A method for semi-active damping coordinated control of a heavy vehicle with hydro-pneumatic suspensions

Abstract

The present application belongs to the technical field of suspension system, and particularly relates to a heavy vehicle whole vehicle semi-active damping coordination control method with an oil-gas suspension. The method comprises the following steps: step 1, establishing a mathematical model of adjustable damping force to obtain valve system damping force; step 2, establishing a whole vehicle reference model motion differential equation; step 3, establishing a whole vehicle elastic force and damping force model based on the oil-gas suspension, and the valve system damping force of step 1 is the input of the model; step 4, using the force model, combining step 2, designing a whole vehicle semi-active damping coordination sliding mode control algorithm, coordinating the controllable damping force of each suspension, and realizing that the vertical, roll and pitch states of the whole vehicle body can follow the state changes of the reference model. The present application realizes the coordination control of the vertical, roll and pitch motions of the special vehicle, studies the semi-active control method meeting the use of the special vehicle on the special vehicle with the same side coupled oil-gas suspension, analyzes the semi-active control method, and models and simulates the whole vehicle semi-active damping coordination control strategy.

Description

Technical Field

[0001] This invention belongs to the technical field of suspension systems, specifically relating to a semi-active damping coordination control method for heavy-duty vehicles equipped with hydropneumatic suspension. Background Technology

[0002] Heavy vehicles require high maneuverability, but the safety of heavy vehicles during high-speed maneuvers and the impact of vibrations on onboard instruments and equipment need further improvement. Vehicle ride comfort is primarily affected by vertical and pitch vibrations, while handling stability is mainly affected by roll vibrations. During heavy vehicle operation on complex road surfaces, vibrations in the vertical, roll, and pitch directions can damage equipment and instruments and affect driver fatigue. Passive hydropneumatic suspensions cannot adjust parameters under external road surface excitation, thus achieving optimal performance only under specific conditions. Semi-active hydropneumatic suspensions, however, do not change the suspension stiffness but only consider altering the damping. They are simple in structure, low in cost, and low in energy consumption, while achieving performance similar to active suspensions.

[0003] Currently, semi-active suspensions mainly achieve stepped or stepless control of the suspension damping coefficient. Stepped control can only be adjusted between a few pre-set different damping levels, while stepless control suspensions can achieve continuous damping through a continuously controllable damping method. Sensors obtain the real-time status of the vehicle and road conditions, and the control unit obtains the damping adjustment amount under the real-time status through control algorithms, and issues control commands to achieve continuous damping adjustment, ensuring the coupled control of the vehicle in vertical, roll, and pitch. Summary of the Invention

[0004] To address the above issues and further meet the high maneuverability requirements of heavy vehicles driving in complex road conditions, while ensuring vehicle ride comfort and equipment reliability, this invention explores an effective semi-active damping control method for heavy vehicles under complex road conditions, based on existing heavy vehicles equipped with same-side coupled hydropneumatic suspension systems. On the basis of controllable damping, the invention studies the semi-active damping control strategy of the vehicle's hydropneumatic suspension to achieve coordinated control of the vehicle's vertical, roll, and pitch movements, thereby further improving the ride comfort of heavy vehicles under high speed and heavy load and improving vehicle vibration characteristics.

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

[0006] A semi-active damping coordinated control method for heavy-duty vehicles equipped with hydropneumatic suspension, characterized in that it includes:

[0007] Step 1: Establish a mathematical model of adjustable damping force to obtain the damping force of the valve system;

[0008] Step 2: Establish the motion differential equations of the whole vehicle reference model;

[0009] Step 3: Establish a model of the vehicle's elastic force and damping force based on the hydropneumatic suspension. The valve system damping force in Step 1 is the input to this model.

[0010] Step 4: Using the force model established in Step 3, and in conjunction with Step 2, design a semi-active damping coordinated sliding mode control algorithm for the whole vehicle to coordinate and control the controllable damping forces of each suspension, so that the vertical, roll and pitch states of the whole vehicle body can follow the state changes of the reference model.

[0011] Preferably, the mathematical model for the adjustable damping force in step 1 is:

[0012] Compressed travel:

[0013]

[0014] Stretching stroke:

[0015]

[0016] In the formula,

[0017] And because:

[0018]

[0019] Valve system damping force is

[0020] F d =ΔpA2 (4)

[0021] In the formula, d c h is the valve orifice diameter; k and l0 are the valve opening degree; k and l0 are the stiffness and initial compression of the preload spring, respectively; Δp is the pressure difference across the valve core, Δp = p out -p in ;F s It is steady-state hydrodynamic force, F s =C d πd c hΔpsin(2θ), where θ is the fluid flow angle. Let A1 be the relative velocity of the piston rod, and A2 be the area of ​​the annular cavity.

[0022] Preferably, step 2 includes:

[0023] Step 2.1: Measure the relative velocity and relative displacement of the hydropneumatic suspension using sensors, thereby obtaining the output force of the hydropneumatic suspension through the hydropneumatic suspension model. The vibration differential equation of the two-degree-of-freedom reference model of the whole vehicle is then:

[0024]

[0025] In the formula, These are the vertical acceleration and velocity of the vehicle's center of mass in the reference model, respectively; C sky It is the ceiling damping coefficient; z b -z t , These are the displacement and velocity of the suspension vibration obtained by the sensors; F k (z b -z t ), These represent the elastic force and damping force of the hydropneumatic suspension hydraulic model, respectively; q is the road surface roughness input, and z... t This refers to the amount of tire deformation; m b m t These are the sprung mass and the unsprung mass, respectively.

