A memory output feedback control method for an automobile active suspension system

Abstract

A memory output feedback control method for an automobile active suspension system belongs to the technical field of automobile suspension control and solves the problem that existing automobile active suspension control models do not consider the influence of time delay on the dynamic performance of the system and cannot meet the control performance of the suspension system. The present invention designs a memory output feedback control method. Taking into account the existence of time delay in actual automobile active suspension systems and the inability of traditional memoryless controllers to eliminate the influence of time delay, a memory output feedback controller is proposed, which introduces the time delay factor into the design of the controller, ensuring that the system can still remain stable and controllable under time delay, improving driving stability and comfort, and having a good control effect.

Description

Technical Field

[0001] The invention belongs to the technical field of automobile suspension control and relates to a memory output feedback control method for an automobile active suspension system. Background Art

[0002] With the development of technology and the improvement of people's living standards, cars have gradually become part of everyday life. As one of the main components of a car, the suspension system, consisting of springs, damping structures, and guide components, ensures driving stability and passenger comfort. Its performance plays a crucial role in the vehicle's operation. Compared to passive suspension systems, active suspension systems incorporate force-generating devices. Through active suspension controllers, the vehicle can continuously adjust the input force as operating conditions and road excitations change, thereby achieving excellent control performance on complex road surfaces. Therefore, active suspension has become a trend in the development of automotive suspension and a hot topic of research for automakers and scholars.

[0003] In existing research on automotive active suspension systems, the impact of time delay on these systems is rarely considered for the sake of theoretical analysis and control design. Furthermore, traditional memoryless control design methods are unable to address the effects of time delay on the system. This approach suffers from the following shortcomings:

[0004] 1) The design model fails to account for time delay. For the sake of convenience in theoretical analysis and control design, time delay is often ignored, resulting in an idealized mathematical model. When the controller of an active suspension system issues a control signal, the actuator does not immediately react; instead, it reacts with a delay. Therefore, the impact of time delay on the system must be considered in the design of active suspension control systems. Compensation methods must be implemented to mitigate or even eliminate this delay, thereby improving control accuracy.

[0005] 2) Traditional memoryless controllers cannot eliminate the effects of time lag. The presence of time lag means that the change in system state depends not only on the current state but also on the state at a previous moment or within a certain period of time. However, memoryless controllers do not incorporate past states and therefore cannot eliminate the impact of time lag on the control system. When the time lag is small, it may still be effective. However, when the time lag is too large, the control effect of the controller becomes ineffective and becomes somewhat conservative.

[0006] 3) Memory-based state feedback control requires the state to be known. In practical engineering, the system state cannot be directly measured or obtained through simple methods. To address this problem, some researchers have proposed the concept of state reconstruction, but this method increases the order of the system and brings difficulties to controller design.

[0007] In the prior art, the Chinese invention patent application "A Method for Controlling an Automobile Active Suspension" with a publication date of August 2, 2019 and publication number CN110077191A discloses a method for controlling an automobile active suspension system, including establishing an automobile active suspension system model, establishing the dynamic differential equation of the automobile active suspension system based on the model, and solving the state-space equation of the automobile active suspension system. Taking into account the uncertainty of the system, a controller for the automobile active suspension system under disturbance interference is designed. This invention considers the output feedback H-infinity controller under four factors, including system parameter uncertainty, actuator delay, road surface unevenness disturbance, and sensor measurement output disturbance, to achieve control of the automobile active suspension system. The controller has a wider adaptability. However, the disadvantage of this technical solution is that the design of the controller only involves a memoryless term, that is, it does not consider the impact of time lag on the control rate, and is somewhat conservative.

