Impact load-oriented electro-hydraulic servo active suspension feedback linearization sliding mode robust control method

Abstract

The invention relates to an impact load-oriented electro-hydraulic servo active suspension feedback linearization sliding mode robust control method, which belongs to the technical field of vehicle active suspension and electro-hydraulic servo control, and comprises the following steps of: firstly, establishing a quarter vehicle two-degree-of-freedom active suspension model; the method comprises the following steps: step 2, constructing a nonlinear dynamic model of the electro-hydraulic servo actuator of the valve-controlled cylinder; step 3, designing a feedback linearization sliding mode composite controller and giving a stability proof; and step 4, carrying out controller parameter setting and simulation comparison. According to the feedback linearization sliding mode robust control method provided by the invention, the nonlinearity and parameter uncertainty of the actuator can be effectively compensated under the impact working conditions of a deceleration strip and the like, the piston displacement tracking error and sliding mode buffeting are remarkably reduced, sprung mass vibration is reduced, the vehicle driving smoothness and attitude stability are improved, and the method is suitable for large-scale popularization and application. The method is suitable for the field of vehicle hydraulic active suspension control.

Description

Technical Field

[0001] This invention relates to the field of vehicle active suspension and electro-hydraulic servo control technology, and in particular to an electro-hydraulic servo active suspension feedback linearized sliding mode robust control method oriented towards impact loads, applicable to vehicle hydraulic active suspension systems that use valve-controlled hydraulic cylinders as actuators. Background Technology

[0002] As a crucial guarantee for vehicle driving safety and ride comfort, the vehicle suspension system's vibration damping and attitude control performance has always been a key focus in automotive engineering. Traditional passive suspensions rely on fixed parameters of springs and damping elements to absorb road excitation, making it difficult to balance ride comfort and handling stability across a wide frequency range. Especially when encountering impacts such as speed bumps and potholes, significant peaks in vehicle acceleration and suspension deflection often occur, easily leading to ride discomfort or even suspension bottoming out. To improve overall vehicle performance, hydraulic active suspension systems incorporate servo actuators to actively output power, adjusting suspension mechanical characteristics in real time according to road conditions and vehicle status, becoming an important development direction for future high-performance vehicles.

[0003] However, electro-hydraulic active suspensions using valve-controlled hydraulic cylinders inherently possess significant nonlinearity and strong coupling characteristics. Their dynamic response is influenced by multiple factors, including hydraulic compressibility, valve flow-pressure relationship, leakage, and frictional hysteresis. Furthermore, changes in sprung mass, hydraulic parameter drift, and random road surfaces and impact loads introduce significant uncertainties and external disturbances. In existing technologies, linear control methods such as PID and LQR are simple in structure and easy to implement, but they struggle to accurately compensate for the aforementioned nonlinearities, often exhibiting large overshoot and slow convergence under strong impact conditions. Model-based optimal control, robust control, and adaptive control improve system performance to some extent, but they generally rely on highly accurate mathematical models or impose significant computational burdens. While sliding mode control possesses good resistance to parameter perturbations and external disturbances, it is prone to high-frequency chattering when directly applied to electro-hydraulic servo actuators, affecting the service life and control quality of the valve-controlled hydraulic cylinders.

[0004] In summary, existing active suspension control methods struggle to simultaneously address nonlinear compensation within the electro-hydraulic servo system, vehicle vibration suppression under impact loads, and the smoothness of control inputs. This is particularly evident when vehicles encounter transient, high-impact conditions such as speed bumps, where issues like excessive suspension deflection and slow vibration decay persist. Therefore, it is necessary to propose a composite control method that organically integrates the precise nonlinear compensation capabilities of feedback linearization with the robust disturbance rejection characteristics of sliding mode control. Based on a refined dynamic model of the electro-hydraulic servo active suspension, this method eliminates inherent nonlinearities in the actuators through input-output feedback linearization. Sliding mode control is then introduced to enhance robustness against modeling errors and external impacts. Furthermore, boundary layer techniques are used to suppress chattering. This approach achieves higher precision and robustness in suspension dynamics control under complex impact conditions, significantly improving vehicle ride comfort and safety. Summary of the Invention

[0005] To address the shortcomings of valve-controlled hydraulic cylinder electro-hydraulic active suspension in the prior art, such as insufficient vehicle vibration suppression under impact loads like speed bumps, weak robustness to parameter perturbations and external disturbances, and susceptibility to chattering in control inputs, this invention proposes a feedback linearized sliding mode robust control method for electro-hydraulic servo active suspension under impact loads. Based on establishing a quarter-vehicle two-degree-of-freedom active suspension dynamic model and a valve-controlled hydraulic cylinder nonlinear dynamic model, this method uses input-output feedback linearization to equate the electro-hydraulic servo actuator to a linear position servo subsystem. Combining sliding mode control with equivalent control and reaching law control, and introducing boundary layer saturation functions and Lyapunov stability analysis, this method achieves high-precision tracking of the desired displacement trajectory of the suspension actuator and robust suppression of vertical vehicle vibrations, thereby significantly improving the ride comfort and safety of the vehicle under impact loads.

[0006] Specifically, the present invention provides an electro-hydraulic servo active suspension feedback linearized sliding mode robust control method for impact loads, characterized by comprising the following steps:

[0007] Step 1: Obtain vehicle parameters and operating status, and establish a one-quarter vehicle two-DOF active suspension dynamics model;

[0008] Step 2: Establish a nonlinear model of the electro-hydraulic servo actuator with servo valve control voltage as input and piston displacement as output, and couple it with the suspension dynamics model;

[0009] Step 3: Based on the nonlinear model of the actuator, an equivalent linear position servo model is constructed using feedback linearization and sliding mode control. Stability analysis is performed using Lyapunov functions, and the global stability of the high-precision composite control algorithm is proven. At the same time, the inner ring displacement trajectory tracking of the suspension and the vibration suppression of the outer ring sprung mass are realized.

[0010] Step 4: Adjust controller parameters and compare simulation results.

