ACTIVE SUSPENSION CONTROL METHOD UNDER VEHICLE-MOUNTED VISUAL PERCEPTION

Abstract

The present disclosure discloses an active suspension control method under vehicle-mounted visual perception preview. It uses a binocular camera combined with multiple visual perception algorithms, and monitors in real time the road surface conditions ahead of the vehicle. By accurately capturing and analyzing the road surface information, based on robust control theory and Lyapunov theory, it designs a matching preview H.sub. controller. The vehicle can effectively reduce bumps and vibrations by timely adjusting the suspension system, providing passengers with a more stable and smooth driving experience. The present disclosure uses a machine vision method to sense in advance the road surface information ahead, improving the time lag problem in the traditional suspension control method, thereby significantly improving the vehicle safety and ride comfort.

Claims

1. An active suspension control method under vehicle-mounted visual perception preview, comprising steps of: S1: training a target identification model: using a YOLOV5 target detection algorithm to identify an instantaneous road surface excitation of a speed bump; S2: obtaining road surface information: using a binocular camera and combining with the target identification model that has been trained in S1, performing contour fitting on an identified target, obtaining an actual height x.sub.f of the target through internal and external parameters of the camera, and calculating an actual distance S of the target with a binocular ranging algorithm; S3: designing a controller: using the excitation information detected in S2, designing a state feedback-based preview H.sub. controller.

2. The active suspension control method according to claim 1, wherein the step S1 comprises: taking different speed bump images under different lighting conditions, annotating the speed bump images using LabelImg and producing a data set; and using YOLOV5 target identification algorithm for training.

3. The active suspension control method according to claim 1, wherein the step S2 comprises: installing the binocular camera in front of the vehicle, and using the YOLOV5 model trained in S1 to perform target identification and determine if there is a speed bump ahead; if there is the speed bump ahead, extracting the target and using the Canny edge detection algorithm to detect the edge of the speed bump, and using the findContours function in OpenCV to extract the contour of the object, and converting a scale of the fitting object contour in the image to a scale in a real world to obtain the actual height x.sub.f of the target; detecting feature points on the road surface image by using a SIFT image processing algorithm, and obtaining corresponding feature point pairs in the image by a RANSAC matching algorithm; calculating a parallax value x.sub.hx.sub.t of the image based on the found feature point pairs, and obtaining the actual distance S based on a triangle similarity principle, as follows: $\begin{array}{cc}\frac{L-\left(x_h-x_t\right)}{L}=\frac{S-f}{S}& \left(1\right)\end{array}$ $\begin{array}{cc}S=\frac{\mathrm{fL}}{x_h-x_t}& \left(2\right)\end{array}$ wherein L is a center distance between left and right cameras of the binocular camera, and f is a focal length of the camera.

