A method for restraining disturbance by using a nonlinear active suspension with preset attenuation performance

Abstract

The present application belongs to the technical field of inversion control of automobile active suspension, and particularly relates to a nonlinear active suspension constraint disturbance suppression method with preset attenuation performance, which comprises the following steps: Step 1: a 1 / 4 vehicle nonlinear uncertain active suspension model is established, and a control equation containing matching disturbance force and unmatched disturbance force is established; Step 2: based on the compensation of matching and unmatched disturbance of the 1 / 4 vehicle nonlinear uncertain active suspension model in Step 1, an error expression of disturbance estimation is obtained through dynamic surface technology, and an adaptive disturbance update law of the system is constructed by introducing a preset attenuation performance function; Step 3: on the basis of Step 2, an inversion control law with preset attenuation performance is established in combination with the disturbance estimation law, and stability and boundedness of the inversion control law are analyzed. The present application can compensate matching and unmatched disturbance simultaneously, coordinate transient and steady-state performance, implement the control scheme of active suspension by using low-cost sensors, and improve the disturbance suppression performance of the suspension.

Description

Technical Field

[0001] This invention belongs to the field of inversion control technology of active suspension for automobiles, and specifically relates to a nonlinear active suspension constraint interference suppression method with preset attenuation performance. Background Technology

[0002] With the rapid development of electrification, intelligentization, connectivity, and sharing, the research demand for active safety and comfort continues to grow, making it one of the key technologies for promoting the development of intelligent connected vehicles. Since active suspension possesses adaptive control and adjustment capabilities, the overall comfort performance of a vehicle can be comprehensively improved by designing appropriate active control methods. Based on this, researchers have proposed some classic control methods, such as LQG control, adaptive control, sliding mode control, and inverse control. Simulation and experimental studies have verified the effectiveness of these active control methods.

[0003] In engineering practice, accurate vehicle parameter calibration is costly, and it is difficult to accurately predict model parameter perturbations, high-order nonlinear dynamics, and external disturbances caused by actual bumpy road conditions. To reduce the cost of parameter measurement and control hardware, some scholars have proposed approximation-free control for electro-hydraulic active suspension, considering the preset performance of the controller; however, this method does not consider compensation for external disturbances. Other studies have investigated sliding mode control methods for automotive active suspension, designing disturbance observers to compensate for the effects of external disturbances, achieving better nonlinear adaptive control performance.

[0004] Disturbance compensation-based control methods are effective disturbance suppression control methods. For nonlinear uncertain systems, this method does not require precise model parameter calibration, significantly reducing implementation costs. Some scholars have applied high-order sliding mode observers and sliding mode controllers to study the disturbance suppression control problem of active suspensions. However, because high-order sliding mode control can map chattering to higher-order dynamics, it reduces comfort. Other scholars have used extended state observers (ESOs) to implement disturbance suppression control of active suspensions, combining them with PD control to form an active disturbance rejection controller, but this does not consider both transient and steady-state performance in disturbance suppression. Current conventional disturbance observer design methods, such as sliding mode disturbance observers, high-order sliding mode observers, and ESOs, do not consider mismatch disturbances in the suspension system. Mismatch disturbances originate from measurement errors and environmental interference in real systems and are widely present in practical nonlinear systems. Furthermore, because mismatch disturbances are not within the control channel, compensation and observation are difficult. Secondly, if the designed observer cannot simultaneously consider transient, steady-state performance and convergence rate, it is prone to overshoot and instability when encountering large shocks. For automotive suspension control, it is often necessary to maintain the control state within a certain limit range for a short period of time in order to achieve the expected transient performance.

[0005] Furthermore, suspension dynamic deflection is also a key performance indicator. To prevent it from exceeding its travel range and damaging the mechanical structure, some researchers have designed a filter-based model reference system. This system uses an adaptive inversion tracking control method to coordinate control objectives under different road conditions, achieving good control results. Therefore, theoretically ensuring strict time-domain constraints on suspension dynamic deflection is crucial. Researchers have already proposed the obstacle Lyapunov boundedness method and H... ∞ Classic constraint control methods such as the / GH2 method.

[0006] In addition to the factors mentioned above, it is difficult to measure the vehicle's vertical absolute displacement and velocity in real time. The method of frequency domain integration of acceleration requires a certain amount of computing power, which increases the cost of hardware. Summary of the Invention

[0007] To address the aforementioned problems, this invention designs an interference suppression control law that considers a preset attenuation performance (PPF), capable of simultaneously compensating for matched and mismatched interferences and coordinating transient and steady-state performance. This invention also references overcurrent protection constraint control methods, designing a nonlinear constraint response mechanism to limit suspension dynamic deflection. This invention utilizes low-cost sensors to implement an active suspension control scheme, and improves suspension interference suppression performance by designing an inverse control method that considers constraint performance. Furthermore, to simultaneously adjust vehicle acceleration and suspension dynamic deflection, a dynamic reference trajectory tracking model with nonlinear damping is provided. The effectiveness of the proposed scheme is verified through simulation and rapid prototyping control experiments.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A nonlinear active suspension constraint disturbance suppression method with preset attenuation performance includes:

[0010] Step 1: Establish a 1 / 4 car nonlinear uncertain active suspension model, and based on the established model, establish control equations with active suspension dynamic deflection as the measured object, including matching disturbance force and mismatch force disturbance, and design a high static and low dynamic oscillator reference model that depends on the active suspension dynamic deflection.