[0011] A further improvement to the technical solution of the present invention is that step one includes the following steps:

[0012] S1: Obtain the state information of the vehicle's hydraulic active suspension system, the state information including state input data and state model data used to describe the dynamic characteristics of the system;

[0013] S2: Based on the state model data obtained in step S1, establish a two-degree-of-freedom dynamic model of the electro-hydraulic servo active suspension, as shown below.

[0014] S21: Establish a dynamic model of the active suspension based on Newton's second law:

[0015]

[0016] In the above formula, F t The expression is as follows:

[0017] F t =K1(q t -z mu )+K2(q t -z mu ) 2

[0018] In the suspension dynamics model, m s The sprung mass is the sum of the mass of the car body frame and the passenger; m u This indicates the unsprung mass, which is the mass of the tire assembly; B p K represents the damping coefficient of the suspension system. t This represents the stiffness coefficient of the suspension system; z ms Indicates the vertical displacement of the sprung mass; z mu Indicates the vertical displacement of the unsprung mass; x p F represents the output displacement of the electro-hydraulic actuator system. t K represents the tire's elastic force; K1 and K2 represent the elastic force coefficients under various operating conditions, and neither is zero; q t This indicates the road surface input.

[0019] S22: Abstract the dynamic model into a mathematical model of the suspension;

[0020] First, the dynamic model is written in the form of a state-space expression:

[0021] Establish the spatial state expression for the vehicle's active suspension, defining the state variables as follows:

[0022] z ms =z1, z mu =z3,

[0023] The dynamic equation above can be rewritten as:

[0024]

[0025] A further improvement to the technical solution of the present invention is that step two includes the following:

[0026] S3: Based on the structural parameters and operating condition data obtained in step S1 and the two-degree-of-freedom dynamic model of the electro-hydraulic servo active suspension established in step S2, a nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo actuator is established. Piston displacement, piston speed, and load pressure are used as state variables. The nonlinear state equation is derived uniformly based on force balance, pressure dynamics, valve flow rate, and servo valve drive relationship, and used as the active... The force / position inputs for the suspension dynamics model are as follows:

[0027] S31: Establish the hydraulic cylinder piston force balance equation;

[0028] The electro-hydraulic servo actuator is considered as being composed of an equivalent load mass m eq Equivalent damping coefficient B p Equivalent stiffness coefficient K t An actuator consisting of the effective working area A of the piston and the piston rod is denoted as x. p Speed ​​is speed is The hydraulic cylinder load pressure is P L External load If the load is F, then the piston force equilibrium equation can be expressed as:

[0029]

[0030] This formula describes the nonlinear motion relationship of a hydraulic cylinder piston under load pressure, suspension equivalent stiffness and damping, and external load.

[0031] S32: Establish the hydraulic cylinder piston force balance equation;

[0032] Considering the compressibility and leakage effect of hydraulic oil, let V be the equivalent total volume of the two chambers of the hydraulic cylinder and β be the bulk modulus of the hydraulic oil. e The total leakage coefficient of the hydraulic cylinder is C. t If the load flow rate of the hydraulic cylinder is Q, then the dynamic balance equation of the load pressure is:

[0033]

[0034] In the formula, C represents the flow rate due to the volume change caused by piston movement. t P L Indicates pressure-related leakage flow rate. This represents the equivalent flow rate caused by compressibility.

[0035] S33: Establish the flow equation and driving relationship of the servo valve orifice;

[0036] The load flow Q of the electro-hydraulic servo actuator is considered to be generated by throttling at the servo valve orifice, and the servo valve orifice flow coefficient is denoted as C. d ,valve The orifice area gradient is ω, and the valve core displacement is x. v If the oil supply pressure is Ps and the hydraulic oil density is ρ, then the load flow rate can be expressed as:

[0037]

[0038] In the formula, sgn() is a sign function used to distinguish between valve opening degree and flow direction;

[0039] Assuming a linear proportional relationship exists between the servo valve spool displacement and the control input voltage u, it can be expressed as:

[0040] x v =K v u

[0041] In the formula, K v The voltage-displacement gain coefficient of the servo valve is used to map the electrical signal u into the adjustment amount of the hydraulic flow.

[0042] S34: Construct a nonlinear state-space model of the electro-hydraulic servo actuator;

[0043] By selecting piston displacement, piston velocity, and load pressure as the system state variables, it can be expressed as:

[0044] x1=x p ,

[0045] Using the servo valve control voltage u as the system input, the force balance equation, pressure dynamic equation, and valve established in S31 to S33 are utilized. The flow rate equation and linear driving relationship lead to the following system differential equations:

[0046]

[0047] Thus, we obtain the state vector The nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo actuator, characterized by the control input u, provides the basis for the design of the feedback linearized sliding mode composite control method in step S4.

[0048] A further improvement to the technical solution of the present invention is that step three includes the following steps;

[0049] S4: Based on the state input data obtained in step S1, the two-degree-of-freedom dynamic model of the electro-hydraulic servo active suspension established in step S2, and the nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo actuator constructed in step S3, a feedback linearized sliding mode composite control method is constructed to achieve accurate tracking of the piston displacement of the electro-hydraulic servo actuator and robustly suppress the vertical vibration of the sprung mass under impact loads and parameter perturbations. The feedback linearized sliding mode composite control method includes equivalent linearized model construction, error dynamics and sliding surface design, equivalent control and... The derivation of Daryl and the sub-steps based on Lyapunov functions, including stability analysis and boundary layer chattering suppression, are detailed below:

[0050] S41: Sub-step for constructing the equivalent linearization model;

[0051] The standard form of the affine nonlinear system corresponding to the state equation of the nonlinear mathematical model of the electro-hydraulic position servo system obtained in step S3. The quasi-form is:

[0052]

[0053] In the formula:

[0054]

[0055]

[0056] h(x) = x1

[0057] According to differential geometry theory, the calculation yields:

[0058]

[0059]

[0060]

[0061]

[0062] According to the definition of relative order, the above calculation results show that the relative order of the system is 3, which is equal to the system dimension. Therefore, the system can achieve state feedback linearization. Based on the feedback linearization method, the transformation relationship between the new state variables and the original state variables is constructed as follows:

[0063]

