solve the technical problems existing in the prior art is: an adaptive sliding mode control method for active air suspension based on a disturbance observer, comprising the following steps:

[0007] S1. Based on thermodynamics and fluid mechanics theory, nonlinear modeling is performed on the main gas chamber, throttling element and auxiliary gas chamber;

[0008] The load-bearing capacity of an air spring is related to the force exerted by the air inside the main air chamber, and the magnitude of this force is related to the air pressure and the effective area of ​​the main air chamber. In an air spring, the force F generated by air compression is expressed as:

[0009]

[0010] In the formula: -Gas pressure in the main air chamber

[0011] -Effective area of ​​the main air chamber of the air spring.

[0012] For the air in the auxiliary air chamber air spring, it mainly consists of nitrogen and oxygen, and its pressure is generally no greater than 2 MPa, so it is considered an ideal gas. Considering the compressibility of air and the continuity of the airflow mass flow rate, the relationship between the gas mass flow rate in the main air chamber and the gas pressure and volume change is as follows:

[0013]

[0014] In the formula, -Main gas mass flow rate in the main gas chamber

[0015] k is the adiabatic index; for a gas undergoing an adiabatic process, k = 1.4.

[0016] R - Universal air constant,

[0017] T - Temperature of the gas inside the air spring.

[0018] - Initial pressure inside the air spring.

[0019] - Main air chamber volume

[0020] The rate of change of gas pressure in the main chamber is:

[0021]

[0022] The pressure change rate of the main chamber consists of two parts: the pressure change caused by the change in the mass of compressed air in the main chamber and the pressure change caused by the change in the effective volume of the main chamber.

[0023] The air mass flow rate on the auxiliary air chamber side is similar to that of the main air chamber of the air spring. The difference is that the auxiliary air chamber is often made of rigid materials, and its volume is a fixed value that does not change.

[0024] Right now:

[0025]

[0026] In the formula, -Additional air chamber volume

[0027] The mass flow rates of the gas in the main chamber and the accessory chamber are the same in magnitude but opposite in direction, satisfying the following:

[0028]

[0029] When the air spring in the auxiliary air chamber is working, the compressed air in the auxiliary air chamber is also compressible and conforms to the continuity relationship of airflow mass flow rate. Combining formulas (2), (3), (4), and (5), the rate of change of gas pressure in the auxiliary air chamber is:

[0030]

[0031] In the formula, -Additional chamber internal pressure.

[0032] Throttling elements are key components for adjusting the stiffness of air spring systems and achieving air damping. Common throttling elements include throttling orifices and throttling tubes, which control the gas mass flow rate between the main air chamber and the auxiliary air chamber. By changing the opening of the throttling element, the stiffness and damping of the air spring system are adjusted, thereby changing the natural frequency of the sprung mass vibration and giving the vehicle a good ride comfort.

[0033] The gas mass flow rate through the throttling orifice is expressed by the following formula:

[0034]

[0035]

[0036]

[0037]

[0038] In the formula:

[0039]

[0040] - Effective flow area of ​​the throttling orifice

[0041] Compared with the actual throttling orifice area

[0042] The ratio of the smaller pressure at both ends of the orifice to the larger pressure is called the pressure ratio. 0.518 represents the critical pressure ratio. When the pressure ratio is greater than the critical pressure ratio, it is called subsonic flow. When the pressure ratio is less than the critical pressure ratio, it is called supersonic flow or congested flow. Equation (7) is the air mass flow rate during subsonic flow through the orifice, and Equation (8) is the air mass flow rate during supersonic flow.

[0043] S2. Linearize the models of each part of the air spring and derive the equivalent stiffness and equivalent damping of the air spring suspension system.

[0044] According to the Taylor expansion formula, ignoring higher-order terms, the pressure change rates of the main chamber and the auxiliary chamber can be obtained using the first-order Taylor expansion formula:

[0045]

[0046]

[0047] Given the initial pressures, initial volumes, and effective area of ​​the main and auxiliary air chambers of the air suspension, the relationship between mass flow rate and the pressures of the two chambers is obtained using equations (9) and (10). The model is then linearized near the suspension equilibrium point using the wire cutting method.

[0048]

[0049] In the formula: This is the orifice resistance coefficient.