4. The active suspension control method according to claim 1, wherein the step S3 is comprises: firstly establishing a suspension model $\begin{array}{cc}\{\begin{array}{c}{m}_s{\stackrel{.Math.}{x}}_1=F-c_s\left({\stackrel{.}{x}}_1-{\stackrel{.}{x}}_2\right)-k_s\left(x_1-x_2\right)\\ m_s{\stackrel{.Math.}{x}}_2=c_s\left({\stackrel{.}{x}}_1-{\stackrel{.}{x}}_2\right)+k_s\left(x_1-x_2\right)-k_t\left(x_2-x_r\right)-F\end{array}& \left(3\right)\end{array}$ wherein, ms is a suspended mass, m.sub.t is a non-suspended mass, x.sub.1 is a vertical displacement of a suspended mass, x.sub.2 is a vertical displacement of the non-suspended mass, x.sub.r is a height of the road surface under a wheel, k.sub.s is a suspension spring stiffness, k.sub.t is a tire stiffness, c.sub.s is a suspension damping, and F is an active suspension control force; establishing an active suspension model according to the equation (3), taking a state variable X=[x.sub.1x.sub.2 {dot over (x)}.sub.1 x.sub.2x.sub.r {dot over (x)}.sub.2].sup.T, an output is Y=[x.sub.1x.sub.2 x.sub.2x.sub.r F {umlaut over (x)}.sub.1].sup.T, a state equation is expressed as follow $\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{X}=\mathrm{AX}+B_1{\stackrel{.}{x}}_r+B_{2}F\\ \stackrel{.}{Y}=C_{1}X+D_{11}{\stackrel{.}{x}}_r+D_{12}F\\ Z=C_{2}X\end{array}& \left(4\right)\end{array}$ $\mathrm{wherein},A=\left[\begin{array}{cccc}0& 1& 0& -1\\ -\frac{k_s}{m_s}& -\frac{c_s}{m_s}& 0& \frac{c_s}{m_s}\\ 0& 0& 0& 1\\ \frac{k_s}{m_t}& \frac{c_s}{m_t}& -\frac{k_t}{m_t}& -\frac{c_s}{m_t}\end{array}\right],B_1={\left[00-10\right]}^T,$ $B_2={\left[0\frac{1}{m_s}0-\frac{1}{m_t}\right]}^T,C_1=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 0\\ -\frac{k_s}{m_s}& -\frac{c_s}{m_s}& 0& \frac{c_s}{m_s}\end{array}\right],$ $D_{11}={\left[0000\right]}^T,D_{12}={\left[001\frac{1}{m_s}\right]}^T,$ $C_2=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right],Z={\left[x_1-x_2{\stackrel{.}{x}}_1{x}_2-x_r{\stackrel{.}{x}}_2\right]}^T$ are status feedback; a relationship between an actual road surface excitation x.sub.r and a preview excitation x.sub.f is as follow: $\begin{array}{cc}\frac{z_r}{z_f}=e^{-\mathrm{ts}}& \left(5\right)\end{array}$ wherein $t=\frac{S}{v}$ is a preview time, and v is a vehicle speed; adopting pade to approach quadratic approximation $\begin{array}{cc}\frac{{\stackrel{.}{z}}_r}{{\stackrel{.}{z}}_f}=\frac{s^2-{}_{1}s+{}_0}{s^2+{}_{1}s+{}_0}& \left(6\right)\end{array}$ $\mathrm{wherein}{}_1=\frac{6}{t},{}_2=\frac{12}{r^2}$ performing Laplace inverse transformation on it to obtain: $\begin{array}{cc}\stackrel{.Math.}{y}+{}_1\stackrel{.}{y}+{}_{0}y={\stackrel{.}{x}}_f& \left(7\right)\end{array}$ $\mathrm{wherein}y={\stackrel{.}{x}}_r-{\stackrel{.}{x}}_f,=-2{}_1$ defining an additional state vector =[.sub.1 .sub.2].sup.T, .sub.1=y, .sub.2={dot over ()}.sub.1{dot over (x)}.sub.f, its state space equation is $\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{}=A_9+B_9{\stackrel{.}{x}}_f\\ {\stackrel{.}{x}}_r=C_9+D_9{\stackrel{.