CN113467233A - Time-lag finite frequency domain output feedback control method based on fuzzy model - Google Patents

Abstract

The fuzzy model-based time-delay finite frequency domain output feedback control method of the present invention includes the following steps: establishing a dynamic model of automobile active suspension mechanics; determining the variation range of the automobile sprung mass and unsprung mass; constructing two key The physical quantity is used to evaluate the performance of the control method; the time-delay state space model of the vehicle suspension is established; the fuzzy state-space model of the vehicle suspension time-delay system is established; the overall time-delay fuzzy control of the vehicle suspension system is obtained Spatial model and establishment of a static output feedback controller satisfying asymptotic stability of finite frequency domain and closed-loop systems. The invention can realize the high-performance control target of the automobile suspension system, and satisfy the high comfort and high safety in the driving process, especially considering the 4-8 Hz frequency range where the human body is most sensitive to vibration and the time-delay problem of sensors and actuators ; And strong robustness and stability, can meet the real-time requirements of automotive suspension systems.

Description

A Time-delay Finite Frequency Domain Output Feedback Control Method Based on Fuzzy Model

technical field

The invention belongs to the field of intelligent automobile manufacturing, and in particular relates to a time-delay limited frequency domain output feedback control method based on a fuzzy model.

Background technique

The suspension system of a car is composed of connecting rods, springs and shock absorbers, which can greatly improve the ride comfort, handling stability and grip of the car. As an important part of automobile chassis, automobile suspension has attracted extensive attention. In order to improve the noise, vibration and harshness (NVH) performance of automotive suspensions, a lot of research has been done on automotive suspension systems, such as passive suspension, energy regenerative suspension, semi/slow active suspension, active suspension Wait. In the current study, active suspension is an effective method to combine independent actuators and controllers to improve suspension performance. It's no secret that these three primary properties are always in conflict with each other, especially when it comes to the trade-off between ride comfort and road hold. In order to improve the ride comfort and maintain the displacement of the suspension and tires within an acceptable range, various control methods are designed and applied, such as sliding mode control, predictive control, model predictive control, H _∞ control. Among them, H ₂ , H _∞ and H ₂ /H _∞ control methods have been extensively discussed especially in the context of robustness and disturbance attenuation.

Time delays are very common in various engineering systems, such as long transmission lines, hydraulic systems, electronic systems, and magnetorheological systems. The presence of skew can be a source of instability and poor performance. In an active suspension system, there is always a time lag in the control channel because the digital controller needs time to do the calculations and the actuator needs time to build up the required force. Obviously, a suspension system with time lag requires careful analysis and synthesis. Therefore, this paper studies the time-delay problem in active suspension control.

It should be pointed out that all the above controllers are designed on the premise that the model parameters are known. Therefore, the above controller may crash when faced with various parameter changes. Uncertainty of some parameters is an inevitable phenomenon, such as the uncertainty of sprung mass and unsprung mass due to the number of passengers, fuel consumption, tire wear and so on. Therefore, the active suspension system has become a complex nonlinear system. For the representation of complex nonlinear systems, the Takagi-Sugeno (T-S) fuzzy model has been shown to be an effective method and a practical tool.

However, the above fuzzy controllers for uncertain nonlinear suspension systems all involve the entire frequency range. A key goal of the controller design was to minimize wheel-to-body vibration while maximizing passenger comfort. According to ISO-2631, the human body is more sensitive to vertical vibration between 4-8Hz. Furthermore, all road excitations only occur in a limited frequency range. Therefore, the controller in a certain frequency range is less conservative and more efficient than the controller in the whole frequency range.

Literature (Pan Huihui. Research on Nonlinear Control of Automotive Active Suspension System [D]. Harbin Institute of Technology, 2017). Only time delay and finite time are considered in the paper, and the frequency range of 4-8 Hz, which is the most sensitive human body, is not considered, nor does Considering the sprung and unsprung masses, this paper considers that some state feedback quantities in the system cannot be measured, and also considers the output feedback control of the lack of state quantities.

Similar to this research, there are existing researches: A reliable fuzzy state feedback controller is proposed for active suspension system with actuator time delay. In addition, some studies have proposed a fuzzy sampling data controller. Dynamic output feedback dissipation control is proposed for T-S fuzzy systems with time-varying input delay and output constraints. A semi-active vehicle suspension with T-S fuzzy control with magnetorheological dampers has been studied and verified experimentally. In addition, some researchers use the dynamic sliding mode control method to fuzzy control the uncertain vehicle active suspension system.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a time-delay limited frequency domain output feedback control method based on a fuzzy model, which is used to solve the time-delay and hard constraints existing in the suspension system, and considers the most sensitive frequency range of the human body, so as to achieve The high-performance control goal of the automotive suspension system, to meet the comfort and high safety during driving.

The present invention is realized by at least one of the following technical solutions.

A time-delay finite frequency domain output feedback control method based on fuzzy model, comprising the following steps:

1) For the time-delay vehicle active suspension system, the following dynamic model of the vehicle suspension system is established according to the mechanics principle;

2) Determine the variation range of sprung mass and unsprung mass according to the characteristics of the mechanical structure of the vehicle and the change in the number of passengers allowed and the effective load mass;

3) Construct two physical quantities to evaluate the performance of the control method;

4) Establish the time-delay state space model of the vehicle suspension system;

5) According to the Takagi-Sugeno fuzzy model, the time-delay fuzzy state space model of the vehicle suspension system is established;

6) Establish a time-delay output feedback controller;

7) Solve the output feedback controller gain of the vehicle suspension system;

8) Optimize the feedback controller;

9) Using the fuzzy finite frequency domain output feedback controller to control the vehicle suspension system online.