[0050] When air flows between the main air chamber and the auxiliary air chamber, it needs to pass through a throttling damping orifice. The throttling damping orifice obstructs the airflow, generating a damping force. Therefore, the air spring forms an equivalent structure of an ideal spring and a damper connected in parallel. From equations (1), (9), (10), and (11), the equivalent stiffness of the spring is obtained as:

[0051]

[0052] Similarly, the equivalent damping is expressed as:

[0053]

[0054] In the formula: - Orifice area

[0055] - The density of the gas inside the air spring.

[0056] The equivalent stiffness and equivalent damping of an air spring vary around the system's equilibrium point; therefore, the equivalent stiffness and equivalent damping can be rewritten in the following form:

[0057]

[0058] In the formula and These represent the stiffness and damping at the equilibrium point of the air spring in the additional air chamber, respectively.

[0059] Represented as:

[0060]

[0061]

[0062] and These represent the changes in stiffness and damping as they deviate from the equilibrium point, respectively.

[0063]

[0064]

[0065] S3. Define the characteristic parameters of each part of the system and establish a two-degree-of-freedom 1 / 4 active suspension model;

[0066] A dynamic model of a two-degree-of-freedom air spring suspension with an additional air chamber is established based on Newton's second law:

[0067]

[0068] In the formula, It is the force control of the active suspension. and Indicates sprung mass and unsprung mass. and It is the displacement of sprung mass and unsprung mass; the road excitation displacement is determined by... express.

[0069] The air spring force is generated by the air spring in the additional air chamber:

[0070]

[0071] It is the damping force of the shock absorber:

[0072]

[0073] The dynamic load generated by the tire is expressed as:

[0074]

[0075] In the formula: - Tire stiffness;

[0076] g - gravitational acceleration.

[0077] Since the tire damping is very small, its impact on the dynamic model is negligible, and the tire damping force is ignored in the formula.

[0078] S4. Based on the two-degree-of-freedom active suspension model, consider the parameter uncertainties and the effects of external disturbances.

[0079] In active suspension control, sensors such as speed sensors and acceleration sensors are needed to collect the state variables of the suspension system. Noise disturbances are unavoidable during data collection, so disturbance terms are added to the sprung mass dynamic equation. .

[0080] When designing a control system, a relatively simple air spring model must be used to describe the actual physical model. In the process of simplifying the actual physical model, linearization is usually performed. The simplified air spring model will inevitably produce a deviation from the actual model. This deviation is called the uncertainty of the model.

[0081] Therefore, in general industrial control processes, in order to make the system model description more accurate and to design a more stable and robust control system, parameter uncertainty is often an important factor that cannot be ignored. As seen in the air spring model with an additional air chamber, its equivalent stiffness and equivalent damping are not constants; both values ​​vary around the static equilibrium position of the suspension. To more accurately describe the suspension system, the uncertainty of the suspension parameters should be considered, i.e., varying stiffness should be added to the dynamic model. With changing damping Meanwhile, considering the model error caused by linearization of the air spring model and the neglect of unmodeled dynamic terms, disturbance terms are added to the sprung mass dynamic equation. .

[0082] Define state variables The state-space equations for an active suspension are defined as follows:

[0083]

[0084] Among them, interference items For noise disturbance; interference term The model error is due to model linearization and the neglect of unmodeled dynamic terms.

[0085] The air spring force is generated by the air spring in the additional air chamber:

[0086]

[0087] It is the damping force of the air spring:

[0088]

[0089] The disturbance force generated by the time-varying spring load:

[0090]

[0091] S5. Design a disturbance observer to observe the changes in disturbance parameters due to uncertainties.

[0092] To achieve a more ideal control effect, it is necessary to estimate unknown external disturbances; therefore, it is necessary to design a disturbance observer to estimate parameter uncertainties and external disturbances, and then combine it with sliding mode control to ensure suspension performance.