[0026] Step 2.2: Establish a whole vehicle ceiling damping reference model based on the two-degree-of-freedom improved ceiling damping model. It is assumed that each suspension connection point has a damping coefficient C between itself and the sky reference frame. sky The damper, in the reference model, assumes that the reference vertical displacement of the vehicle's center of gravity, the reference roll angle, and the reference pitch angle are respectively... Under vertical motion, the damping force generated by the damper on the vehicle body During the roll motion, the roll velocity is The damping force generated by the damper is The anti-rolling moment on the left side is: The right anti-roll moment is Total anti-rolling moment B is the mounting distance between the left and right suspensions. Similarly, based on the anti-roll moment analysis method, the anti-pitch moment generated by the damper can be obtained: Where a1, a2, b2, and b1 are the distances from the vehicle's center of gravity to the first, second, third, and fourth axles, respectively, in meters. b It is the vehicle body weight, m ti It is the unsprung mass; I r It is the moment of inertia of vehicle body roll, I p It is the pitch inertia of the vehicle body; k t It refers to tire stiffness; z gi It is the road surface input for each wheel; F i The output forces of each suspension element are used to obtain the differential equations of motion for the whole vehicle reference model:

[0027]

[0028] Step 2.3: Define the generalized vehicle body mass matrix Let the output force F = [F1 ... F8] T The differential equations of motion for the vehicle body of the reference model with roof damping are expressed in matrix form:

[0029]

[0030] In the formula,

[0031]

[0032] Similarly, the matrix expression for the vehicle body's motion equations is obtained as follows:

[0033]

[0034] In the formula,

[0035] Preferably, step 3 specifically comprises:

[0036] Oil-air suspension output force F i Including the elastic force F generated by gas compression in the accumulator ki The damping force F generated by the oil passing through the damping valve system and pipeline di According to the same-side coupled hydropneumatic suspension system, the four cylinders on the left and right sides each share one accumulator. To simplify the output force model, the elastic force is expressed as:

[0037]

[0038]

[0039] In the formula, P g0 V represents the initial pressure of the accumulator. g0 The initial volume of the accumulator is given by A; the cross-sectional area of ​​the accumulator is given by m. i Let r be the equivalent mass of the oil-gas spring support, r be the gas index, Q be the flow rate out of the accumulator per unit time, and z be the suspension deformation.

[0040] Assuming the damping force changes linearly and the damping coefficient is constant, the output damping force of the gas spring is:

[0041]

[0042] In the formula, C is the damping coefficient of the passive hydropneumatic suspension, and ΔF di It is the output damping force of the semi-active damping coordinated sliding mode control system.

[0043] Preferably, step 4 includes:

[0044] Step 4.1: Based on the vehicle semi-active damping coordination control system, determine the control forces and torques output by the vertical, roll and pitch sliding mode controllers, calculate the controllable damping forces of each suspension cylinder, define the tracking error vector of the vehicle dynamics system, and then obtain the sliding mode surface function;

[0045] Step 4.2: By using the equivalent control torque and the switching control torque, the output torque in the vertical, roll and pitch sliding mode control of the whole vehicle is obtained;

[0046] Step 4.3: Using sliding mode control, the equivalent control torque and switching control torque of step 4.2 are controlled, thereby enabling the vertical, roll and pitch states of the vehicle body to follow the changes in the state of the reference model.

[0047] Preferably, step 4.1 specifically includes:

[0048] Step 4.1.1: The control forces and torques output by the vertical, tilt, and pitch sliding mode controllers are as follows: The control force and torque M are determined by the controllable damping force ΔF di Generate, let ΔF d =[ΔF d1 ... ΔF d8 ] T ,have to:

[0049] M = HΔF d (12)

[0050] Step 4.1.2: The controllable damping force of each hydraulic cylinder of the suspension is obtained by equation (12):

[0051] ΔF d =Η + M (13)

[0052] In the formula, H is the transfer matrix, H + This is the pseudo-inverse of H;

[0053] Step 4.1.3: Based on the semi-active suspension damping constraint conditions, the damping force control quantity ΔF di This can be further expressed as:

[0054]

[0055] Step 4.1.4: Define the tracking error vector of the vehicle dynamics system:

[0056]

[0057] Where e is the output deviation of the state variable; Zs is the state variable;

[0058] Step 4.1.5: Use a linear switching function to determine the sliding surface S, as follows:

[0059] definition, C is the sliding mode parameter matrix. And if the Hurwitz condition is satisfied, then:

[0060]

[0061] Preferably, step 4.2 specifically includes:

[0062] The output torque in the sliding mode control of the vehicle's vertical, roll, and pitch should include the equivalent control torque M. eq and switching control torque M sw ,Right now:

[0063] M = M eq +M sw (17)

[0064] Equivalent control torque M eq Its function is to drive the vehicle's dynamic system state along the sliding surface, while switching the control torque M sw Its function is to drive the vehicle's dynamics system to the sliding surface.

[0065] Preferably, the sliding mode control process in step 4.3 includes an equivalent control torque M. eq and switching control torque M sw Control.

[0066] Preferably, the equivalent control torque M eq Specifically:

[0067] Sliding surface function satisfies Then the equivalent control torque M eq for:

[0068]

[0069] By combining equations (7), (8), (16), and (18), we obtain:

[0070]

[0071] Preferably, the switching control torque M sw Specifically:

[0072] S1: Using the constant velocity approximation method, switch the control torque M. sw If the state of the vehicle dynamics system approaches the sliding mode switching surface S=0, then the switching control torque is:

[0073] M sw =-Ksgn(S) (20)

[0074] In the formula, K is the switching control gain coefficient matrix;

[0075] S2: Define the Lyapunov function as follows The conditions for ensuring the reachability and existence of sliding mode are: Where η is a positive constant, the stability condition of the vehicle sliding mode control system is:

[0076]

[0077] In the formula, η z , η θ Each of them is an arbitrarily small positive number;

[0078] S3: Due to equivalent control M eq The purpose is to ensure that S = 0, so equation (21) can be rewritten as:

[0079]

[0080] From equation (22), it can be seen that when the switching control gain coefficient satisfies The sliding mode control system satisfies the Lyapnov stability condition;

[0081] S4: To prevent chattering in the sliding mode control system, the switching control torque M in equation (19) is replaced by a saturation function. sw The sign function in the expression employs feedback control within the boundary layer to reduce chattering during rapid switching, thus yielding the final switching control torque M. sw :

[0082] M sw =-KSat(σ -1 S) (23)

[0083] In the formula, σ is the boundary layer thickness matrix of the quasi-sliding mode.

[0084]

[0085] S5: By combining equations (13), (14), (17), (19), and (23), the optimal damping force ΔF output by each suspension in the semi-active damping coordinated sliding mode control of the whole vehicle can be obtained. d .

[0086] Compared with the prior art, the beneficial effects of the present invention are:

[0087] 1. Continuously controllable suspension can obtain the real-time status of the vehicle and road conditions through sensors in a continuously controllable damping manner. The control unit obtains the damping adjustment amount in the real-time status through the control algorithm and adjusts the damping force output of the suspension in real time.