}{x}}_f\end{array}& \left(8\right)\end{array}$ $\mathrm{Wherein}{A}_9=\left[\begin{array}{cc}0& 1\\ -{}_0& -{}_1\end{array}\right],B_9=\left[\begin{array}{c}-2{}_1\\ 2{}_1^2\end{array}\right],C_9=\left[10\right],D_9=1;$ combining with equation (4) to obtain an active suspension state equation containing preview information, as shown in equation $\begin{array}{cc}\{\begin{array}{c}{\stackrel{.}{X}}_{}=A_{}{X}_{}+B_1{\stackrel{.}{x}}_f+B_{2}F\\ Y_{}=C_1{X}_{}+D_{11}{\stackrel{.}{x}}_f+D_{12}F\\ Z_{}=C_2{X}_{}\end{array}& \left(9\right)\end{array}$ $\mathrm{wherein}{\stackrel{.}{X}}_{}=\left[\begin{array}{c}\stackrel{.}{X}\\ \stackrel{.}{}\end{array}\right],Y_{}=\left[\begin{array}{c}Y\\ \stackrel{.}{}\end{array}\right],Z_{}=\left[\begin{array}{c}Z\\ \stackrel{.}{}\end{array}\right],X_{}=\left[\begin{array}{c}X\\ \stackrel{.}{}\end{array}\right],A_{}=\left[\begin{array}{cc}A& B_1{C}_9\\ 0& A_9\end{array}\right],$ $B_1=\left[\begin{array}{c}{B}_1{D}_9\\ B_9\end{array}\right],B_2=\left[\begin{array}{c}{B}_2\\ 0\end{array}\right].$ $C_1=\left[\begin{array}{cc}{C}_1& D_{11}{C}_9\\ 0& A_9\end{array}\right],D_{11}=\left[\begin{array}{c}{D}_{11}{D}_9\\ B_9\end{array}\right],D_{12}=\left[\begin{array}{c}{D}_{12}\\ 0\end{array}\right],$ $C_2=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right];$ secondly, designing an LMI-based suspension H.sub. controller, a transfer function G from an external excitation to the output satisfies the following relationship: $\begin{array}{cc}.Math.G.Math.& \left(10\right)\end{array}$ wherein is a specified positive scalar; assuming that a state feedback gain is K, and substituting F=KX.sub. into the equation (9) to obtain: $\begin{array}{cc}\{\begin{array}{c}{\stackrel{.}{X}}_{}=A_c{X}_{}+B_1{\stackrel{.}{x}}_f\\ Y_{}=C_l{X}_{}+D_{11}{\stackrel{.}{x}}_f\\ Z_{}=C_2{X}_{}\end{array}& \left(11\right)\end{array}$ $\mathrm{wherein}{A}_C=A_{}+B_2,C_l=C_1+D_{12};$ theorem: for a given positive scalar , if there exists a positive definite matrix P.sub.0 and a matrix Q, a following LMI is established: $\begin{array}{cc}\left[\begin{array}{ccc}{P}_0{A}_{}+Q^T{B}_2+A_{}{P}_0+B_{2}Q& P_0{C}_2^T& B_2\\ C_2{P}_0& -I& 0\\ B_2^T& 0& -{}^{2}I\end{array}\right]<0& \left(12\right)\end{array}$ then a closed-loop control system has the following H.sub. performance: $\begin{array}{cc}{}_0^T{Z}^T\left(t\right)Z\left(t\right)\mathrm{dt}<{}_{\max }\left(P\right){.Math.X\left(0\right).Math.}^2+{}^2{}_0^T{z}_f^T\left(t\right)z_f\left(t\right)\mathrm{dt}& \left(13\right)\end{array}$ $\mathrm{where}Q={\mathrm{KP}}_0,P_0=P^{-1};$ setting a Lyapunov function as $\begin{array}{cc}V=X_{}^T{\mathrm{PX}}_{}& \left(14\right)\end{array}$ taking a derivative of this to give: $\begin{array}{cc}\stackrel{.}{V}=X_{}^T\left(A_c^{T}P+{\mathrm{PA}}_c\right)X_{}+x_f^T{B}_2^T{\mathrm{PX}}_{}+X_{}^T{\mathrm{PB}}_2{z}_f& \left(15\right)\end{array}$ in order to ensure a performance of the H.sub. controller, an evaluation index J.sub.1 is introduced: $\begin{array}{cc}\begin{array}{c}{J}_1=\stackrel{.