[0093] Since the road excitation in the two-degree-of-freedom suspension model is unknown, the spring force and damping force in the two-degree-of-freedom suspension model cannot be calculated from the model. Therefore, the spring force, damping force, external disturbance force acting on the sprung mass, model error caused by model linearization, and the sum of neglected unmodeled dynamic terms are taken as the input disturbance force of the active suspension control system. Thus, a new state-space equation is defined as follows:

[0094]

[0095]

[0096] The nonlinear perturbation observer is designed as follows:

[0097]

[0098] In the formula: h - intermediate variables of the state observer;

[0099] - The estimated variable of the disturbance variable d;

[0100] v-Perturbation observer gain.

[0101] S6. Design of an adaptive sliding mode control method based on a disturbance observer;

[0102] Based on the observation results of the perturbation observer in step S5, a novel sliding surface considering mismatch perturbation is designed. The sliding surface S is defined as:

[0103]

[0104] In the formula: , The controller parameters need to be designed to ensure the asymptotic stability of the sliding mode motion;

[0105] , The tracking errors are as follows:

[0106]

[0107] in: It is the expected reference variable.

[0108] An adaptive sliding mode control law based on a disturbance observer is proposed:

[0109]

[0110] in:

[0111]

[0112] The sat function selected in equation (32) is a saturation function to reduce chattering in the control system. Its expression is:

[0113]

[0114] Parameters used to adjust the stability of the sliding mode control algorithm. To adjust the rate at which the sliding surface approaches zero. To adjust the parameters for controlling the chattering.

[0115] The advantages and positive effects of this invention are:

[0116] 1) Based on thermodynamics and fluid mechanics theory, this invention establishes an accurate air spring model for the auxiliary air chamber, which can better represent the airflow motion between the main air chamber and the auxiliary air chamber, and at the same time obtains its equivalent stiffness and equivalent damping model.

[0117] 2) The active suspension model of the present invention takes into account the uncertainty of some parameters under actual working conditions and various unavoidable sensor noise disturbance factors, and establishes a two-degree-of-freedom active suspension model that considers parameter uncertainty and external disturbance, so that the mathematical model can better fit the actual operating conditions.

[0118] 3) This method designs a disturbance observer to offset the uncertainty of air spring parameters in the system and the influence of external disturbances on suspension performance. Furthermore, by designing a new sliding surface based on disturbance estimation, the main control objective is sprung mass motion. The controller parameters are adjusted to ensure that the three indicators of suspension body vertical acceleration, suspension dynamic travel, and wheel dynamic load are significantly improved. This satisfies the control performance of the suspension system to cope with the influence of uncertain parameters and disturbances on the control effect of the system, thereby achieving better control effect. Attached Figure Description

[0119] Figure 1 It is a two-degree-of-freedom system model with an additional air chamber for air suspension;

[0120] Figure 2 This is a sliding mode control structure diagram based on a disturbance observer;

[0121] Figure 3 This is a time-domain waveform diagram of a Class B random road surface.

[0122] Figure 4 It is a disturbance and disturbance estimation Comparison chart;

[0123] Figure 5 It is a disturbance and disturbance estimation Comparison chart;

[0124] Figure 6 It is a disturbance and disturbance estimation Observation error diagram;

[0125] Figure 7 It is a graph showing the relationship between the vertical acceleration of the vehicle body.

[0126] Figure 8 It is a curve showing the relationship between wheel dynamic load;

[0127] Figure 9 It is a curve showing the relationship between the suspension dynamic travel. Detailed Implementation

[0128] To further understand the invention's content, features, and effects, the following description and demonstration of the invention are provided in conjunction with the accompanying drawings and specific implementation examples of active air spring suspension control.

[0129] The adaptive sliding mode control method for active air suspension based on disturbance observer of the present invention is applied to the active control of suspension system to improve the reliability and stability of vehicle ride comfort design.

[0130] S1. Based on thermodynamics and fluid mechanics theory, nonlinear modeling is performed on the main gas chamber, throttling element and auxiliary gas chamber.

[0131] First, the relevant parameters of the auxiliary air chamber air spring system must be determined. The relevant parameters are shown in Table 1.

[0132] Table 1. Parameters of the Additional Air Chamber Air Spring System

[0133]

[0134] The load-bearing capacity of an air spring is related to the force exerted by the air inside the main air chamber, and the magnitude of this force is related to the air pressure and the effective area of ​​the main air chamber. In an air spring, the force F generated by air compression is expressed as:

[0135]

[0136] In the formula: -Gas pressure in the main air chamber

[0137] -Effective area of ​​the main air chamber of the air spring.