[0088] 2. Establish a coupled model of the vehicle in the vertical, roll, and pitch directions, and achieve multi-dimensional control of the vehicle through sliding mode decoupling control. Attached Figure Description

[0089] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0090] In the attached diagram:

[0091] Figure 1 Semi-active damping coordinated sliding mode control system for special vehicles

[0092] Figure 2 For a two-degree-of-freedom reference model

[0093] Figure 3 For the whole vehicle reference model

[0094] Figure 4 Vehicle body center of gravity vertical acceleration time domain response

[0095] Figure 5 Vertical acceleration power spectral density of vehicle body center of mass

[0096] Figure 6 Time-domain response of vertical displacement of vehicle body center of mass

[0097] Figure 7 Time-domain response of vehicle roll angle

[0098] Figure 8 Power spectral density of vehicle body roll angle

[0099] Figure 9 Time-domain response of vehicle pitch angle

[0100] Figure 10 Power spectral density of vehicle body pitch angle

[0101] Figure 11 Time-domain response of dynamic deflection of left axle suspension

[0102] Figure 12 Power spectral density of dynamic deflection of the left suspension of axle

[0103] Figure 13 Time-domain response of dynamic load on the left tire of axle

[0104] Figure 14 Power spectral density of dynamic load on the left tire of axle

[0105] Figure 15 The root mean square value of the vertical acceleration of the vehicle's center of mass at different vehicle speeds

[0106] Figure 16 The root mean square value of the left side dynamic deflection of the axle at different vehicle speeds

[0107] Figure 17 The root mean square value of the vehicle body roll angle at different vehicle speeds

[0108] Figure 18 The root mean square value of vehicle pitch angle at different vehicle speeds

[0109] Figure 19 The root mean square value of the dynamic load on the left tire of the axle at different vehicle speeds

[0110] Figure 20 Comparison of vertical acceleration of the vehicle's center of mass under bump excitation

[0111] Figure 21 Comparison of vertical displacement of the vehicle's center of gravity under convexity excitation

[0112] Figure 22 Comparison of dynamic deflection of the left suspension of the lower axle under cam excitation

[0113] Figure 23 Comparison of dynamic loads on the left tire of the next axle under bump excitation

[0114] Figure 24 Schematic diagram of damping adjustable valve system

[0115] Figure 25 Cone valve structure diagram

[0116] Among them, 1. hydraulic cylinder, 2. voltage signal one, 3. accumulator, 4. first proportional relief valve, 5. check valve, 6. adjustable flow valve, 7. second proportional relief valve, 8. voltage signal two, 9. control signal, 10. suspension input. Detailed Implementation

[0117] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0118] Example:

[0119] To improve the ride comfort of multi-axle special vehicles equipped with hydropneumatic suspension, this study investigates a vehicle-wide semi-active damping coordination control strategy for special vehicles equipped with same-side coupled hydropneumatic suspension, based on the method of adjusting the proportional overflow valve voltage and building upon the semi-active control of independent hydropneumatic suspension. The vehicle-wide semi-active damping coordination control system for special vehicles is as follows: Figure 1 As shown, an 11-DOF dynamic model of a four-axle special vehicle is established. Using the vehicle's roof damping model as a reference, the tracking errors of the vehicle's vertical, roll, and pitch vibrations are obtained. Based on this, a sliding mode controller for the vehicle's vertical, roll, and pitch motions is designed. The output force and torque of the sliding mode controller are obtained, and the controllable damping force output by each cylinder of the suspension is calculated. This enables the vehicle's vibration response to follow the vibration response of the reference model, thereby improving the vertical, roll, and pitch vibration characteristics of the controlled special vehicle.

[0120] Therefore, a semi-active damping coordinated control method for heavy-duty vehicles equipped with hydropneumatic suspension includes:

[0121] Step 1: Establish a mathematical model for adjustable damping force.

[0122] like Figure 24 The diagram shows the semi-active damping control valve system structure of each suspension in a same-side coupled hydropneumatic suspension system. The adjustable damping valve system mainly includes a first proportional relief valve 4 and a second proportional relief valve 7 during the extension and compression strokes. Voltage signals 1 and 2 adjust the opening pressure of the proportional relief valves to achieve continuous damping adjustment. The check valve 5 and adjustable flow valve 6 function identically to the check valves and damping orifices in ordinary hydropneumatic suspensions. The adjustable flow valve is a normally open orifice, and its flow area can be adjusted.

[0123] Its semi-active damping adjustable working principle is as follows: During the compression stroke, the oil flows from the rodless chamber into the rod chamber through the valve system. When the relative speed of the piston rod is low, the oil only flows through the adjustable flow valve 6 and the check valve 5. When the speed increases, the pressure rises, and the second proportional relief valve 7 opens. At this time, the oil flows into the rod chamber through the check valve 5, the adjustable flow valve 6, and the second proportional relief valve 7. During the extension stroke, the oil flows from the rod chamber into the rodless chamber, the check valve closes, and the oil flows through the adjustable flow valve 6 and the second proportional relief valve 4 through the rodless chamber. The principle is the same as that of the extension stroke. The opening pressure of the proportional relief valve is proportional to the pre-compression of the preload spring, and the preload of the spring is proportional to the voltage signal, that is, the opening pressure is proportional to the voltage. When the system pressure is low, the relief valve is closed; after reaching the opening pressure, the relief valve opens. If the system pressure does not reach the opening pressure of the relief valve when the voltage U=0V, the damping cannot be adjusted. However, the appropriate opening pressure of the relief valve when U=0V can be set according to the actual needs of the special vehicle through design parameters. Taking the compression stroke as an example, when the damping is within the adjustable range, if the system requires greater damping force, the voltage can be increased. This increases the opening pressure of the relief valve, thereby increasing the pressure difference across the valve system and thus increasing the damping force.

[0124] like Figure 25 As shown, the adjustable valve system includes a flow-regulating valve, a check valve, and a proportional relief valve connected in parallel. Flow-pressure differential models need to be established for each of these valves to obtain the adjustable damping force model. To simplify the model, the compressibility and temperature effects of the oil are not considered.