}{V}+Z_{}^T{Z}_{}-{}^2{z}_f^2\\ =\left[X_{}{z}_f\right]\left[\begin{array}{cc}{A}_c^{T}P+{\mathrm{PA}}_c+C_2^T{C}_2& {\mathrm{PB}}_2\\ B_2^{T}P& -{}^{2}I\end{array}\right]\left[\begin{array}{c}{X}_{}\\ z_f\end{array}\right]\end{array}& \left(16\right)\end{array}$ according to Schur's complement theorem, the evaluation index J.sub.1 can be equivalent to J.sub.2, $\begin{array}{cc}\left[\begin{array}{cc}{P}^{-1}& 0\\ 0& I\end{array}\right]\left[\begin{array}{cc}{A}_c^{T}P+{\mathrm{PA}}_c+C_2^T{C}_2& {\mathrm{PB}}_2\\ B_2^{T}P& -{}^{2}I\end{array}\right]\left[\begin{array}{cc}{P}^{-1}& 0\\ 0& I\end{array}\right]& \left(17\right)\end{array}$ $\begin{array}{cc}\mathrm{that}\mathrm{is}{J}_2=\left[\begin{array}{ccc}{p}^{-1}{A}_c^T+A_c{P}^{-1}& B_2& P^{-1}{C}_2^T\\ B_2^T& -{}^{2}I& 0\\ C_2{P}^{-1}& 0& -I\end{array}\right]& \left(18\right)\end{array}$ substituting A.sub.c=A.sub.+B.sub.2 into the equation (18) and performing elementary transformations to give: $\begin{array}{cc}{J}_2=\left[\begin{array}{ccc}{p}_0{A}_{}^T+Q^T{B}_2^T+A_{}{P}_0+B_{2}Q& P^{-1}{C}_2^T& B_2\\ C_2{P}^0& -I& 0\\ B_2^T& 0& -{}^{2}I\end{array}\right]& \left(19\right)\end{array}$ given a positive scalar , if there exists a positive definite matrix P.sub.0 and a matrix Q such that J.sub.2<0, then J.sub.1<0 holds, by integrating J.sub.1, it gives: $\begin{array}{cc}{}_0^T{J}_1\mathrm{dt}={}_0^T\left(\stackrel{.}{V}+Z_{}^T{Z}_{}-{}^2{z}_f^2\right)\mathrm{dt}<0& \left(20\right)\end{array}$ according to Lyapunov's definition of stability, it gives: $\begin{array}{cc}{}_0^T\stackrel{}{V}\mathrm{dt}=V\left(T\right)-V\left(0\right)<0& \left(21\right)\end{array}$ substituting the Lyapunov function into the equation (21), it gives: $\begin{array}{cc}{}_0^T\stackrel{}{V}\mathrm{dt}=X_{}^T\left(T\right){\mathrm{PX}}_{}\left(T\right)-X_{}^T\left(0\right){\mathrm{PX}}_{}\left(0\right)<0& \left(22\right)\end{array}$ due to $X_{}^T\left(T\right){\mathrm{PX}}_{}\left(T\right)>0,P<-{}_{\max }\left(P\right)I,$ obtaining: $\begin{array}{cc}{}_0^T\stackrel{}{V}\mathrm{dt}>-{}_{\max }\left(P\right){.Math.X_{}\left(0\right).Math.}^2& \left(23\right)\end{array}$ then the equation (20) is equivalent to $\begin{array}{cc}{}_0^T{Z}^T\left(t\right)Z\left(t\right)\mathrm{dt}<{}_{\max }\left(P\right){.Math.X\left(0\right).Math.}^2+{}^2{}_0^T{z}_f^T\left(t\right)z_f\left(t\right)\mathrm{dt}& \left(24\right)\end{array}$ given a positive scalar , solving for the positive definite matrix P.sub.0 and the matrix Q, a closed-loop system obtains a control gain of K=QP, then the closed-loop system has the H.sub. performance; using the LMI solver in MATLAB to solve the state feedback gain as K, and find an optimal control force, the designed preview H.sub. controller is used to improve a suspension dynamic route, a tire dynamic displacement and a vehicle body acceleration, so that vehicle comfort and safety are improved.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0046] FIG. 1 is a flowchart of an implementation process of the present disclosure;