[0138] For the air in the auxiliary air chamber air spring, it mainly consists of nitrogen and oxygen, and its pressure is generally no greater than 2 MPa, so it is considered an ideal gas. Considering the compressibility of air and the continuity of the airflow mass flow rate, the relationship between the gas mass flow rate in the main air chamber and the gas pressure and volume change is as follows:

[0139]

[0140] In the formula, -Main gas mass flow rate in the main gas chamber

[0141] k is the adiabatic index; for a gas undergoing an adiabatic process, k = 1.4.

[0142] R - Universal air constant,

[0143] T - Temperature of the gas inside the air spring.

[0144] - Initial pressure inside the air spring.

[0145] - Main air chamber volume

[0146] The rate of change of gas pressure in the main chamber is:

[0147]

[0148] The pressure change rate of the main chamber consists of two parts: the pressure change caused by the change in the mass of compressed air in the main chamber and the pressure change caused by the change in the effective volume of the main chamber.

[0149] The air mass flow rate on the auxiliary air chamber side is similar to that of the main air chamber of the air spring. The difference is that the auxiliary air chamber is often made of rigid materials, and its volume is a fixed value that does not change.

[0150] Right now:

[0151]

[0152] The mass flow rates of the gas in the main chamber and the accessory chamber are the same in magnitude but opposite in direction, satisfying the following:

[0153]

[0154] When the air spring in the auxiliary air chamber is working, the compressed air in the auxiliary air chamber is also compressible and conforms to the continuity relationship of airflow mass flow rate. Combining formulas (2), (3), (4), and (5), the rate of change of gas pressure in the auxiliary air chamber is:

[0155]

[0156] In the formula, -Additional air chamber volume

[0157] -Additional chamber internal pressure.

[0158] Throttling elements are key components for adjusting the stiffness of air spring systems and achieving air damping. Common throttling elements include throttling orifices and throttling tubes, which control the gas mass flow rate between the main air chamber and the auxiliary air chamber. By changing the opening of the throttling element, the stiffness and damping of the air spring system are adjusted, thereby changing the natural frequency of the sprung mass vibration and giving the vehicle a good ride comfort.

[0159] The gas mass flow rate through the throttling orifice is expressed by the following formula:

[0160]

[0161]

[0162]

[0163]

[0164] In the formula:

[0165]

[0166] - Effective flow area of ​​the throttling orifice

[0167] Compared with the actual throttling orifice area

[0168] The ratio of the smaller pressure at both ends of the orifice to the larger pressure is called the pressure ratio. 0.518 represents the critical pressure ratio. When the pressure ratio is greater than the critical pressure ratio, it is called subsonic flow. When the pressure ratio is less than the critical pressure ratio, it is called supersonic flow or choking flow. Equation (40) is the air mass flow rate during subsonic flow through the orifice, and Equation (41) is the air mass flow rate during supersonic flow (choking flow).

[0169] S2. Linearize the models of each part of the air spring and derive the equivalent stiffness and equivalent damping of the air spring suspension system.

[0170] According to the Taylor expansion formula, ignoring higher-order terms, the pressure change rates of the main chamber and the auxiliary chamber can be obtained using the first-order Taylor expansion formula:

[0171]

[0172]

[0173] Given the initial pressures and volumes of the main and auxiliary air chambers of the air suspension, and the effective area of ​​the main air chamber, the relationship between mass flow rate and the pressures of the two chambers is obtained from equations 1 and 2. The model is then linearized near the suspension equilibrium point using the wire cutting method.

[0174]

[0175] In the formula: This is the orifice resistance coefficient.

[0176] When air flows between the main air chamber and the auxiliary air chamber, it must pass through a throttling damping orifice. The obstruction of airflow by the throttling damping orifice generates a damping force. Therefore, the air spring can be considered as an equivalent structure of an ideal spring and a damper connected in parallel. Near the static equilibrium position of the suspension, linearizing the spring model yields the equivalent spring stiffness as:

[0177]

[0178] Similarly, the equivalent damping is expressed as:

[0179]

[0180] In the formula: - Orifice area

[0181] - The density of the gas inside the air spring.

