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yabo亚博问题
yabo亚博
体积21.那Number6.,2020年
文章编号 611.
页数) 8.
迪伊 https://doi.org/10.1051/meca/2020081
在线发布 1920年11月19日

©AFM,EDP Sciences 2020

1介绍

骑行舒适和道路处理能力取决于悬架系统的性能。然而,在车辆悬架系统中乘坐舒适和道路之间存在矛盾。传统的被动悬浮液对于获得对这个问题的最佳控制影响是痛苦的。为了解决这个问题,研究人员提出了半主动悬架[1] 和active suspensions [2]。在哪里as, the active suspension is better than semi-active suspension for improved ride comfort due to structural constraints. Therefore, the design of active suspensions is a hot spot in modern vehicle control research.

V.arious control methods have proposed to achieve active control of the suspension. Sun et al [3.]讨论了有限频域车辆有源悬架系统的H∞控制问题。结果表明,通过线性矩阵不等式优化,乘坐舒适性得到改善,以及保证的时域约束。jamil等[4.f]研究了致动器输出的最优问题orce in suspension, combining optimal control with intelligent control technology. The suspension system has a high damping characteristic of LQR control. The actuator produces moderate peak and stable amplitude control force to improve the ride quality and handle stability of to automobile and comfort of passengers. Wang et al [5.使用车身加速器与控制目标一起,并利用改进的模糊PID控制策略优化控制规则,以加快优化。实验结果取得了良好的全球优化性能。他们的测试结果表明,它可以显着抑制车身的垂直加速度,提高了驾驶舒适性。基于多绩效目标优化算法,船员等[6.]considered the performance objectives of ride comfort and damping power dissipation and used the multi-objective genetic algorithm (MOGA) to determine the optimal performance of the controller. The results show that the two performance goals improved. By those control methods, we know that researchers have considered different optimization goals to achieve the requirements of active control. However, they all assume the vehicle model as a linear structure.

不考虑悬浮液的弹簧刚度和阻尼的非线性问题。实际上,车辆悬架是非线性系统,操作条件也在发生变化,并且在车辆的操作期间总是存在噪声干扰以及传感器的信号获取[7.]。T.he measurement of the state variable of the suspension is still incomplete in the actual procedure. These have limitations on the design of the controller. Therefore, if we only consider the linear vehicle model when designing the controller, the control effect is not satisfactory in practical engineering applications.

本文采用可变结构控制方法来解决系统的非线性问题。由于滑模控制结构易于设计,并且如果满足条件,系统完全适应系统干扰和参数扰动,系统具有强大的鲁棒性[8.-10.]。系统的状态是需要设计the sliding mode controller, and the acquired state signal uses the Kalman filter to remove the noise to get the actual value. The proportional integral PI method is used to the sliding surface, which provides greater freedom and reduces stability error. The simulation results demonstrate the effectiveness and robust of the proposed active suspension control method.

2季度汽车模型

在以前的经典悬架模型中,弹簧和阻尼通常似乎是线性组件,简化了研究。但是,这并没有充分描述真正的汽车暂停;当应用于实际悬架时,效果有限。本文考虑了车辆悬架系统的固有非线性和参数不确定性[11.]。

过滤器和控制机构的设计需要悬架的动态方程。本文适用于所示的经典四分之一悬架模型图1那W.heremS.代表汽车身体的质量和mR.epresents the mass of the tire system. The suspension and shock absorbers that connect the body, and the tire have stiffness and damping coefficients ofK.S.B.S.,而橡胶轮胎近似为弹性构件,刚度K.T.。在模型中,Z.S.代表车身的位移,Z.是轮胎的位移,Z.R.是路面的输入激励。变量力量表示控制器生成主动控制的力。

根据牛顿的第二律,模型的力方程是

(1)

在该公式中悬浮液的阻尼力和弹力考虑其非线性特性,以及简化的轮胎力分别如下

(2)

这里,非线性阻尼系数B.S.由...组成B.S.B.B.S.描述阻尼器的线性部分,和BSN.R.epresents the performance of the nonlinear part of the damper. The nonlinear stiffnessK.S.通过组合线性系数部分获得悬架K.S.和非线性系数部分K.

替换国家矢量进入公式(1)(2)产生简单的非线性状态方程如下

(3)

在哪里D.X,T.)=δFX)+ EZ.R.

在哪里D.XT.)contains nonlinear and uncertain structures in the suspension system.

一种S.S.你mption:有一个已知的β∊R+这样的||D.XT.)||≤.β,其中|| · || represents the spectral norm of the vector or matrix.