[0011] Step 2: Based on the compensation matching and mismatch disturbances of the 1 / 4 vehicle nonlinear uncertain active suspension model in Step 1, the error expression of disturbance estimation is obtained through dynamic surface technology. An adaptive disturbance update law of active suspension is constructed by introducing a preset attenuation performance function, and the preset attenuation performance of disturbance estimation error is analyzed by using a quadratic Lyapunov function.

[0012] Step 3: Based on Step 2, an inversion control law with preset attenuation performance is established by combining the adaptive disturbance update law. The inversion control law includes a virtual control law and a constraint control law. Then, dynamic surface technology is used, and a nonlinear constraint response mechanism is introduced to limit the range of active suspension dynamic deflection. Finally, stability and boundedness analysis are performed on the inversion control law.

[0013] Preferably, step 1 includes:

[0014] Step 1.1: Establish a 1 / 4 car nonlinear uncertain active suspension model, and apply Newton's second law to establish the dynamic equations based on the structural characteristics of the active suspension;

[0015] Step 1.2: Model the damping force and footprint tire force of the active suspension damper:

[0016] Step 1.3: Based on steps 1.1 and 1.2, establish the nonlinear active suspension control equation with the active suspension dynamic deflection as the measured object;

[0017] Step 1.4: Based on Step 1.3, establish a reference model for a high static and low dynamic oscillator that depends on the dynamic deflection of the suspension.

[0018] Preferably, step 2 includes:

[0019] Step 2.1: Construct the dynamic surface expression for the error;

[0020] Step 2.2: Introduce the PPF function to apply a preset attenuation performance constraint;

[0021] Step 2.3: Combining Step 2.1 and Step 2.2, obtain the error transformation function;

[0022] Step 2.4: Based on Step 2.3, establish an adaptive disturbance update law;

[0023] Step 2.5: The adaptive disturbance update law in Step 2.4 is analyzed for stability using a quadratic Lyapunov function.

[0024] Preferably, step 3 includes:

[0025] Step 3.1: Based on the adaptive disturbance update law obtained in Step 2, establish an inversion control law with preset attenuation performance;

[0026] Step 3.2: Analyze the stability and boundedness of the inversion control law in Step 3.1.

[0027] Compared with the prior art, the beneficial effects of the present invention are:

[0028] 1. The present invention designs an interference suppression controller that takes into account a preset attenuation performance (PPF), which can simultaneously compensate for matched and mismatched interferences and coordinate transient and steady-state performance;

[0029] 2. This invention also references the overcurrent protection constraint control method, and limits the suspension dynamic deflection by designing a nonlinear constraint response mechanism;

[0030] 3. This invention utilizes low-cost sensors to implement an active suspension control scheme, and improves the suspension's disturbance suppression performance by designing an inverse control method that considers constraint performance;

[0031] 4. In order to simultaneously adjust vehicle body acceleration and suspension dynamic deflection, this invention provides a dynamic reference trajectory tracking model with nonlinear damping, and applies simulation and rapid prototyping control tests to verify the effectiveness of the proposed scheme. Attached Figure Description

[0032] 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.

[0033] In the attached diagram:

[0034] Figure 1 This is a flowchart of the method of the present invention;

[0035] Figure 2 This is a nonlinear 1 / 4-car active suspension model;

[0036] Figure 3 The time-domain curve of the preset decay performance function;

[0037] Figure 4 shows a schematic diagram of road surface interference: (a) excitation of block road surface; (b) excitation of sloping road surface;

[0038] Figure 5 For vehicle body response under block road surface;

[0039] Figure 6 For the hard constraint response of the suspension under the block road surface;

[0040] Figure 7 This is the estimation error for the disturbance under the block road surface;

[0041] Figure 8 To reduce trajectory tracking error on roads without enclosing blocks;

[0042] Figure 9 PSD (Power Detector) of vehicle acceleration under the road surface block;

[0043] Figure 10 Vehicle response on sloping roads;

[0044] Figure 11For the hard-constraint response of the suspension on a sloping road surface;

[0045] Figure 12 This is for the estimation of disturbances and trajectory tracking errors under the sloping road surface;

[0046] Figure 13 For rapid prototyping control test platform;

[0047] Figure 14 Vehicle body response under harmonic excitation;

[0048] Figure 15 For trajectory tracking error;

[0049] Figure 16 The vehicle body acceleration PSD under harmonic excitation. Detailed Implementation

[0050] 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.

[0051] Example:

[0052] See attached document Figure 1-16 As shown, in order to improve the steady-state and transient disturbance suppression performance of the active suspension system, this invention establishes a nonlinear 1 / 4-vehicle active suspension model and designs a disturbance compensation control law with a preset attenuation performance (PPF). By tracking the dynamic reference trajectory, the active suspension achieves model-free tracking (MFT) control. In the control scheme, a nonlinear constraint response mechanism is designed to limit the suspension dynamic deflection, thereby realizing PPF-MFT control of the active suspension.