Preferably, the dynamic model of the vehicle suspension system is as follows:

和

为簧载质量的加速度和速度；z_u(t)为m_u(t)以水平地面为起始点垂直向上方向上的簧下质量的垂直位移，单位为m；

和

为簧下质量的加速度和速度；z_r(t)为以水平地面为起始点垂直向上方向上路面与轮胎接触点的垂直位移，单位为m；

为路面输入的速度；c_s为汽车悬架系统的阻尼系数，单位为N/(m/s)；k_s为汽车悬架系统的刚度系数，单位为N/m；c_t为汽车轮胎的阻尼系数，单位为N/(m/s)；k_t为汽车轮胎的刚度系数，单位为N/m。Among them, m _s (t) is the sprung mass composed of the mass of the car body, unit: Kg; m _u (t) is the unsprung mass composed of the mass of the car tire assembly, unit: Kg; u (t) is the car active suspension System control input, unit: N; z _s (t) is m _s (t) the vertical displacement of the sprung mass in the vertical upward direction with the horizontal ground as the starting point, unit: m;

and

is the acceleration and velocity of the sprung mass; z _u (t) _is the vertical displacement of the unsprung mass in the vertical upward direction with the horizontal ground as the starting point, and the unit is m;

and

is the acceleration and velocity of the unsprung mass; z _r (t) is the vertical displacement of the contact point between the road surface and the tire in the vertical upward direction with the horizontal ground as the starting point, in m;

is the speed input by the road surface; c _s is the damping coefficient of the automobile suspension system, in N/(m/s); k _s is the stiffness coefficient of the automobile suspension system, in N/m; c _t is the Damping coefficient, the unit is N/(m/s); k _t is the stiffness coefficient of the car tire, the unit is N/m.

Preferably, the variation range of the sprung mass m _s (t) and the unsprung mass _mu (t) is: m _s (t)∈[m _smin , m _smax ] and _mu (t)∈[m _umin , m _umax ], m _smin and m _smax are the minimum and maximum values of the sprung mass, and m _umin and m _umax are the minimum and maximum values of the unsprung mass.

Preferably, the evaluation control method is:

Among them, g is the acceleration of gravity, unit; N/Kg; and it is necessary to ensure that |z _s (t)-z _u (t)|≤z _max and k _t (z _u (t)-z _r (t))<( m _s (t)+m _u (t))g is established at the same time, z ₁ (t) is the acceleration of the sprung mass, z ₂ (t) is the relative dynamic deflection of the suspension z ₂₁ (t) and the relative dynamic of the wheel Matrix composed of load z ₂₂ (t), z _max is the maximum displacement stroke of the vehicle suspension system, unit: m.

Preferably, the time-delay state space model of the vehicle suspension system:

为状态变量的导数，x₁(t)＝z_s(t)-z_u(t)为悬架的动挠度，x₂(t)＝z_u(t)-z_r(t)为车轮的动挠度，

为簧载质量的速度，

为簧下质量的速度，

为路面输入的速度，

为系统三个状态变量输出矩阵，A(t)为系统空间状态变量系数矩阵，B₁(t)系统状态空间路面干扰系数矩阵，B₂(t)系统状态空间变量控制输入系数矩阵，C₁(t)为簧载质量加速度输出状态空间系数矩阵，D₁(t)为簧载质量加速度输出状态空间中控制系数系数矩阵，C₂(t)悬架相对动挠度和车轮相对动载荷的系数矩阵，C单位矩阵，τ为时滞值参数，

是一个初始连续函数；Among them, define x(t)=[x ₁ (t)x ₂ (t)x ₃ (t)x ₄ (t)] ^T is the system state variable matrix,

is the derivative of the state variable, x ₁ (t)=z _s (t)-z _u (t) is the dynamic deflection of the suspension, x ₂ (t)=z _u (t)-z _r (t) is the wheel dynamic deflection,

is the velocity of the sprung mass,

is the velocity of the unsprung mass,

the speed entered for the road surface,

is the output matrix of three state variables of the system, A(t) is the system space state variable coefficient matrix, B ₁ (t) system state space pavement disturbance coefficient matrix, B ₂ (t) system state space variable control input coefficient matrix, C ₁ (t) is the sprung mass acceleration output state space coefficient matrix, D ₁ (t) is the control coefficient coefficient matrix in the sprung mass acceleration output state space, C ₂ (t) is the coefficient of the relative dynamic deflection of the suspension and the relative dynamic load of the wheel matrix, C identity matrix, τ is the delay value parameter,

is an initial continuous function;

Preferably, in step 5), according to the changes of m _s (t) and _mu (t), two fuzzy variables are selected as ζ ₁ (t)=1/m _s (t) and ζ ₂ (t) =1/m _u (t), and use the Takagi-Sugeno fuzzy model to establish the time-delay fuzzy state space model of the vehicle suspension system:

Rule 1. If ζ ₁ (t) is M ₁ (ζ ₁ (t)) for heavy, and ζ ₂ (t) is N ₁ (ζ ₂ (t)) for "heavy", then:

Rule 2. If ζ ₁ (t) is M ₁ (ζ ₁ (t)) represents heavy and ζ ₂ (t) is N ₂ (ζ ₂ (t)) represents light, then

Rule 3. If ζ ₁ (t) is M ₂ (ζ ₁ (t)) represents light and ζ ₂ (t) is N ₁ (ζ ₂ (t)) represents heavy, then

Rule 4. If ζ ₁ (t) is M ₂ (ζ ₁ (t)) represents light and ζ ₂ (t) is N ₂ (ζ ₂ (t)) represents light, then

代表簧载质量权重函数重，

代表簧载质量权重函数轻，

代表簧下质量权重函数重，

代表簧下质量权重函数轻，M₁(ζ₁(t))表示簧载质量偏重，M₂(ζ₁(t))表示簧载质量偏轻，N₁(ζ₁(t))表示簧下质量偏重，N₂(ζ₁(t))表示簧下质量偏轻，A₁、B₁₁、B₂₁、C₁₁、D₁₁、C₂₁均表示簧载质量和非簧载质量取最小值时的系统状态空间矩阵，即：in,

represents the sprung mass weight function weight,

represents the sprung mass weight function is light,

represents the weight of the unsprung mass weight function,

Represents a light weight function of unsprung mass, M ₁ (ζ ₁ (t)) indicates that the sprung mass is heavy, M ₂ (ζ ₁ (t)) indicates that the sprung mass is light, and N ₁ (ζ ₁ (t)) indicates that the sprung mass is light. The lower mass is heavy, N ₂ (ζ ₁ (t)) indicates that the unsprung mass is light, A ₁ , B ₁₁ , B ₂₁ , C ₁₁ , D ₁₁ , C ₂₁ all indicate the minimum value of the sprung mass and the unsprung mass The system state space matrix when , namely:

In the formula, A ₂ , B ₁₂ , B ₂₂ , C ₁₂ , D ₁₂ , and C ₂₂ represent the system state space matrix when the minimum value of sprung mass and the maximum value of unsprung mass are taken, namely:

In the formula, A ₃ , B ₁₃ , B ₂₃ , C ₁₃ , D ₁₃ , C ₂₃ represent the system state space matrix when the maximum value of sprung mass and the minimum value of unsprung mass are:

Among them, A ₄ , B ₁₄ , B ₂₄ , C ₁₄ , D ₁₄ , C ₂₄ represent the system state space matrix when the maximum value of sprung mass and the maximum value of unsprung mass are:

According to the fuzzy modeling method, the overall fuzzy state space model of the vehicle suspension system is obtained as:

为模糊权重系数之和，

i取1、2、3、4，并且where, h ₁ (ζ(t)) represents the fuzzy weight coefficient under heavy and recombination, h ₂ (ζ(t)) represents the fuzzy weight coefficient under heavy and light combination, h ₃ (ζ(t) ) represents the fuzzy weight coefficient under the light and heavy combination, h ₄ (ζ(t)) represents the fuzzy weight coefficient under the light and light combination, let

is the sum of fuzzy weight coefficients,

i takes 1, 2, 3, 4, and

h ₁ (ζ(t))=M ₁ (ζ ₁ (t))×N ₁ (ζ ₂ (t))

h ₂ (ζ(t))=M ₁ (ζ ₁ (t))×N ₂ (ζ ₂ (t))

h ₃ (ζ(t))=M ₂ (ζ ₁ (t))×N ₁ (ζ ₂ (t))

h ₄ (ζ(t))=M ₂ (ζ ₁ (t))×N ₂ (ζ ₂ (t))

Among them, C _1h , D _1h , and C _2h are all derived state space matrices after adding fuzzy weight coefficients.

Preferably, the time delay output feedback controller is:

为控制增益矩阵加权和，h_i＝h_i(ζ(t))，h_j＝h_j(ζ(t-d(t)))，ζ(t)代表ζ₁(t)和ζ₂(t)，h_i和h_j均为模糊权重系数，i和j为系数取何值时的角标，取1、2、3、4时分别对应h₁、h₂、h₃、h₄。where K _j is the local control gain matrix, let

is the weighted sum of the control gain matrix, hi = hi (ζ(t)), _{h j = h j (} ζ(td(t))), ζ(t) represents ζ ₁ (t) and ζ ₂ (t) , h _i and h _j are fuzzy weight coefficients, i and j are the index when the coefficients are taken, and when 1, 2, 3, and 4 are taken, they correspond to h ₁ , h ₂ , h ₃ , and h ₄ respectively.

From steps 6) and 7), the closed-loop fuzzy wired frequency domain state space model of the active suspension system considering nonlinearity, time delay and uncertainty is obtained:

并且在ω(t)∈L₂[0,∞)L₂代表二范数，频率和零初始条件下需要满足：in

And in ω(t)∈L ₂ [0,∞)L ₂ represents the second norm, frequency and zero initial conditions need to satisfy:

i. The closed-loop system is asymptotically stable;

为路面输入到车身加速度的传递函数，γ为H_∞范数性能优化指标，其值为迭代求解时的变量；

和

为路面输入最小和最大输入频率；ii. Under condition i, the normative H _∞ performance satisfies:

is the transfer function input from the road surface to the acceleration of the vehicle body, γ is the H _∞ norm performance optimization index, and its value is the variable during the iterative solution;

and

Enter the minimum and maximum input frequencies for the road surface;

iii. Under condition i, the generalized H ₂ performance satisfies: |[z ₂ (t)] _q |≤1 q=1,2;

Preferably, the output feedback controller gain of the vehicle suspension system is solved:

where the general matrices L _i and L _j , i,j=1,2,3,4 are obtained by satisfying the following matrix inequality conditions:

ξ _ij ^T Ξ _ij ξ _ij +Γ _ij +Γ _ij ^T <0 (34)

here,

Γ _sij =[0 K -I] ^T ×[0 L _j C -F _j ]

Γ _ij =[0 K 0 -I] ^T ×[0 L _j C 0 -F _j ]

P_j、Q_j、Z_j、L_j、F_j、X_j为任意维数矩阵，

ξ_sij为Ξ_sij的系数矩阵，ξ_ij为Ξ_ij的系数矩阵，Ξ_sij、Γ_sij、Γ_ij和Ξ_ij公式推导中相应的变换矩阵，I为单位矩阵，ρ大于0的任意常数，K原始控制增益矩阵；Among them, P _1j , S _1j , R _1j are any symmetric positive definite matrix,

P _j , Q _j , Z _j , L _j , F _j , X _j are matrices of any dimension,

ξ _sij is the coefficient matrix of Ξ _sij , ξ _ij is the coefficient matrix of Ξ _ij , the corresponding transformation matrix in the derivation of Ξ _sij , Γ _sij , Γ _ij and Ξ _ij formulas, I is the identity matrix, ρ is an arbitrary constant greater than 0, K original control gain matrix;

For step 9), by solving the fuzzy state feedback control gain K _fsf as the value of K, K _fsf is solved as follows:

Among them, K _fsf is obtained by solving the following linear matrix inequality conditions:

-Q _j +τZ _j <0 (38)

Among them, α _j , ρ are scalars greater than 0, q is the index of the matrix, J _j , V _j are both matrices, S _1j , P _1j , A _i , B _2i , R _1j , Q _j , P _j , Both X _j and Z _j are matrices, and j is the index when the matrix is transformed.

Preferably, the optimization needs to use the following two algorithms as the optimization of the problem, including the following steps:

Algorithm one:

Step 1. By solving K _fsf , let K _initial-fsf =K _fsf be the initial control gain matrix;

Step 2, solve the optimization problem 2, get

F_j表示矩阵；Step 3. Take the gain in step 2 as the initial value and bring it into optimization problem 1 to get

F _j represents the matrix;

Algorithm two:

设置i＝0为初始增益矩阵角标；Step 1. By solving K _fsf and let

Set i=0 as the initial gain matrix index;

作为初始值，带入到优化问题二中，得到

Step 2, use

As the initial value, it is brought into the optimization problem 2, and we get

Step 3. Bring the value obtained in step 2 into the optimization problem 1, and get

然后返回到步骤二。Step 4: If a satisfactory control gain is obtained, exit, otherwise, let i=i+1,

Then return to step two.

Preferably, the optimization problem one: satisfying the minimum H _∞ performance

Minimize: γ ²

Satisfy:

Wherein P _1j , R _1j , S _1j , Q _j , Z _j , P _j , X _j , K, L _j , F _j , i, j = 1, 2, 4, K is a priori fixed value : K=K _initial-fsf ;

The second optimization problem: the initial K _fsf should be close to K _fsof C; that is, η = ‖K _fsf -K _fsof C‖ is the 2-norm, minimize: η

Satisfy:

Among them, P _1j , R _1j , S _1j , Q _j , Z _j , P _j , X _j , K, L _j , F _j , i, j = 1 to 4, K is a priori value and the fixed value is: K = K _initial-fsf , and replace C with the identity matrix I, and C ^⊥ represents a set of null-space orthonormal bases of C;

The vehicle's suspension system is controlled online using the optimized controller gain, and the closed-loop system is asymptotically stable, limited by the output constraints, and satisfies the H _∞ performance index γ minimum.