[0182] The equivalent stiffness and equivalent damping of an air spring vary around the system's equilibrium point; therefore, the equivalent stiffness and equivalent damping can be rewritten in the following form:

[0183]

[0184] In the formula and These represent the stiffness and damping at the equilibrium point of the air spring in the additional air chamber, respectively.

[0185] Represented as:

[0186]

[0187]

[0188] The calculated equivalent stiffness of the air spring in the additional air chamber at its static equilibrium position is 16000. The equivalent damping is 960. .

[0189] and These represent the changes in stiffness and damping as they deviate from the equilibrium point, respectively.

[0190]

[0191]

[0192] S3. Define the characteristic parameters of each part of the system and establish a two-degree-of-freedom 1 / 4 active suspension model;

[0193] Figure 1 This is a simplified diagram of a two-degree-of-freedom air spring suspension with an additional air chamber. A dynamic model of the two-degree-of-freedom air spring suspension with an additional air chamber is established based on Newton's second law.

[0194]

[0195] In the formula, It is the force control of the active suspension. and Indicates sprung mass and unsprung mass. and It is the displacement of sprung mass and unsprung mass; the road excitation displacement is determined by... express.

[0196] Table 2 Suspension System Related Parameters

[0197]

[0198] The air spring force is generated by the air spring in the additional air chamber:

[0199]

[0200] It is the damping force of the shock absorber:

[0201]

[0202] The dynamic load generated by the tire is expressed as:

[0203]

[0204] In the formula: - Tire stiffness

[0205] g - acceleration due to gravity

[0206] Since the tire damping is very small, its impact on the dynamic model is negligible, and the tire damping force is ignored in the formula.

[0207] S4. Based on the two-degree-of-freedom active suspension model, consider the parameter uncertainties and the effects of external disturbances.

[0208] In active suspension control, sensors such as speed sensors and acceleration sensors are needed to collect the state variables of the suspension system. Noise disturbances are unavoidable during data collection, so disturbance terms are added to the sprung mass dynamic equation. .

[0209] When designing a control system, a relatively simple air spring model must be used to describe the actual physical model. In the process of simplifying the actual physical model, linearization is usually performed. The simplified air spring model will inevitably produce a deviation from the actual model. This deviation is called the uncertainty of the model.

[0210] Therefore, in general industrial control processes, in order to make the system model description more accurate and to design a more stable and robust control system, parameter uncertainty is often an important factor that cannot be ignored. As seen in the air spring model with an additional air chamber, its equivalent stiffness and equivalent damping are not constants; both values ​​vary around the static equilibrium position of the suspension. To more accurately describe the suspension system, the uncertainty of the suspension parameters should be considered, i.e., varying stiffness should be added to the dynamic model. With changing damping Meanwhile, considering the model error caused by linearization of the air spring model and the neglect of unmodeled dynamic terms, disturbance terms are added to the sprung mass dynamic equation. .

[0211] Define state variables The state-space equations for an active suspension are defined as follows:

[0212]

[0213] Among them, interference items For noise disturbance; interference term This includes model errors introduced by model linearization and the neglect of unmodeled dynamic terms. The disturbance term is represented in this example as a sinusoid with an amplitude of 0.02 and a period of 2. .

[0214] The air spring force is generated by the air spring in the additional air chamber:

[0215]

[0216] It is the damping force of the shock absorber:

[0217]

[0218] The disturbance force generated by the time-varying spring load:

[0219]

[0220] The time-varying spring load mass function is: .

[0221] S5. Design a disturbance observer to observe the changes in disturbance parameters due to uncertainties.

[0222] To achieve a more ideal control effect, it is necessary to estimate unknown external disturbances; therefore, it is necessary to design a disturbance observer to estimate parameter uncertainties and external disturbances, and then combine it with sliding mode control to ensure suspension performance.