[0125] (1) Proportional relief valve model

[0126] The basic physical model of the proportional relief valve adopts the cone valve model, and the cone valve structure is as follows: Figure 25 As shown.

[0127] Assuming the valve is installed horizontally, the force balance equation for the valve core in the horizontal direction is:

[0128]

[0129] In the formula, d c h is the valve orifice diameter; k and l0 are the valve opening degree; k and l0 are the stiffness and initial compression of the preload spring, respectively; Δp is the pressure difference across the valve core, Δp = p out -p in ;F s It is steady-state hydrodynamic force, F s =C d πd c hΔpsin(2θ), where θ is the fluid flow angle.

[0130] The relationship between valve core opening h and pressure difference can be obtained from equation (5.1):

[0131]

[0132] When h = 0, the relief valve is in the critical opening state, and the pressure difference at this time is the valve opening pressure, i.e.

[0133]

[0134] When h = h cmax At this time, the relief valve is at its maximum opening, and the pressure at this time is

[0135]

[0136] The flow-pressure relationship in the cone valve model is as follows:

[0137]

[0138] P is the oil density. The flow-pressure difference relationship of the cone valve model can be obtained through equations (5.1) to (5.5):

[0139]

[0140] For a proportional relief valve, when a voltage signal is input, the electromagnet generates electromagnetic force, compressing the preload spring. The preload compression determines the relief pressure, and the compression is proportional to the armature displacement, i.e., proportional to the input voltage signal. Therefore, the valve opening pressure is proportional to the voltage signal. Because the electromagnet generates force acting on the preload spring, changing the spring's preload, the proportional relief valve has three states: closed, open, and maximum valve opening.

[0141] Assuming the voltage is U, based on the fact that the preload of the preload spring is proportional to the input voltage, we can obtain...

[0142]

[0143] In the formula, K is the proportionality coefficient of the relationship between pre-compression and voltage. U maxThe maximum adjustable voltage of the proportional relief valve is l. max l1 represents the maximum pre-compression amount corresponding to the maximum voltage value. l1 represents the pre-compression amount of the pre-tensioned spring when the voltage U = 0V.

[0144] The flow-pressure differential relationship of the proportional relief valve is:

[0145]

[0146] In the formula, q s This refers to the flow rate of the proportional relief valve; d s h smax These are the valve orifice diameter and maximum opening of the proportional relief valve, respectively.

[0147] (2) Check valve and throttle valve model

[0148] The check valve also adopts the cone valve model, but the opening pressure of the check valve is relatively small, so the process from opening to full opening of the check valve is ignored. Therefore, the flow-pressure difference relationship of the check valve is obtained as follows:

[0149]

[0150] The throttle valve is equivalent to a normally open orifice. Assume the throttle valve diameter and flow coefficient are d and d, respectively. z C z The flow rate-pressure difference relationship of the throttle valve is obtained:

[0151]

[0152] During the compression stroke, when the relative speed of the piston rod is low, the proportional relief valve is closed. However, considering the low opening pressure of the check valve (assuming the check valve only has two states during the compression stroke: closed and at its maximum opening), the check valve opens from the beginning. Therefore, during the low speed and low pressure of the compression stroke, the oil flows through the throttle valve and the check valve. As the piston rod speed increases, the valve system pressure rises. When it reaches the opening pressure of the relief valve, the oil flows through the throttle valve, the check valve, and the proportional relief valve. During the extension stroke, at low speed and low pressure, the oil only flows through the throttle valve. As the piston rod speed increases, the proportional relief valve opens, and the oil flows through the throttle valve and the proportional relief valve. The flow-pressure differential relationships of the valve systems for each process are as follows:

[0153] Compression stroke, flow rate - pressure difference:

[0154]

[0155] The stretching stroke, flow rate - pressure difference is:

[0156]

[0157] To simplify the solution process and facilitate the use of Cardan's formula to solve the relationship between pressure difference and flow rate in the valve system during the opening to maximum opening process, we assume 2θ = π, which is a flat valve structure. The relationship between pressure difference and flow rate in the valve system can be obtained through equations (5.8) to (5.12).

[0158] Compressed travel:

[0159]

[0160] Stretching stroke:

[0161]

[0162] In the formula,

[0163] And because

[0164]

[0165] Valve system damping force is

[0166] F d =ΔpA2(5.16)

[0167] In the formula, Let A1 be the relative velocity of the piston rod, and A2 be the area of ​​the annular cavity.

[0168] The mathematical model of adjustable damping force is obtained from equations (5.13) to (5.16).

[0169] Step 2: Establish the motion differential equations of the whole vehicle reference model; including:

[0170] Step 2.1: As Figure 2 The diagram shows a two-degree-of-freedom dynamic roof reference model. Special vehicles operate under complex road conditions, making it difficult to obtain the road surface input required for an ideal roof-mounted hydropneumatic suspension reference model, and resulting in significant errors. Therefore, to reduce the dynamic load on the vehicle body and minimize the damage to onboard instruments and driver fatigue caused by vehicle vibration, sensors are used to measure the relative velocity and displacement of the hydropneumatic suspension. This allows the output force of the hydropneumatic suspension to be obtained through the hydropneumatic suspension model. The vibration differential equation of the two-degree-of-freedom reference model of the entire vehicle is then:

[0171]

[0172] In the formula, These are the vertical acceleration and velocity of the vehicle's center of mass in the reference model, respectively; C sky It is the ceiling damping coefficient; z b -z t , These are the displacement and velocity of the suspension vibration obtained by the sensors; F k(z b -z t ), These represent the elastic force and damping force of the hydropneumatic suspension hydraulic model, respectively; q is the road surface roughness input, and z... t This refers to the amount of tire deformation; m b m t These are the sprung mass and the unsprung mass, respectively.