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

Existing fuzzy controllers for uncertain nonlinear suspension systems involve the entire frequency range, while the human body is more sensitive to vertical vibrations between 4-8 Hz according to ISO-2631. Therefore, a finite frequency controller suitable for active suspension system is designed, which can effectively reduce the acceleration of the vehicle body in the wired frequency domain. GYKP (Generalized Kalman-Yakubovic-Popov) is an effective method to deal with Frequency Domain Inequality (FDI) with equivalent Linear Matrix Inequality (LMI, Linear Matrix Inequality). The present invention applies this method to analyze and synthesize the controller of the active control system in the relevant frequency range. In the actual suspension system, since not all state vectors are measurable online, the controller considers that the states cannot be all measured, and uses the output feedback method to deal with time delay or inertia nonlinearity and uncertainty. This greatly improves the control accuracy and driving comfort of the vehicle suspension system, and the effectiveness of the controller is verified through simulation experiments.

Description of drawings

Fig. 1 is a kind of time-delay limited frequency domain output feedback control method flow chart based on fuzzy model of the present invention;

Fig. 2 is the mechanism model diagram of the suspension system of the present invention;

3 is a frequency domain response diagram of a vehicle body vertical acceleration involving a fuzzy finite frequency domain according to an embodiment of the present invention;

FIG. 4 is a time domain response diagram of the vertical relative displacement of a vehicle body in a fuzzy finite frequency domain according to an embodiment of the present invention;

FIG. 5 is a time-domain response diagram of a vertical relative dynamic load in a fuzzy finite frequency domain according to an embodiment of the present invention.

Detailed ways

The invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the invention and implement it, but the examples are not intended to limit the invention.

A time-delay finite frequency domain output feedback control method based on fuzzy model shown in FIG. 1 includes the following steps:

(1) For the time-delay vehicle active suspension system, the dynamic model of the vehicle suspension system is established according to Newton's second theorem;

(2) Considering the characteristics of the mechanical structure of the automobile and the changes in the number of passengers allowed and the mass of the payload, determine the variation range of m _s (t) and m _u (t) as: m _s (t)∈[m _smin , m _smax ] and m _u (t)∈[m _umin ,m _umax ];

(3) Considering the main influencing factors related to passenger and driver's ride comfort and high safety, construct two physical quantities to evaluate the performance of the control method;

(4) According to the dynamic model of the vehicle active suspension mechanics established in (1), the time-delay state space model of the vehicle suspension system is established;

(5) Since m _s (t) and _mu (t) are variable, two fuzzy variables are selected as ζ ₁ (t)=1/m _s (t) and ζ ₂ (t)=1/ m _u (t), and use the Takagi-Sugeno fuzzy model to establish the time-delay fuzzy state space model of the vehicle suspension system;

(6) According to the fuzzy modeling method, the overall fuzzy state space model of the vehicle suspension system is obtained;

(7) A time-delay output feedback controller is established for the holistic fuzzy state space model of the vehicle suspension system in step (6);

(8) The state space of the time-delay closed-loop system of the nonlinear uncertain active suspension system can be rewritten by steps (6) and (7);

(9) Solving the gain of the output feedback controller of the automobile suspension system;

(10) For K in step (9), the fuzzy state feedback control gain K _fsf can be solved as the K initial value input;

(11) In order to better meet the performance requirements, two algorithms are designed to optimize K _fsof in step 9);

(12) Using the fuzzy finite frequency domain controller given in the step (7), the suspension system of the automobile can be controlled online.

A fuzzy finite frequency domain control method for an automobile suspension system based on the present invention can be applied to various active suspension systems. The following takes the 1/4 suspension system with two degrees of freedom as an example to carry out the actual control application.

Specifically, the specific working process of the fuzzy finite frequency domain output feedback control method of the automobile suspension system involved in the present invention includes the following steps:

1) According to the mechanical principle, the following dynamic model of the vehicle suspension system is established:

Among them, m _s (t) is the sprung mass of the car, unit: Kg; m _u (t) is the unsprung mass of the car, unit: Kg; u (t) is the control input of the car active suspension system. Unit: N; z _s (t) is the vertical displacement of the sprung mass in the vertical upward direction of m _s with the horizontal ground as the starting point, unit: m; z _u (t) is the vertical upward direction of m _u with the horizontal ground as the starting point The vertical displacement of the unsprung mass above, the unit is m; z _r (t) is the vertical displacement of the contact point between the road surface and the tire in the vertical upward direction with the horizontal ground as the starting point, the unit is m; c _s is the vehicle suspension system. Damping coefficient, the unit is N/(m/s); k _s is the stiffness coefficient of the automobile suspension system, the unit is N/m; c _t is the damping coefficient of the automobile tire, the unit is N/(m/s); k _t is the stiffness coefficient of the car tire, in N/m.

The main technical performance indicators and equipment parameters of the quarter suspension system using two degrees of freedom in this embodiment are: m _s (t)∈[256Kg, 384Kg], m _u (t)∈[35Kg, 45Kg], k _s =18000N/m, k _t =200000N/m, c _s =1000N/(m/s), c _t =10N/(m/s), z _max =0.1m,u _max =2500N,w ₁ =4Hz , w ₂ =8Hz, ρ=1, τ=5ms.

2) Considering the characteristics of the mechanical structure of the car and the changes in the number of passengers allowed and the mass of the payload, the range of changes of m _s (t) and _mu (t) is determined as: m _s (t)∈[m _smin ,m _smax ]=[256Kg, 384Kg] and m _u (t)∈[m _umin ,m umax ]=[35Kg, _45Kg ];

3) Considering the main influencing factors related to passenger and driver's ride comfort and high safety, the following two physical quantities are used to evaluate the performance of the control method;

Among them, the maximum displacement stroke of the automobile suspension system z _max = 0.1m, unit: m; g is the acceleration of gravity g = 9.8N/Kg, unit; N/Kg; and it is necessary to ensure |z _s (t)-z _u ( t)|≤0.1m and k _t (z _u (t)-z _r (t))<(m _s (t)+m _u (t))×9.8N/Kg) are established at the same time, z ₁ (t) is the acceleration of the sprung mass, z ₂ (t) is the matrix composed of the relative dynamic deflection z ₂₁ (t) of the suspension and the relative dynamic load z ₂₂ (t) of the wheel, and z _max is the maximum displacement stroke of the vehicle suspension system , unit: m.

