Event-triggered control method for vehicle suspension with position constraints and input saturation

Abstract

The present invention discloses an event-triggered control method for automobile suspension with position constraints and input saturation, which is characterized by comprising the following steps: (a) establishing a state space model of an automobile nonlinear active suspension control system; (b) setting constraints; (c) selecting a candidate Lyapunov function at each step in the controller design process to construct a virtual controller until the last step to construct a real controller; (d) defining tracking error variables; (e) constructing a virtual control law; (e) constructing a virtual control law; (g) constructing a virtual control law; (h) designing an adaptive law. The method models the automobile active suspension system into a more realistic nonlinear system, and then combines the network system with the adaptive backstepping control technology to design a finite-time adaptive neural network controller; the method saves communication resources and reduces the communication burden, making the controller simple and easy to implement.

Description

Technical Field

[0001] The invention relates to an automobile active suspension control technology, in particular to an automobile suspension event triggering control method with position constraints and input saturation. Background Art

[0002] With the improvement of people's living standards, cars have entered thousands of households. The popularity of cars has also prompted people to have higher and higher requirements for cars. Since the conventional automobile suspension controller is designed based on time triggering, that is, the controller can only transmit to the actuator in a fixed period sampling manner regardless of the road conditions, this will increase the communication burden and waste communication resources. In addition, in order to provide drivers and passengers with a more comfortable experience during vehicle driving, the present invention designs an adaptive controller. In summary, how to design a controller to make drivers and passengers more comfortable and save network communication resources and reduce communication burden while ensuring safety is the core content of the present invention. Summary of the invention

[0003] The purpose of the present invention is to address the deficiencies of the prior art and propose an event-triggered control method for automobile suspension with position constraints and input saturation. This method addresses the problem that the automobile active suspension system cannot be accurately modeled. First, the automobile active suspension system is modeled as a nonlinear system that is more in line with reality, and then the neural network system and the adaptive backstepping control technology are combined to design a finite-time adaptive neural network controller. In addition, this method addresses the problem of limited network bandwidth and proposes an event trigger mechanism that acts between the controller and the actuator, which saves communication resources and reduces the communication burden, making the controller simple and easy to implement.

[0004] The event-triggered control method for vehicle suspension with position constraints and input saturation includes the following steps:

[0005] (a) Establish the state space model of the nonlinear active suspension control system of the vehicle. For the nonlinear quarter active suspension model with two degrees of freedom, its dynamic differential equation is:

[0006]

[0007]

[0008] Among them, f1(z s ,z us ) = k s1 (z s -z us )+k s2 (z s -z us ) 2 +k s3 (z s -zus ) 3 ,

[0009]

[0010] m s Represents the vehicle body mass, m us Represents the wheel mass, k s1 ,k s2 ,k s3 are the linear coefficient, quadratic coefficient and cubic coefficient of the suspension spring respectively, B s represents the suspension damping, k us represents the linear spring constant of the tire, and Represent the linear coefficient and quadratic coefficient of suspension damping, z s Represents the vertical displacement of the vehicle body, z us represents the displacement of the unsprung mass, z r represents the road input, u(v(t)) represents the control input of the active suspension system, and there is input saturation in the following form:

[0011]

[0012] The vertical displacement of the vehicle body, the velocity of the vehicle body, the displacement of the unsprung mass and the velocity of the unsprung mass are selected as state variables, that is, x1 = z s , x3=z us , The suspension dynamics differential equation is converted into a state space mathematical model:

[0013]

[0014] The states of all systems are strictly constrained to be in the following compact set:

[0015] Ω x :={x i ∈R||x i |≤k ci ,i=1,2,3,4};

[0016] (b) Set constraints:

[0017] (i) Ride comfort: Ride comfort is usually evaluated by the body acceleration in the vertical direction. Therefore, one of the main control objectives is to make the body acceleration in the vertical direction as small as possible.