[0223] Since the road excitation in the two-degree-of-freedom suspension model is unknown, the spring force and damping force in the two-degree-of-freedom suspension model cannot be calculated from the model. Therefore, the spring force, damping force, external disturbance force acting on the sprung mass, model error caused by model linearization, and the sum of neglected unmodeled dynamic terms are taken as the input disturbance force of the active suspension control system. Thus, a new state-space equation is defined as follows:

[0224]

[0225]

[0226] The nonlinear perturbation observer is designed as follows:

[0227]

[0228] In the formula:

[0229]

[0230] S6. Design of an adaptive sliding mode control method based on a disturbance observer;

[0231] Figure 2 This is a simplified diagram of the sliding mode control strategy based on the disturbance observer. Based on the observation results of the disturbance observer in step S5, a novel sliding surface considering mismatched disturbances is designed. The sliding surface S is defined as:

[0232]

[0233] In the formula: , The controller parameters need to be designed to ensure the asymptotic stability of the sliding mode motion;

[0234] , The tracking errors are as follows:

[0235]

[0236] in: It is the expected reference variable.

[0237] An adaptive sliding mode control law based on a disturbance observer is proposed:

[0238]

[0239] in:

[0240]

[0241] The sat function selected in equation (30) is a saturation function to reduce chattering in the control system. Its expression is:

[0242]

[0243] Parameters used to adjust the stability of the sliding mode control algorithm. To adjust the rate at which the sliding surface approaches zero. To adjust the parameters for controlling the chattering.

[0244] Table 3 Controller Parameters

[0245]

[0246] When the vehicle speed and road surface are constant, the speed power spectrum of road surface irregularity The power spectral density remains constant throughout the entire time history and does not change with frequency. To make the road surface model more realistically reflect the actual road conditions, since vehicle driving conditions are not unique and vehicle speed and road roughness change constantly, the road surface time-domain power spectral density varies with the road roughness coefficient and vehicle speed. A filtered white noise method is used to reconstruct the road time-domain model that satisfies the given power spectral density. This involves abstracting the road surface elevation changes into random white noise that meets certain conditions, and then transforming it to obtain the expression for the single-wheel random road roughness velocity time-domain model:

[0247]

[0248] Introducing the pavement spatial cutoff frequency into equation (34) The time-domain mathematical model expression for the filtered white noise is obtained (35), due to the introduction of Equation (35) more accurately reflects the working conditions of the road surface at low frequencies.

[0249]

[0250] Class B random road surface input model, such as Figure 3 As shown. The disturbance signal, disturbance signal estimation, and disturbance observation error are as follows: Figures 4 to 6 As shown in the figure. The effectiveness of the proposed control strategy is verified by comparing it with a passive suspension system using a random signal as the input excitation. The simulation results are as follows. Figures 7 to 9 As shown in Table 4, the root mean square values ​​of the three evaluation indicators are compared.

[0251] Table 4. Root Mean Square Values ​​of Random Road Suspension Performance Evaluation Indicators

[0252] passive suspension 0.1452 0.0104 222.253 Active suspension 0.0495 0.0069 87.575 Compared to improvement 65% 33% 60%

[0253] Figure 7 The graph shows the relationship between the vehicle's vertical acceleration and the passive suspension. As can be seen from the graph, the active additional air chamber air spring suspension with adaptive sliding mode control based on the disturbance observer optimizes the vehicle's vertical acceleration by 65%, significantly reduces the vertical acceleration, and significantly improves the vehicle's ride comfort. Figure 8 The dynamic deflection relationship curve of the suspension shows that the dynamic deflection has been optimized by 33%, and the active auxiliary air spring suspension has a lower suspension dynamic travel than the passive suspension. Figure 9 The wheel dynamic load relationship curve shows that the dynamic load was optimized by 60%, resulting in lower dynamic load and safer driving with the active suspension. Comparisons reveal that under Class B random road excitation, the designed active suspension exhibits significantly reduced vertical acceleration, suspension travel, and tire dynamic load, greatly minimizing vehicle vibration and damage to the road surface. This significantly improves vehicle ride comfort, handling stability, and driving safety.

Claims

1. An adaptive sliding mode control method for active air suspension based on a disturbance observer, characterized by: Includes the following steps, S1. Based on thermodynamics and fluid mechanics theory, nonlinear modeling is performed on the air spring with additional air chamber; The load-bearing capacity of an air spring is related to the force exerted by the air inside the main air chamber. The magnitude of this force is related to the air pressure and the effective area of ​​the main air chamber. In an air spring, the force F generated by air compression is expressed as: (1) In the formula: -Gas pressure in the main air chamber -Effective area of ​​the main air chamber of the air spring The air in the auxiliary air chamber air spring is mainly composed of nitrogen and oxygen, with a pressure not exceeding 2 MPa. The relationship between the gas mass flow rate and the gas pressure and volume change in the main air chamber is as follows: (2) In the formula, -Main gas mass flow rate in the main gas chamber k is the adiabatic index; for a gas undergoing an adiabatic process, k = 1.