[0064] Therefore, the state equation of the original nonlinear system can be transformed into the state equation in linear space, which can be expressed as:

[0065]

[0066] In the formula, v is the control quantity of the linear system in the new coordinate system, and its relationship with the control quantity u of the nonlinear system in the original coordinate system is as follows:

[0067] v=α(x)+β(x)u

[0068] In the formula: α(x)=L 3 f h(x), β(x) = L g L 2 f h(x)

[0069] By performing an inverse coordinate transformation on the control quantity v of the linear system, we can obtain the control quantity u of the nonlinear system in the original coordinate system as follows:

[0070]

[0071] S42: Error dynamics and sliding surface design sub-steps;

[0072] Based on the third-order equivalent linear position servo model obtained in step S41, the piston rod displacement tracking error is defined as:

[0073] e = z d -z5

[0074] In the formula, z d Let be the desired displacement of the piston rod;

[0075] The tracking error vector of the system is defined as follows:

[0076]

[0077] Since the system model obtained after feedback linearization is a third-order linear system, the sliding surface can be designed as follows:

[0078]

[0079] In the formula, c1 > 0 and c2 > 0 are the sliding surface design parameters. This sliding surface is equivalent to configuring the closed-loop characteristic equation of the error polynomial. When the system state is restricted to around s = 0, the error dynamics satisfy the expected exponential convergence characteristics.

[0080] S43: Sub-steps for derivation of equivalent control and arrival law control laws;

[0081] Based on the error variable and sliding surface defined in step S42, it can be expressed as follows:

[0082]

[0083] The equivalent linear model obtained in step S41 is:

[0084]

[0085] Based on this, taking the derivative with respect to the sliding surface yields:

[0086]

[0087] To ensure the system remains on the sliding surface under the ideal model, let The equivalent control quantity can be obtained by solving:

[0088]

[0089] Considering the parameter uncertainties and external disturbances in real-world systems, in order to ensure that the system state can reach the sliding mode from any initial conditions... To address this, a switching control term v in the form of an arrival law is introduced. si Using the exponential reaching law, it can be expressed as:

[0090]

[0091] In the formula, k > 0 represents the arrival law gain;

[0092] The arrival law and By comparing the expressions, the switching control quantity can be obtained:

[0093] v si = -k sgn(s)

[0094] Thus, the complete form of the virtual control quantity is obtained:

[0095]

[0096] Under ideal conditions where high-frequency chattering is ignored, the virtual control quantity can ensure that the system state arrives at and remains in the neighborhood of the sliding surface within a finite time, thereby achieving robust suppression of model uncertainties and shock disturbances.

[0097] S44: Stability analysis and boundary layer chattering suppression sub-steps based on Lyapunov functions;

[0098] Based on the virtual control quantity obtained in step S43, a Lyapunov function is introduced to analyze the stability of the closed-loop system.

[0099]

[0100] For this feedback-linearized third-order linear system, we have Taking the derivative with respect to V, we get:

[0101]

[0102] Decompose the virtual control quantity into:

[0103] v = v eq +v si +Δ(x,t)

[0104] Where v eq As an equivalent control term, v si The switching control term is denoted by Δ(x,t), which represents the merged modeling error and external disturbance term. It is assumed that a constant Δ exists. max >0, such that |Δ(x,t)|≤Δ max ;

[0105] In equivalent control v eq In an ideal scenario, accurate compensation for the modeled partial dynamics can be expressed as:

[0106]

[0107] At this point:

[0108]

[0109] Using the inequality |sΔ(x,t)|≤|s|Δ max ,get:

[0110]

[0111] Therefore, when the arrival law gain satisfies k>Δ max hour, The Lyapunov function is monotonically decreasing, and the sliding surface variable s converges to zero in finite time, thus ensuring the asymptotic stability of the system on the sliding surface and its robustness to bounded uncertainties.

[0112] Considering that electro-hydraulic servo actuators are highly sensitive to high-frequency switching control, in order to reduce chattering in the actual system, the sign function in the switching control item in step S43 can be replaced with a saturation function with a defined boundary layer thickness, which can be expressed as:

[0113]

[0114] In the formula, φ>0 represents the boundary layer thickness parameter. The switching control term is then rewritten as:

[0115]

[0116] The virtual control quantity is:

[0117]

[0118] Substituting the above virtual control quantity into the input transformation relationship obtained in step S41, we get:

[0119]

[0120] Finally, the expression for the servo valve control voltage is obtained as follows:

[0121]

[0122] The control voltage is used as the drive input of the valve-controlled cylinder electro-hydraulic servo actuator to achieve high-precision tracking of the desired displacement trajectory and robust suppression of sprung mass vibration under impact loads such as speed bumps and under conditions of parameter uncertainty in the electro-hydraulic servo active suspension system.

[0123] A further improvement to the technical solution of the present invention is that step four includes the following steps:

[0124] A: For the equivalent impact condition and the given desired piston displacement trajectory, by adjusting the sliding surface parameters, switching gain and boundary layer thickness, the simulation results of the piston displacement of the electro-hydraulic servo actuator were compared using PID control, sliding mode control and feedback linearized sliding mode composite control, respectively, and the controller parameter group that minimizes displacement tracking error and chattering was selected.

[0125] B: After A determines the controller parameters, the simulation results of the vertical displacement of the sprung mass under the same impact conditions are compared. The peak value, convergence speed and root mean square index of the composite control of PID, sliding mode and feedback linearized sliding mode are compared to verify the superiority of the composite control in terms of sprung mass vibration suppression and ride comfort improvement.

[0126] The technological advancements achieved by this invention due to the adoption of the above technical solutions are as follows:

[0127] This invention addresses the problems of large displacement tracking errors and severe chattering in electro-hydraulic servo-driven active suspension systems under conditions of strong nonlinearity, parameter uncertainty, and impact loads. It establishes a refined nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo active suspension, proposes a composite control strategy combining feedback linearization and sliding mode control, and provides a global stability proof for the closed-loop system based on Lyapunov functions. Simultaneously, it introduces a boundary layer saturation function to weaken sliding mode chattering, improving engineering feasibility while ensuring robustness, and significantly enhancing the system's resistance to parameter perturbations and external impact disturbances.