[0018] (ii) Driving safety: Regardless of the driving conditions, the wheels should not leave the ground, otherwise it will cause traffic accidents and losses. Therefore, in order to ensure that the wheels are in constant contact with the ground, the dynamic load of the tire should not exceed its static tire load, i.e., k us (z us -z r )<(m s +m us )g, g is the acceleration due to gravity;

[0019] (iii) Maximum dynamic deflection: The dynamic deflection of the suspension satisfies |z s -z us |≤z max ,z max is the maximum allowable dynamic deflection;

[0020] (c) In the controller design process, a candidate Lyapunov function is selected at each step to construct a virtual controller until the last step to construct a real controller. The control method is as follows:

[0021] Lemma 1. If there exist some constants a>0, b>0, 0<l<1, 0<c<∞ such that the following inequality holds:

[0022]

[0023] Then, the trajectory of the system is practically stable for finite time;

[0024] Since f(x):R n →R is an unknown continuous function, so the following neural network is introduced to process it:

[0025]

[0026] in, is the output vector of the neural network with dimension r, Φ=[Φ1,Φ2,...,Φ k ] T ∈R k is defined as a weight vector, k greater than 1 is defined as the number of neural network nodes, P(Z) = [p1(Z), p2(Z), ..., p k (Z)] T ∈R k , the selected Gaussian function p i (Z) is:

[0027]

[0028] in, is the center of the receiving field, σ i is the width of the Gaussian function. For sufficiently large k, we have:

[0029]

[0030] Where δ(x) is defined as the approximation error and satisfies |δ(x)|≤ε; define the unknown ideal weight constant Φ * for:

[0031]

[0032] Lemma 2. (Young's inequality) For any vector ψ, have:

[0033]

[0034] holds true, where η>0, i>1, j>1, (i-1)(j-1)=1;

[0035] Lemma 3. For any given real number x1, x2, …, x n and 0≤l≤1, the following inequality holds:

[0036] (|x1|+…+|x n |) l ≤|x1| l +…|x n | l ;

[0037] (d) Define the tracking error variable as:

[0038]

[0039] Among them, y d is the reference signal |y d |≤Y0<k c1 , α1 is defined as the virtual control law to be designed and δ is the state signal of the auxiliary system designed to handle input saturation as follows:

[0040]

[0041]

[0042] Among them, p1>0, p2>0 are the parameters to be designed; taking the derivative of e1, we get:

[0043]

[0044] Select the following candidate Lyapunov functions:

[0045]

[0046] Among them, k b1 =k c1 -Y0, calculate the derivative of V1 and get:

[0047]

[0048] (e) Construct the virtual control law α1 as:

[0049]

[0050] Among them, k 11 >0,k 22 >0,0<l1<1 are the parameters to be designed;

[0051] Substituting (5) into (4) yields:

[0052]

[0053] when When, obviously there is It is established, so it can be proved that when 0<l<1, there is Established;

[0054] Rewrite (6) as follows:

[0055]

[0056] Next, design the real controller and derive e2 to get:

[0057]

[0058] Select the following candidate Lyapunov functions:

[0059]

[0060] in, Defined as the estimation error and θ=||Φ|| 2 , Define an estimate of θ;

[0061] Calculate the derivative of V1 and get:

[0062]

[0063] Then, it can be concluded that:

[0064]

[0065] in, According to (2), it can be concluded that the neural network system has good approximation ability, so the following formula is established:

[0066]

[0067] ||δ(X)||≤τ;

[0068] Where δ(X) is defined as the approximation error and τ>0, according to Young's inequality, we have:

[0069]

[0070] Where a1 is a given positive constant, from (9) and (10) we get:

[0071]

[0072] Will Substituting into (11), we can obtain:

[0073]

[0074] (f) Design an adaptive finite-time event-triggered controller and event-triggered mechanism as follows:

[0075]