[0173] Step 2.2: Establish a whole vehicle ceiling damping reference model based on the two-degree-of-freedom improved ceiling damping model. It is assumed that each suspension connection point has a damping coefficient C between itself and the sky reference frame. sky The damper, in the reference model, assumes that the reference vertical displacement of the vehicle's center of gravity, the reference roll angle, and the reference pitch angle are respectively... Under vertical motion, the damping force generated by the damper on the vehicle body During the roll motion, the roll velocity is The damping force generated by the damper is The anti-rolling moment on the left side is: The right anti-roll moment is Total anti-rolling moment B is the mounting distance between the left and right suspensions. Similarly, based on the anti-roll moment analysis method, the anti-pitch moment generated by the damper can be obtained: Where a1, a2, b2, and b1 are the distances from the vehicle's center of gravity to the first, second, third, and fourth axles, respectively, in meters. b It is the vehicle body weight, m ti It is the unsprung mass; I r It is the moment of inertia of vehicle body roll, I p It is the pitch inertia of the vehicle body; k t It refers to tire stiffness; z gi It is the road surface input for each wheel; F i The output forces of each suspension element are used to obtain the differential equations of motion for the whole vehicle reference model:

[0174]

[0175] Step 2.3: Define the generalized vehicle body mass matrix Let the output force F = [F1 ... F8] T The differential equations of motion for the vehicle body of the reference model with roof damping are expressed in matrix form:

[0176]

[0177] In the formula,

[0178]

[0179] Similarly, the matrix expression for the vehicle body's motion equations is obtained as follows:

[0180]

[0181] In the formula,

[0182] Step 3: Establish the vehicle's elastic and damping forces based on the hydropneumatic suspension; specifically:

[0183] Oil-air suspension output force F i Including the elastic force F generated by gas compression in the accumulator ki The damping force F generated by the oil passing through the damping valve system and pipeline di According to the same-side coupled hydropneumatic suspension system, the four cylinders on the left and right sides each share one accumulator. To simplify the output force model, the elastic force is expressed as:

[0184]

[0185]

[0186] In the formula, P g0 V represents the initial pressure of the accumulator. g0 The initial volume of the accumulator is given by A; the cross-sectional area of ​​the accumulator is given by m. i Let r be the equivalent mass of the oil-gas spring support, r be the gas index, and Q be the flow rate out of the accumulator per unit time.

[0187] Assuming the damping force changes linearly and the damping coefficient is constant, the output damping force of the gas spring is:

[0188]

[0189] In the formula, C is the damping coefficient of the passive hydropneumatic suspension, and ΔF di It is the output damping force of the semi-active damping coordinated sliding mode control system.

[0190] Step 4: Design a semi-active damping coordinated sliding mode control algorithm for the entire vehicle to coordinate and control the controllable damping forces of each suspension, enabling the vehicle's vertical, roll, and pitch states to follow the changes in the reference model's state. This includes:

[0191] Step 4.1: Based on the vehicle's semi-active damping coordinated control system, determine the control forces and torques output by the vertical, roll, and pitch sliding mode controllers, calculate the controllable damping forces of each suspension cylinder, define the tracking error vector of the vehicle dynamics system, and then obtain the sliding mode surface function; Step 3.1 specifically involves:

[0192] Step 4.1.1: The control forces and torques output by the vertical, tilt, and pitch sliding mode controllers are as follows: The control force and torque M are determined by the controllable damping force ΔFdi Generate, let ΔF d =[ΔF d1 ... ΔF d8 ] T ,have to:

[0193] M = HΔF d (5.24)

[0194] Step 4.1.2: The controllable damping force of each hydraulic cylinder of the suspension is obtained by equation (5.24):

[0195] ΔF d =Η + M (5.25)

[0196] In the formula, H is the transfer matrix, H + This is the pseudo-inverse of H;

[0197] Step 4.1.3: Based on the semi-active suspension damping constraint conditions, the damping force control quantity ΔF di This can be further expressed as:

[0198]

[0199] Step 4.1.4: Define the tracking error vector of the vehicle dynamics system:

[0200]

[0201] Where e is the output deviation of the state variable; Zs is the state variable;

[0202] Step 4.1.5: Use a linear switching function to determine the sliding surface S, as follows:

[0203] definition, C is the sliding mode parameter matrix. And if the Hurwitz condition is satisfied, then:

[0204]

[0205] Step 4.2: By using the equivalent control torque and the switching control torque, the output torque in the vertical, roll, and pitch sliding mode control of the entire vehicle is obtained; specifically:

[0206] The output torque in the sliding mode control of the vehicle's vertical, roll, and pitch should include the equivalent control torque M. eq and switching control torque M sw ,Right now:

[0207] M = M eq +M sw (5.29)

[0208] Equivalent control torque M eq Its function is to drive the vehicle's dynamic system state along the sliding surface, while switching the control torque M sw Its function is to drive the vehicle's dynamics system to the sliding surface.

[0209] Step 4.3: Sliding mode control is employed to control the equivalent control torque and switching control torque of Step 4.2, thereby enabling the vehicle's vertical, roll, and pitch states to follow the changes in the reference model's state. The sliding mode control process in Step 4.3 includes the equivalent control torque M. eq and switching control torque M sw Control.

[0210] The equivalent control torque M eq Specifically:

[0211] Sliding surface function satisfies Then the equivalent control torque M eq for:

[0212]

[0213] Combining equations (5.19), (5.20), (5.28), and (5.30), we obtain:

[0214]

[0215] The switching control torque M sw Specifically:

[0216] S1: Using the constant velocity approximation method, switch the control torque M. sw If the state of the vehicle dynamics system approaches the sliding mode switching surface S=0, then the switching control torque is:

[0217] M sw =-Ksgn(S) (5.32)

[0218] In the formula, K is the switching control gain coefficient matrix;

[0219] S2: Define the Lyapunov function as follows The conditions for ensuring the reachability and existence of sliding mode are: Where η is a positive constant, the stability condition of the vehicle sliding mode control system is:

[0220]

[0221] In the formula, η z , η θ Each of them is an arbitrarily small positive number;

[0222] S3: Due to equivalent control M eq Its purpose is to ensure Equation (5.33) can be rewritten as:

[0223]

[0224] From equation (5.34), it can be seen that when the switching control gain coefficient satisfies The sliding mode control system satisfies the Lyapnov stability condition;

[0225] S4: To prevent chattering in the sliding mode control system, the switching control torque M in equation (5.32) is replaced by a saturation function. sw The sign function in the expression employs feedback control within the boundary layer to reduce chattering during rapid switching, thus yielding the final switching control torque M. sw :

[0226] M sw =-KSat(σ -1 S) (5.35)

[0227] In the formula, σ is the boundary layer thickness matrix of the quasi-sliding mode.