[0128] Simulation results show that, under impact conditions such as equivalent speed bumps, compared with PID control and sliding mode control, the control method of this invention can significantly reduce the root mean square error of piston displacement tracking of electro-hydraulic servo actuators and suppress high-frequency chattering, thereby greatly reducing the root mean square of vertical displacement of sprung mass. It comprehensively achieves simultaneous improvement in three aspects: suspension dynamic stroke constraint, sprung mass vibration suppression, and high-precision trajectory tracking, thus significantly improving the ride comfort and vehicle posture stability under impact loads, and has good engineering application prospects. Attached Figure Description

[0129] Figure 1 This is a flowchart of the invention;

[0130] Figure 2 This is a model diagram of the suspension system of the present invention;

[0131] Figure 3 This is a schematic diagram of the road surface input method of the present invention;

[0132] Figure 4 This is a diagram of the inner loop position tracking curve of the electro-hydraulic servo actuator obtained by the PID control method in an embodiment of the present invention.

[0133] Figure 5 This is a diagram showing the inner loop position tracking curve of the electro-hydraulic servo actuator obtained by the SMC control method in an embodiment of the present invention.

[0134] Figure 6 This is a diagram of the inner loop position tracking curve of the electro-hydraulic servo actuator obtained by the FLSMC control method according to an embodiment of the present invention;

[0135] Figure 7 This is a comparison chart of the inner loop position tracking error curves of the electro-hydraulic servo actuator obtained by different control methods according to embodiments of the present invention;

[0136] Figure 8 This is a comparison diagram of the vertical response of the active suspension outer ring spring load mass after compensation by an electro-hydraulic servo actuator, obtained by different control methods according to embodiments of the present invention. Detailed Implementation

[0137] Exemplary embodiments, features, and aspects of the present invention will now be described in detail with reference to the accompanying drawings. Although various parameter values ​​and aspects of the embodiments are shown, the simulation process need not be performed with exactly the same parameters and aspects unless specifically indicated.

[0138] The following will combine Figures 1-8 The present invention will be further described in detail with reference to the embodiments:

[0139] The present invention provides a feedback linearized sliding mode robust control method for an electro-hydraulic servo active suspension oriented to impact loads, such as... Figure 1As shown, it includes:

[0140] Step 1: Obtain vehicle parameters and operating status, and establish a one-quarter vehicle two-DOF active suspension dynamics model;

[0141] S1: Obtain the state information of the vehicle's hydraulic active suspension system, the state information including state input data and state model data used to describe the dynamic characteristics of the system;

[0142] S2: Based on the state model data obtained in step S1, establish a two-degree-of-freedom dynamic model of the electro-hydraulic servo active suspension, as follows: As shown:

[0143] like Figure 2 The diagram shown is a model of the suspension system. In the suspension dynamics model, m s The sprung mass is the sum of the mass of the car body frame and the passenger; m u This indicates the unsprung mass, which is the mass of the tire assembly; B p K represents the damping coefficient of the suspension system. t This represents the stiffness coefficient of the suspension system; z ms Indicates the vertical displacement of the sprung mass; z mu Indicates the vertical displacement of the unsprung mass; x p This indicates the output displacement of the electro-hydraulic actuator; F t K represents the tire's elastic force; K1 and K2 represent the elastic force coefficients under various operating conditions, and neither is zero; q t This indicates the road surface input.

[0144] S21: Establish a dynamic model of the active suspension based on Newton's second law:

[0145]

[0146] In the above formula, F t The expression is as follows:

[0147] F t =K1(q t -z mu )+K2(q t -z mu ) 2

[0148] S22: Abstract the dynamic model into a mathematical model of the suspension;

[0149] Let z ms =z1, z mu =z3,

[0150] z1 represents the first state variable, z2 represents the first state variable, z3 represents the first state variable, and z4 represents the first state variable.

[0151] The dynamic equation above can be rewritten as:

[0152]

[0153] Step 2: Establish a nonlinear model of the electro-hydraulic servo actuator with servo valve control voltage as input and piston displacement as output, and couple it with the suspension dynamics model;

[0154] S3: Based on the structural parameters and operating data of the electro-hydraulic servo system obtained in step S1 and the two-degree-of-freedom dynamic model of the electro-hydraulic servo active suspension established in step S2, a nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo actuator is constructed. Using piston displacement, piston speed, and load pressure as state variables, the nonlinear state equations are derived uniformly based on force balance, pressure dynamics, valve flow rate, and servo valve drive relationship. The force / position inputs for the active suspension dynamics model are as follows:

[0155] S31: Establish the hydraulic cylinder piston force balance equation;

[0156] The electro-hydraulic servo actuator is considered as being composed of an equivalent load mass m eq Equivalent damping coefficient B p Equivalent stiffness coefficient K t An actuator consisting of the effective working area A of the piston and the piston rod is denoted as x. p Speed ​​is speed is The hydraulic cylinder load pressure is P L External load If the load is F, then the piston force equilibrium equation can be expressed as:

[0157]

[0158] This formula describes the nonlinear motion relationship of a hydraulic cylinder piston under load pressure, suspension equivalent stiffness and damping, and external load.

[0159] S32: Establish the hydraulic cylinder piston force balance equation;

[0160] Considering the compressibility and leakage effect of hydraulic oil, let V be the equivalent total volume of the two chambers of the hydraulic cylinder and β be the bulk modulus of the hydraulic oil. e The total leakage coefficient of the hydraulic cylinder is C. t If the load flow rate of the hydraulic cylinder is Q, then the dynamic balance equation of the load pressure is:

[0161]

[0162] In the formula, C represents the flow rate due to the volume change caused by piston movement. t P L Indicates pressure-related leakage flow rate. This represents the equivalent flow rate caused by compressibility.