[0076] v(t)=χ(t k ),t k ≤t<t k+1 ,

[0077] t k+1 = inf{t>t k ‖ψ(t)|≥γ|v(t)|+d1}

[0078] Among them, ψ(t)=χ(t)-v(t), d1>0, 0<γ<1,∈>0 and is a designed normal constant; α2 is the virtual controller to be designed;

[0079] From the event trigger mechanism, we can conclude that χ(t)=(1+λ1(t)γ)v(t)+λ2(t)d1,t k ≤t<t k+1 , where |λ1(t)|≤1,|λ2(t)|≤1; therefore, the following equation holds:

[0080]

[0081] Substituting (12) into (11), we obtain:

[0082]

[0083] From λ1(t)∈[-1,1],λ2(t)∈[-1,1], we get:

[0084]

[0085]

[0086] From (13), (14) and (15), we can get:

[0087]

[0088] According to the properties of the hyperbolic tangent function, we can conclude that Then combined with (16), we get:

[0089]

[0090] (g) Construct the virtual control law α2 as:

[0091]

[0092] Among them, k 12 >0,k 22 >0,a1>0,0<l1<1 are the parameters to be designed;

[0093] Substituting (18) into (17), we obtain:

[0094]

[0095] Then, by have to:

[0096]

[0097] (h) Design the following adaptive law:

[0098]

[0099] Where σ is the constant to be designed, (19) can be rewritten as:

[0100]

[0101] When |e1|<k b1 When, obviously there is It is established, and it can be proved that when 0<l<1, there is Established; then, we have:

[0102]

[0103] Applying Young's inequality again, we get:

[0104]

[0105] From (20) and (21), we can get:

[0106]

[0107]

[0108] (i) Zero dynamics analysis: From the above design process, only the signal of the second-order system is proved to be bounded; next, we discuss the boundedness of x3 and x4, and let e1 = 0, that is, input saturation will not occur. Therefore, the state of the auxiliary system δ = 0, so the derivative of e1 is:

[0109]

[0110] Then continue to The derivative is:

[0111]

[0112] From (22), we can get:

[0113]

[0114] Substituting u into the system equation (1) we obtain:

[0115]

[0116] Rewrite (23) as:

[0117]

[0118] in

[0119] The selected Lyapunov function is as follows:

[0120] V=X T PX,

[0121] Among them, P is a positive definite symmetric matrix, and its derivative is:

[0122]

[0123] In the above formula, A has a negative real eigenvalue, so A T P+PA=-Q holds, where Q is a positive definite symmetric matrix;

[0124] From Young's inequality we get:

[0125]

[0126] Among them, ε>0 is the parameter to be designed;

[0127]

[0128]

[0129] in, ω≥εΔ T Δ;

[0130] Therefore, we can conclude that:

[0131]

[0132] in, Then there is Established;

[0133] From the above results, it can be concluded that all signals in the closed-loop system are bounded; by selecting appropriate parameters, it can be concluded that the proposed control scheme can ensure driving safety;

[0134] (j) Next, prove that Zeno's behavior will not occur;

[0135] Prove that Zeno behavior will not occur, that is, there exists υ>0 so that There is k+1 -t k ≥υ;

[0136] The event trigger mechanism can be obtained:

[0137]

[0138] According to the designed event trigger mechanism, have By ψ(t k )=0 and The inequality Established; that is, it proves that Zeno's behavior will not occur;

[0139] The method aims at the problem that the automobile active suspension system cannot be accurately modeled. First, the automobile active suspension system is modeled as a nonlinear system that is more in line with reality. Then, the Shenjiang network system and the adaptive backstepping control technology are combined to design a finite-time adaptive neural network controller. The main features of the present invention are:

[0140] (1) The controller designed in the existing control scheme is time-triggered, that is, no matter whether the system needs to update the controller or not, the time trigger will update the value of the controller at a fixed period, which will increase communication resources and lead to resource waste. Different from the existing control scheme, the controller proposed in the present invention is event-triggered, that is, the controller is updated only when the system does not meet the designed event. Therefore, the controller proposed in the present invention can greatly save communication resources and reduce the communication burden.