[0047] FIG. 2 is a schematic diagram of a binocular ranging principle provided by the present disclosure.

DESCRIPTION OF EMBODIMENTS

[0048] As shown in FIG. 1, an active suspension control method under vehicle-mounted visual perception preview is provided, it includes the steps as follows: [0049] S1: training a target identification model: Use a YOLOV5 target detection algorithm to identify the instantaneous road surface excitation of speed bumps; [0050] Step S1 is specifically as follows: [0051] Taking different speed bump images under different lighting conditions, annotating them using LabelImg and producing a data set; and using YOLOV5 target identification algorithm for training; [0052] S2: Obtaining road surface information: Use a binocular camera and combine with the target identification model trained in S1 to perform contour fitting on the identified target, obtain the actual height x.sub.f of the target through the internal and external parameters of the camera, and calculate the actual distance S of the target with the binocular ranging algorithm; [0053] Step S2 is specifically as follows: [0054] Installing the binocular camera in front of the vehicle, and using the YOLOV5 model trained in S1 to perform target identification and determine if there is a speed bump ahead.

[0055] If so, extracting the target and using the Canny edge detection algorithm to detect the edge of the speed bump. Meanwhile, the findContours function in OpenCV is used to extract the contour of the object, and the scale of the fitting object contour in the image is converted to the scale in the real world to obtain the actual height x.sub.f of the target;

[0056] The SIFT image processing algorithm is then used to detect feature points on the road surface image, and the corresponding feature point pairs in the image are obtained by the RANSAC matching algorithm. The parallax value x.sub.hx.sub.t of the image is calculated based on the found feature point pairs, and the actual distance S can be obtained based on the triangle similarity principle, as shown in FIG. 2, as follows:

[00026]$\begin{array}{cc}\frac{L-\left(x_h-x_t\right)}{L}=\frac{S-f}{S}& \left(1\right)\end{array}$$\begin{array}{cc}S=\frac{\mathrm{fL}}{x_h-x_t}& \left(2\right)\end{array}$

[0057] Wherein L is the center distance between the left and right cameras of the binocular camera, and f is the focal length of the camera.

[0058] S3: Designing a controller; [0059] Using the excitation information detected in S2, a preview H.sub. controller based on the state feedback is designed; [0060] Step S3 is specifically as follows: [0061] First, establishing a suspension model.

[00027]$\begin{array}{cc}\{\begin{array}{c}{m}_s{\stackrel{.Math.}{x}}_1=F-c_s\left({\stackrel{.}{x}}_1-{\stackrel{.}{x}}_2\right)-k_s\left(x_1-x_2\right)\\ m_t{\stackrel{.Math.}{x}}_2=c_s\left({\stackrel{.}{x}}_1-{\stackrel{.}{x}}_2\right)+k_s\left(x_1-x_2\right)-k_t\left(x_2-x_r\right)-F\end{array}& \left(3\right)\end{array}$

[0062] Wherein, ms is the suspended mass, m.sub.t is the non-suspended mass, x.sub.1 is the vertical displacement of the suspended mass, x.sub.2 is the vertical displacement of the non-suspended mass, x.sub.r is the height of the road surface under the wheel, k.sub.s is the suspension spring stiffness, k.sub.t is the tire stiffness, c.sub.s is the suspension damping, and F is the active suspension control force.