[0163] S33: Establish the flow equation and driving relationship of the servo valve orifice;

[0164] The load flow Q of the electro-hydraulic servo actuator is considered to be generated by throttling at the servo valve orifice, and the servo valve orifice flow coefficient is denoted as C. d The valve port area gradient is ω, and the valve core displacement is x. v If the oil supply pressure is Ps and the hydraulic oil density is ρ, then the load flow rate can be expressed as:

[0165]

[0166] In the formula, sgn() is a sign function used to distinguish between valve opening degree and flow direction;

[0167] Assume that the servo valve spool displacement and the control input voltage u satisfy a linear proportional relationship:

[0168] x v =K v u

[0169] Where K v The voltage-displacement gain coefficient of the servo valve is used to map the electrical signal u into the adjustment amount of the hydraulic flow.

[0170] S34: Construct a nonlinear state-space model of the electro-hydraulic servo actuator;

[0171] Piston displacement, piston velocity, and load pressure are selected as the system state variables, i.e.

[0172] x1=x p ,

[0173] Using the servo valve control voltage u as the system input, and leveraging the force balance equation, pressure dynamic equation, valve orifice flow equation, and linear drive relationship established in S31-S33, the system differential equation is reorganized as follows:

[0174]

[0175] Thus, we obtain the state vector The nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo actuator, characterized by the control input u, provides the basis for the design of the feedback linearized sliding mode composite control method in step S4.

[0176] Step 3: Based on the nonlinear model of the actuator, an equivalent linear position servo model is constructed using feedback linearization-sliding mode composite control. The global stability of the control algorithm is proved based on the Lyapunov function, thereby realizing the tracking of the inner ring displacement trajectory of the suspension and the suppression of the outer ring sprung mass vibration.

[0177] S4: Based on the state input data obtained in step S1, the two-degree-of-freedom dynamic model of the electro-hydraulic servo active suspension established in step S2, and the nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo actuator constructed in step S3, a feedback linearized sliding mode composite control method is constructed to achieve precise tracking control of the piston displacement of the electro-hydraulic servo actuator and robustly suppress the vertical vibration of the sprung mass under impact loads and parameter perturbations. The composite control method includes sub-steps such as equivalent linearized model construction, error dynamics and sliding mode surface design, equivalent control and arrival law derivation, and stability analysis and boundary layer chattering suppression based on Lyapunov functions, as detailed below:

[0178] S41: Sub-step for constructing the equivalent linearization model;

[0179] The standard form of the affine nonlinear system corresponding to the state equation of the nonlinear mathematical model of the electro-hydraulic position servo system obtained in step S34 is:

[0180]

[0181] In the formula:

[0182]

[0183]

[0184] h(x) = x1

[0185] According to differential geometry theory, the calculation yields:

[0186]

[0187]

[0188]

[0189]

[0190] According to the definition of relative order, the above calculation results show that the relative order of the system is 3, which is equal to the system dimension. Therefore, the system can achieve state feedback linearization. Based on the feedback linearization method, the transformation relationship between the new state variables and the original state variables is constructed as follows:

[0191]

[0192] Therefore, the state equations of the original nonlinear system can be transformed into state equations in linear space, that is:

[0193]

[0194] In the formula, v is the control quantity of the linear system in the new coordinate system, and its relationship with the control quantity u of the nonlinear system in the original coordinate system is as follows:

[0195] v=α(x)+β(x)u

[0196] In the formula:

[0197] α(x)=L 3 f h(x)

[0198] β(x)=L g L 2 f h(x)

[0199] By performing an inverse coordinate transformation on the control quantity v of the linear system, we can obtain the control quantity u of the nonlinear system in the original coordinate system as follows:

[0200]

[0201] S42: Error dynamics and sliding surface design sub-steps;

[0202] Based on the third-order equivalent linear position servo model obtained in step S41, the piston rod displacement tracking error is defined as:

[0203] e = z d -z5

[0204] In the formula, z d Let be the desired displacement of the piston rod;

[0205] The tracking error vector of the system is defined as follows:

[0206]

[0207] Since the system model obtained after feedback linearization is a third-order linear system, the sliding surface can be designed as follows:

[0208]

[0209] In the formula, c1>0 and c2>0 are the sliding surface design parameters. The sliding surface is equivalent to the configuration of the closed-loop characteristic equation of the error polynomial. When the system state is restricted to around s=0, the error dynamics satisfy the expected exponential convergence characteristics.

[0210] S43: Sub-steps for derivation of equivalent control and arrival law control laws;

[0211] Based on the error variables and sliding surface defined in step S42 and the equivalent linear model obtained in step S41, the derivative of the sliding surface can be obtained as follows:

[0212]

[0213] To ensure the system remains on the sliding surface under the ideal model, let The equivalent control quantity can be obtained by solving:

[0214]

[0215] Considering the parameter uncertainties and external disturbances in real-world systems, in order to ensure that the system state can reach the sliding mode from any initial conditions... To address this, a switching control term v in the form of an arrival law is introduced. si Using the exponential reaching law:

[0216]

[0217] In the formula, k > 0 represents the arrival law gain;

[0218] By comparing the arrival law with the expression for s, the switching control quantity can be obtained:

[0219] v si = -k sgn(s)

[0220] Thus, the complete form of the virtual control quantity is obtained:

[0221]

[0222] Under ideal conditions where high-frequency chattering is ignored, the virtual control quantity can ensure that the system state arrives at and remains in the neighborhood of the sliding surface within a finite time, thereby achieving robust suppression of model uncertainties and shock disturbances.

[0223] S44: Stability analysis and boundary layer chattering suppression sub-steps based on Lyapunov functions;

[0224] Based on the virtual control quantity obtained in step S43, a Lyapunov function is introduced to analyze the stability of the closed-loop system:

[0225]

[0226] For this feedback-linearized third-order linear system, we have Taking the derivative with respect to V, we get:

[0227]

[0228] Decompose the virtual control quantity into:

[0229] v = v eq +v si +Δ(x,t)

[0230] Where v eq As an equivalent control term, v si The switching control term is denoted by Δ(x,t), which represents the merged modeling error and external disturbance term. It is assumed that a constant Δ exists. max >0, such that |Δ(x,t)|≤Δ max ;

[0231] In equivalent control v eq In an ideal scenario, accurate compensation for the modeled partial dynamics can be expressed as:

[0232]

[0233] At this point:

[0234]

[0235] Using the inequality |sΔ(x,t)|≤|s|Δ max ,get:

[0236]

[0237] Therefore, when the arrival law gain satisfies k > Δ max When V < 0, the Lyapunov function is monotonically decreasing, and the sliding surface variable s converges to zero in a finite time, thus ensuring the asymptotic stability of the system on the sliding surface and its robustness to bounded uncertainties.

