CN111487870A - Design method of adaptive inversion controller in flexible active suspension system - Google Patents

Abstract

The invention discloses a design method of a self-adaptive inversion controller in a flexible active suspension system, which comprises the steps of building an active suspension model, designing a self-adaptive inversion controller based on a neural network, aiming at the two-degree-of-freedom flexible active suspension system containing unknown nonlinear dynamics, constructing a control condition meeting the system stability by selecting a B L function in the control design of the automobile active suspension system, and realizing the compensation of asymmetric control saturation by introducing a second-order auxiliary system, designing the self-adaptive inversion controller based on the neural network by the method, wherein a hardware loop experiment shows that the method can better attenuate the vertical vibration of the sprung mass in the automobile active suspension system and improve the grounding performance of the automobile active suspension system under sine and impact excitation compared with the traditional PD and L QR control in the control design of the automobile active suspension system.

Description

A Design Method of Adaptive Inversion Controller in Flexible Active Suspension System

technical field

The invention belongs to the field of automobile automatic control, and particularly relates to a design method of an adaptive inversion controller in a flexible active suspension system.

Background technique

Automobile suspension system is a key part of the car. It can improve the vibration and comfort of the car during use. When the suspension system is used, in addition to attenuating the vibration transmitted to the body by road interference, it must also ensure the suspension moving stroke and grounding. It is very important to study advanced active control methods to realize the vibration control of suspension system. In the research process of automobile suspension system, certain research results have been achieved so far: for example, the research on the Network control of active suspension, and reduce communication burden through event-triggered mechanism; and propose a class of self-organizing fuzzy controller to control active suspension system, which all contribute to the stability and comfort of vehicle suspension system. improved to some extent;

In car driving, the body mass usually changes with the driver's weight and load, and the perturbation of the car needs to be considered at this time; Sun Weichao et al. proposed a nonlinear suspension adaptive inversion control strategy, through the adaptive method To estimate the change of the body mass; and on this basis, the saturation of the control force is compensated by adding a state constraint compensation module, and the adaptive road control method of the active suspension is studied, and the ideal effect is achieved;

However, since the actual suspension system contains unknown nonlinear dynamics, ideal feedback linearization is difficult to implement, and the extended state observer is used to estimate the unknown dynamics of the system in the prior art, which requires the unknown dynamics to be Lipschitz continuous and bounded; although Some control methods of adaptive fuzzy and neural network are proposed for the uncertainty of suspension system, but most of their researches are mainly based on numerical simulation, and only stay at the level of simulation, and the related hardware loop experiments are still relatively rare;

Therefore, in the design process of automotive active suspension system, there is an urgent need for a system that can not only consider the unknown nonlinear dynamics of the system, parameter perturbation and asymmetric control saturation effects, but also can consider the friction contained in the active suspension system at the same time. Force, gap and other hard nonlinear characteristics, and can also meet the Lipschitz continuous and bounded control method, so as to design a control method that can compensate for the asymmetric saturation phenomenon of the control force, and at the same time can better attenuate the vertical vibration of the sprung mass, while improving the Automotive active suspension system with good grounding performance and stability.

SUMMARY OF THE INVENTION

In order to overcome the above-mentioned defects in the prior art, the purpose of the present invention is to provide a design method of an adaptive inversion controller in a flexible active suspension system, aiming at a two-degree-of-freedom flexible active suspension system with unknown nonlinear dynamics, In the control design of the automotive active suspension system, the Barrier-Lyapunov (BL) function is selected to construct the control condition that satisfies the system stability, and a second-order auxiliary system is introduced to realize the compensation of the asymmetric control saturation. The adaptive law of convergence is used to estimate neural network weights and body mass; hardware loop experiments show that this control method in the control design of automotive active suspension system, compared with traditional PD and LQR control, under sinusoidal and shock excitation, The method can better attenuate the vertical vibration of the sprung mass in the active suspension system of the vehicle, and at the same time it can improve the grounding performance.

In order to achieve the above object, the technical scheme of the present invention is achieved in this way:

A design method of an adaptive inversion controller in a flexible active suspension system, the design method of the adaptive inversion controller comprises:

Step 1: Build the Flexible Active Suspension Model

In a two-degree-of-freedom flexible active suspension system with unknown nonlinear dynamics, a flexible active suspension is built. The dynamic relationship of the model is:

Step 2: Design a neural network-based adaptive inversion controller

According to the flexible active suspension model established in step 1, the BL function is introduced to construct the control conditions that satisfy the system stability, and a second-order auxiliary system is introduced to realize the compensation of the asymmetric control saturation in the flexible active suspension system. Inversion control method, an adaptive inversion controller based on neural network is designed to improve the control performance of active suspension.

Preferably, the construction process of the flexible active suspension model described in step 1 is as follows:

S1. Set in the flexible active suspension model: m _s is the sprung mass; m _u is the unsprung mass; z _s is the vertical displacement at the center of mass of the sprung mass, and _zu is the vertical displacement at the center of mass of the unsprung mass ; z _r is the road roughness excitation; F _s is the force generated by the nonlinear spring of the suspension, F _d is the force generated by the damper; F _t is the elastic force generated by the tire stiffness, and F _b is the damping force generated by the damping; u is the active control force generated by the DC servo motor in the active suspension;

S2. The dynamic relationship of the flexible active suspension model is:

Among them: F _Δ is the unknown disturbance force caused by friction and control error, and F _Δ is bounded but not continuously bounded with respect to Lipschitz, in the flexible active suspension model, the spring force F _s and damping force F _d are not measurable is an unknown nonlinear dynamic, and m _s is the parameter perturbation term;

x₃＝z_u，

则被控系统式(1)的状态空间方程为：S3. Let the state variable of the system be x ₁ =z _s ,

x ₃ = _zu ,

Then the state space equation of the controlled system equation (1) is:

Preferably, the design steps of the neural network-based adaptive inversion controller described in step 2 include:

S1. First consider the saturation phenomenon of the active control force u, introduce a second-order auxiliary system to compensate for the control error caused by saturation, and define the saturation condition of the control force u;

S2. Define the tracking errors e ₁ =x ₁ -x _r -λ ₁ , e ₂ =x ₂ -α, and select the BL function to construct a control condition that satisfies the stability of the flexible active suspension system;

渐近收敛到原点或者原点附近，

为一个估计量；S3. Use an adaptive neural network algorithm to design a virtual control law f, so that the variables e ₁ , e ₂ ,

asymptotically converges to or near the origin,

is an estimator;

S4. Design an adaptive law based on error convergence to estimate NN weights and sprung mass;

S5. Use the Lyapunov function to analyze the stability of the flexible active suspension system and to classify and discuss the error convergence set.

Preferably, the specific design process of step 2 S1 is:

(1) According to the type of flexible active suspension system, considering the adaptive NN inversion control law of the asymmetric input saturation of the active suspension model, a second-order auxiliary system is introduced to compensate the control error caused by saturation. for:

为簧载质量倒数θ＝1/m_s的估计量；Where: Δu=uf, λ ₁ and λ ₂ represent the state variables of the auxiliary system, and the zero initial states λ ₁ (0) and λ ₂ (0) are zero; c ₁ and c ₂ are constants,

is an estimate of the reciprocal sprung mass θ=1/m _s ;

(2) According to the introduced second-order auxiliary system, considering the saturation phenomenon of the control force in the active suspension model, the saturation conditions that the control force u satisfies are defined as follows:

Where: f is the virtual control law to be designed.

Preferably, the specific design process of step 2 S2 is:

(1) Define the tracking error: e ₁ =x ₁ -x _r -λ ₁ , e ₂ =x ₂ -α;

Among them: x ₁ is the state variable of the closed-loop system formula (2), x _r is the reference trajectory of the system state x ₁ , x _r is generally zero, and α is the virtual trajectory of the system state x ₂ ;

(2) Set the initial tracking error |e ₁ (0)|<δ ₁ , where δ ₁ is an arbitrarily small positive number;

(3) Select the BL function, the expression of the BL function is as follows:

Among them: V ₁ (e ₁ ) represents the BL function, δ ₁ is an arbitrarily small positive number, and e ₁ represents the tracking error;

(4) Derivation of formula (7), we can get:

k₁＞0，e₂表示跟踪误差，in

k ₁ >0, e ₂ represents the tracking error,

Then formula (8) can be transformed into:

故e₁渐近收敛到零，且满足V₁(e₁)≤V₁(e₁(0))；取x_r为零，从步骤(2)可得|x₁(0)|＜δ₁，当t→∞，有|x₁(t)|＜||λ₁||_∞；(5) It can be seen from formula (9) that if the error e ₂ →0, then

Therefore, e ₁ converges to zero asymptotically, and satisfies V ₁ (e ₁ )≤V ₁ (e ₁ (0)); if x _r is zero, from step (2) we can obtain |x ₁ (0)|<δ ₁ , when t→∞, there is |x ₁ (t)|＜||λ ₁ || _∞ ;

对公式(6)进行数值仿真，得到仿真曲线，从仿真曲线可以看出，当控制误差Δu＝10N时，||λ₁||∞仍然小于3mm；因此可以通过调节控制参数c₁和c₂来调节||λ₁||_∞，从而减小|x₁(t)|。(6) In order to study the variation law of ||λ ₁ || _∞ with Δu, the parameters c ₁ =50, c ₁ =60,

Numerical simulation of formula (6) is carried out, and the simulation curve is obtained. It can be seen from the simulation curve that when the control error Δu=10N, ||λ ₁ ||∞ is still less than 3mm; therefore, the control parameters c ₁ and c ₂ can be adjusted by adjusting to adjust ||λ ₁ || _∞ to reduce |x ₁ (t)|.

Preferably, the specific design process of step 2 S3 is:

(1) Derivation of the tracking error e ₂ , we can get:

可以看出-F_d-F_s-F_Δ为未知非线性动态，θ＝1/m_s为摄动参数；where φ=-F _d -F _s -F _Δ +u,

It can be seen that -F _d -F _s -F _Δ is the unknown nonlinear dynamic, and θ=1/m _s is the perturbation parameter;

(2) Design an adaptive neural network algorithm to approximate the above-mentioned unknown nonlinear dynamic φ, and the neural network algorithm is:

T _NN =W ₁ ^T φ ₁ +ε ₁ =θ(-F _d -F _s -F _Δ ) (11)

where: T _NN represents the approximation of unknown nonlinear dynamics, W ₁ represents the ideal NN weight, φ ₁ represents the activation function vector, ε ₁ represents the bounded approximation error, namely |ε ₁ |<ε _1N , ε _1N >0;

(3) Substituting formula (11) into formula (10), we can get:

where Θ ₁ =[W ₁ ^T θ] ^T ,

为

的估计量，式(12)可重写为：(4) Definition

for

The estimator of , equation (12) can be rewritten as:

in

渐近收敛到原点或者原点附近，设计虚拟控制律如下：(5) In order to ensure the asymptotic stability of the closed-loop system formula (2), and make the error variables e ₁ , e ₂ ,

Asymptotically converge to the origin or near the origin, and design the virtual control law as follows:

Wherein: k ₂ is the control gain, and k ₂ >0.