4) According to the dynamic model of the vehicle active suspension mechanics established in step 1), the state space model of the vehicle suspension system is established:

z ₁ (t)=C ₁ (t)x(t)+D ₁ (t)u(td(t))

z ₂ (t)=C ₂ (t)x(t)

y(t)=Cx(t)

x(t)=φ(t),t∈[-τ,0]

为状态变量的导数，x₁(t)＝z_s(t)-z_u(t)为悬架的动挠度，x₂(t)＝z_u(t)-z_r(t)为车轮的动挠度，

为簧载质量的速度，

为簧下质量的速度，

为路面输入的速度，

为系统三个状态变量输出矩阵，A(t)为系统空间状态变量系数矩阵，B₁(t)系统状态空间路面干扰系数矩阵，B₂(t)系统状态空间变量控制输入系数矩阵，C₁(t)为簧载质量加速度输出状态空间系数矩阵，D₁(t)为簧载质量加速度输出状态空间中控制系数系数矩阵，C₂(t)悬架相对动挠度和车轮相对动载荷的系数矩阵，C单位矩阵，τ为时滞值参数，

是一个初始连续函数；Among them, define x(t)=[x ₁ (t)x ₂ (t)x ₃ (t)x ₄ (t)] ^T is the system state variable matrix,

is the derivative of the state variable, x ₁ (t)=z _s (t)-z _u (t) is the dynamic deflection of the suspension, x ₂ (t)=z _u (t)-z _r (t) is the wheel dynamic deflection,

is the velocity of the sprung mass,

is the velocity of the unsprung mass,

the speed entered for the road surface,

is the output matrix of three state variables of the system, A(t) is the system space state variable coefficient matrix, B ₁ (t) system state space pavement disturbance coefficient matrix, B ₂ (t) system state space variable control input coefficient matrix, C ₁ (t) is the sprung mass acceleration output state space coefficient matrix, D ₁ (t) is the control coefficient coefficient matrix in the sprung mass acceleration output state space, C ₂ (t) is the coefficient of the relative dynamic deflection of the suspension and the relative dynamic load of the wheel matrix, C identity matrix, τ is the delay value parameter,

is an initial continuous function;

5) Since m _s (t) and _mu (t) are variable, two fuzzy variables are selected as ζ ₁ (t)=1/m _s (t) and ζ ₂ (t)=1/m _u (t), and use the Takagi-Sugeno fuzzy model to establish the time-delay fuzzy state space model of the vehicle suspension system:

Rule 1. If ζ ₁ (t) is M ₁ (ζ ₁ (t)) for heavy and ζ ₂ (t) is N ₁ (ζ ₂ (t)) for heavy, then

z ₁ (t)=C ₁₁ x(t)+D ₁₁ u(td(t))

z ₂ (t)=C ₂₁ x(t)

Rule 2. If ζ ₁ (t) is M ₁ (ζ ₁ (t)) represents heavy and ζ ₂ (t) is N ₂ (ζ ₂ (t)) represents light, then

z ₁ (t)=C ₁₂ x(t)+D ₁₂ u(td(t))

z ₂ (t)=C ₂₂ x(t)

Rule 3. If ζ ₁ (t) is M ₂ (ζ ₁ (t)) represents light and ζ ₂ (t) is N ₁ (ζ ₂ (t)) represents heavy, then

z ₁ (t)=C ₁₃ x(t)+D ₁₃ u(td(t))

z ₂ (t)=C ₂₃ x(t)

Rule 4. If ζ ₁ (t) is M ₂ (ζ ₁ (t)) represents light and ζ ₂ (t) is N ₂ (ζ ₂ (t)) represents light, then

z ₁ (t)=C ₁₄ x(t)+D ₁₄ u(td(t))

z ₂ (t)=C ₂₄ x(t)

代表簧载质量权重函数重，

代表簧载质量权重函数轻，

代表簧下质量权重函数重，

代表簧下质量权重函数轻，所述重和轻为无明显界限的模糊概念，M₁(ζ₁(t))表示簧载质量偏重，M₂(ζ₁(t))表示簧载质量偏轻，N₁(ζ₁(t))表示簧下质量偏重，N₂(ζ₁(t))表示簧下质量偏轻，A₁、B₁₁、B₂₁、C₁₁、D₁₁、C₂₁均表示簧载质量和非簧载质量取最小值时的系统状态空间矩阵，即：in,

represents the sprung mass weight function weight,

represents the sprung mass weight function is light,

represents the weight of the unsprung mass weight function,

Represents the lightness of the weight function of unsprung mass, the heavy and light are fuzzy concepts with no obvious boundaries, M ₁ (ζ ₁ (t)) represents the unsprung mass partial weight, M ₂ (ζ ₁ (t)) represents the sprung mass partial weight Light, N ₁ (ζ ₁ (t)) means the unsprung mass is heavy, N ₂ (ζ ₁ (t)) means the unsprung mass is light, A ₁ , B ₁₁ , B ₂₁ , C ₁₁ , D ₁₁ , C ₂₁ Both represent the state space matrix of the system when the sprung mass and the unsprung mass take the minimum value, namely:

In the formula, A ₃ , B ₁₃ , B ₂₃ , C ₁₃ , D ₁₃ , C ₂₃ represent the system state space matrix when the maximum value of sprung mass and the minimum value of unsprung mass are:

Among them, A ₄ , B ₁₄ , B ₂₄ , C ₁₄ , D ₁₄ , C ₂₄ represent the system state space matrix when the maximum value of sprung mass and the maximum value of unsprung mass are:

6) According to the fuzzy modeling method, the overall fuzzy state space model of the vehicle suspension system can be obtained:

为模糊权重系数之和，

i取1、2、3、4，并且where, h ₁ (ζ(t)) represents the fuzzy weight coefficient under heavy and recombination, h ₂ (ζ(t)) represents the fuzzy weight coefficient under heavy and light combination, h ₃ (ζ(t) ) represents the fuzzy weight coefficient under the light and heavy combination, h ₄ (ζ(t)) represents the fuzzy weight coefficient under the light and light combination, let

is the sum of fuzzy weight coefficients,

i takes 1, 2, 3, 4, and

h ₁ (ζ(t))=M ₁ (ζ ₁ (t))×N ₁ (ζ ₂ (t))

h ₂ (ζ(t))=M ₁ (ζ ₁ (t))×N ₂ (ζ ₂ (t))

h ₃ (ζ(t))=M ₂ (ζ ₁ (t))×N ₁ (ζ ₂ (t))

h ₄ (ζ(t))=M ₂ (ζ ₁ (t))×N ₂ (ζ ₂ (t))

Among them, C _1h , D _1h , and C _2h are all derived state space matrices after adding fuzzy weight coefficients.