[0238] Considering that electro-hydraulic servo actuators are quite sensitive to high-frequency switching control, in order to reduce chattering in the actual system, the switching control in step S43 will be adjusted. Replacing the symbolic function in the control term with a saturation function that limits the boundary layer thickness, it can be expressed as:

[0239]

[0240] In the formula, φ>0 is the boundary layer thickness parameter; at this time, the switching control term can be rewritten as:

[0241]

[0242] Therefore, the virtual control quantity can be expressed as:

[0243]

[0244] Substituting the above virtual control quantity into the input transformation relationship obtained in step S41, we get:

[0245]

[0246] Finally, the expression for the servo valve control voltage is obtained as follows:

[0247]

[0248] The control voltage is used as the drive input of the valve-controlled cylinder electro-hydraulic servo actuator to achieve high-precision tracking of the desired displacement trajectory and robust suppression of sprung mass vibration under impact loads such as speed bumps and under conditions of parameter uncertainty in the electro-hydraulic servo active suspension system.

[0249] Step 4: Adjust controller parameters and compare simulation results;

[0250] S51: Values ​​of suspension system parameters and controller parameters;

[0251] Simulation verification

[0252] The suspension system parameters are shown in Table 1.

[0253] Table 1

[0254]

[0255] Considering the generality of sinusoidal road surfaces, the simulation verification in this paper mainly selects sinusoidal road surfaces such as... Figure 3 As shown.

[0256] The selected controller parameters are as follows:

[0257] c1=89.172, c2=1592.025, k=31, Φ=0.002;

[0258] Based on the above controller parameters, adjust the controller and verify the effectiveness of the feedback linearized sliding mode robust control strategy.

[0259] S52: Adjust the controller and analyze the effect of applying the feedback linearized sliding mode robust control strategy to the suspension system;

[0260] The equivalent speed bump sinusoidal displacement excitation road surface input is selected as:

[0261] q t =0.04sin(0.8πt)

[0262] The following graphical comparison further illustrates the controller's control effect, such as... Figures 4-7As shown, this invention compares the inner ring piston displacement tracking curves of an electro-hydraulic servo actuator under three control strategies. The results show that PID exhibits significant phase lag and a large amplitude error; while SMC improves tracking performance to some extent, it still suffers from strong high-frequency chattering. In contrast, under FLSMC, the actuator displacement is almost identical to the desired trajectory in amplitude, with only a very small steady-state deviation; the error curve is smooth and virtually chatter-free. Table 2 shows that the displacement tracking error RMS of FLSMC is approximately 6.2 × 10⁻⁶. -6 m, significantly lower than SMC's 6.1 × 10 -5 m and PID 1.9×10 -4 The error is reduced by approximately 96.74% compared to PID, and by approximately 89.84% compared to SMC, which fully demonstrates that the FLSMC method of this invention is significantly superior to PID and SMC strategies in terms of tracking accuracy, chatter suppression, and phase lag elimination.

[0263] Table 2

[0264]

[0265] pass Figure 8 The displacement response of the sprung mass of the suspension outer ring under the three control strategies can be further compared to evaluate their ability to compensate for and suppress sudden road impacts. The results show that the sprung mass response amplitude is the largest and the phase lag is significant under PID control, resulting in the worst compensation effect; while SMC can significantly reduce the peak value, there is still a relatively obvious residual oscillation; under the FLSMC strategy of this invention, the sprung mass displacement can quickly converge to near the equilibrium position with almost no overshoot and oscillation, exhibiting the best transient performance. Table 3 shows the RMS error and optimization rate of the sprung mass displacement under the corresponding operating conditions: the RMS values ​​for PID, SMC, and FLSMC are approximately 1.7 × 10⁻⁶. -4 m, 6.4×10 -5 m and 1.8×10 -5 Based on PID control, SMC and FLSMC are reduced by approximately 62.35% and 89.41% respectively, with FLSMC further reduced by approximately 71.87% compared to SMC. This demonstrates that the FLSMC scheme of this invention significantly outperforms the comparative controller in both inner-loop position tracking and outer-loop impact compensation. It effectively suppresses the inherent high-frequency chattering and suspension overshoot of sliding mode control, while improving trajectory tracking accuracy, robustness, and stability, exhibiting superior overall control performance compared to existing technologies.

[0266] Table 3

[0267]

[0268] In summary, through Figures 4-8As can be seen from the comparison of the simulation results in Tables 2 and 3, the feedback linearized sliding mode control algorithm of the present invention, when applied to the vehicle hydraulic active suspension system, not only significantly reduces the actuator displacement tracking error and the amplitude of sprung mass vibration, but also effectively suppresses the excessive dynamic deflection of the suspension and high-frequency vibration, thereby further improving the vehicle's ride comfort, driving smoothness and handling safety, demonstrating a comprehensive performance advantage over existing control strategies.

[0269] The above are preferred embodiments of this application, and are not intended to limit the scope of protection of this invention. It should be noted that those skilled in the art can make several improvements without departing from the principles of this technology, and these improvements should also be considered within the scope of protection of this application.

Claims

1. A robust sliding mode control method for electro-hydraulic servo active suspension with feedback linearization oriented to impact loads, characterized in that: The method includes the following steps: Step 1: Obtain vehicle parameters and operating status, and establish a one-quarter vehicle two-DOF active suspension dynamics model; Step 2: Establish a nonlinear model of the electro-hydraulic servo actuator with servo valve control voltage as input and piston displacement as output, and couple it with the suspension dynamics model; Step 3: Based on the nonlinear model of the actuator, an equivalent linear position servo model is constructed using feedback linearization-sliding mode composite control, and the global stability of the control algorithm is proved based on the Lyapunov function, thereby realizing the tracking of the inner ring displacement trajectory of the suspension and the suppression of the outer ring sprung mass vibration. Step 4: Adjust controller parameters and compare simulation results.