Preferably, the specific design process of step 2 S4 is:

所述滤波变量e_2f、

的关系式如下：(1) Define a virtual filter variable e _2f ,

The filtering variable e _2f ,

The relationship is as follows:

Where: k>0 is a design parameter;

(2) Define the virtual filter matrix P ₁ and the vector Q ₁ to satisfy the following relationship:

Where: l>0 is a design parameter;

(3) Design the following adaptive law based on error convergence:

where: Γ ₁ is a diagonal matrix, σ > 0 is a learning gain value, and

(4) According to formula ( ₁₆ ), H1 can be further decomposed into:

ε_1f是ε₁的滤波因子，即

in:

ε _1f is the filter factor of ε ₁ , i.e.

持续激励时，矩阵P₁＞0为一个正定矩阵，且其最小特征值满足条件

即完成了主动悬架控制策略的设计。(5) It can be seen from equation (18) that for all bounded active control forces u and state vectors x, ||Δ ₁ ||<ε _1Nf , ε _1Nf is a bounded constant; when the regression vector

When continuously excited, the matrix P ₁ >0 is a positive definite matrix, and its minimum eigenvalue satisfies the condition

That is, the design of the active suspension control strategy is completed.

Preferably, the specific design process of step 2 S5 is:

(1) In order to analyze the stability and error convergence set of the flexible active suspension system, the following Lyapunov function is selected:

并且Γ₁是对角矩阵；Where: V ₁ represents the BL function,

and Γ ₁ is a diagonal matrix;

Substituting equation (14) into equation (13), we can get:

After derivation of Equation (19), combining Equation (20) and Equation (18), we can get:

Where: k ₁ , k ₂ are control gains, and k ₁ >0, k ₂ >0;

(2) Equation (21) is discussed in two cases, the first case: if the neural network algorithm can ideally approximate the nonlinear dynamics of the flexible active suspension system, the approximation error ε ₁ =0, and Δ ₁ = 0, then formula (21) satisfies:

将收敛到原点，且在整个时域范围内满足|e₁(t)|＜δ₁；According to Lyapunov stability theory, V(t)≤V(0), when time t→∞, the error variables e ₁ , e ₂ ,

will converge to the origin and satisfy |e ₁ (t)|<δ ₁ in the entire time domain;

(3) The second case: when the approximation error ε ₁ ≠0, the young inequality can be used to obtain:

Wherein: n and _n are both positive setting parameters;

Substitute equation (23) into equation (21) to get:

始终存在η₁保证

表示

的最大奇异值；in:

There is always an η ₁ guarantee

express

the largest singular value of ;

So the Lyapunov function satisfies:

是最终一致有界的，并将收敛到集合：According to the Lyapunov stability theory, it can be known that the error variables e ₁ , e ₂ ,

is eventually consistently bounded and will converge to the set:

表示

的最小奇异值；in:

express

The smallest singular value of ;

It can be seen from equation (26) that |e ₁ (t)|<δ ₁ can also be satisfied in equation (26), and the radius of the set depends on the size of the approximation error ε ₁ , that is, when ε ₁ →0 , the same conclusion as in case 1 can be obtained, that is, the set is as follows:

Preferably, the method for designing an adaptive inversion controller in the flexible active suspension system further includes step 3: a hardware loop test experiment to detect the performance of the adaptive inversion controller, and the specific process of the experiment includes:

(1) Sine wave excitation experiment

Under the excitation of sinusoidal action, the adaptive inversion control method can control the vibration very well. At the same time, under the road excitation of the resonance frequency, the comfort and grounding stability of the adaptive inversion control method are better than those of the traditional PD, LQR and passive control;

(2) Square wave shock excitation experiment

Under the shock excitation, compared with the traditional PD, LQR and passive control, the adaptive inversion control method has smaller overshoot displacement and acceleration, and also has the control force output of saturation effect, and its control effect is obviously better than the traditional one. PD and LQR control.

The beneficial effects of the present invention are as follows: the present invention discloses a design method of an adaptive inversion controller in a flexible active suspension system. Compared with the prior art, the improvements of the present invention are:

(1) The present invention is aimed at a two-degree-of-freedom flexible active suspension system with unknown nonlinear dynamics, and introduces the Barrier-Lyapunov (BL) function to construct a control condition that satisfies the system stability, and obtains a less conservative controller design method ; And by introducing a second-order auxiliary system in the design method to realize the compensation of asymmetric control saturation, an adaptive inversion controller based on neural network is designed;

(2) At the same time, through the hardware loop experiment, the adaptive inversion controller designed by the present invention using the adaptive inversion control method is compared with the traditional classical PD control and LQR control, through the sinusoidal excitation experiment and the square wave shock excitation experiment It is proved that under sinusoidal and shock excitation, the active suspension of the adaptive inversion controller designed by this method can better attenuate the vertical vibration of the sprung mass and improve the grounding performance. Therefore, it is further verified that the adaptive inversion controller is used. The effectiveness of the adaptive inversion controller designed by the inversion control method is proved, thus proving the superiority of the adaptive inversion control method of the present invention.

Description of drawings

FIG. 1 is a model diagram of the active suspension of the flexible active suspension system of the present invention.

FIG. 2 is a graph showing the variation law of ||λ ₁ || _∞ with Δu in the present invention.

FIG. 3 is a diagram of the vertical displacement of the sprung mass in the sine wave excitation experiment in Example 1 of the present invention.

FIG. 4 is a graph of the vertical acceleration of the sprung mass of the sine wave excitation experiment in Example 1 of the present invention.

FIG. 5 is a diagram of the suspension dynamic stroke of the sine wave excitation experiment in Embodiment 1 of the present invention.

FIG. 6 is a tire dynamic stroke diagram of a sine wave excitation experiment in Example 1 of the present invention.

FIG. 7 is a diagram of the motor control force of the sine wave excitation experiment in Embodiment 1 of the present invention.

FIG. 8 is a diagram of the vertical displacement of the sprung mass in the square wave shock excitation experiment in Example 1 of the present invention.

FIG. 9 is a diagram of the vertical acceleration of the sprung mass of the square wave shock excitation experiment in Example 1 of the present invention.