7) According to the fuzzy finite frequency domain state space model of the overall vehicle suspension system described in step 6), a time-delay output feedback controller is established:

为控制增益矩阵加权和，h_i＝h_i(ζ(t))，h_j＝h_j(ζ(t-d(t)))，ζ(t)代表ζ₁(t)和ζ₂(t)，h_i和h_j均为模糊权重系数，i和j为系数取何值时的角标，取1、2、3、4时分别对应h₁、h₂、h₃、h₄。where K _j is the local control gain matrix, let

is the weighted sum of the control gain matrix, hi = hi (ζ(t)), _{h j = h j (} ζ(td(t))), ζ(t) represents ζ ₁ (t) and ζ ₂ (t) , h _i and h _j are fuzzy weight coefficients, i and j are the index when the coefficients are taken, and when 1, 2, 3, and 4 are taken, they correspond to h ₁ , h ₂ , h ₃ , and h ₄ respectively.

8) The state space of the rewritable closed-loop system and nonlinear active suspension system by steps 6) and 7) is as follows:

并且在ω∈L₂[0,∞)频率和零初始条件下满足：in

and at ω∈L ₂ [0,∞) frequency and zero initial conditions:

i. The closed-loop system is asymptotically stable;

ii. Under condition i, H _∞ performance satisfies:

iii. Under condition i, the generalized _H2 performance satisfies:

9) Solve the gain of the output feedback control of the automobile suspension system:

where the general matrices L _j and L _j (i,j=1,2,3,4) can be obtained by satisfying the following matrix inequality conditions:

ξ _ij ^T Ξ _ij ξ _ij +Γ _ij +Γ _ij ^T <0

here,

Γ _sij =[0 K -I] ^T ×[0 L _j C -F _j ]

Γ _ij =[0 K 0 -I] ^T ×[0 L _j C 0 -F _j ]

Due to the existence of matrix K, the above condition is not a linear matrix inequality. However, if K is an a priori fixed matrix, then the above condition becomes an a priori matrix inequality for the remaining unknown matrix. Next, the gain of the initial fuzzy state feedback controller can be solved with K, and K is brought into the fuzzy static output feedback controller to obtain the output K _fsof . In addition, the above conditions replace the measurement output matrix C with the identity matrix I, which can be used to update and improve the gain of the fuzzy state feedback controller.

10) For step 9), the gain K _fsf can be controlled by solving the fuzzy state feedback as the K input:

where K _fsf can be obtained by solving the following linear matrix inequality conditions:

-Q _j +τZ _j <0

Among them, α _j , ρ are scalars greater than 0, q is the index of the matrix, J _j , V _j are both matrices, S _1j , P _1j , A _i , B _2i , R _1j , Q _j , P _j , Both X _j and Z _j are matrices, and j is the index when the matrix is transformed.

11) In order to better meet the performance requirements, the following two algorithms need to be used as the optimization of the problem

Algorithm one:

Step 1, by solving 10), let K _initial-fsf =K _fsf ;

Step 2, solve the optimization problem 2, get

Step 3. Take the gain in step 2 as the initial value and bring it into optimization problem 1 to get

Algorithm two:

设置i＝0；Step 1. By solving 10) and let

set i = 0;

作为初始值，带入到优化问题二中，得到

Step 2, use

As the initial value, it is brought into the optimization problem 2, and we get

Step 3. Bring the value obtained in step 2 into the optimization problem 1, and get

然后返回到步骤二。Step 4. Exit if a satisfactory control gain is obtained. Otherwise, let i=i+1,

Then return to step two.

Optimization Problem 1: Satisfy Minimum H _∞ Performance

Minimize: γ ²

Satisfy:

ξ _ij ^T Ξ _ij ξ _ij +Γ _ij +Γ _ij ^T <0

P _1j ＞0, R _1j ＞0, S _1j ＞0, Q _j ＞0, Z _j ＞0

Among them, P _1j , R _1j , S _1j , Q _j , Z _j , P _j , X _j , K, L _j , F _j , i, j = 1, 2, 4, K are a priori fixed values is: K=K _initial-fsf .

Optimization problem 2: The initial K _fsf should be close to K _fsof C; then,

Minimize: η

Satisfy:

ξ _ij ^T Ξ _ij ξ _ij +Γ _ij +Γ _ij ^T <0

P _1j ＞0, R _1j ＞0, S _1j ＞0, Q _j ＞0, Z _j ＞0

Among them, P _1j , R _1j , S _1j , Q _j , Z _j , P _j , X _j , K, L _j , F _j , i, j = 1, 2, 4, K are a priori fixed values is: K=K _initial-fsf , and replace C with the identity matrix I. C ^⊥ represents a set of null-space orthonormal basis of C. Through the above steps, it can be obtained: K _fsf =10 ⁴ ×[1.2759 -0.2647-0.2649 -0.0723], K _fsof =10 ⁴ ×[1.2738 -0.2684 -0.0709].

12) Using the controller gain given in step 7), the suspension system of the vehicle can be controlled online, and the closed-loop system is asymptotically stable and satisfies the H _∞ performance index γ minimum.

In this embodiment, the maximum value of the executive force of the actuator is u _max =2500N, the frequency range is set to w ₁ =4Hz, w ₂ =8Hz, the time delay is set to τ=5ms, and other values ρ=1. γ is the suppression index value for external disturbance in the control system, and the user should make it as small as possible if the conditions are satisfied.

Fig. 2 shows a simplified control model of the method of the present invention, which is intended for the user to more clearly apply the method to a specific example. Fig. 3 shows the frequency domain response curve of the closed-loop system of the present invention. Obviously, in the frequency range of 4-8 Hz, which is the most sensitive of the human body, compared with the passive suspension, the present invention can significantly reduce the acceleration of the vehicle body, and greatly reduce the acceleration of the vehicle body. Improve ride comfort. Figure 4 shows a comparison chart of the relative displacement of the suspension of the present invention. It can be seen from the figure that the relative displacement has been greatly reduced, which can effectively reduce the probability of hitting the suspension limit and improve the ride comfort of the vehicle. Figure 5 shows a comparison diagram of the vertical relative dynamic load of the wheel and the body of the present invention. From the figure, it can be seen that the relative dynamic load is significantly reduced, the probability of the wheel jumping off the ground is reduced, and the steering stability of the vehicle is improved.