[0053] Specifically, it is a nonlinear active suspension constraint interference suppression method with preset attenuation performance, comprising:

[0054] Step 1: Establish a 1 / 4-car nonlinear uncertain active suspension model. Based on this model, establish control equations that take the active suspension dynamic deflection as the measured object and include both matched and mismatched disturbances. Design a high static low dynamic oscillator reference model that depends on the suspension dynamic deflection. Specifically:

[0055] Step 1.1: To fully consider the nonlinearity and unknown dynamics of the system, establish as follows: Figure 2 The 1 / 4-car nonlinear uncertain active suspension model shown is used to establish the dynamic equations of the active suspension based on the structural characteristics of the active suspension and applying Newton's second law:

[0056]

[0057] like Figure 2 As shown, where m sFor the sprung mass of the vehicle body, m b For unsprung mass; u is the active control force, F s F represents the spring force of the active suspension. b This indicates the damping force of the active suspension;

[0058] The tire model is simplified to a parallel distribution of springs and dampers, with a resultant force F. t The vertical displacement of the sprung mass of the vehicle body is z. s The vertical displacement of the unsprung mass is z. b The vertical displacement of the unsprung mass is z. b The road surface elevation is z(y); The coordinates represent the length of the tire footprint, where L represents the contact length between the tire and the road surface.

[0059] The spring force of the suspension has the following third-order nonlinear form:

[0060] F s =k s (z s -z b )+k sn (z s -z b ) 3 (2)

[0061] In the formula: k s and k sn These are the linear and nonlinear coefficients of the spring, respectively;

[0062] Step 1.2: Due to the piecewise nonlinearity of the active suspension damper's extension and retraction, the damping force is modeled as follows:

[0063]

[0064] In the formula: b e and b c These are the linear and nonlinear coefficients of the damper, respectively;

[0065] The footprint tire force model is as follows:

[0066]

[0067] In the formula: L represents the contact length between the tire and the road surface, z c This indicates the amount of tire deformation under static load. Therefore The road surface elevation is the independent variable; V represents the vehicle's forward speed; k t and b t The coefficients represent the values ​​in a single spring-damped model; g is the acceleration due to gravity.

[0068] Step 1.3: Since the relative displacement of the active suspension is easy to measure in practice, based on steps 1.1 and 1.2, the control equations for the active suspension are established with the dynamic deflection of the active suspension as the measured object:

[0069]

[0070] In the formula: x1=z s -z b +Δ;

[0071] x1 represents state variable 1 of the active suspension, x2 represents state variable 2 of the active suspension, and m represents the mass ratio. u For unsprung mass, Δ represents the mismatch between the measured value and the true value. Therefore, d1 represents the mismatch disturbance of the active suspension model. In practice, the value of Δ is usually small, but its rate of change is large. Therefore, d1 affects the stability of the system.

[0072] Step 1.4: Based on Step 1.3, implement the control scheme, let u = υ / b, and define d2 as the matching nonlinear disturbance force of the system, where d2 satisfies

[0073]

[0074] In the formula: b is the nominal value of m, which is estimated by recursive least squares method in open-loop mode.

[0075] Step 1.5: To coordinate vehicle acceleration and suspension dynamic deflection, a high static and low dynamic oscillator reference model dependent on suspension dynamic deflection is established. The output of the uncertain active suspension model will track the output of the oscillator reference model. The oscillator reference model satisfies the following state-space equations:

[0076]

[0077] In the formula: Represents the state vector in the state-space equation; ν(t) represents the vertical acceleration of the unsprung mass; ν(t) represents the output vector of the oscillator reference model; y d and These represent the reference trajectory and its rate of change, respectively; F n (t) represents the nonlinear damping force to be designed;

[0078] The matrices in equation (7) satisfy:

[0079]

[0080] k d The stiffness of the oscillator is expressed by the following formula:

[0081]

[0082] In the formula: z max This represents the maximum working stroke of the active suspension space; Indicates relative active suspension travel; γ represents the safety threshold; z s z represents the vertical displacement of the sprung mass. b This indicates the vertical displacement of the unsprung mass.

[0083] Its working principle can be described as follows: when the relative active suspension travel is less than the safety threshold, the oscillator stiffness is relatively soft, which can better isolate external vibrations, while the damping can attenuate the system's kinetic energy; when the relative active suspension travel is greater than the safety threshold, the oscillator stiffness increases to save suspension working space. To strictly ensure |y d |≤z max A saturation function is connected in series at the output.

[0084] Step 1.6: The larger the damping coefficient, the better the vibration reduction performance of the oscillator at the natural frequency, but the weaker the vibration reduction performance at high frequencies. Therefore, the nonlinear damping in Step 1.5 satisfies the following: the damping coefficient is large at the natural frequency and small at high frequencies. Therefore, for F in equation (7) n (t) Taking the Laplace transform, we get (9) The following formula for the second-order quasi-bandpass damping force is designed:

[0085] F n (s)=U(s)y d (s)s (9)

[0086] In the formula: s represents the Laplace operator;

[0087] U(s) represents a second-order quasi-bandpass filter, and its complex domain calculation formula is:

[0088]

[0089] In the formula: k l =20 represents the bandpass gain; ξ l Indicates the damping ratio; ω l Represents the center frequency, when k l =1 and a l When ω = 1, the nonlinear damping force simplifies to a conventional linear damping force. To satisfy the vibration damping performance at the natural frequency and high frequencies, ω l Approaching the natural frequency of the oscillator For second-order systems, to prevent overshoot, the damping ratio is typically taken as 0.4-0.8, while when the damping ratio is ξ... l When the value is 0.707, the overshoot is less than 5% and the settling time is the shortest, which meets the engineering requirements.

[0090] Design goals:

[0091] In the tracking control performance indicators of active suspension, in order to simultaneously meet the preset error decay rate, maximum overshoot, and small steady-state error, the following PPF function is defined:

[0092]

[0093] In the formula: ρ i0 ρ i∞ κ i ρ is a preset positive constant; i0 ρ represents the initial error bound; i∞ κ represents the steady-state error bound; i The convergence rate is represented by the PPF time-domain curve as shown below. Figure 3 As shown.