[0228]

[0229] S5: By combining equations (5.25), (5.26), (5.29), (5.31), and (5.35), the optimal damping force ΔF output by each suspension in the semi-active damping coordinated sliding mode control of the whole vehicle can be obtained. d .

[0230] Simulation Analysis

[0231] I. Vibration Characteristics Analysis under Random Road Surface Input:

[0232] Based on Matlab / Simulink, using C and D level random road roughness as input, a simulation analysis of the semi-active damping sliding mode coordinated control strategy of the whole vehicle is performed at a vehicle speed u = 60 km / h. The time-domain simulation results of the vehicle vibration characteristics and the power spectral density analysis of the vibration characteristics under the D level random road input are as follows: Figures 4-14 As shown. Figures 4-6 These are the time-domain response of the vertical acceleration of the vehicle body's center of mass, the power spectral density of the vehicle body's center of mass acceleration, and the time-domain response of the vertical vibration displacement of the vehicle body's center of mass, respectively.

[0233] from Figure 4 It can be seen that under the active coordinated sliding mode control of the whole and half, the peak value and root mean square value of the vertical acceleration of the vehicle body center of gravity both decreased, with the peak value and root mean square value decreasing by 13.67% and 14.59%, respectively. Figure 5The results show that semi-active sliding mode control can effectively reduce the vertical acceleration of the vehicle body at low frequencies (below 5Hz), while at f=10~20Hz, the vehicle acceleration of semi-active sliding mode control is basically consistent with that of passive suspension. Sliding mode control reduces the vertical acceleration of the vehicle body at low frequencies, which can effectively prevent the vehicle body from resonating at low frequencies, thereby improving the life and safety of the suspension. Figure 6 The time-domain response of the vertical vibration displacement of the vehicle body's center of gravity shows that, under sliding mode control, the root mean square value of the vertical displacement of the vehicle body's center of gravity decreased by 6.41%, and the maximum vertical displacement decreased by 18.09%, which further demonstrates that sliding mode control can effectively reduce the vertical motion of the vehicle body's center of gravity.

[0234] Figure 7 , 8 The comparisons are as follows: time-domain response of vehicle roll angle and power spectral density analysis of vehicle roll angle. It can be seen that under semi-active sliding mode control, the time-domain response of vehicle roll angle is reduced, with the root mean square value decreasing by 14.52% and the maximum roll angle decreasing by 9.68%. Figure 8 The roll angle power spectral density analysis shows that the semi-active control mainly reduces the time domain response of the vehicle roll angle at low frequencies f = 1 to 5 Hz.

[0235] The comparison of the time-domain response of the vehicle pitch angle and the comparison of the power spectral density analysis of the vehicle pitch angle are as follows: Figure 9 and 10 As shown. From Figure 9 As can be seen, compared with passive suspension, the semi-active sliding mode control of the whole vehicle can reduce the maximum value and root mean square value of the vehicle pitch angle time domain response by 22.66% and 11.5%, respectively. Figure 10 The mid-power spectral density analysis shows that the peak value of the vehicle body roll angle mainly decreases in the low-frequency range of f = 1 to 3 Hz.

[0236] Figure 11 This section compares the time-domain response of the dynamic deflection of the left-side hydropneumatic suspension on a single axle. Compared to the passive suspension, the dynamic deflection of the suspension under semi-active sliding mode control is reduced, with a root mean square value decrease of 14.60%, thus improving the suspension's service life and safety. The power spectrum analysis of the dynamic deflection response of the left-side hydropneumatic suspension on the single axle is shown below. Figure 12 As shown, semi-active sliding mode control effectively controls the suspension dynamic deflection mainly at low frequencies below f=4Hz, while at high frequencies it is basically consistent with passive suspension.

[0237] Figure 13 A comparison of the time-domain response of the dynamic load on the left tire of one axle. Figure 14 For tire dynamic load power spectral density analysis. From Figure 13The results show that the semi-active damping coordinated sliding mode control of the whole vehicle can improve ride comfort compared to the passive suspension. However, after the semi-active damping coordinated sliding mode control, the root mean square value of the tire dynamic load increased by 3.81%. The reason for this is that the semi-active damping coordinated sliding mode control strategy of the whole vehicle uses the improved roof damping reference model as the reference model, which mainly improves the vibration characteristics of the vehicle body, thus sacrificing the tire dynamic load. Figure 14 Power spectral density analysis of tire dynamic load shows that the tire dynamic load mainly increases in the frequency range of f = 10 to 20 Hz.

[0238] Table 1 compares the root mean square (RMS) and maximum values ​​of the vehicle ride comfort indexes under random road surface inputs of levels C and D, and a vehicle speed u = 60 km / h. As can be seen from Table 1, under different levels of random road surface inputs, the semi-active sliding mode control strategy reduces the maximum and RMS values ​​of the vehicle's vertical acceleration, roll angle, pitch angle, and suspension dynamic deflection compared to the passive suspension, effectively suppressing the time-domain response of the vehicle's vertical, roll, and pitch motions, although the tire dynamic load increases slightly. Therefore, the semi-active damping coordinated control strategy can improve vehicle ride comfort under different levels of random road surface inputs.

[0239] Table 1 Comparison of overall vehicle vibration characteristics

[0240]

[0241] II. Performance Analysis of Semi-Active Damping Control at Different Vehicle Speeds:

[0242] To verify the control effect of the semi-active damping sliding mode coordinated control strategy for the whole vehicle, the impact of the semi-active sliding mode damping control strategy on the ride comfort of special vehicles at different vehicle speeds was simulated and analyzed under D-level random road input. Figures 15-19 The comparisons are as follows: vertical acceleration of the vehicle's center of gravity, roll angle, pitch angle, dynamic deflection of the left suspension of the first axle, and root mean square values ​​of dynamic load on the left tire of the first axle at different vehicle speeds.