4. R - Universal air constant, T - Temperature of the gas inside the air spring. - Initial pressure inside the air spring. - Main air chamber volume The rate of change of gas pressure in the main chamber is: (3) The pressure change rate of the main chamber consists of two parts: the pressure change caused by the change in the mass of compressed air in the main chamber and the pressure change caused by the change in the effective volume of the main chamber. The air mass flow rate on the auxiliary air chamber side is similar to that of the main air chamber of the air spring. The difference is that the auxiliary air chamber is mostly made of rigid materials, and its volume is a fixed value that will not change. (4) In the formula, -Additional air chamber volume The gas mass flow rates in the main gas chamber and the accessory gas chamber are the same in magnitude but opposite in direction, satisfying the following: (5) When the air spring in the auxiliary air chamber is working, the compressed air in the auxiliary air chamber is compressible and conforms to the continuity relationship of airflow mass flow rate. Combining formulas (2), (3), (4), and (5), the rate of change of gas pressure in the auxiliary air chamber is: (6) In the formula, -Additional chamber internal pressure. Throttling elements are key components for adjusting the stiffness of the air spring system and achieving air damping. Common throttling elements include throttling orifices and throttling tubes. Their function is to control the gas mass flow rate between the main air chamber and the auxiliary air chamber. By changing the opening of the throttling element, the stiffness and damping of the air spring system are adjusted, and the natural frequency of the sprung mass vibration is changed, so that the vehicle has good ride comfort. The gas mass flow rate through the throttling orifice is expressed by the following formula: (7) (8) In the formula: - The effective flow area of ​​the throttling orifice, compared with the actual throttling orifice area. The smaller pressure at both ends of the throttle orifice compared to the larger pressure is called the pressure ratio. 0.518 represents the critical pressure ratio. When the pressure ratio is greater than the critical pressure ratio, it is called subsonic flow. When the pressure ratio is less than the critical pressure ratio, it is called supersonic flow or choking flow. Equation (7) is the air mass flow rate when the throttle orifice is in subsonic flow, and Equation (8) is the air mass flow rate when the throttle orifice is in supersonic flow. S2. Linearize the air spring model to obtain the equivalent stiffness and equivalent damping of the air spring suspension system; According to the Taylor expansion formula, ignoring higher-order terms, the pressure change rates of the main chamber and the auxiliary chamber can be obtained using the first-order Taylor expansion formula: (9) (10) Given the initial pressure, initial volume, and effective area of ​​the main air chamber and auxiliary air chamber of the air suspension, the relationship between mass flow rate and pressure of the two air chambers is obtained from equations (9) and (10). The model is then linearized near the suspension equilibrium point using the wire cutting method. (11) In the formula: The resistance coefficient of the throttling orifice. When air flows between the main air chamber and the auxiliary air chamber, it needs to pass through the throttling damping orifice. Due to the obstruction of the air by the throttling damping orifice, a damping force is generated. The air spring forms an equivalent structure with the spring and damping connected in parallel. From equations (1), (9), (10), and (11), the equivalent stiffness of the spring is obtained as follows: (12) Similarly, the equivalent damping is expressed as: (13) In the formula: - Orifice area -Gas density inside the air spring The equivalent stiffness and equivalent damping of an air spring vary around the system's equilibrium point; therefore, the equivalent stiffness and equivalent damping can be rewritten in the following form: (14) In the formula and These represent the stiffness and damping at the equilibrium point of the air spring in the additional air chamber, respectively. Represented as: (15) (16) and These represent the changes in stiffness and damping as they deviate from the equilibrium point, respectively. (17) (18) S3. Define the system parameters and establish an active suspension model; A dynamic model of a two-degree-of-freedom air spring suspension with an additional air chamber is established based on Newton's second law: (19) In the formula, It is the force control of the active suspension. and Indicates sprung mass and unsprung mass. and It is the displacement of sprung mass and unsprung mass; the road excitation displacement is determined by... express, The air spring force is generated by the air spring in the additional air chamber: (20) It is the damping force of the shock absorber: (21) The dynamic load generated by the tire is expressed as: (22) In the formula: - Tire stiffness g - acceleration