FIG. 10 is a diagram of the suspension dynamic stroke of the square wave shock excitation experiment in Example 1 of the present invention.

FIG. 11 is a tire dynamic stroke diagram of a square wave shock excitation experiment in Example 1 of the present invention.

FIG. 12 is a diagram of the motor control force of the square wave shock excitation experiment in Example 1 of the present invention.

Among them: Pass represents passive control, and AB control represents the adaptive inversion control of the present invention.

Detailed ways

In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention are further described below with reference to the accompanying drawings and embodiments;

1-12, a design method of an adaptive inversion controller in a flexible active suspension system, the design method of the adaptive inversion controller includes:

Step 1: Build the Flexible Active Suspension Model

In a two-degree-of-freedom flexible active suspension system with unknown nonlinear dynamics, a flexible active suspension is built. The dynamic relationship of the model is:

The construction process of the active suspension model includes the construction of the active suspension model and the performance evaluation of the active suspension model:

(1) The specific process of building the active suspension model is as follows:

S1. Study the two-degree-of-freedom active suspension model shown in Figure 1, set in the active suspension model: m _s is the sprung mass; m _u is the unsprung mass; z _s is the vertical displacement at the center of mass of the sprung mass , z _u is the vertical displacement at the center of mass of the unsprung mass; z _r is the road roughness excitation; F _s is the force generated by the nonlinear spring of the suspension, F _d is the force generated by the damper; F _t is the tire stiffness generated , F _b is the damping force generated by the damping; u is the active control force generated by the DC servo motor in the active suspension;

S2. The dynamic relationship of the flexible active suspension model is:

where F _Δ is the unknown disturbance force caused by friction and control error, and F _Δ is bounded but not continuously bounded with respect to Lipschitz. In the flexible active suspension model, the spring force F _s and damping force F _d are not measurable , belongs to the unknown nonlinear dynamic, and because the body mass changes with the driver's weight, the system contains a parameter perturbation term m _s , where m _s is a parameter perturbation term;

x₃＝z_u，

则被控系统式(1)的状态空间方程为：S3. Let the state variable of the system be x ₁ =z _s ,

x ₃ = _zu ,

Then the state space equation of the controlled system equation (1) is:

(2) Performance evaluation of the active suspension model (generally, when implementing the control strategy of the active suspension, the following four aspects need to be considered)

1. Vibration attenuation: Since the vertical motion of the body is closely related to the comfort of the suspension, the main goal of the controller is to suppress the vibration transmitted from the road disturbance to the body, and make it tend to be near the zero point;

2. Suspension dynamic stroke: Due to the limitation of the chassis structure, the suspension dynamic stroke must move within the specified range, that is, it is required to meet the time domain constraint |z _s -z _u |≤z _max , where z _max is allowed by the structure safety threshold;

3. Ground contact: In order to ensure the safety and maneuverability of the vehicle, the dynamic load of the tire is required to be less than its static load, that is, it is required to satisfy the time domain constraint |F _t +F _b |<(m _s +m _u )g; Note that the tire dynamic load is proportional to the tire dynamic stroke ||z _u -z _r || _∞ , so it is hoped that the smaller the amplitude, the better;

4. Asymmetric input saturation: Limited by the output of the motor, in order to ensure the stability of the closed-loop system, the control force saturation must be considered, and the following constraints are taken: u _min ≤ u ≤ u _max , where u _min and u _max respectively are the upper and lower limits of the control force;

In the performance evaluation, the root mean square value and maximum value of vibration can reflect the quality of vibration damping performance, so it is necessary to consider the mean square value and maximum value of the design output. The design formula is as follows:

|χ(t)| _max =max{χ(t)|,t∈[0,T]} (4)

where χ(t) represents the vibration output, and T represents the system response time;

And make the following mark in the present invention:

||x|| _∞ =max(x _i ), i=1...n,

λ _min/max (A) represents the minimum/large eigenvalue of matrix A,

A>0 means it is a positive definite matrix.

Step 2: Design a neural network-based adaptive inversion controller

According to the flexible active suspension model established in step 1, the Barrier-Lyapunov (BL) function is introduced to construct the control conditions that satisfy the system stability, and a second-order auxiliary system is introduced to realize the compensation of asymmetric control saturation in the flexible active suspension system. , through the saturated adaptive inversion control method, an adaptive inversion controller based on neural network is designed to improve the control performance of the active suspension;

The design steps of the neural network-based adaptive inversion controller include (the method used is an adaptive inversion control method):

S1. First consider the saturation phenomenon of the active control force u, introduce a second-order auxiliary system to compensate for the control error caused by saturation, and define the saturation condition of the control force u. The specific design process is as follows:

(1) According to the type of flexible active suspension system, considering the adaptive NN inversion control law of the asymmetric input saturation of the active suspension model, a second-order auxiliary system is introduced to compensate the control error caused by saturation. for:

为簧载质量倒数θ＝1/m_s的估计量；where Δu=uf, λ ₁ and λ ₂ represent the state variables of the auxiliary system, and the zero initial state is zero; c ₁ and c ₂ are positive numbers,

is an estimate of the reciprocal sprung mass θ=1/m _s ;

(2) According to the introduced second-order auxiliary system, considering the saturation phenomenon of the control force in the active suspension model, the saturation conditions that the control force u satisfies are defined as follows:

where f is the virtual control law of .