[0094] The PPF function has the following properties:

[0095] (1)ρ i (t) is a positive and decreasing monotonic function;

[0096] (2)lim t→∞ ρ i (t)=ρ i∞ >0, lim t→0 ρ i (t)=ρ i0 .

[0097] By indirectly reducing the vehicle's acceleration by tracking a reference trajectory, the controlled state x i Tracking error z i Need to meet

[0098] -ρ i (t)<z i <ρ i (t),

[0099] Since the external disturbances of the active suspension are time-varying and continuous, the steady-state error ρ ∞ Not equal to zero.

[0100] In addition, to ensure that the suspension dynamic deflection is bounded, x1 satisfies

[0101] |x1|<z max ,

[0102] To improve vehicle handling stability, the tire dynamic-to-static load ratio must meet the following requirements.

[0103] |F t | / G<1,

[0104] In the formula: G=(m s +m b g represents the static load of the suspension; g represents the acceleration due to gravity.

[0105] In the comprehensive performance evaluation of the suspension, the root mean square value (RMS) is calculated as follows.

[0106]

[0107] In the formula: n represents the number of signal samples; χ represents the signal to be evaluated.

[0108] For ease of calculation and proof, we first define the following strictly smooth increasing function:

[0109]

[0110] In the formula: e represents the base of the natural logarithm function; ε i It represents an independent variable.

[0111] S(ε i ) is a strictly smooth increasing function with the following properties:

[0112] (1)-1<S(ε i ) < 1,

[0113] (2)

[0114] The inverse function of an increasing function exists and satisfies:

[0115]

[0116] In the formula: θ i =z i / ρ i Let represent the normalized error variable. For ease of stability analysis and proof, the following lemma is introduced.

[0117] Lemma 1: If the inverse function S(ε) i ) is bounded, that is |ε i If |<∞, then -ρ i (t)<z i <ρ i (t), Established.

[0118] Lemma 2: Define Lyapunov functions satisfy in If Ω and Ω are positive constants, then the following inequality holds.

[0119]

[0120] Step 2: Based on the compensation matching and mismatch disturbances of the 1 / 4-car nonlinear uncertain active suspension model from Step 1, the error expression for disturbance estimation is obtained through dynamic surface techniques. An adaptive disturbance update law for the system is constructed by introducing a preset attenuation performance function, and the preset attenuation performance of the disturbance estimation error is analyzed using a quadratic Lyapunov function. The specific steps are as follows:

[0121] Step 2.1: Construct the dynamic expression for the error;

[0122] Step 2.1.1: Establish the following dynamic surface:

[0123]

[0124] In the formula: k f It is a time constant, and k f >0, its value is greater than the signal sampling frequency; x f ω f and x1 and x2 are the state variables of the dynamic surface, and x1 and x2 are the state variables of the active suspension.

[0125] Further, there are:

[0126]

[0127] In the formula: d 1f =(x1-x f ) / k f -ω f ,

[0128] Step 2.1.2: Define dummy intermediate variables N and Z, with their rates of change as follows:

[0129]

[0130] In the formula: l is a filtering parameter, and l > 0. The solution to equation (12) is:

[0131]

[0132]

[0133] In the formula: t represents time, r represents the integral, and e represents a natural number;

[0134] definition Then (13) and (14) can be written as

[0135]

[0136] Construct the following error variable:

[0137]

[0138] In the formula: S and T are error variables, and These are the estimators for d1 and d2, respectively;

[0139] Substituting (15) into (16), we define the disturbance estimation error. and achievable

[0140]

[0141] Therefore:

[0142]

[0143] Step 2.2: Introduce the PPF function to apply a preset attenuation performance constraint;

[0144] Based on step 2.1, the following preset attenuation performance function (PPF) is introduced:

[0145]

[0146] In the formula: η i0 >0 indicates initial error; η i∞ >0 indicates the maximum steady-state error; v i >0 indicates an exponential decay rate;

[0147] Then (19) satisfies the following performance

[0148] (1)η i (t) is a monotonically decreasing positive function;

[0149] (2)lim t→∞ η i (t)=η i∞ >0,lim t→0 η i (t)=η i0 >0;

[0150] The dynamic error estimation of the disturbance, including the preset attenuation performance (PPF), must meet the following requirements:

[0151]

[0152]

[0153] Step 2.3: Combining Step 2.1 and Step 2.2, obtain the error transformation function;

[0154] Define a y iLet be a strictly smooth increasing function of the independent variable, with the following form:

[0155]

[0156] In the formula: y i Indicates the transformation error variable;

[0157] Equation (22) obviously satisfies:

[0158] a:-1<H(y i ) < 1,

[0159] b:

[0160] Combining (18) and (22), define for:

[0161]

[0162] According to Lemma 1, if y i If it is bounded, then (20) and (21) hold, where y i It can be represented as

[0163]

[0164] In the formula:

[0165]

[0166] η2 is the preset decay performance function η2(t);

[0167] According to equation (24), we can further obtain

[0168]

[0169] y1 and y2 are transformation error variables. Indicates tracking error The ratio to the preset attenuation performance function η2(t).

[0170] Step 2.4: Based on Step 2.3, establish an adaptive disturbance update law;

[0171] In order to establish an adaptive disturbance update law and Calculating the derivative of (25) yields...