due to gravity; S4. Based on the two-degree-of-freedom active suspension model, consider the parameter uncertainties and the effects of external disturbances. Active suspension control requires the use of sensors such as speed sensors and acceleration sensors to collect the state variables of the suspension system. Noise disturbances are always present during data collection, necessitating the addition of disturbance terms to the sprung mass dynamics equations. ; When designing a control system, a relatively simple air spring model must be used to describe the actual physical model. In the process of simplifying the actual physical model, linearization is usually performed. The simplified air spring model will inevitably produce a deviation from the actual model. This deviation is called the model uncertainty. Therefore, in general industrial control processes, in order to make the system model description more accurate and to design a more stable and robust control system, parameter uncertainty is often one of the important factors that cannot be ignored. The equivalent stiffness and equivalent damping of an air spring model with an additional air chamber are not constants; both values ​​vary around the static equilibrium position of the suspension. To more accurately describe the suspension system, the uncertainties in the suspension parameters should be considered, i.e., varying stiffness should be incorporated into the dynamic model. With changing damping Meanwhile, considering the model error caused by linearization of the air spring model and the neglect of unmodeled dynamic terms, disturbance terms are added to the sprung mass dynamic equation. ; Define state variables Active suspension state-space equations: (23) Among them, interference items For noise disturbance; interference term The model error resulting from model linearization and the neglect of unmodeled dynamic terms; The air spring force is generated by the air spring in the additional air chamber: (24) It is the damping force of the air spring: (25) The disturbance force generated by the time-varying spring load: (26) The time-varying spring mass function is: . S5. Design a disturbance observer to observe the changes in disturbance parameters due to uncertainties. To achieve a more ideal control effect, it is necessary to estimate unknown external disturbances; therefore, it is necessary to design a disturbance observer to estimate parameter uncertainties and external disturbances, and then combine it with sliding mode control to ensure suspension performance. Since the road excitation of the two-degree-of-freedom suspension model is unknown, the spring force and damping force in the two-degree-of-freedom suspension model cannot be calculated from the model. Therefore, the sum of the spring force, damping force, external disturbance force acting on the sprung mass, model error caused by model linearization, and neglected unmodeled dynamic terms is used as the input disturbance force of the active suspension control system. A new state-space equation is defined as follows: (27) The nonlinear perturbation observer is designed as follows: (28) In the formula: h - intermediate variables of the state observer, - The estimated variable for the disturbance variable d v-Gain of the perturbation observer In step S5, the sum of the spring force, damping force, external disturbance force acting on the sprung mass, model error caused by model linearization, and neglected unmodeled dynamic terms in the air spring suspension model is used as the input disturbance force of the active suspension control system. S6. Design of an adaptive sliding mode control method based on a disturbance observer; Based on the observation results of the perturbation observer in step S5, a novel sliding surface considering mismatch perturbation is designed. The sliding surface S is defined as: (29) In the formula: , The controller parameters need to be designed to ensure the asymptotic stability of the sliding mode motion; , The tracking errors are as follows: (30) in: It is the expected reference variable. An adaptive sliding mode control law based on a disturbance observer is proposed: (31) in: (32) The sat function selected in equation (32) is a saturation function to reduce chattering in the control system. Its expression is: (33) To adjust the parameters for the stability of the sliding mode control algorithm, To adjust the speed at which the sliding surface approaches zero, To adjust the parameters for controlling chattering; In step S6, a perturbation observer is used to counteract the mismatch uncertainty in the system. A new sliding surface is designed based on the perturbation estimate. In the presence of mismatch perturbation, the system state is asymptotically driven to the desired equilibrium by sliding motion along the sliding surface.

2. The adaptive sliding mode control method for active air suspension based on a disturbance observer according to claim 1, characterized in that: In step S5, the noise disturbance factor of the sensor is taken into account.

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