The above embodiments only illustrate the technical ideas and features of the present invention, and are intended to enable those skilled in the art to better understand and implement them. The scope of the present invention is not limited to the above-mentioned embodiments, and all equivalent changes or modifications made according to the principles and design ideas disclosed in the present invention are within the scope of the present invention.

Claims (10)

1. A time lag limited frequency domain output feedback control method based on a fuzzy model is characterized by comprising the following steps:

1) aiming at a time-lag automobile active suspension system, establishing a dynamic model of the following automobile suspension system according to a mechanical principle;

2) determining the variation range of the sprung mass and the unsprung mass according to the characteristics of the mechanical structure of the vehicle and the allowable number of passengers and the variation of the effective load mass;

3) constructing two physical quantities to evaluate the performance of the control method;

4) establishing a time-lag state space model of an automobile suspension system;

5) establishing a time-lag fuzzy state space model of the automobile suspension system according to the Takagi-Sugeno fuzzy model;

6) establishing a time-lag output feedback controller;

7) solving the gain of an output feedback controller of the automobile suspension system;

8) optimizing a feedback controller;

9) and a fuzzy finite frequency domain output feedback controller is adopted to carry out online control on the automobile suspension system.

2. The fuzzy model-based time-lag finite frequency domain output feedback control method according to claim 1, wherein the dynamic model of the automobile suspension system is as follows:

wherein m is_s(t) is the sprung mass formed by the mass of the automobile body, unit: kg; m is_u(t) unsprung mass, unit, of vehicle tire component mass: kg; u (t) is the control input quantity of the automobile active suspension system, and the unit is as follows: n; z is a radical of_s(t) is m_s(t) verticality of sprung mass in vertically upward direction with horizontal ground as starting pointDisplacement, unit: m;

and

acceleration and velocity of the sprung mass; z is a radical of_u(t) is m_u(t) vertical displacement of the unsprung mass in the vertical upward direction with the horizontal ground as the starting point, in units of m;

and

acceleration and velocity of the unsprung mass; z is a radical of_r(t) is the vertical displacement of the road surface and the tire contact point in the vertical upward direction with the horizontal ground as the starting point, and the unit is m;

the speed input for the road surface; c. C_sThe damping coefficient of the automobile suspension system is expressed in the unit of N/(m/s); k is a radical of_sThe unit is N/m, and the rigidity coefficient is the rigidity coefficient of the automobile suspension system; c. C_tThe damping coefficient of the automobile tire is expressed by the unit of N/(m/s); k is a radical of_tThe rigidity coefficient of the automobile tire is N/m.

3. The fuzzy model-based time-lag finite frequency domain output feedback control method according to claim 2, wherein the sprung mass m_s(t) and unsprung mass m_u(t) ranges of variation are: m is_s(t)∈[m_smin，m_smax]And m_u(t)∈[m_umin,m_umax]，m_sminAnd m_smaxMinimum and maximum values of sprung mass, m_uminAnd m_umaxThe minimum and maximum values of the unsprung mass.

4. The fuzzy model-based time-lag finite frequency domain output feedback control method according to claim 3, wherein the evaluation control method comprises:

wherein g is the acceleration of gravity in units; N/Kg; and it is necessary to ensure | z_s(t)-z_u(t)|≤z_maxAnd k_t(z_u(t)-z_r(t))＜(m_s(t)+m_u(t)) g is simultaneously true, z₁(t) acceleration of the sprung mass, z₂(t) is the relative dynamic deflection z of the suspension₂₁(t) and relative dynamic load z of the wheel₂₂(t) a matrix of_maxThe maximum displacement stroke of the automobile suspension system is represented by the following unit: and m is selected.

5. The fuzzy model-based time lag finite frequency domain output feedback control method according to claim 4, wherein the time lag state space model of the automobile suspension system is:

wherein, x (t) ═ x is defined₁(t) x₂(t) x₃(t) x₄(t)]^TIn the form of a matrix of state variables of the system,

as derivatives of state variables, x₁(t)＝z_s(t)-z_u(t) dynamic deflection of the suspension, x₂(t)＝z_u(t)-z_r(t) is the dynamic deflection of the wheel,

is the velocity of the sprung mass,

is the velocity of the unsprung mass,

the speed of the road surface input is used,

three state variable output matrices for the system, A (t) is a system space state variable coefficient matrix, B₁(t) System State space road surface disturbance coefficient matrix, B₂(t) the system state space variable controls the input coefficient matrix, C₁(t) is a sprung mass acceleration output state space coefficient matrix, D₁(t) is a control coefficient matrix in the sprung mass acceleration output state space, C₂(t) coefficient matrix of suspension relative dynamic deflection and wheel relative dynamic load, C unit matrix, tau is time lag parameter,

is an initial continuous function;

6. the fuzzy model-based time-lag finite frequency domain output feedback control method as claimed in claim 5, wherein in step 5), the feedback control method is based on m_s(t) and m_u(t) change, two fuzzy variables are selected as zeta₁(t)＝1/m_s(t) and ζ₂(t)＝1/m_u(t), and establishing a time-lag fuzzy state space model of the automobile suspension system by using a Takagi-Sugeno fuzzy model:

rule 1, if ζ₁(t) is M₁(ζ₁(t)) represents weight, and ζ₂(t) is N₁(ζ₂(t)) represents weight, then:

rule 2, if ζ₁(t) is M₁(ζ₁(t)) represents weight and ζ₂(t) is N₂(ζ₂(t)) represents light, then

Rule 3, if ζ₁(t) is M₂(ζ₁(t)) represents light and ζ₂(t) is N₁(ζ₂(t)) represents weight, then

Rule 4, if ζ₁(t) is M₂(ζ₁(t)) represents light and ζ₂(t) is N₂(ζ₂(t)) represents light, then