[0172]

[0173] In the formula:

[0174]

[0175] in, Design the following adaptive disturbance update law model:

[0176]

[0177] In the formula: Γ1>0 and Γ2>0 are both learning rate parameters. It is the reciprocal of j1.

[0178]

[0179] In order to obtain and Employing dynamic surface technology:

[0180]

[0181] In the formula: D 1e and D 2e For the state variables of the dynamic surface;

[0182] but and It can be approximated as:

[0183]

[0184] Combining (27) and (29), the following adaptive disturbance estimation update law can be obtained:

[0185]

[0186] Further combining (26)-(30), we can obtain the dynamic equation for the error transformation variable:

[0187]

[0188] Step 2.5: The adaptive disturbance update law in Step 2.4 is analyzed for stability using a quadratic Lyapunov function.

[0189] To demonstrate the pre-defined attenuation performance of the interference estimation error, the following quadratic Lyapunov function is selected for verification:

[0190]

[0191] Taking its derivative, we get:

[0192]

[0193] In the formula: Γ m =min{Γ1,Γ2};

[0194] According to Lemma 2, the transformation error variable yi It is bounded, that is, y i ∈L ∞ Furthermore, according to Lemma 1, With this assurance, the preset attenuation performance is satisfied. Thus, the design of the disturbance estimator is complete, and its output can be used to compensate for the unknown nonlinear dynamics of the system and improve the control accuracy.

[0195] Step 3: Based on Step 2, an inversion control law with preset attenuation performance is established by combining the disturbance estimation law. The inversion control law includes a virtual control law and a constraint control law. To avoid calculating the derivative of the virtual control law in the inversion control, dynamic surface technology is used, and a nonlinear constraint response mechanism is introduced to limit the range of suspension dynamic deflection. Finally, stability and boundedness analysis are performed. Specifically, this includes:

[0196] Step 3.1: Combine the disturbance estimation law to establish an inversion control law with preset attenuation performance; the specific steps are as follows:

[0197] Step 3.1.1: Define the trajectory tracking error of the active suspension:

[0198] z1 = x1 - y d (34)

[0199] Step 3.1.2: Based on the preset attenuation performance function, design the tracking error as the target, satisfying:

[0200] -ρ1(t)<z1<ρ1(t),

[0201] ρ1(t) represents the upper and lower bounds of the tracking error;

[0202] Step 3.1.3: Design the conversion error ε1 as:

[0203]

[0204] In the formula:

[0205] Step 3.1.4: Based on Step 3.1.3, design the virtual control law:

[0206]

[0207] In the formula: k1>0 is the control gain; P = -z max -y d Notice |y d |≤z max Therefore, and P <0,

[0208] Step 3.1.5: Define the error variable z2 as:

[0209] z² = x² - α² (38)

[0210] Meanwhile, the transformation error ε2 is defined as follows:

[0211]

[0212] In the formula:

[0213] Step 3.1.6: Combining the parameters obtained from steps 3.1.1 to 3.1.5, design the following constraint control law:

[0214]

[0215] In the formula: k2>0 is the control gain, and Λ satisfies:

[0216] Step 3.1.7: To avoid the tediousness of engineering calculations, the derivative of the virtual control law is approximated by the dynamic surface technique as equation (41):

[0217]

[0218] In the formula: α 2f For the state variables of the dynamic surface;

[0219] Based on the above analysis, the following conclusions can be drawn:

[0220] Inference: For the nonlinear suspension system (5), by applying the preset attenuation performance disturbance estimator (30), virtual control law (37), and constraint control law (40), if the initial conditions satisfy |z i (0)|<ρ i (0), then all error signals are uniformly bounded and satisfy the tracking error equation (35); if Then the suspension dynamic deflection constraint satisfies |x1|<z max ,t∈[0,+∞);

[0221] Step 3.2: Prove the stability and boundedness of the inversion control law obtained in Step 3.1:

[0222] Step 3.2.1: Stability Analysis:

[0223] Step 3.2.1.1: Based on the error variable z1 = x1 - y d Given z² = x² - α², calculate the following derivatives:

[0224]

[0225] Step 3.2.1.2: Substituting the virtual control law α2 into (42) yields the dynamic equation of θ1:

[0226]

[0227] Step 3.2.1.3: Similarly, the derivative of θ² can be obtained as:

[0228]

[0229] Step 3.2.1.4: Substituting the constraint control law υ obtained in step 3.1.6 into (44) yields:

[0230]

[0231] It can be seen that, and They are all continuous functions;

[0232] Step 3.2.1.5: Further solving for the derivative of the conversion error ε1 yields:

[0233]

[0234] In the formula:

[0235] Step 3.2.1.6: Similarly, solve for the derivative of the conversion error ε2:

[0236]

[0237] In the formula:

[0238] Define a positive constant γ M such that 0 < γ 1,2 <γ M γ M Indicates γ 1,2 The supremum;

[0239] Step 3.2.1.7: Use the following quadratic Lyapunov function:

[0240]

[0241] Its derivative is:

[0242]

[0243] Therefore:

[0244]

[0245] because Therefore It is bounded and satisfies the following conditions:

[0246]

[0247] According to (48), the following inequality can be obtained:

[0248] -ε1 2 -ε2 2 ≤-2V (51)

[0249] Combining (50) and (51), we can obtain:

[0250]

[0251] In the formula:

[0252]

[0253] π=min{2γ1(k1-0.5),2γ2(k2-0.5)}>0;

[0254] When V≥C / π, we have According to Lemma 2, V will converge to a compact set Ω = {V|V≤C / π} in finite time, therefore ε i It is bounded; therefore, according to Lemma 1, θ i ∈(-1,1), and -ρ i (t)<z i <ρ i (t), Q.E.D.