TH.你mB.nail Fig. 1

四分之一车模型。

3.Sliding surface and controller design

B.ecause of the nonlinearity of the vehicle model and the disturbance of the road, the riding comfort and road handing of the vehicle depends on the performance of the suspension system. This paper applies the sliding mode control method to design the active control force. Firstly, the sliding surface needs to be designed to ensure that the system motion track slides along the specified line to the equilibrium point. In our paper, we use the proportional integral sliding surface expression as follows:(4)

在哪里CΕℝ.m×nE.Εℝ.n×n是恒定的矩阵,使系统进入滑动模式,必须确保S. = 0是建立的。同时,等效控制力eq.T.)是从[12.]

(5)

如果TH.ere is a matrixC这样CB.是非奇异的基质,等同的控制力eq.(6)

Substituting Equation(6)进入系统(3),反馈闭环系统动态方程如下(7)

T.heorem如果系统(7)在滑动表面S = 0上界定且稳定。

证明。为了简化认证过程,我们让(7a)(7B)

然后等式(7)是S.implified to(8)

We choose the following Lyapunov function related to the vectorXT.)。(9)

衍生V.T.)沿着轨迹XT.),给予(10)

在哪里问:是an arbitrary positive definite symmetric matrix, thenP.是对应于等式的独特解决方案。E.问:你ation(10)can be rewritten as(11)

众所周知λ问:)>0, the是S.atisfied for allXT.)满意

T.herefore, the suspension system is bounded stability.

在本文中,使用恒定的达到法,并且使用饱和函数来削弱抖动。最后,获得了不确定系统的控制定律。(12)(13)

如果(14)

T.hus,。通过比较方程式(5)(12)(14)那TH.e hitting condition is satisfied.

4卡尔曼滤波器

T.he sensor measures the state quantity of the suspension. Nevertheless, due to the actual constraints, only certain state variables can be tested, and there is noise in the process of signal acquisition. Therefore, the Kalman filter is used to filter out the noises, and all state variables are estimated [13.]。最后,控制器基于状态估计设计。

In order to meet the design conditions of the Kalman filter, we can rewrite the system Equation(3)作为:(15)

在哪里G= [B.E.] 和一种FX)是一种时变矩阵,其可以根据系统状态的变化而变化。一般来说,相对位移Z.S.-Z.和相对速度B.etween the body and the tire can be measured by sensors. Converting a continuous state equation to a discrete state equation by a zero-order keeper is shown below.(16)(17)。在哪里K.是个K.TH.样本数据,φ(XK.-1),K.-1),Γ和γ.W.代表离散状态方程的系统参数矩阵,控制输入矩阵和外部干扰矩阵。H是个output matrix, andW.V.表示分别在传感器测量中的悬架操作和噪声向量中的过程噪声载体。然后我们可以如下获取卡尔曼过滤器:(18)(19)在哪里are the estimated state and output vectors, respectively.

(20)

这里。P.K.|K.)估计误差方差矩阵,以及K.K.)代表卡尔曼收益;在哪里R. = E.[V.K.V.T.K.)] 和问: = E.[W.K.W.T.K.)]R.epresent the covariance matrices of noisesW.V., 分别。使用估计的状态向量后通过滤波获得,实际输出控制力计算如下(21)

In the actual damping system, it is required to decouple the control from the external disturbance, since the external disturbanceZ.R.是challenging to detect and estimate online. When (CB.-1CE. = 0,满足要求。最后,控制功率降低到(22)

5绩效措施

Due to the limited space between the car body and the tire, its size must not exceed the maximum valueXR.。本文使用相对暂停偏转(RSD)来评估悬架是否与主体干扰,由ζ表示为(23)

为了确保车轮不留地,使用相对轮胎力(RTF)来表明轮胎的动态载荷是否超过静电轮胎负载,表示为φ,被定义为(24)

必须保证RSD和RTF值都小于1,因此汽车可以平稳和安全地行进。垂直加速度车辆衡量乘坐的舒适度。

6仿真和讨论

For reflecting the performance of the control method proposed in this paper, we compare it with the linear quadratic regulator (LQR) control approach and passive suspension. Vehicle model parameters are shown in表格1,以及状态矢量的初始值X是S.et toX(0.)=[0.0.0.0.]T.