[0008] A Chinese invention patent application, "A Finite-Time Hybrid Control Method for an Automobile Active Suspension," published on July 18, 2017, with publication number CN106956559A, discloses a finite-time hybrid control method for an automobile active suspension. The method involves three main steps: 1) constructing a mathematical model of the system based on the dynamic equations of the automobile active suspension system; 2) selecting the vehicle body vertical acceleration as the control output and conducting a finite-time hybrid performance analysis of the open-loop suspension system; 3) selecting the suspension travel, tire dynamic and static loads, and actuator output force as constraint outputs, designing a state feedback controller based on the finite-time hybrid performance analysis results, and calculating an upper bound on the road disturbance energy. This method effectively improves vehicle ride comfort while satisfying the suspension's hard constraints. However, the technical solution has the following drawbacks: 1) the automobile active suspension model used does not consider the influence of time lag, which reduces the control accuracy of the designed controller when applied to an actual automobile active suspension system; and 2) the controller considered is a state feedback controller, which is more practical than output feedback control.

[0009] Because automotive active suspension systems are essentially discrete control systems, time lags in signal acquisition, transmission, controller calculations, and actuator actuation can all lead to timely control. This can prevent disturbances from being eliminated, degrading control quality. Excessive time lag can even lead to system instability, resulting in irreparable damage. For discrete automotive active suspension systems with time lag, stability and robustness analysis of the control system are essential industrial practices. Therefore, when designing controllers, it is important to consider the impact of time lag on the control system and other performance indicators, such as robustness and interference rejection, to enhance driving comfort. Summary of the Invention

[0010] The purpose of the present invention is to design a memory output feedback control method for an automobile active suspension system to solve the problem that the existing automobile active suspension control model does not consider the influence of time delay on the dynamic performance of the system and cannot meet the control performance of the suspension system.

[0011] The present invention solves the above technical problems through the following technical solutions:

[0012] A memory output feedback control method for an automobile active suspension system comprises the following steps:

[0013] S1. Based on the mechanical model of the automobile active suspension system, a model of the automobile active suspension system with time delay is established, and the model is discretized to obtain a discrete model of the automobile active suspension system with time delay;

[0014] S2. Designing a memory output feedback controller for the discrete model of the vehicle active suspension system with time delay described in step S1, obtaining a closed-loop control system for the vehicle active suspension with time delay, and designing a vehicle ride comfort disturbance suppression performance index;

[0015] S3. Based on the closed-loop control system of the active suspension of the automobile with time delay described in step S2, design a nonlinear matrix inequality constraint condition that meets the asymptotic stability requirement thereof, select a Lyapunov function, and prove that the nonlinear matrix inequality constraint condition can ensure the asymptotic stability of the closed-loop control system of the active suspension of the automobile with time delay and meet the disturbance rejection performance index;

[0016] S4. Using the projection theorem, the nonlinear matrix inequality constraints described in step S3 are converted into linear matrix inequality constraints. By solving the minimum value of the disturbance suppression performance index in the linear matrix inequality constraints, the gain matrix of the output feedback controller with memory is obtained.

[0017] The present invention designs a memory output feedback control method. Taking into account the existence of time lag in actual automobile active suspension systems and the inability of traditional memoryless controllers to eliminate the influence of time lag, a memory output feedback controller is proposed, which introduces the time lag factor into the design of the controller, ensuring that the system can still remain stable and controllable under time lag, improving driving stability and comfort, and having a good control effect.

[0018] Furthermore, the method for establishing the model of the automobile active suspension system with time delay described in step S1 is specifically as follows:

[0019] The dynamic equations of the vehicle active suspension system are as follows:

[0020]

[0021] Among them, ms Refers to the mass on the spring; m u refers to the unsprung mass; u(t) is the control input of the suspension system; c s ,k s ,c t and k t Respectively represent the suspension damping coefficient, spring stiffness coefficient, tire damping coefficient and tire stiffness coefficient; z s Indicates the vehicle distance. Indicates the vertical speed of the vehicle body, is the vertical acceleration of the vehicle body, z u represents the unsprung mass displacement, is the unsprung mass velocity, is the unsprung mass acceleration, z r Indicates road roughness, represents the road disturbance velocity, u(t-τ) is the control input of the suspension system with time delay at time t;

[0022] Select the system state variable: x1(t)=z s (t)-z u (t) is the dynamic deflection of the suspension, x2(t)=z u (t)-z r (t) is the tire dynamic displacement, represents the velocity of the sprung mass; represents the velocity of the unsprung mass; is the road disturbance input; u(t-τ) is the control input of the vehicle active suspension system with time delay at time t, and the system state variables are defined as:

[0023] x(t)=[x1(t)x2(t)x3(t)x4(t)] T (2)

[0024] The vertical acceleration of the vehicle body is selected as the control output of the system, that is:

[0025]

[0026] The state equation of the vehicle active suspension system with time delay is obtained as follows:

[0027]

[0028] Among them, the matrices A, B, B1, C1, D1 are defined as:

[0029]

[0030] Among them, A is the system matrix, B is the input matrix, B1 is the disturbance matrix, C1 is the state-output matrix, and D1 is the input-output matrix.