[0255] Step 3.2.2: Boundedness Analysis:

[0256] Step 3.2.2.1: Theoretically derive the condition for the boundedness of the suspension dynamic deflection and define a range. x1∈(-z max ,z max ) is equivalent to Analyzing the range of z1, we can obtain the following by taking the derivative with respect to z1:

[0257]

[0258] In the formula:

[0259] Step 3.2.2.2: For any There exists a time constant T such that t∈[0,T), as can be seen from the above analysis, Since it is bounded, there exists a positive constant N such that t∈[0,T), the range of z1 is divided into three intervals for analysis. First, define and P2∈( P Let's discuss the following three cases, 0, respectively:

[0260] Case 1: Let In the formula when t∈[0,T), we have

[0261]

[0262] Based on (53) and (54), we can deduce that:

[0263]

[0264] Obviously, at this time there is Therefore, z1 will converge to the boundary ( P ,P1);

[0265] Scenario 2: Order When z1(t)∈( P When t∈[0,T), P2 ...

[0266]

[0267] Based on (53) and (56), we can deduce that:

[0268]

[0269] Obviously, at this time there is Therefore, z1 will converge to the boundary.

[0270] Case 3: When z1(t)∈(P2,P1), t∈[0,T), it is obvious that... t∈[0,T), and when z1 enters the range or( P According to cases 1 and 2, z1 will eventually enter the range (P2, P1). Furthermore, according to the preset performance constraints of z1, z1 will eventually be less than the steady-state error limit, so there will be no infinite jump phenomenon.

[0271] A comprehensive analysis of the above three cases shows that when the set t∈[0,T), we have T = +∞, therefore the time-domain constraint x1 ∈ (-z) of the suspension dynamic deflection can be guaranteed. max ,z max ), Q.E.D.

[0272] Simulation results:

[0273] To verify the effectiveness of the control scheme of this invention, Simulink was used for co-simulation verification, leveraging the real-time capabilities of dSPACE, to analyze four key performance indicators: vehicle vertical acceleration, suspension dynamic deflection, tire dynamic-to-static load ratio, and control force. In the proposed control scheme, the sensor outputs are x1, x2, ... Note that the output and control variables do not explicitly contain sprung mass dynamics, making it easy to extend the control equations to the entire vehicle suspension. Considering that ESO feedback control and NDO inversion control are both classic disturbance suppression control methods already applied in many engineering fields, the simulation compares ESO feedback control, NDO inversion control, robust approximation-free control (RAF-PPF), and passive suspension.

[0274] The suspension simulation parameters and PPF-MFT control parameters are shown in Tables 1 and 2. The nonlinear damping parameter is taken as k. l =20、ξ l =0.707, a l =2. Note that besides the PPF function parameters, the only controller parameters that need to be selected are k1, k2, and l, which reduces the complexity of the design. To avoid control saturation, smaller control parameters should be chosen. In the design of the disturbance estimator, high gain is more sensitive to noise, so smaller parameters should be selected.

[0275] Table 1 Suspension Simulation Parameters

[0276]

[0277] Table 2 PPF Functions and Control Parameters

[0278]

[0279] The sampling frequency is set to 1000Hz, the initial estimation error of the matched interference is taken as 1N, the mismatched interference is taken as the harmonic interference of the high and low frequency combination d1=0.001sin(2πt)+0.0001sin(20πt), and the sampling noise level of the velocity quantity x2 is taken as 10. - 3 m·s -1 First, a simulation test was conducted using a continuous block pavement with short-term high strength as shown in Figure 4(a), with the vehicle speed set at 12.5 m / s. -1 Each block is 5m long and 0.05m high.

[0280] Figure 5 The output shows the response curves of the vehicle body's vertical displacement and acceleration under block excitation. From... Figure 5It can be seen that the active suspension controlled by PPF-MFT has the smallest response amplitude under block excitation, lower than other control schemes and passive suspension, thus significantly improving the ride comfort of the vehicle. In terms of convergence speed, the vehicle acceleration controlled by PPF-MFT can stabilize at 6 seconds, while other control methods are difficult to stabilize quickly.

[0281] Figure 6 For the response curves of the other three performance indicators of the suspension under block excitation, from Figure 6 (a) It can be observed that under PPF-MFT control, the dynamic deflection of the active suspension did not increase significantly, thus effectively protecting the mechanical structure of the suspension. Furthermore, Figure 6 (b) and (c) show that the PPT-MFT has a smaller tire dynamic and static load ratio and a smaller amplitude of control force, which avoids wheel hopping, improves vehicle handling stability, and has lower energy consumption.

[0282] Figure 7 and Figure 8 The figures compare the interference estimation and trajectory tracking errors. As can be seen, the preset performance interference estimator designed in this invention has the smallest estimation error compared to ESO and NDO, and the estimation error under block excitation meets the PPF performance. The trajectory tracking error also has the smallest error amplitude, and both transient and steady-state errors are better than the other three control methods, indicating that this method has a smaller convergence bound. Calculations show that the peak values ​​of transient and steady-state errors in the PPF-MFT control for nonlinear interference force estimation are reduced by more than 50% compared to other control methods; the peak values ​​of transient and steady-state errors in trajectory tracking are also reduced by more than 40%. Although NDO inversion control also has a small trajectory tracking error, it requires a large control gain, resulting in relatively large control chattering.