S2. Define the tracking error e ₁ =x ₁ -x _r -λ ₁ , e ₂ =x ₂ -α, and select the BL function to construct a control condition that satisfies the stability of the flexible active suspension system. The specific design process is:

(1) Define the tracking error: e ₁ =x ₁ -x _r -λ ₁ , e ₂ =x ₂ -α, where x ₁ is the state variable of the controlled system equation (2), and x _r is the state variable of the system state x ₁ Reference trajectory, x _r is generally zero, α is the virtual trajectory of the system state x ₂ ;

(2) Let the initial tracking error |e ₁ (0)|<δ ₁ , where δ ₁ is an arbitrarily small positive number (because in the suspension system, the initial static position of x ₁ is zero, and setting x _r is zero, and the zero initial state of the state quantity λ ₁ is also zero, so δ ₁ can meet the requirements as long as it takes any small positive number);

(3) Select the BL function, the expression of the BL function is as follows:

Among them: V ₁ (e ₁ ) represents the BL function, δ ₁ is an arbitrarily small positive number, and e ₁ represents the tracking error;

(4) Derivation of formula (7), we can get:

k₁＞0，e₂表示跟踪误差，in

k ₁ >0, e ₂ represents the tracking error,

Then formula (8) can be transformed into:

故e₁渐近收敛到零，且满足V₁(e₁)≤V₁(e₁(0))；取x_r为零，从步骤(2)可得|x₁(0)|＜δ₁，当t→∞，有|x₁(t)|＜||λ₁||_∞；(5) It can be seen from formula (9) that if the error e ₂ →0, then

Therefore, e ₁ converges to zero asymptotically, and satisfies V ₁ (e ₁ )≤V ₁ (e ₁ (0)); if x _r is zero, from step (2) we can obtain |x ₁ (0)|<δ ₁ , when t→∞, there is |x ₁ (t)|＜||λ ₁ || _∞ ;

对公式(6)进行数值仿真，得到仿真曲线(如图2所示)，从仿真曲线可以看出当控制误差Δu＝10N时，||λ₁||_∞仍然小于3mm；因此可以通过调节控制参数c₁和c₂来调节||λ₁||_∞，从而减小|x₁(t)|。(6) In order to study the variation law of ||λ ₁ || _∞ with Δu, the parameters c ₁ =50, c ₁ =60,

Numerical simulation of formula (6) is carried out to obtain a simulation curve (as shown in Figure 2). It can be seen from the simulation curve that when the control error Δu=10N, ||λ ₁ || _∞ is still less than 3mm; therefore, it can be controlled by adjusting The parameters c ₁ and c ₂ adjust ||λ ₁ || _∞ to reduce |x ₁ (t)|.

渐近收敛到原点或者原点附近，

为一个估计量，其设计的具体过程为：S3. Use an adaptive neural network algorithm to design a virtual control law f, so that the variables e ₁ , e ₂ ,

asymptotically converges to or near the origin,

is an estimator, and the specific process of its design is:

(1) Derivation of the tracking error e ₂ , we can get:

可以看出-F_d-F_s-F_Δ为未知非线性动态，θ＝1/m_s为摄动参数；where φ=-F _d -F _s -F _Δ +u,

It can be seen that -F _d -F _s -F _Δ is the unknown nonlinear dynamic, and θ=1/m _s is the perturbation parameter;

(2) Design an adaptive neural network algorithm to approximate the above-mentioned unknown nonlinear dynamic φ, and the neural network algorithm is:

T _NN =W ₁ ^T φ ₁ +ε ₁ =θ(-F _d -F _s -F _Δ ) (11)

where: T _NN represents the approximation of unknown nonlinear dynamics, W ₁ represents the ideal NN weight, φ ₁ represents the activation function vector, ε ₁ represents the bounded approximation error, namely |ε ₁ |<ε _1N , ε _1N >0;

(3) Substituting formula (11) into formula (10), we can get:

where Θ ₁ =[W ₁ ^T θ] ^T ,

为Θ₁＝[W₁ ^T θ]^T的估计量，式(12)可重写为：(4) Definition

is the estimator of Θ ₁ =[W ₁ ^T θ] ^T , equation (12) can be rewritten as:

in

渐近收敛到原点或者原点附近，设计虚拟控制律如下：(5) In order to ensure the asymptotic stability of the closed-loop system (2), and make the error variables e ₁ , e ₂ ,

Asymptotically converge to the origin or near the origin, and design the virtual control law as follows:

where k ₂ is the control gain, and k ₂ >0 (see S5 below for the detailed proof process).

S4. Design an adaptive law based on error convergence to estimate NN weights and sprung mass. The specific design process is as follows:

所述滤波变量e_2f、

的关系式如下：(1) Define a virtual filter variable e _2f ,

The filter variable e _2f ,

The relationship is as follows:

where k>0 is a design parameter;

(2) Define the virtual filter matrix P ₁ and the vector Q ₁ to satisfy the following relationship:

where l>0 is a design parameter;

(3) Design the following adaptive law based on error convergence:

where: Γ ₁ is a diagonal matrix, σ > 0 is a learning gain value, and

(4) According to formula ( ₁₆ ), H1 can be further decomposed into:

ε_1f是ε₁的滤波因子，即

in

ε _1f is the filter factor of ε ₁ , i.e.

持续激励时，矩阵P₁＞0为一个正定矩阵，且其最小特征值满足条件

即完成了主动悬架控制策略的设计，下面对主动悬架的稳定性进行进一步讨论；(5) It can be seen from equation (18) that for all bounded active control forces u and state vectors x, ||Δ ₁ ||<ε _1Nf , ε _1Nf is a bounded constant; when the regression vector

When continuously excited, the matrix P ₁ >0 is a positive definite matrix, and its minimum eigenvalue satisfies the condition

That is, the design of the active suspension control strategy is completed, and the stability of the active suspension is further discussed below;

S5. Use the Lyapunov function to analyze the stability of the flexible active suspension system and classify and discuss the error convergence set. The specific design process is as follows:

(1) In order to analyze the stability and error convergence set of the flexible active suspension system, the following Lyapunov function is selected:

并且Γ₁是对角矩阵；Where: V ₁ represents the BL function,

and Γ ₁ is a diagonal matrix;

Substituting equation (14) into equation (13), we can get:

After derivation of Equation (19), combining Equation (20) and Equation (18), we can get:

Where: k ₁ , k ₂ are control gains, and k ₁ >0, k ₂ >0;

(2) Equation (21) is discussed in two cases, the first case: if the neural network algorithm can ideally approximate the nonlinear dynamics of the flexible active suspension system, the approximation error ε ₁ =0, and Δ ₁ = 0, then formula (21) satisfies:

将收敛到原点，且在整个时域范围内满足|e₁(t)|＜δ₁；According to Lyapunov stability theory, V(t)≤V(0), when time t→∞, the error variables e ₁ , e ₂ ,

will converge to the origin and satisfy |e ₁ (t)|<δ ₁ in the entire time domain;

(3) The second case: when the approximation error ε ₁ ≠0, the young inequality can be used to obtain:

where η and η ₁ are both positive tuning parameters;

Substitute equation (23) into equation (21) to get:

始终存在η₁保证

表示

的最大奇异值；in

There is always an η ₁ guarantee

express

the largest singular value of ;

So the Lyapunov function satisfies:

是最终一致有界的，并将收敛到集合：According to the Lyapunov stability theory, it can be known that the error variables e ₁ , e ₂ ,

is eventually consistently bounded and will converge to the set:

表示

的最小奇异值；in:

express

The smallest singular value of ;

It can be seen from equation (26) that |e ₁ (t)|<δ ₁ can also be satisfied in equation (26), and the radius of the set depends on the size of the approximation error ε ₁ , that is, when ε ₁ →0 , the same conclusion as in case 1 can be obtained, that is, the set is as follows:

According to the universal approximation principle of the neural network, the approximation error will be very small, so that x ₁ (t) will converge to the residual set near the origin; therefore, the stability proof is completed, and the system state can converge to an arbitrarily small set.

Step 3: Hardware loop test experiment (Example 1)

In order to test the performance of the adaptive inversion controller designed in step 2, a hardware loop experiment (HIL) was implemented. The control program was programmed with S-function in C language, and a TLC file was inlined for hardware acceleration operation, and the reference was set. The trajectory x _r is zero;

In the control parameter setting, according to the user manual of the system, take the maximum suspension stroke as z _max =0.02cm, the maximum control force as |u|≤10N, and the zero initial parameter of the adaptive law

In the experiment, the precise parameters of the system are not needed, and only the feedback of the sprung mass displacement x ₁ is required, the vertical displacement of each part is measured by the encoder, the acceleration of the sprung mass is measured by the accelerometer, and the vertical velocity is obtained by the filter;

The activation function vector φ ₁ and the adaptive gain vector of NN are taken as:

φ ₁ =[x ₂ -x ₄ x ₁ -x ₃ (x ₁ -x ₃ ) ³ ] ^T

Γ ₁ =diag([50 100 500 1×10 ^-5 ])

Where x ₁ -x ₃ is the suspension travel, x ₂ -x ₄ is its derivative; the controller parameters after tuning are shown in Table 1:

Table 1: Controller Gain Parameters

In the experiment, the road excitation is generated by the DC servo motor at the bottom, and two typical road excitations are considered, the first is sine wave excitation, and the second is square wave shock excitation; set the gain of the PD controller as k _P = 5, k _Q =6; the gain of the LQR controller is K = [24.66 48.87 -0.47 3.68];

Therefore, when the excitation frequency is close to the natural frequency of the flexible active suspension system, the vibration is most obvious, so the waveform of the sine wave is set to z _r =0.002×sin(6πt)m, and the excitation frequency is the same as the natural frequency of the sprung mass;

(1) Sine wave excitation experiment:

Figure 3-Figure 7 are the test results under sinusoidal excitation, and the excitation time is 15s; Figure 3 is the displacement response of the sprung mass; Figure 4 is the acceleration response of the sprung mass; Figure 5 is the dynamic stroke response of the suspension; Figure 6 is the tire dynamic response Stroke; Figure 7 is the active control force generated by the controller; In the figure: Pass represents passive control, AB control represents the adaptive inversion control of the present invention; as can be seen from the figure, relative to typical PD control and LQR control, Without the need for precise parameters of the system, the adaptive inversion control proposed by the present invention achieves a good vibration control effect;

Further, the root mean square value of the sprung mass acceleration can be calculated by using formula (3), wherein the root mean square value of the uncontrolled case is 0.9813m/s ² , and the root mean square value of the PD is 0.8882m/s ² , the root mean square value of LQR is 0.3819m/s ² , and the root mean square value of adaptive inversion control is 0.0421m/s ² ; it can be seen that, compared with PD control and LQR passive control, the adaptive inversion of the present invention is The controlled acceleration rms value has dropped by 95%;

It can also be seen from Figure 5 that the maximum suspension dynamic stroke of adaptive inversion control is less than 0.02cm, which is smaller than that of passive control; the size of tire dynamic stroke directly reflects the quality of grounding stability, while adaptive inversion The control can obtain a smaller tire moving stroke;

Therefore, it can be seen from the above that under the road excitation at the resonance frequency, the comfort and grounding stability of the adaptive inversion control are better than those of the traditional PD, LQR and passive control.

(2) Square wave shock excitation experiment

In order to test the anti-shock performance of the active suspension system, a set of square waves were used to excite it, and the excitation time was 15s; Figure 8-Figure 12 are the test results under shock excitation; in order to verify the anti-saturation performance of the active suspension system, Connect an asymmetric saturation module at the control input, where the maximum and minimum values are respectively set as u _max =1N, u _min =-3N;

It can be seen from Fig. 8 and Fig. 9 that under shock excitation, the adaptive inversion control method proposed by the present invention has smaller overshoot displacement and acceleration;

It can be seen from Fig. 10 and Fig. 11 that the suspension dynamic stroke and tire dynamic stroke of the adaptive inversion control method proposed by the present invention are also less than the given limit values;

Fig. 12 is the control force output with saturation effect, it can be seen that the control effect of the adaptive inversion control method proposed by the present invention is obviously better than the traditional PD and LQR control;

It can be seen from FIG. 2 that when the control error is not large, ||λ ₁ || _∞ is a very small value, which further verifies the effectiveness of the adaptive inversion control method proposed by the present invention.