[0243] from Figures 15-18 As can be seen, with increasing vehicle speed, the root mean square values ​​of vehicle acceleration, roll angle, and pitch angle all tend to increase for vehicles equipped with sliding semi-active damping control suspension and those equipped with passive suspension. Compared to passive suspension, the vehicle semi-active sliding control strategy can significantly reduce the root mean square values ​​of the time-domain response of vehicle center of gravity acceleration, roll angle, and pitch angle, further improving vehicle ride comfort. The higher the vehicle speed, the more obvious the effect of sliding semi-active damping control on the time-domain response of vehicle center of gravity acceleration and roll angle, while with increasing vehicle speed, the effect of sliding semi-active damping control on the time-domain response of pitch angle is not significant. Figure 19 This indicates that the tire dynamic load of vehicles equipped with sliding mode control suspension increases slightly, but vehicle speed has little effect on the magnitude of the increase.

[0244] III. Vibration Characteristics Analysis under Bump Pulse Excitation:

[0245] To further verify the effectiveness of the sliding mode semi-active control strategy, simulation analysis was conducted on passive suspension and semi-active control suspension at different speeds u = 20, 30, and 40 km / h under cam pulse excitation. Figures 20-23 A comparison of the overall vehicle vibration characteristics at a vehicle speed u = 20 km / h.

[0246] Figure 20 and Figure 21 The comparisons are as follows: time-domain response of vehicle body center of gravity vibration acceleration and time-domain response of vehicle body vertical displacement. It can be seen that, compared to passive suspension, under sliding mode control, the peak vibration values ​​at all four points are reduced when the vehicle passes over the bump, with the maximum peak value decreasing by 12.63%. After passing the bump, the vehicle body's vertical acceleration stabilizes more quickly. Regarding the vehicle body's vertical displacement, after passing the bump, sliding mode control reduces the peak vertical displacement value, decreasing by 29.55%. Furthermore, after passing the bump, sliding mode control effectively stabilizes the vehicle body's vertical displacement.

[0247] The time-domain responses of the left suspension dynamic deflection and tire dynamic load under bump excitation on the lower axle are compared as follows: Figure 22 and 23 As shown, the semi-active sliding mode coordinated control strategy of the whole vehicle can reduce the dynamic deflection of the hydropneumatic suspension, with a maximum reduction of 11.48%, thus reducing the probability of hydropneumatic suspension failure. After passing the bump, the dynamic deflection of the suspension can be stabilized more quickly than that of the passive suspension. However, the tire dynamic load increases slightly, mainly reflected in the slight increase in tire dynamic load when passing the bump, with a maximum increase of 5.27%.

[0248] The maximum values ​​of the vehicle vibration characteristic index at a vehicle speed u = 20 km / h are shown in Table 2.

[0249] Table 2 Comparison of maximum vibration characteristics under bump pulse excitation.

[0250]

[0251] Summarize:

[0252] Using an improved roof-damped vehicle model as a reference, a semi-active damping coordinated sliding mode control system was constructed. Simulation tests were conducted under random road surface input and bump pulse excitation. Simulation results show that the semi-active damping coordinated sliding mode control system effectively reduces the vertical acceleration of the vehicle's center of gravity, body roll angle, body pitch angle, and the root mean square and maximum values ​​of suspension dynamic deflection compared to a passive suspension, improving vehicle ride comfort. However, it slightly increases tire dynamic load and reduces handling stability. The effectiveness of the semi-active control method was also verified at different vehicle speeds. The semi-active damping coordinated sliding mode control system effectively reduces the vertical acceleration of the vehicle's center of gravity, body roll angle, and body pitch angle response at different vehicle speeds.

[0253] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A semi-active damping coordinated control method for a heavy-duty vehicle equipped with an air-fuel suspension, characterized in that: include: Step 1: Establish a mathematical model of adjustable damping force to obtain the damping force of the valve system; Step 2: Establish the motion differential equations of the whole vehicle reference model; Step 3: Establish a model of the vehicle's elastic force and damping force based on the hydropneumatic suspension. The valve system damping force in Step 1 is the input to this model. Step 4: Using the model established in Step 3, and combining it with Step 2, design a semi-active damping coordinated sliding mode control algorithm for the entire vehicle. This algorithm coordinates and controls the controllable damping forces of each suspension, enabling the vehicle's vertical, roll, and pitch states to follow the changes in the reference model's state. This includes: Step 4.1: Based on the vehicle semi-active damping coordination control system, determine the control forces and torques output by the vertical, roll and pitch sliding mode controllers, calculate the controllable damping forces of each suspension cylinder, define the tracking error vector of the vehicle dynamics system, and then obtain the sliding mode surface function; Step 4.2: By using the equivalent control torque and the switching control torque, the output torque in the vertical, roll and pitch sliding mode control of the whole vehicle is obtained; Step 4.3: Using sliding mode control, the equivalent control torque and switching control torque of step 4.2 are controlled, thereby enabling the vertical, roll and pitch states of the vehicle body to follow the changes in the state of the reference model. Among them, the damping adjustable valve system structure includes a first proportional relief valve and a second proportional relief valve in the extension and compression strokes. Voltage signal one and voltage signal two adjust the opening pressure of the proportional relief valve to achieve continuous damping adjustment. During the compression stroke, the oil flows from the rodless chamber into the rod chamber through the valve system. When the relative speed of the piston rod is low, the oil only flows through the adjustable flow valve and the check valve. When the speed increases, the pressure rises, and the second proportional relief valve opens. At this time, the oil flows into the rod chamber through the check valve, the adjustable flow valve, and the second proportional relief valve. During the extension stroke, the oil flows from the rod chamber into the rodless chamber, the check valve closes, and the oil flows through the rodless chamber through the adjustable flow valve and the second proportional relief valve.

2. The semi-active damping coordination control method for a heavy-duty vehicle with an air-fuel suspension as described in claim 1, characterized in that: The mathematical model for the adjustable damping force in step 1 is as follows: Compressed stroke: (1) Stretching stroke: (2) In the formula, , , ; And because: (3) Valve system damping force is (4) In the formula, d c h is the valve orifice diameter; h is the valve opening degree. , These are the stiffness and initial compression of the preload spring, respectively. It is the pressure difference across the valve core. ; It is steady-state hydrodynamics. , It is the flow angle. The relative velocity of the piston rod, It is the area of ​​the annular cavity.