[0283] Table 3 shows the RMS values ​​of vehicle acceleration, tire dynamic / static load ratio, control force, and its derivative. The RMS value of the control force derivative is used to evaluate the chattering situation; the larger the value, the more pronounced the chattering. From the table, it can be calculated that the suspension acceleration RMS of PPF-MFT control is reduced by more than 50% compared to passive suspension and by more than 20% compared to NDO inversion control. The tire dynamic / static load ratio RMS is reduced by more than 20% compared to passive suspension and by more than 60% compared to the other three control schemes. Furthermore, the control force RMS required by PPF-MFT control is only 70% of that of NDO inversion control, and its chattering RMS is only 60% of that of RAF-PPF control. This demonstrates that the proposed control scheme achieves better control performance while exhibiting lower energy consumption and chattering. Figure 9The figure shows the power spectral density (PSD) of the vehicle acceleration. It compares the NDO and PPF-MFT methods, which have similar time-domain performance. The figure shows that the PPF-MFT has better frequency domain performance than the NDO control method at low-frequency and high-frequency excitation peaks.

[0284] Table 3. Root mean square values ​​of suspension performance under block road surfaces

[0285]

[0286] Vehicles typically experience a strong impact when going uphill, which severely affects ride comfort and handling stability. To verify the effectiveness of the proposed control scheme on sloping roads, a test was conducted... Figure 5 (b) Simulations were performed on a hybrid road surface consisting of a ramp and bumps. The ramp slope was 0.14, the vehicle speed was 12.5 m / s, the bump excitation frequency was 3 Hz, and the bump height was 0.1 m. Note that this road surface amplitude represents a relatively large excitation input, which can lead to significant suspension deformation.

[0287] Figure 10 The suspension-body response curves on sloping roads are shown. It's noted that the body displacement adaptively adjusts to the road slope, while the body acceleration amplitude under PPF-MFT control is relatively small, effectively improving ride comfort on sloping roads. Meanwhile... Figure 11 In (a), the suspension dynamic deflection has a larger amplitude at the moment of uphill movement because the excitation amplitude at the moment of contact is larger. However, under the trajectory tracking strategy, it still does not exceed the maximum limit of 0.1m. In subsequent road conditions, the suspension dynamic deflection returns to a smaller amplitude. Calculations show that the RMS value of the suspension dynamic deflection of the PPF-MFT is 0.0369m, and the RMS value of the passive suspension dynamic deflection is 0.0379m, so no excessive suspension deformation occurs. Figure 11 (b) and (c) show that the tire dynamic and static load ratio and the required control force amplitude are minimized under PPF-MFT control, which can ensure steering stability during uphill driving.

[0288] Figure 12 The curves for disturbance estimation error and trajectory tracking error show that PPF-MFT control has the smallest transient error during uphill acceleration. Compared to the other three control schemes, PPF-MFT control reduces trajectory tracking error by more than 60% and disturbance estimation error by more than 40%. Simultaneously, PPF-MFT control also achieves a minimum steady-state error, meeting the preset attenuation performance targets.

[0289] Table 4 shows the root mean square (RMS) values ​​of suspension performance indicators under sloping road conditions. Among the four performance indicators of interest, the PPF-MFT control exhibits the lowest RMS values. Specifically, the RMS value of vehicle acceleration, related to ride comfort, is reduced by more than 40%, while the RMS value of the tire dynamic-to-static load ratio, related to handling stability, is reduced by more than 13%. Furthermore, the PPF-MFT control requires the least control force and exhibits the lowest vibration, demonstrating a significant improvement in overall performance compared to the closest comparable RAF-PPF control.

[0290] Table 4. Root mean square values ​​of suspension performance on sloping roads

[0291]

[0292] To verify the vibration reduction performance of the proposed control scheme under random road conditions, the RMS value of the suspension under Gaussian white noise random road conditions was calculated. The road elevation model is as follows:

[0293]

[0294] In the formula: vehicle speed V = 20 m / s, n0 = 0.1 m -1 For spatial frequency, G q (n0) is the road surface roughness coefficient, W(t) represents the Gaussian white noise signal with zero mean, and f c =0.01Hz is the road surface time cutoff frequency. The paper uses a Class D random road surface for simulation analysis, i.e., G. q (n0) = 1024 × 10 -6 m 3 .

[0295] Table 5 shows the root mean square (RMS) values ​​of suspension performance indicators under D-level random road surface excitation. Comparison reveals that the acceleration RMS value of PPF-MFT is lower than other control schemes, and only 72% of that of passive suspension. The tire dynamic / static load ratio RMS value of PPF-MFT is only 82% of that of passive suspension. Due to the larger trajectory tracking errors of the other two control schemes, the expected vibration isolation target was not achieved. It is noted that the control force and its chatter RMS value under random road surface conditions are slightly higher than those of RAF-PPF control. This is because RAF-PPF control does not estimate external disturbances, and therefore does not transmit high-frequency chatter to the control channel. However, considering various road conditions, the designed PPF-MFT control still exhibits good control performance.