[0031] Furthermore, the method for discretizing to obtain the discrete model of the vehicle active suspension system with time delay in step S1 is as follows:

[0032] Let the time delay amount τ in the state equation of the vehicle active suspension system with time delay be τ=(d - 1)T+τ', where d is an integer, d≥0, 0<=τ'<T. Since the solution of the state equation of the vehicle active suspension system with time delay is:

[0033]

[0034] In the formula, t0 is the initial sampling time; σ is the sampling time;

[0035] Take the sampling values at adjacent sampling times kT (integer k≥0) and (k + 1)T for observation. Let t0 = kT, t=(k + 1)T, and take:

[0036]

[0037] Substitute equation (7) into (6), take s=(k + 1)T - σ, and simplify the sampling time kT to k. When τ'≠0 and d = 1, the discrete-time model of the system is obtained as:

[0038]

[0039] where

[0040] Take the following augmented state variable matrix:

[0041]

[0042] Then the discrete model of the vehicle active suspension system with time delay is:

[0043]

[0044] where the matrices G, H, V, C are respectively:

[0045]

[0046] where G1 is the system matrix, H1, H2 are the input matrices, V1 is the disturbance matrix, C1 is the state-output matrix, and D1 is the input-output matrix.

[0047] Furthermore, the method for designing a memory output feedback controller to obtain the closed-loop control system of the vehicle active suspension with time delay in step S2 is as follows:

[0048] The memory output feedback controller is:

[0049] u(k)=k0y(k)+k1y(k-1)+k2y(k-2) (12)

[0050] in, is the controller gain matrix;

[0051] Define state variables:

[0052]

[0053] Substituting formula (12) into formula (10), the closed-loop control system of the vehicle active suspension with time delay is obtained as follows:

[0054]

[0055] Among them, the matrix E, They are:

[0056]

[0057] Where diag{} represents a diagonal block matrix, where I (ny+ny+nx) represents the ny+ny+nx dimensional identity matrix, 0 (nu×nu) Represents a nu×nu-dimensional rank-0 matrix.

[0058] Furthermore, the designed vehicle ride comfort disturbance suppression performance index in step S2 is as follows:

[0059]

[0060] Among them, γ represents the disturbance suppression performance index, γ>0, the smaller its value is, the stronger the anti-disturbance ability of the vehicle active suspension closed-loop control system with time delay is, y T (t), w T (t) are the transposed matrices of y(t) and w(t) respectively.

[0061] Furthermore, the method for designing the nonlinear matrix inequality constraint condition that satisfies the asymptotic stability requirement described in step S3 is as follows:

[0062] According to the dynamic equation of the automobile active suspension system given by formula (1), if there exists a positive definite matrix P>0 and γ>0, then the memory output feedback controller of formula (12) can make the automobile active suspension closed-loop control system with time delay of formula (14) asymptotically stable and meet the disturbance suppression performance index γ>0;

[0063] That is, the nonlinear matrix inequality constraint condition is:

[0064]

[0065] in, Represent the state matrix and disturbances The transposed matrix of .