[0063] According to equation (3), the active suspension model is established, and the state variable is taken as X=[x.sub.1x.sub.2 {dot over (x)}.sub.1 x.sub.2x.sub.r {dot over (x)}.sub.2].sup.T. The output is Y=[x.sub.1x.sub.2 x.sub.2x.sub.r F {umlaut over (x)}.sub.1].sup.T. The state equation is expressed as follows

[00028]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{X}=\mathrm{AX}+B_1{\stackrel{.}{x}}_r+B_{2}F\\ \stackrel{.}{Y}=C_{1}X+D_{11}{\stackrel{.}{x}}_r+D_{12}F\\ Z=C_{2}X\end{array}& \left(4\right)\end{array}$$\mathrm{Wherein},A=\left[\begin{array}{cccc}0& 1& 0& -1\\ -\frac{k_s}{m_s}& -\frac{c_s}{m_s}& 0& \frac{c_s}{m_s}\\ 0& 0& 0& 1\\ \frac{k_s}{m_t}& \frac{c_s}{m_t}& -\frac{k_t}{m_t}& -\frac{c_s}{m_t}\end{array}\right],B_1={\left[00-10\right]}^T$$B_2={\left[0\frac{1}{m_s}0-\frac{1}{m_t}\right]}^T,C_1=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 0\\ -\frac{k_s}{m_s}& -\frac{c_s}{m_s}& 0& \frac{c_s}{m_s}\end{array}\right],$$D_{11}={\left[0000\right]}^T,D_{12}={\left[001\frac{1}{m_s}\right]}^T,$$C_2=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right],Z={\left[x_1-x_2{\stackrel{.}{x}}_1{x}_2-x_r{\stackrel{.}{x}}_2\right]}^T$

are status feedback.

[0064] The relationship between the actual road surface excitation x.sub.r and the preview excitation x.sub.f is as follows:

[00029]$\begin{array}{cc}\frac{z_r}{z_f}=e^{-\mathrm{ts}}& \left(5\right)\end{array}$

[0065] Wherein

[00030]$t=\frac{S}{v}$

is the preview time, and v is the vehicle speed.

[0066] Adopting pade to approach quadratic approximation

[00031]$\begin{array}{cc}\frac{{\stackrel{.}{z}}_r}{{\stackrel{.}{z}}_f}=\frac{s^2-{}_{1}s+{}_0}{s^2+{}_{1}s+{}_0}& \left(6\right)\end{array}$$\mathrm{Wherein}{}_1=\frac{6}{t},{}_2=\frac{12}{t^2}$

[0067] Performing the Laplace inverse transformation on it to obtain

[00032]$\begin{array}{cc}\stackrel{.Math.}{y}+{}_1\stackrel{.}{y}+{}_{0}y={\stackrel{.}{x}}_f& \left(7\right)\end{array}$$\mathrm{Wherein}y={\stackrel{.}{x}}_r-{\stackrel{.}{x}}_f,=-2{}_1.$

[0068] Defining the additional state vector =[.sub.1 .sub.2].sup.T, .sub.1=y, .sub.2={dot over ()}.sub.1{dot over (x)}.sub.f. Its state space equation is

[00033]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{}=A_9+B_9{\stackrel{.}{x}}_f\\ {\stackrel{.}{x}}_r=C_9+D_9{\stackrel{.}{x}}_f\end{array}& \left(8\right)\end{array}$$\mathrm{Wherein}{A}_9=\left[\begin{array}{cc}0& 1\\ -{}_0& -{}_1\end{array}\right],B_9=\left[\begin{array}{c}-2{}_1\\ 2{}_1^2\end{array}\right],C_9=\left[10\right],D_9=1.$

[0069] Combined with equation (4), the active suspension state equation containing preview information can be obtained, as shown in equation