[0141] (2) Since the actuators of the actual suspension system have amplitude limitations, when the value transmitted by the controller exceeds the amplitude of the actuator, input saturation will occur. Input saturation will reduce the performance of the system and lead to system instability. The existing control scheme does not consider the occurrence of input saturation, so based on the actual situation, the present invention designs an auxiliary system to handle input saturation.

[0142] (3) Since the suspension travel of the automobile suspension system must be within a certain range, the present invention introduces an obstacle Lyapunov function to solve the problem of the state of the suspension system being constrained.

[0143] (4) The existing control scheme of automobile suspension system considers that the dynamic travel of suspension and the acceleration of vehicle body can converge to a sufficiently small range when time tends to infinity. Different from the existing control scheme, the present invention proposes a finite time control scheme, so that the suspension system can achieve the desired control target within a finite time. BRIEF DESCRIPTION OF THE DRAWINGS

[0144] Figure 1 It is the trajectory of the vertical acceleration of the vehicle body given by the present invention.

[0145] Figure 2 It is the displacement trajectory of the vehicle body given by the present invention.

[0146] Figure 3 It is the trajectory of the suspension dynamic deflection given by the present invention.

[0147] Figure 4 is the trajectory of the controller given by the present invention.

[0148] Figure 5 It is a comparison diagram of the trajectories of the real controller and the virtual controller given by the present invention.

[0149] Figure 6 It is the triggering time interval given by the present invention, that is, the time interval for controller update. DETAILED DESCRIPTION

[0150] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0151] (a) Establish the state space model of the nonlinear active suspension control system of the vehicle:

[0152] For the two-degree-of-freedom nonlinear quarter active suspension model, its dynamic differential equation is:

[0153]

[0154]

[0155] in,

[0156] f1(z s ,z us ) = k s1 (z s -z us )+k s2 (z s -z us ) 2 +k s3 (z s -z us ) 3 ,

[0157] In addition, m s Represents the vehicle body mass, m us Represents the wheel mass, k s1 ,k s2 ,k s3 are the linear coefficient, quadratic coefficient and cubic coefficient of the suspension spring respectively, and Represent the linear coefficient and quadratic coefficient of suspension damping, k us Represents the linear spring coefficient of the tire, B us Represents the linear damping coefficient of the tire, z s Represents the vertical displacement of the vehicle body, z us represents the displacement of the unsprung mass, z r represents the road input, u(v(t)) represents the control input of the active suspension system, and there is an input saturation of the following form

[0158]

[0159] The vertical displacement of the vehicle body, the velocity of the vehicle body, the displacement of the unsprung mass and the velocity of the unsprung mass are selected as state variables, that is, x1 = z s , x3=z us , The suspension dynamics differential equation (1) is transformed into a state space mathematical model:

[0160]

[0161] (b) Set constraints:

[0162] Ride comfort: Ride comfort is usually evaluated by the body acceleration in the vertical direction; therefore, one of the main control objectives is to make the body acceleration in the vertical direction as small as possible;

[0163] Driving safety: No matter what driving conditions the vehicle is in, the wheels should not leave the ground, otherwise it will cause traffic accidents and losses. Therefore, in order to ensure that the wheels are in constant contact with the ground, the dynamic load of the tire should not exceed its static tire load; that is, k us (z us -z r )<(m s +m us )g, g is the acceleration due to gravity;

[0164] Maximum dynamic deflection: The dynamic deflection of the suspension satisfies |z s -z us |≤z max ,z max is the maximum allowable dynamic deflection;

[0165] (c) In the controller design process, a candidate Lyapunov function is selected at each step to construct a virtual controller until the last step to construct a real controller. The control method is as follows:

[0166] Since f(x):R n →R is an unknown continuous function, so the following neural network is introduced to process it

[0167]

[0168] in, is the output vector of the neural network with dimension r, Φ=[Φ1,Φ2,...,Φ k ] T ∈R k is defined as a weight vector, k greater than 1 is defined as the number of neural network nodes, P(Z) = [p1(Z), p2(Z), ..., p k (Z)] T ∈R k , the selected Gaussian function p i (Z) is

[0169]

[0170] in, is the center of the receiving field, σ i is the width of the Gaussian function; for sufficiently large k,

[0171]

[0172] Where δ(x) is defined as the approximation error and satisfies |δ(x)|≤ε; define the unknown ideal weight constant Φ * for

[0173]

[0174] (d) Define the tracking error variable as:

[0175]

[0176] Among them, y d is the reference signal |y d |≤Y0<k c1 , α1 is defined as the virtual control law to be designed and δ1,δ2 are the status signals of the auxiliary system designed to handle input saturation as follows

[0177]

[0178]

[0179] Among them, p1>0, p2>0 are the parameters to be designed;

[0180] (e) Construct the virtual control law α1 as:

[0181]

[0182] Among them, k b1 =k c1 -Y0,k 11 >0,k 21 >0,0<l1<1 are the parameters to be designed;

[0183] (f) Design the adaptive neural network event trigger controller and event trigger mechanism as follows:

[0184]

[0185] v(t)=χ(t k ),t k ≤t<t k+1 ,

[0186] t k+1 = inf{t>t k ‖ψ(t)|≥γ|v(t)|+d1}

[0187] Among them, ψ(t)=χ(t)-v(t), d1>0, 0<γ<1,∈>0 and is a designed normal constant; α2 is the virtual controller to be designed;

[0188] (g) Construct the virtual control law α2 as:

[0189]

[0190] in, k 12 >0,k 22 >0,a1>0,0<l1<1 are the parameters to be designed;

[0191] (h) Design the adaptive law as:

[0192]

[0193] Among them, σ is the constant to be designed;

[0194] (i) Zero kinetic analysis;

[0195] (j) Prove that Zeno's behavior does not occur.

[0196] The above description is only a preferred feasible embodiment of the present invention, and does not limit the scope of rights of the present invention. All equivalent structural changes made using the contents of the present invention description and drawings are included in the scope of rights of the present invention.

[0197] In this embodiment, the parameters of the active suspension system are set as shown in Table 1:

[0198] Table 1: Active suspension system model parameters

[0199]

[0200] The event-triggered controller and adaptive law parameters given during simulation are shown in Table 2:

[0201] Table 2: Parameters of the event-triggered controller and adaptive law given during simulation.

[0202]

[0203]

[0204] The initial conditions are x1(0) = 0.002, x2(0) = 0, x3(0) = 0, x4(0) = 0, δ1(0) = 0.1, δ2(0) = 0.1, Give the system a sinusoidal excitation z r =Asin2πft, 0≤t≤10s, A=20mm, f=1Hz, under the disturbance of this road surface and the designed event-triggered controller, the vehicle body vertical acceleration, vehicle body displacement, suspension dynamic deflection, the trajectories of the controller, the real controller and the virtual controller, the trigger time interval and Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown. Figure 1 It can be concluded that the proposed controller design can greatly reduce the acceleration of the vehicle body, thereby increasing the comfort of the driver and passengers. Figure 2 and Figure 3 It can be seen that the proposed solution can not only ensure that the vertical displacement of the vehicle body is very small but also ensure that the vehicle suspension moves within the allowable range. Figure 4 It can be concluded that the proposed controller design can ensure that the controller trajectory does not exceed the maximum and minimum values ​​of saturation. Figure 6 It can be seen that the proposed controller can save network communication resources and reduce the communication burden compared with the traditional periodic sampling controller design.