[0296] Table 5. Root mean square values ​​of suspension performance under random road conditions

[0297]

[0298] Rapid Prototyping Control Experiments:

[0299] To further study the real-time performance of the control scheme, Figure 13 The rapid prototyping control test platform shown was used to verify the scheme. The three control structures, passive suspension, ESO and NDO, were compared respectively. The road excitation was harmonic excitation with an amplitude of 2mm and an excitation frequency of 3Hz, which was the resonant frequency of the sprung mass. The PPF-MFT controller parameters are shown in Table 6.

[0300] Table 6 PPF Functions and Control Parameters

[0301]

[0302] Figure 14 The test results under PPF-MFT control show good performance of the vehicle body response curve under harmonic excitation, which is consistent with the simulation results, further verifying the effectiveness of the proposed scheme. Figure 15 To track the error curve, the PPF-MFT achieves the minimum steady-state error peak while still satisfying PPF performance. The PSD of vehicle acceleration (e.g., Figure 16 As shown in the figure, PPF-MFT exhibits the best frequency domain performance, outperforming the other two control schemes at both low and high frequencies. The RMS formula for calculating the root mean square value is also used. Figure 15 The RMS value of the vehicle body acceleration was found to be 0.1381 m / s². 2 The RMS values ​​for passive suspension, ESO feedback control, and NDO inversion control are 0.7474 m / s². 2 0.5628m / s 2 0.2505m / s 2 This further verifies that PPF-MFT has good vibration reduction performance, and also shows that it suppresses the main interference of the system.

[0303] in conclusion:

[0304] (1) To address the impact of matched and mismatched disturbances in active suspension systems, this invention proposes a disturbance suppression control method with preset attenuation performance. By introducing a PPF function, the disturbance estimation and the transient and steady-state performance of the controller are both taken into account. The stability and convergence are proved using the Lyapunov method.

[0305] (2) By comparing the responses of the four control schemes under road excitation, it was found that the four key performance characteristics of PPF-MFT control were improved; the suspension dynamic deflection of the control scheme was close to that of the passive suspension, so it did not lead to excessive suspension deformation; the reduction in the peak error of disturbance estimation and trajectory tracking indicates that PPF-MFT control has strong disturbance suppression capability.

[0306] (3) Due to the large noise and chattering of the high-frequency random disturbance estimation, the control force and chattering of PPF-MFT under Class D random road surface are slightly higher than those of RAF-PPF control, but still much lower than those of ESO feedback control. The RMS values ​​of vehicle acceleration and tire dynamic load ratio are lower than those of other control schemes, indicating that PPF-MFT can improve the ride comfort and stability of the vehicle under random road surface.

[0307] (4) The results of the rapid prototype control experiment further verified the effectiveness of the PPF-MFT control method. It achieved good control effect without the need for precise parameter calibration. The frequency domain performance and root mean square value also verified the advantages of the proposed method in suspension control applications.

[0308] 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 nonlinear active suspension constraint interference suppression method with preset attenuation performance, characterized in that: include: Step 1: Establish a 1 / 4 car nonlinear uncertain active suspension model, and based on the established model, establish control equations with active suspension dynamic deflection as the measured object, including matching disturbance force and mismatch force disturbance, and design a high static and low dynamic oscillator reference model that depends on the active suspension dynamic deflection. Step 2: Based on the compensation matching and mismatch disturbances of the 1 / 4 vehicle nonlinear uncertain active suspension model in Step 1, the error expression of disturbance estimation is obtained through dynamic surface technology. An adaptive disturbance update law of active suspension is constructed by introducing a preset attenuation performance function, and the preset attenuation performance of the disturbance estimation error is analyzed by using a quadratic Lyapunov function. Step 3: Based on Step 2, an inversion control law with preset attenuation performance is established by combining the adaptive disturbance update law. The inversion control law includes a virtual control law and a constraint control law. Then, dynamic surface technology is used, and a nonlinear constraint response mechanism is introduced to limit the range of active suspension dynamic deflection. Finally, stability and boundedness analysis are performed on the inversion control law.

2. The nonlinear active suspension constraint interference suppression method with preset attenuation performance according to claim 1, characterized in that: Step 1 includes: Step 1.1: Establish a 1 / 4 car nonlinear uncertain active suspension model, and apply Newton's second law to establish the dynamic equations based on the structural characteristics of the active suspension; Step 1.2: Model the damping force and footprint tire force of the active suspension damper: Step 1.3: Based on steps 1.1 and 1.2, establish the nonlinear active suspension control equation with the active suspension dynamic deflection as the measured object; Step 1.4: Based on Step 1.3, establish a reference model for a high static and low dynamic oscillator that depends on the dynamic deflection of the suspension.

3. The nonlinear active suspension constraint interference suppression method with preset attenuation performance according to claim 2, characterized in that: Step 2 includes: Step 2.1: Construct the dynamic surface expression for the error; Step 2.2: Introduce the PPF function to apply a preset attenuation performance constraint, where the PPF function is the preset attenuation performance function; Step 2.3: Combining Step 2.1 and Step 2.2, obtain the error transformation function; Step 2.4: Based on Step 2.3, establish an adaptive disturbance update law; Step 2.5: The adaptive disturbance update law in Step 2.4 is analyzed for stability using a quadratic Lyapunov function.

4. The nonlinear active suspension constraint interference suppression method with preset attenuation performance according to claim 3, characterized in that: Step 3 includes: Step 3.1: Based on the adaptive disturbance update law obtained in Step 2, establish an inversion control law with preset attenuation performance; Step 3.2: Analyze the stability and boundedness of the inversion control law in Step 3.1.

Images