[00034]$\begin{array}{cc}\{\begin{array}{c}{\stackrel{.}{X}}_{}=A_{}{X}_{}+B_1{\stackrel{.}{x}}_f+B_{2}F\\ Y_{}=C_1{X}_{}+D_{11}{\stackrel{.}{x}}_f+D_{12}F\\ Z_{}=C_2{X}_{}\end{array}& \left(9\right)\end{array}$$\mathrm{Wherein}{\stackrel{.}{X}}_{}=\left[\begin{array}{c}\stackrel{.}{X}\\ \stackrel{.}{}\end{array}\right],Y_{}=\left[\begin{array}{c}Y\\ \stackrel{.}{}\end{array}\right],Z_{}=\left[\begin{array}{c}Z\\ \stackrel{.}{}\end{array}\right],X_{}=\left[\begin{array}{c}X\\ \stackrel{.}{}\end{array}\right],A_{}=\left[\begin{array}{cc}A& B_1{C}_9\\ 0& A_9\end{array}\right],$$B_1=\left[\begin{array}{c}{B}_1{D}_9\\ B_9\end{array}\right],B_2=\left[\begin{array}{c}{B}_2\\ 0\end{array}\right],C_1=\left[\begin{array}{cc}{C}_1& D_{11}{C}_9\\ 0& A_9\end{array}\right],D_{11}=\left[\begin{array}{c}{D}_{11}{D}_9\\ B_9\end{array}\right],$$D_{12}=\left[\begin{array}{c}{D}_{12}\\ 0\end{array}\right],C_2=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right].$

[0070] Next, the LMI-based suspension H.sub. controller is designed. The transfer function G from the external excitation to the output should satisfy the following relationship:

[00035]$\begin{array}{cc}.Math.G.Math.& \left(10\right)\end{array}$

[0071] Wherein is a specified positive scalar.

[0072] Assuming that the state feedback gain is K, and substituting F=KX.sub. into equation (9) to obtain:

[00036]$\begin{array}{cc}\{\begin{array}{c}{\stackrel{.}{X}}_{}=A_c{X}_{}+B_1{\stackrel{.}{x}}_f\\ Y_{}=C_l{X}_{}+D_{11}{\stackrel{.}{x}}_f\\ Z_{}=C_2{X}_{}\end{array}& \left(11\right)\end{array}$$\mathrm{Wherein}{A}_c=A_{}+B_{2}K,C_l=C_1+D_{12}K.$

[0073] Theorem: For a given positive scalar , if there exists a positive definite matrix P.sub.0 and a matrix Q, the following LMI can be established:

[00037]$\begin{array}{cc}\left[\begin{array}{ccc}{P}_0{A}_{}+Q^T{B}_2+A_{}{P}_0+B_{2}Q& P_0{C}_2^T& B_2\\ C_2{P}_0& -I& 0\\ B_2^T& 0& -{}^{2}I\end{array}\right]<0& \left(12\right)\end{array}$

[0074] Then the closed-loop control system has the following H.sub. performance:

[00038]$\begin{array}{cc}{}_0^T{Z}^T\left(t\right)Z\left(t\right)\mathrm{dt}<{}_{\max }\left(P\right){.Math.X\left(0\right).Math.}^2+{}^2{}_0^T{z}_f^T\left(t\right)z_f\left(t\right)\mathrm{dt}& \left(13\right)\end{array}$$\mathrm{Wherein}Q={\mathrm{KP}}_0,P_0=P^{-1}.$

[0075] Setting the Lyapunov function as

[00039]$\begin{array}{cc}V=X_{}^T{\mathrm{PX}}_{}& \left(14\right)\end{array}$

[0076] Taking the derivative of this, it gives:

[00040]$\begin{array}{cc}\stackrel{.}{V}=X_{}^T\left(A_c^{T}P+{\mathrm{PA}}_c\right)X_{}+x_f^T{B}_2^T{\mathrm{PX}}_{}+X_{}^T{\mathrm{PB}}_2{z}_f& \left(15\right)\end{array}$

[0077] In order to ensure the performance of the H.sub. controller, the evaluation index J.sub.1 is introduced:

[00041]$\begin{array}{cc}\begin{array}{c}{J}_1=\stackrel{.}{V}+Z_{}^T{Z}_{}-{}^2{z}_f^2\\ =\left[X_{}{z}_f\right]\left[\begin{array}{cc}{A}_c^{T}P+{\mathrm{PA}}_c+C_2^T{C}_2& {\mathrm{PB}}_2\\ B_2^{T}P& -{}^{2}I\end{array}\right]\left[\begin{array}{c}{X}_{}\\ z_f\end{array}\right]\end{array}& \left(16\right)\end{array}$