Claims

1. An event-triggered control method for automobile suspension with position constraints and input saturation, characterized in that The following steps are involved: (a) Establish the state space model of the nonlinear active suspension control system of the vehicle. For the nonlinear quarter active suspension model with two degrees of freedom, its dynamic differential equation is: where: f1(z s ,z us ) = k s1 (z s -z us ) + k s2 (z s -z us ) 2 +k s3 (z s -z us ) 3 , Among them, m s Represents the vehicle body mass, m us Represents the wheel mass, k s1 ,k s2 ,k s3 are the linear coefficient, quadratic coefficient and cubic coefficient of the suspension spring respectively, and Represent the linear coefficient and quadratic coefficient of suspension damping, k us Represents the linear spring coefficient of the tire, B us Represents the linear damping coefficient of the tire, z s Represents the vertical displacement of the vehicle body, z us represents the displacement of the unsprung mass, z r represents the road input, u(v(t)) represents the control input of the active suspension system, and there is input saturation in the following form: The vertical displacement of the vehicle body, the velocity of the vehicle body, the displacement of the unsprung mass and the velocity of the unsprung mass are selected as state variables, that is, The suspension dynamics differential equation is converted into a state space mathematical model: The states of all systems are strictly constrained to be in the following compact set: Ω x :={x i ∈R||x i |≤k ci ,i=1,2,3,4}; (b) Set constraints: (i) Ride comfort: Ride comfort is usually evaluated by the body acceleration in the vertical direction. Therefore, one of the main control objectives is to make the body acceleration in the vertical direction as small as possible. (ii) Driving safety: Regardless of the driving conditions, the wheels should not leave the ground, otherwise it will cause traffic accidents and losses. Therefore, in order to ensure that the wheels are in constant contact with the ground, the dynamic load of the tire should not exceed its static tire load, i.e., k us (z us -z r )<(m s +m us )g, g is the acceleration due to gravity; (iii) Maximum dynamic deflection: The dynamic deflection of the suspension satisfies |z s -z us |≤z max ,z max is the maximum allowable dynamic deflection; (c) In the controller design process, a candidate Lyapunov function is selected at each step to construct a virtual controller until the last step to construct a real controller. The control method is as follows: Since f(x):R n →R is an unknown continuous function, so the following neural network is introduced to process it: in, is the output vector of the neural network with dimension r, Φ=[Φ1,Φ2,...,Φ k ] T ∈R k is defined as a weight vector, k greater than 1 is defined as the number of neural network nodes, P(Z) = [p1(Z), p2(Z), ..., p k (Z)] T ∈R k , the selected Gaussian function p i (Z) is: in, is the center of the receiving field, σ i is the width of the Gaussian function. For sufficiently large k, we have: Where δ(x) is defined as the approximation error and satisfies |δ(x)|≤ε; define the unknown ideal weight constant Φ * for: (d) Define the tracking error variable as: Among them, y d is the reference signal, |y d |≤Y0<k c1 , α1 is defined as the virtual control law to be designed and δ1,δ2 are status signals of the auxiliary system designed to handle input saturation as follows: Among them, p1>0, p2>0 are the parameters to be designed; (e) Construct the virtual control law α1 as: Among them, k b1 =k c1 -Y0,k 11 >0,k 21 >0,0<l1<1 are the parameters to be designed; (f) Design the adaptive neural network event trigger controller and event trigger mechanism as follows: v(t)=χ(t k ),t k ≤t<t k+1 , t k+1 =inf{t>t k ‖ψ(t)|≥γ|v(t)|+d1} Among them, ψ(t)=χ(t)-v(t), d1>0, 0<γ<1,∈>0 and is a designed normal constant; α2 is the virtual controller to be designed; (g) Construct the virtual control law α2 as: in, k 12 >0,k 22 >0,a1>0,0<l1<1 are the parameters to be designed; (h) Design the adaptive law as: Here, σ is a constant to be designed.

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