2. The method for feedback linearized sliding mode robust control of an electro-hydraulic servo active suspension oriented to impact loads according to claim 1, characterized in that: To obtain an accurate dynamic description of the suspension side and provide a foundation for subsequent electro-hydraulic servo actuator modeling and control law design, the process of establishing a quarter-vehicle two-degree-of-freedom active suspension dynamic model in step one specifically includes: S1: Obtain the state information of the vehicle's hydraulic active suspension system, the state information including state input data and state model data used to describe the dynamic characteristics of the system; S2: Based on the state model data obtained in step S1, establish a two-degree-of-freedom dynamic model of the electro-hydraulic servo active suspension, as shown below: S21: Establish the dynamic model of the active suspension according to Newton's second law: In the above formula, F t The expression is as follows: F t =K1(q t -With mu )+K2(q t -With mu ) 2 In the suspension dynamics model, m s The sprung mass is the sum of the mass of the car body frame and the passenger; m u This indicates the unsprung mass, which is the mass of the tire assembly; B p K represents the damping coefficient of the suspension system. t This represents the stiffness coefficient of the suspension system; z ms Indicates the vertical displacement of the sprung mass; z mu Indicates the vertical displacement of the unsprung mass; x p F represents the output displacement of the electro-hydraulic actuator system. t K represents the tire's elastic force; K1 and K2 represent the elastic force coefficients under various operating conditions, and neither is zero; q t This indicates the road surface input. S22: Abstract the dynamic model into a mathematical model of the suspension; First, the dynamic model is written in the form of a state-space expression: Establish the spatial state expression for the vehicle's active suspension, defining the state variables as follows: The dynamic equation above can be rewritten as:

3. The method for feedback linearized sliding mode robust control of an electro-hydraulic servo active suspension oriented to impact loads according to claim 2, characterized in that: Based on the aforementioned quarter-vehicle two-degree-of-freedom active suspension dynamics model, in order to achieve integrated modeling of the valve-controlled cylinder electro-hydraulic servo actuator and the suspension dynamics model, and to provide an actuator-side mathematical model for feedback linearization and sliding mode control, the construction process of the nonlinear dynamics model of the valve-controlled cylinder electro-hydraulic servo actuator in step two includes: S3: Based on the structural parameters and operating data of the electro-hydraulic servo system obtained in step S1 and the two-degree-of-freedom dynamic model of the electro-hydraulic servo active suspension established in step S2, a nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo actuator is constructed. This yields a nonlinear state equation with piston displacement, piston velocity, and load pressure as state variables, and provides actuator force / position input for the active suspension dynamic model. The construction process includes force balance relationships, pressure dynamic equations, valve orifice flow equations, and servo valve drive relationships, which are then uniformly written into a nonlinear dynamic model, as detailed below: S31: Establish the hydraulic cylinder piston force balance equation; The electro-hydraulic servo actuator is considered as being composed of an equivalent load mass m eq Equivalent damping coefficient B p Equivalent stiffness coefficient K t An actuator consisting of the effective working area A of the piston and the piston rod is denoted as x. p Speed ​​is speed is The hydraulic cylinder load pressure is P L If the external load force is F, then the piston force balance equation can be expressed as: This formula describes the nonlinear motion relationship of a hydraulic cylinder piston under load pressure, suspension equivalent stiffness and damping, and external load. S32: Establish the hydraulic cylinder piston force balance equation; Considering the compressibility and leakage effect of hydraulic oil, let V be the equivalent total volume of the two chambers of the hydraulic cylinder and β be the bulk modulus of the hydraulic oil. e The total leakage coefficient of the hydraulic cylinder is C. t If the load flow rate of the hydraulic cylinder is Q, then the dynamic balance equation of the load pressure is: In the formula, C represents the flow rate due to the volume change caused by piston movement. t P L Indicates pressure-related leakage flow rate. This represents the equivalent flow rate caused by compressibility. S33: Establish the flow equation and driving relationship of the servo valve orifice; The load flow Q of the electro-hydraulic servo actuator is considered to be generated by throttling at the servo valve orifice, and the servo valve orifice flow coefficient is denoted as C. d The valve port area gradient is ω, and the valve core displacement is x. v The oil supply pressure is P s If the density of the hydraulic oil is ρ, then the load flow rate can be expressed as: In the formula, sgn() is a sign function used to distinguish between valve opening degree and flow direction; Assuming a linear proportional relationship exists between the servo valve spool displacement and the control input voltage u, it can be expressed as: x v =K v u In the formula, K v The voltage-displacement gain coefficient of the servo valve is used to map the electrical signal u into the adjustment amount of the hydraulic flow. S34: Construct a nonlinear state-space model of the electro-hydraulic servo actuator; By selecting piston displacement, piston velocity, and load pressure as the system state variables, it can be expressed as: x1=x p , Using the servo valve control voltage u as the system input, and leveraging the force balance equation, pressure dynamic equation, valve orifice flow equation, and linear drive relationship established in S31-S33, the system differential equation is reorganized as follows: Thus, we obtain the state vector The nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo actuator, characterized by the control input u, provides the basis for the design of the feedback linearized sliding mode composite control method in step S4.