道路输入干扰由(25)

在哪里D.T.)= 0.002(2Πt.)+ 0.002(7.。5.Πt.)是一个周期性的干扰,并且时间间隔被描述为T.1 = T. - 3.5,T.2 = T. - 6.5,T.3. = T. - 8.5和T.4. = T. - 11.5. This road input excitation was applied in Chen [14.] 和P.你S.adkar [15.] 研究。

T.he parameters of the LQR controller are as follows: the objective performance functions considered in this article includeZ.S.- Z.Z.- Z.R.。加权矩阵问:R.被选为问: = diag [问:1问:1问:3.]W.here问:1 = 20,问:2 = 问:3. = 1 × 104., 和R. = 1×10-4。根据不同时间的悬架系统的参数来解决Riccati代数方程,并且获得每个时刻的最佳反馈增益。选择仿真期间滑动模式控制的结构参数C = [−300, 300, 1000, 0],E. = Diag [20,5,11,-5],K. = 1δ = 0.001。

在道路输入和噪声干扰的情况下,悬架系统使用卡尔曼滤波器在传感器编号受到限制时估计悬架状态向量。

图2.A-D示出了估计悬架位移,弹簧质量,轮胎位移和难簧速度的模拟结果。估计值与实际成本之间的误差显示在T.able 2。可以看出,Unsprung质量位移误差RM大于簧上位位移误差,并且两者之间的速度误差率差异很小。结果表明,在允许的误差范围内过滤后的估计值可以充分描述悬架的真实状态。

为了验证所提出的PISMC控制方法的性能,LQR控制策略和被动悬架用作参考物体。结果显示在T.able 3图3.是悬浮位移的反应。可以看出,PISMC可以更有效地抑制簧上质量的位移。弹簧质量的加速度是S.hown in图4.。Compared with passive suspension, the vertical acceleration of the car body is reduced by about 27.8%, and the LQR control method is increased.图5.6.S.how the results of RSD and RSF, respectively. The relative suspension deflection has increased a lot due to the characteristics of active control. This increase is acceptable within the allowable space. In terms of operational stability, the PISMC method is similar to passive suspension, and the LQR method is superior.

表格1

P.arameter values of the quarter suspension model

TH.你mB.nail Fig. 2

E.S.T.imation results of Kalman filter.

TH.你mB.nail Fig. 3

R.esponses of suspension displacement.

T.able 2

卡尔曼滤波器估计误差结果摘要

T.able 3

仿真性能参数结果

TH.你mB.nail Fig. 4

悬浮加速的响应。

TH.你mB.nail Fig. 5

相对悬浮偏转。

TH.你mB.nail Fig. 6

相对轮胎力量。

7.Discussion

本文提出了基于信号滤波的滑模主动控制,并考虑了悬架系统的非线性和外部不确定干扰的影响。采用了PISMC控制策略来改善系统的稳健性与参数变化和外部干扰。此外,为了实现更好的控制效果,控制力所需的系统所需的系统更具系统状态变量。由于实际的工程限制,传感器只能收集状态信号的一部分,并且悬架系统在采集信号工程中具有很多噪声。为了避免对控制系统的不利影响,卡尔曼滤波器估计的悬架状态以满足设计要求。

结果表明,过滤的估计与实际值一致,使控制器能够执行准确的控制。在控制效果方面,与LQR和被动悬架的性能相比,PIMSC大大降低了车身的位移和加速度,这可以显着提高乘坐舒适性和同时。

资金

T.his research was funded by the subproject of the National Key Research and Development Program of China (No. 2018YFB2001400), National Natural Science Foundation of China (51705051); Basic Natural Science and Frontier Technology Research Program (ccstc2017jcyjAX0169); China Postdoctoral Science Foundation (2018M643420 and 2019T120813); Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems (GZKF-201808). Open Foundation of the State Key Laboratory of Mechanical Transmission (SKLMT-KFKT-201804).

Conflicts of Interest

作者宣称没有利益冲突。

一种你T.hor contribution statement

概念化,XC.和s.h ;;数据策委,S.H ;;正式分析,XC.和s.h ;;资金收购,X.c。和t. l ;;调查,XC.和s.h ;;方法论,S.H; project administration, X.C.; resources, D.G.; software, S.H.; supervision, X.C.; validation, S.H.; visualization, S.H.; writing—original draft preparation, S.H.; writing—review and editing, S.H., X.C. and T.L.

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Cite this article as:X. Chen,S. Han,T. Luo,D. Guo,具有状态估计,力学和工业的非线性悬架系统的滑模控制的调查yabo亚博21.那611.(20.20.)

所有表格

表格1

P.arameter values of the quarter suspension model

T.able 2

卡尔曼滤波器估计误差结果摘要

T.able 3

仿真性能参数结果

所有数字

TH.你mB.nail Fig. 1

四分之一车模型。

在文中
TH.你mB.nail Fig. 2

E.S.T.imation results of Kalman filter.

在文中
TH.你mB.nail Fig. 3

R.esponses of suspension displacement.

在文中
TH.你mB.nail Fig. 4

悬浮加速的响应。

在文中
TH.你mB.nail Fig. 5

相对悬浮偏转。

在文中
TH.你mB.nail Fig. 6

相对轮胎力量。

在文中

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