3. The semi-active damping coordination control method for a heavy-duty vehicle with an air-fuel suspension as described in claim 1, characterized in that: Step 2 includes: Step 2.1: Measure the relative velocity and relative displacement of the hydropneumatic suspension using sensors, thereby obtaining the output force of the hydropneumatic suspension through the hydropneumatic suspension model. The vibration differential equation of the two-degree-of-freedom reference model of the whole vehicle is then: (5) In the formula, , These are the vertical acceleration and velocity of the vehicle's center of mass in the reference model, respectively. It is the ceiling damping coefficient; , These are the displacement and velocity of the suspension vibration obtained by the sensors; , These represent the elastic force and damping force of the hydropneumatic suspension hydraulic model, respectively; q is the road surface roughness input. This refers to the amount of tire deformation. , These are the sprung mass and the unsprung mass, respectively. Step 2.2: Establish a whole vehicle ceiling damping reference model based on the improved two-degree-of-freedom ceiling damping model. Assume that each suspension connection point to the vehicle body has a damping coefficient between itself and the sky reference frame. The damper, in the reference model, assumes that the reference vertical displacement of the vehicle's center of gravity, the reference roll angle, and the reference pitch angle are respectively... , , Under vertical motion, the damping force generated by the damper on the vehicle body During the roll motion, the roll velocity is The damping force generated by the damper is Then the anti-rolling moment on the left side is: The anti-rolling moment on the right side is Total anti-rolling moment , The mounting distance between the left and right suspensions is used as an example. Similarly, based on the anti-roll moment analysis method, the anti-pitch moment generated by the damper can be obtained: ,in , , , These are the distances from the vehicle's center of gravity to the first, second, third, and fourth axles, respectively. Is it the vehicle body quality, It is the unsprung mass; It is the moment of inertia of vehicle body roll. It is the pitch inertia of the vehicle body; It refers to tire stiffness; It is the road surface input for each wheel; The output forces of each suspension element are used to obtain the differential equations of motion for the whole vehicle reference model: (6) Step 2.3: Define the generalized vehicle body mass matrix Make the output force The differential equations of motion for the vehicle body of the reference model with roof damping are expressed in matrix form: (7) In the formula, , , ； Similarly, the matrix expression for the vehicle body's motion equations is obtained as follows: (8) In the formula, .

4. The semi-active damping coordination control method for a heavy-duty vehicle with an air-fuel suspension as described in claim 3, characterized in that: Step 3 specifically involves: Oil-air suspension output force Including the elastic force generated by gas compression in the accumulator The damping force generated by the oil passing through the damping valve system and pipeline According to the same-side coupled hydropneumatic suspension system, the four cylinders on the left and right sides each share one accumulator. To simplify the output force model, the elastic force is expressed as: (9) (10) In the formula, This is the initial pressure of the accumulator; This represents the initial volume of the accumulator. The cross-sectional area of ​​the accumulator; Let r be the equivalent mass of the oil-gas spring support, and r be the gas index. denoted as the flow rate out of the accumulator per unit time, and z as the suspension deformation; Assuming the damping force changes linearly and the damping coefficient is constant, the output damping force of the gas spring is: (11) In the formula, It is the damping coefficient of the passive hydropneumatic suspension. It is the output damping force of the semi-active damping coordinated sliding mode control system.

5. The semi-active damping coordination control method for a heavy-duty vehicle with an air-fuel suspension as described in claim 4, characterized in that: Step 4.1 specifically involves: Step 4.1.1: The control forces and torques output by the vertical, tilt, and pitch sliding mode controllers are as follows: Control force and torque Controllable damping force Generate, cause ,have to: (12) Step 4.1.2: The controllable damping force of each hydraulic cylinder of the suspension is obtained by equation (12): (13) In the formula, H is the transfer matrix. for The false reversal; Step 4.1.3: Based on the semi-active suspension damping constraint conditions, control the damping force. This can be further expressed as: (14) Step 4.1.4: Define the tracking error vector of the vehicle dynamics system: (15) Where e is the output deviation of the state variable; Zs is the state variable; Step 4.1.5: Use a linear switching function to determine the sliding surface. The sliding surface is as follows: definition, , Let be the sliding mode parameter matrix, then: (16) in, And it satisfies the Hurwitz condition.

6. The semi-active damping coordination control method for a heavy-duty vehicle with an air-fuel suspension as described in claim 5, characterized in that: Step 4.2 specifically involves: The output torque in the sliding mode control of the vehicle's vertical, roll, and pitch parameters should include the equivalent control torque. and switching control torque ,Right now: (17) Equivalent control torque Its function is to drive the vehicle's dynamic system state along the sliding surface, and to switch the control torque. Its function is to drive the vehicle's dynamics system to the sliding surface.

7. The semi-active damping coordination control method for a heavy-duty vehicle with an air-fuel suspension as described in claim 6, characterized in that: The sliding mode control process in step 4.3 includes the equivalent control torque. and switching control torque Control.

8. The semi-active damping coordination control method for a heavy-duty vehicle with an air-fuel suspension as described in claim 7, characterized in that: The equivalent control torque Specifically: Sliding surface function satisfies , (18) By combining equations (7), (8), (16), and (18), we obtain... : (19) in, This is the equivalent control torque.

9. A semi-active damping coordination control method for a heavy-duty vehicle with an air-fuel suspension as described in claim 8, characterized in that: The switching control torque Specifically: S1: Using the constant velocity approach method, switch the control torque. This makes the state of the vehicle's dynamics system approach the sliding mode switching surface. Then the switching control torque is: (20) In the formula, , To switch the control gain coefficient matrix; S2: Define the Lyapunov function as follows Then the conditions for ensuring the accessibility and existence of sliding mode are: ,in, If the integer is a positive constant, then the stability condition of the vehicle sliding mode control system is: (21) In the formula, , , Each of them is an arbitrarily small positive number; S3: Due to equivalent control Its purpose is to ensure Then equation (21) can be rewritten as: (22) From equation (22), it can be seen that when the switching control gain coefficient satisfies The sliding mode control system satisfies the Lyapnov stability condition; S4: To prevent chattering in the sliding mode control system, the switching control torque in equation (19) is replaced by a saturation function. The sign function in the expression employs feedback control within the boundary layer to reduce chattering during rapid switching, thus yielding the final switching control torque. : (23) In the formula, , It is the boundary layer thickness matrix of the quasi-sliding mode. (24) S5: By combining equations (13), (14), (17), (19), and (23), the optimal damping force output of each suspension in the semi-active damping coordinated sliding mode control of the whole vehicle can be obtained. .

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