Wherein,

representing the sprung mass weight function weight,

the weight function representing the sprung mass is light,

represents the unsprung mass weight function weight,

representing unsprung mass weight function light, M₁(ζ₁(t)) represents the sprung mass imbalance, M₂(ζ₁(t)) shows a lighter sprung mass, N₁(ζ₁(t)) represents the unsprung mass weight, N₂(ζ₁(t)) means unsprung weight is lighter, A₁、B₁₁、B₂₁、C₁₁、D₁₁、C₂₁Each represents the system state space matrix at which the sprung and unsprung masses take a minimum value, namely:

in the formula, A₂、B₁₂、B₂₂、C₁₂、D₁₂、C₂₂A system state space matrix representing the minimum and maximum values of the sprung mass, namely:

in the formula, A₃、B₁₃、B₂₃、C₁₃、D₁₃、C₂₃The system state space matrix when the maximum value of the sprung mass and the minimum value of the unsprung mass are expressed is as follows:

wherein A is₄、B₁₄、B₂₄、C₁₄、D₁₄、C₂₄The system state space matrix representing the maximum value of the sprung mass and the maximum value of the unsprung mass is:

according to the fuzzy modeling method, the overall fuzzy state space model of the automobile suspension system is obtained as follows:

wherein, in the formula, h₁(ζ (t)) represents a fuzzy weight coefficient under the combination of weight and weight, h₂(ζ (t)) represents the blur weight coefficient in the heavy and light combination, h₃(ζ (t)) represents the fuzzy weight coefficient at the combination of light and heavy, h₄(ζ (t)) represents the blur weight coefficient for a combination of light and light, such that

Is the sum of the blur weight coefficients,

i is 1,2,3,4, and

h₁(ζ(t))＝M₁(ζ₁(t))×N₁(ζ₂(t))

h₂(ζ(t))＝M₁(ζ₁(t))×N₂(ζ₂(t))

h₃(ζ(t))＝M₂(ζ₁(t))×N₁(ζ₂(t))

h₄(ζ(t))＝M₂(ζ₁(t))×N₂(ζ₂(t))

wherein, C_1h、D_1h、C_2hAll are derived state space matrices after adding the fuzzy weight coefficients.

7. The fuzzy model-based time-lag limited frequency domain output feedback control method of claim 6, wherein the time-lag output feedback controller is:

wherein K_jIs a local control gain matrix, such that

To control the gain matrix weighted sum, h_i＝h_i(ζ(t))，h_j＝h_j(ζ (t-d (t))), ζ (t) represents ζ₁(t) and ζ₂(t)，h_iAnd h_jAll are fuzzy weight coefficients, i and j are angle indexes when the coefficients take which values, and h respectively corresponds to 1,2,3 and 4₁、h₂、h₃、h₄；

Obtaining a closed-loop fuzzy wired frequency domain state space model of the active suspension system considering nonlinearity, time lag and uncertainty through the steps 6) and 7):

wherein

And at ω (t) ∈ L₂[0,∞)L₂Representing a two-norm, the frequency and zero initial conditions need to be satisfied:

i. the closed loop system is asymptotically stable;

norm H under condition i_∞The performance satisfies:

for the transfer function of road surface input to vehicle body acceleration, gamma is H_∞Norm performance optimization indexes, wherein the values of the norm performance optimization indexes are variables during iterative solution;

and

inputting a minimum and a maximum input frequency for the road surface;

under condition i, generalized H₂The performance satisfies: [ z ]₂(t)]_q|≤1 q＝1,2。

8. The fuzzy model-based time-lag finite frequency domain output feedback control method of claim 7, wherein the output feedback controller gain of the automotive suspension system is solved:

wherein a general matrix L_iAnd L_jI, j ═ 1,2,3,4, and is obtained by satisfying the following matrix inequality condition:

here, ,

Γ_sij＝[0 K -I]^T×[0 L_jC -F_j]

Γ_ij＝[0 K 0 -I]^T×[0 L_jC 0 -F_j]

wherein, P_1j、S_1j、R_1jIs an arbitrary symmetrical positive definite matrix,

P_j、Q_j、Z_j、L_j、F_j、X_jin the form of a matrix of any dimension,

ξ_sijis xi_sijCoefficient matrix of (xi), xi_ijIs xi_ijXi, xi_sij、Γ_sij、Γ_ijXi and xi_ijCorresponding transformation matrix in formula derivation, wherein I is a unit matrix, rho is an arbitrary constant larger than 0, and K is used for originally controlling a gain matrix;

for step 9), the gain K is feedback controlled by solving for the fuzzy state_fsfAs the value of K, K_fsfThe solution is as follows:

wherein, K_fsfSolving for a linear matrix inequality condition satisfying:

-Q_j+τZ_j＜0 (17)

wherein alpha is_jRho is a scalar greater than 0, q is a corner mark of the matrix, J_j、V_jAre all matrix, S_1j、P_1j、A_i、B_2i、R_1j、Q_j、P_j、X_j、Z_jAre all matrixes, and j is a corner mark during matrix transformation.

9. The fuzzy model-based time-lag finite frequency domain output feedback control method of claim 8, wherein the optimization using the following two algorithms as the optimization of the problem comprises the following steps:

the first algorithm is as follows:

step one, solving K_fsfLet K_initial-fsf＝K_fsfAs an initial control gain matrix;

step two, solving the optimization problem two to obtain

Step three, taking the gain in the step two as an initial value to be brought into the optimization problem one to obtain

F_jRepresenting a matrix;

and (3) algorithm II:

step 1, solving K_fsfAnd order

Setting i to 0 as an initial gain matrix corner mark;

step 2, use

As an initial value, the initial value is brought into an optimization problem II to obtain

And 3, substituting the value obtained in the step 2 into the optimization problem I to obtain

And 4, step 4: if a satisfactory control gain is obtained, the operation is exited, otherwise, i is made to be i +1,

and then returns to step two.

10. The method according to claim 9, wherein the first optimization problem is that: satisfies the minimum H_∞Performance of

And (3) minimizing: gamma ray²

Satisfies the following conditions:

wherein P is_1j、R_1j、S_1j、Q_j、Z_j、P_j、X_j、K、L_j、F_j1,2, · · 4, K is a priori fixed value:

K＝K_initial-fsf；

the second optimization problem is as follows: initial K_fsfShould be and K_fsofC should be close; i.e. eta | K_fsf-K_fsofC | is a 2-norm, minimize: eta

Satisfies the following conditions:

wherein, P_1j、R_1j、S_1j、Q_j、Z_j、P_j、X_j、K、L_j、F_jAnd i and j are 1-4, and K is a priori value, and the fixed value is as follows: k ═ K_initial-fsfAnd replacing C, C by identity matrix I^⊥A set of null-space orthogonal bases representing C;

the optimized controller gain is used for controlling the suspension system of the automobile on line, and the closed loop system is enabled to be asymptotically stable, the output constraint is limited and H is met_∞The performance index γ is minimal.

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