[0078] According to Schur's complement theorem, the evaluation index J.sub.1 can be equivalent to J.sub.2,

[00042]$\begin{array}{cc}\left[\begin{array}{cc}{P}^{-1}& 0\\ 0& I\end{array}\right]\left[\begin{array}{cc}{A}_c^{T}P+{\mathrm{PA}}_c+C_2^T{C}_2& {\mathrm{PB}}_2\\ B_2^{T}P& -{}^{2}I\end{array}\right]\left[\begin{array}{cc}{P}^{-1}& 0\\ 0& I\end{array}\right]& \left(17\right)\end{array}$$\begin{array}{cc}\mathrm{That}\mathrm{is}{J}_2=\left[\begin{array}{ccc}{p}^{-1}{A}_c^T+A_c{P}^{-1}& B_2& P^{-1}{C}_2^T\\ B_2^T& -{}^{2}I& 0\\ C_2{P}^{-1}& 0& -I\end{array}\right]& \left(18\right)\end{array}$

[0079] Substituting A.sub.c=A.sub.+B.sub.2 into equation (18) and performing elementary transformations, it gives:

[00043]$\begin{array}{cc}{J}_2=\left[\begin{array}{ccc}{P}_0{A}_{}^T+Q^T{B}_2^T+A_{}{P}_0+B_{2}Q& P^{-1}{C}_2^T& B_2\\ C_2{P}_0& -I& 0\\ B_2^T& 0& -{}^{2}I\end{array}\right]& \left(19\right)\end{array}$

[0080] Given a positive scalar , if there exists a positive definite matrix P.sub.0 and a matrix Q such that J.sub.2<0, then J.sub.1<0 holds. By integrating J.sub.1, it gives:

[00044]$\begin{array}{cc}{}_0^T{J}_{1}dt={}_0^T(\stackrel{.}{V}+Z_{}^T{Z}_{}-r^2{z}_f^2\}\mathrm{dt}<0& \left(20\right)\end{array}$

[0081] According to Lyapunov's definition of stability, it gives:

[00045]$\begin{array}{cc}{}_0^T\stackrel{}{V}\mathrm{dt}=V\left(T\right)-V\left(0\right)<0& \left(21\right)\end{array}$

[0082] Substituting the Lyapunov function into equation (21), it gives:

[00046]$\begin{array}{cc}{}_0^T\stackrel{}{V}\mathrm{dt}=X_{}^T\left(T\right){\mathrm{PX}}_{}\left(T\right)-X_{}^T\left(0\right){\mathrm{PX}}_{}\left(0\right)<0& \left(22\right)\end{array}$

[0083] Due to X.sub..sup.T(T)PX.sub.(T)>0, P<.sub.max (P)I, the following is obtained:

[00047]$\begin{array}{cc}{}_0^T\stackrel{}{V}\mathrm{dt}>-{}_{\max }\left(P\right){.Math.X_{}\left(0\right).Math.}^2& \left(23\right)\end{array}$

[0084] Then equation (20) can be equivalent to

[00048]$\begin{array}{cc}{}_0^T{Z}^T\left(t\right)Z\left(t\right)\mathrm{dt}<{}_{\max }\left(P\right){.Math.X\left(0\right).Math.}^2+{}^2{}_0^T{z}_f^T\left(t\right)z_f\left(t\right)\mathrm{dt}& \left(24\right)\end{array}$

[0085] Given a positive scalar , solving for the positive definite matrix P.sub.0 and the matrix Q, the closed-loop system obtains a control gain of K=QP, then the closed-loop system has H.sub. performance.

[0086] Using the LMI solver in MATLAB to solve the state feedback gain as K, and find the optimal control force. The designed preview H.sub. controller is used to improve the suspension dynamic route, the tire dynamic displacement and the vehicle body acceleration, so that the vehicle comfort and safety are improved.