Through the adaptive inversion control method proposed in the present invention, an adaptive inversion controller based on neural network is designed for a two-degree-of-freedom flexible active suspension system with unknown nonlinear dynamics and asymmetric control saturation; The adaptive inversion control method is also different from the traditional QL function. The BL function is selected to analyze the control conditions for the stability of the closed-loop system, and a less conservative controller design method is obtained. Symmetric saturation phenomenon; further through the hardware loop experiment, the effectiveness of the neural network-based adaptive inversion controller designed by the adaptive inversion control method proposed in the present invention is verified. Compared with the classical PD and LQR control, in the sinusoidal and impact excitation, the adaptive inversion control method proposed in the present invention can better attenuate the vertical vibration of the sprung mass and improve the grounding performance at the same time.

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 by the above-mentioned embodiments, and the descriptions in the above-mentioned embodiments and the description are only to illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have Various changes and modifications fall within the scope of the claimed invention. The claimed scope of the present invention is defined by the appended claims and their equivalents.

Claims (9)

1. a design method of adaptive inversion controller in a flexible active suspension system, is characterized in that, the design method of described adaptive inversion controller comprises: Step 1: Build the Flexible Active Suspension Model In a two-degree-of-freedom flexible active suspension system with unknown nonlinear dynamics, a flexible active suspension is built. The dynamic relationship of the model is:

Step 2: Design a neural network-based adaptive inversion controller According to the flexible active suspension model established in step 1, the BL function is introduced to construct the control conditions that satisfy the system stability, and a second-order auxiliary system is introduced to realize the compensation of the asymmetric control saturation in the flexible active suspension system. Inversion control method, an adaptive inversion controller based on neural network is designed to improve the control performance of active suspension. 2. the design method of the adaptive inversion controller in a kind of flexible active suspension system according to claim 1, is characterized in that, the building process of the flexible active suspension model described in step 1 is: S1. Set in the flexible active suspension model: m _s is the sprung mass; m _u is the unsprung mass; z _s is the vertical displacement at the center of mass of the sprung mass, and _zu is the vertical displacement at the center of mass of the unsprung mass ; z _r is the road roughness excitation; F _s is the force generated by the nonlinear spring of the suspension, F _d is the force generated by the damper; F _t is the elastic force generated by the tire stiffness, and F _b is the damping force generated by the damping; u is the active control force generated by the DC servo motor in the active suspension; S2. The dynamic relationship of the flexible active suspension model is:

Among them: F _Δ is the unknown disturbance force caused by friction and control error, and F _Δ is bounded but not continuously bounded with respect to Lipschitz, in the flexible active suspension model, the spring force F _s and damping force F _d are not measurable is an unknown nonlinear dynamic, and m _s is the parameter perturbation term; S3. Let the state variable of the system be x ₁ =z _s ,

x ₃ = _zu ,

Then the state space equation of the controlled system equation (1) is:

3. the design method of the adaptive inversion controller in a kind of flexible active suspension system according to claim 1, is characterized in that, the described design step of the neural network-based adaptive inversion controller of step 2 comprises : S1. First consider the saturation phenomenon of the active control force u, introduce a second-order auxiliary system to compensate for the control error caused by saturation, and define the saturation condition of the control force u; S2. Define the tracking errors e ₁ =x ₁ -x _r -λ ₁ , e ₂ =x ₂ -α, and select the BL function to construct a control condition that satisfies the stability of the flexible active suspension system; S3. Use an adaptive neural network algorithm to design a virtual control law f, so that the variables e ₁ , e ₂ ,

asymptotically converges to or near the origin,

is an estimator; S4. Design an adaptive law based on error convergence to estimate NN weights and sprung mass; S5. Use the Lyapunov function to analyze the stability of the flexible active suspension system and to classify and discuss the error convergence set. 4. the design method of adaptive inversion controller in a kind of flexible active suspension system according to claim 3, is characterized in that, the concrete design process of step 2 S1 is: (1) According to the type of flexible active suspension system, considering the adaptive NN inversion control law of the asymmetric input saturation of the active suspension model, a second-order auxiliary system is introduced to compensate the control error caused by saturation. for:

Where: Δu=uf, λ ₁ and λ ₂ represent the state variables of the auxiliary system, and the zero initial states λ ₁ (0) and λ ₂ (0) are zero; c ₁ and c ₂ are constants,

is an estimate of the reciprocal sprung mass θ=1/m _s ; (2) According to the introduced second-order auxiliary system, considering the saturation phenomenon of the control force in the active suspension model, the saturation conditions that the control force u satisfies are defined as follows:

Where: f is the virtual control law to be designed. 5. the design method of adaptive inversion controller in a kind of flexible active suspension system according to claim 4, is characterized in that, the concrete design process of step 2 S2 is: (1) Define the tracking error: e ₁ =x ₁ -x _r -λ ₁ , e ₂ =x ₂ -α; Among them: x ₁ is the state variable of the closed-loop system formula (2), x _r is the reference trajectory of the system state x ₁ , x _r is generally zero, and α is the virtual trajectory of the system state x ₂ ; (2) Set the initial tracking error |e ₁ (0)|<δ ₁ , where δ ₁ is an arbitrarily small positive number; (3) Select the BL function, the expression of the BL function is as follows:

Among them: V ₁ (e ₁ ) represents the BL function, δ ₁ is an arbitrarily small positive number, and e ₁ represents the tracking error; (4) Derivation of formula (7), we can get:

in

k ₁ >0, e ₂ represents the tracking error, Then formula (8) can be transformed into:

(5) It can be seen from formula (9) that if the error e ₂ →0, then

Therefore, e ₁ converges to zero asymptotically, and satisfies V ₁ (e ₁ )≤V ₁ (e ₁ (0)); if x _r is zero, from step (2) we can obtain |x ₁ (0)|<δ ₁ , when t→∞, there is |x ₁ (t)|＜||λ ₁ || _∞ ; (6) In order to study the variation law of ||λ ₁ || _∞ with Δu, the parameters c ₁ =50, c ₁ =60,

Numerical simulation of formula (6) is carried out, and the simulation curve is obtained. It can be seen from the simulation curve that when the control error Δu=10N, ||λ ₁ || _∞ is still less than 3mm; therefore, the control parameters c ₁ and c ₂ can be adjusted by adjusting to adjust ||λ ₁ || _∞ to reduce |x ₁ (t)|. 6. the design method of adaptive inversion controller in a kind of flexible active suspension system according to claim 5, is characterized in that, the concrete design process of step 2 S3 is: (1) Derivation of the tracking error e ₂ , we can get:

where φ=-F _d -F _s -F _Δ +u,

It can be seen that -F _d -F _s -F _Δ is the unknown nonlinear dynamic, and θ=1/m _s is the perturbation parameter; (2) Design an adaptive neural network algorithm to approximate the above-mentioned unknown nonlinear dynamic φ, and the neural network algorithm is:

where: T _NN represents the approximation of unknown nonlinear dynamics, W ₁ represents the ideal NN weight, φ ₁ represents the activation function vector, ε ₁ represents the bounded approximation error, namely |ε ₁ |<ε _1N , ε _1N >0; (3) Substituting formula (11) into formula (10), we can get:

in

(4) Definition

for

The estimator of , equation (12) can be rewritten as:

in

(5) In order to ensure the asymptotic stability of the closed-loop system formula (2), and make the error variables e ₁ , e ₂ ,

Asymptotically converge to the origin or near the origin, and design the virtual control law as follows:

Wherein: k ₂ is the control gain, and k ₂ >0. 7. the design method of adaptive inversion controller in a kind of flexible active suspension system according to claim 6, is characterized in that, the concrete design process of step 2 S4 is: (1) Define a virtual filter variable e _2f ,

The filtering variable e _2f ,

The relationship is as follows:

Where: k>0 is a design parameter; (2) Define the virtual filter matrix P ₁ and the vector Q ₁ to satisfy the following relationship:

Where: l>0 is a design parameter; (3) Design the following adaptive law based on error convergence:

where: Γ ₁ is a diagonal matrix, σ > 0 is a learning gain value, and

(4) According to formula ( ₁₆ ), H1 can be further decomposed into:

in:

ε _1f is the filter factor of ε ₁ , i.e.

(5) It can be seen from equation (18) that for all bounded active control forces u and state vectors x, ||Δ ₁ ||<ε _1Nf , ε _1Nf is a bounded constant; when the regression vector

When continuously excited, the matrix P ₁ >0 is a positive definite matrix, and its minimum eigenvalue satisfies the condition

That is, the design of the active suspension control strategy is completed. 8. the design method of adaptive inversion controller in a kind of flexible active suspension system according to claim 7, is characterized in that, the concrete design process of step 2 S5 is: (1) In order to analyze the stability and error convergence set of the flexible active suspension system, the following Lyapunov function is selected:

Where: V ₁ represents the BL function,

and Γ ₁ is a diagonal matrix; Substituting equation (14) into equation (13), we can get:

After derivation of Equation (19), combining Equation (20) and Equation (18), we can get:

Where: k ₁ , k ₂ are control gains, and k ₁ >0, k ₂ >0; (2) Equation (21) is discussed in two cases, the first case: if the neural network algorithm can ideally approximate the nonlinear dynamics of the flexible active suspension system, the approximation error ε ₁ =0, and Δ ₁ = 0, then formula (21) satisfies:

According to Lyapunov stability theory, V(t)≤V(0), when time t→∞, the error variables e ₁ , e ₂ ,

will converge to the origin and satisfy |e ₁ (t)|<δ ₁ in the entire time domain; (3) The second case: when the approximation error ε ₁ ≠0, the young inequality can be used to obtain:

Wherein: n and _n are both positive setting parameters; Substitute equation (23) into equation (21) to get:

in:

There is always an η ₁ guarantee

express

The largest singular value of ; So the Lyapunov function satisfies:

According to the Lyapunov stability theory, it can be known that the error variables e ₁ , e ₂ ,

is eventually consistently bounded and will converge to the set:

in:

express

The smallest singular value of ; It can be seen from equation (26) that |e ₁ (t)|<δ ₁ can also be satisfied in equation (26), and the radius of the set depends on the size of the approximation error ε ₁ , that is, when ε ₁ →0 , the same conclusion as in case 1 can be obtained, that is, the set is as follows:

9. The design method of an adaptive inversion controller in a flexible active suspension system according to claim 3, wherein the design method of the adaptive inversion controller in the flexible active suspension system is further Including step 3: a hardware loop test experiment to detect the performance of the adaptive inversion controller, the specific process of the experiment includes: (1) Sine wave excitation experiment Under the excitation of sinusoidal action, the adaptive inversion control method can control the vibration very well. At the same time, under the road excitation of the resonance frequency, the comfort and grounding stability of the adaptive inversion control method are better than those of the traditional PD, LQR and passive control; (2) Square wave shock excitation experiment Under the shock excitation, compared with the traditional PD, LQR and passive control, the adaptive inversion control method has smaller overshoot displacement and acceleration, and also has the control force output of the saturation effect, and its control effect is obviously better than the traditional control method. PD and LQR control.

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