4. The method for feedback linearized sliding mode robust control of an electro-hydraulic servo active suspension oriented to impact loads according to claim 3, characterized in that: Based on the active suspension dynamics model of claim 2 and the nonlinear dynamics model of the valve-controlled cylinder electro-hydraulic servo actuator of claim 3, in order to achieve accurate tracking of the piston displacement of the electro-hydraulic servo actuator and improve the robustness of the system under impact loads and parameter uncertainties, the design process of the feedback linearized sliding mode composite control method in step four includes: S4: Based on the state input data obtained in step S1, the two-degree-of-freedom dynamic model of the electro-hydraulic servo active suspension established in step S2, and the steps... The nonlinear dynamic model of the valve-controlled cylinder electro-hydraulic servo actuator constructed by S3 is used to build a feedback linearized sliding mode composite control method to accurately track and control the piston displacement of the electro-hydraulic servo actuator, and to achieve robust suppression of the vertical vibration of the sprung mass under impact load and parameter perturbation. The feedback linearized sliding mode composite control method includes sub-steps for constructing an equivalent linearized model, sub-steps for error dynamics and sliding surface design, sub-steps for deriving equivalent control and arrival law control laws, and sub-steps for stability analysis and boundary layer chattering suppression based on Lyapunov functions, as detailed below: S41: Sub-step for constructing the equivalent linearization model; The standard form of the affine nonlinear system corresponding to the state equation of the nonlinear mathematical model of the electro-hydraulic position servo system obtained in step S34 is: In the formula: h(x) = x1 According to differential geometry theory, the calculation yields: According to the definition of relative order, the above calculation results show that the relative order of the system is 3, which is equal to the system dimension. Therefore, the system can achieve state feedback linearization. Based on the feedback linearization method, the transformation relationship between the new state variables and the original state variables is constructed as follows: Therefore, the state equation of the original nonlinear system can be transformed into the state equation in linear space, which can be expressed as: In the formula, v is the control quantity of the linear system in the new coordinate system, and its relationship with the control quantity u of the nonlinear system in the original coordinate system is as follows: v=α(x)+β(x)u In the formula: α(x)=L 3 f h(x),β(x)=L g L 2 f h(x) By performing an inverse coordinate transformation on the control quantity v of the linear system, we can obtain the control quantity u of the nonlinear system in the original coordinate system as follows: u = [(v - α(x)] / β(x) =[v-L 3 f h(x)] / [L g L 2 f h(x)] S42: Error dynamics and sliding surface design sub-steps; Based on the third-order equivalent linear position servo model obtained in step S41, the piston rod displacement tracking error is defined as: e=z d -z5 In the formula, z d Let be the desired displacement of the piston rod; The tracking error vector of the system is defined as follows: Since the system model obtained after feedback linearization is a third-order linear system, the sliding surface can be designed as follows: In the formula, c1>0 and c2>0 are the sliding surface design parameters. The sliding surface is equivalent to the configuration of the closed-loop characteristic equation of the error polynomial. When the system state is restricted to around s=0, the error dynamics satisfy the expected exponential convergence characteristics. S43: Sub-steps for derivation of equivalent control and arrival law control laws; Based on the error variable and sliding surface defined in step S42, it can be expressed as follows: The equivalent linear model obtained in step S41 is: Based on this, taking the derivative with respect to the sliding surface yields: To ensure the system remains on the sliding surface under the ideal model, let The equivalent control quantity can be obtained by solving: Considering the parameter uncertainties and external disturbances in the actual system, in order to ensure that the system state can reach the sliding surface from any initial conditions, a switching control term v in the form of an arrival law is introduced. si Using the exponential reaching law, it can be expressed as: In the formula, k > 0 represents the arrival law gain; The arrival law and By comparing the expressions, the switching control quantity can be obtained: v si =-ksgn(s) Thus, the complete form of the virtual control quantity is obtained: Under ideal conditions where high-frequency chattering is ignored, the virtual control quantity can ensure that the system state arrives at and remains in the neighborhood of the sliding surface within a finite time, thereby achieving robust suppression of model uncertainties and shock disturbances. S44: Stability analysis and boundary layer chattering suppression sub-steps based on Lyapunov functions; Based on the virtual control quantity obtained in step S43, a Lyapunov function is introduced to analyze the stability of the closed-loop system: For this feedback-linearized third-order linear system, we have Taking the derivative with respect to V, we get: Decompose the virtual control quantity into: v=v eq +v si +Δ(x,t) Where v eq As an equivalent control term, v si The switching control term is denoted by Δ(x,t), which represents the merged modeling error and external disturbance term. It is assumed that a constant Δ exists. max >0, such that |Δ(x,t)|≤Δ max ; In equivalent control v eq In an ideal scenario, accurate compensation for the modeled partial dynamics can be expressed as: At this point: Using the inequality |sΔ(x,t)|≤|s|Δ max ,get: Therefore, when the arrival law gain satisfies k > Δ max hour, The Lyapunov function is monotonically decreasing, and the sliding surface variable s converges to zero in finite time, thus ensuring the asymptotic stability of the system on the sliding surface and its robustness to bounded uncertainties. Considering that electro-hydraulic servo actuators are highly sensitive to high-frequency switching control, in order to reduce chattering in the actual system, the sign function in the switching control item in step S43 can be replaced with a saturation function with a defined boundary layer thickness, which can be expressed as: In the formula, φ>0 is the boundary layer thickness parameter; at this time, the switching control term is rewritten as: Therefore, the virtual control quantity can be expressed as: Substituting the above virtual control quantity into the input transformation relationship obtained in step S41, we get: u = [(v - α(x)] / β(x) =[v-L 3 f h(x)] / [L g L 2 f h(x)] Finally, the expression for the servo valve control voltage is obtained as follows: The control voltage is used as the drive input of the valve-controlled cylinder electro-hydraulic servo actuator to achieve high-precision tracking of the desired displacement trajectory and robust suppression of sprung mass vibration under impact loads such as speed bumps and under conditions of parameter uncertainty in the electro-hydraulic servo active suspension system.

5. The method for feedback linearized sliding mode robust control of an electro-hydraulic servo active suspension oriented to impact loads according to claim 1, characterized in that: The method for adjusting controller parameters and comparing simulation results in step four specifically includes: A: For the equivalent impact condition and the given desired piston displacement trajectory, by adjusting the sliding surface parameters, switching gain and boundary layer thickness, the simulation results of the piston displacement of the electro-hydraulic servo actuator were compared using PID control, sliding mode control and feedback linearized sliding mode variable structure composite control, respectively. The set of controller parameters that minimizes displacement tracking error and chattering was selected. B: Under the controller parameters determined by A, the simulation results of the vertical displacement of the sprung mass under the same impact conditions are compared. The peak value, convergence speed and root mean square index of PID control, sliding mode control and feedback linearized sliding mode variable structure composite control are compared to verify the superiority of the composite control in terms of sprung mass vibration suppression and ride comfort improvement.

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