[0066] Furthermore, the method for selecting the Lyapunov function in step S3 to prove that the nonlinear matrix inequality constraint can ensure the asymptotic stability of the vehicle active suspension closed-loop control system with time delay and meet the disturbance suppression performance index is as follows:

[0067] The Lyapunov function is:

[0068]

[0069] Where P is a positive definite matrix, Represent the state vector and its transposed vector respectively;

[0070] The forward difference of V(k) is:

[0071] ΔV(k)=V(k+1)-V(k)<0 (19)

[0072] Where ΔV(k) is the forward difference of V(k);

[0073] Further we can get:

[0074]

[0075] Where W(k) is the perturbation vector after discretization;

[0076] We further obtain the following inequality:

[0077]

[0078] Consider the disturbance suppression performance index, as shown in the following formula:

[0079] y T (t)y(t)-γ 2 w T (t)w(t)<0 (22)

[0080] Among them, y T (t), w T (t) represents the transposed vector of the output and perturbation vectors respectively;

[0081] Then, by adding formula (21) and formula (22), we can get the following inequality:

[0082]

[0083] If formula (17) holds true, it can be guaranteed that ΔV(t)<0, that is, the closed-loop control system of the active suspension of the vehicle with time delay is asymptotically stable.

[0084] Furthermore, the method described in step S4 for converting the nonlinear matrix inequality constraint condition described in step S3 into a linear matrix inequality constraint condition by using the projection theorem, and obtaining the gain matrix of the output feedback controller with memory by solving the minimum value of the disturbance rejection performance index in the constraint condition of the linear matrix inequality is as follows:

[0085] In the case of asymptotic stability of the closed-loop system of active suspension of automobile, if there is a matrix Then the memory output feedback controller gain matrix can be obtained by the following linear matrix inequality constraints:

[0086]

[0087] in:

[0088]

[0089] Sym{} represents a symbolic function;

[0090] According to formula (24), the gain matrix of the memory output feedback controller is:

[0091]

[0092] Using the projection theorem, the nonlinear matrix inequality constraint of formula (17) is transformed into a linear matrix inequality constraint, which can be written as follows:

[0093]

[0094] Among them, the matrix X i Defined as:

[0095] X i =[X1 X2 X3 MN] (28)

[0096] in, Define new variables:

[0097]

[0098] Substituting formula (28) and formula (29) into formula (27), we can obtain the linear matrix inequality constraint condition of formula (24).

[0099] Furthermore, the disturbance suppression performance index γ is solved 2 The constraints on the minimum value of are as follows:

[0100] P>0

[0101] γ>0

[0102]

[0103] The above formula can be used to obtain the minimum disturbance suppression performance index γ, thereby maximizing the ride comfort of the car. At the same time, the above algorithm can be used to obtain matrices P and K, thereby obtaining the memory output feedback controller gain matrix.

[0104] The advantages of the present invention are:

[0105] The present invention designs a memory output feedback control method. Taking into account the existence of time lag in actual automobile active suspension systems and the inability of traditional memoryless controllers to eliminate the influence of time lag, a memory output feedback controller is proposed. The time lag factor is introduced into the controller design, ensuring that the system can remain stable and controllable under time lag, improving driving stability and comfort, and achieving good control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 This is a flow chart of a method for controlling a vehicle active suspension system with memory output feedback according to a first embodiment of the present invention;

[0107] Figure 2 is a model diagram of an automobile active suspension system according to a first embodiment of the present invention;

[0108] Figure 3 is a response curve of the input force of the automobile active suspension system over time according to the first embodiment of the present invention;

[0109] Figure 4 1 is a response curve of the vertical displacement of the vehicle body over time according to the first embodiment of the present invention. DETAILED DESCRIPTION

[0110] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0111] The technical solution of the present invention is further described below with reference to the accompanying drawings and specific embodiments:

[0112] Example 1

[0113] like Figure 1 As shown, a memory output feedback control method for an automobile active suspension system includes the following steps:

[0114] First, based on the mechanical model of the automobile active suspension system, a model of the automobile active suspension system with time delay is established, and the discrete model of the automobile active suspension system with time delay is obtained by discretization.

[0115] (1) The method for establishing a model of an automobile active suspension system with time delay is as follows:

[0116] like Figure 2 As shown, the dynamic equation of the vehicle active suspension system is established as follows:

[0117]

[0118] Among them, m s Refers to the mass on the spring; m u refers to the unsprung mass; u(t) is the control input of the suspension system; c s ,k s ,c t and k t Represent the suspension damping coefficient, spring stiffness coefficient, tire damping coefficient and tire stiffness coefficient respectively. s Indicates the vehicle distance. Indicates the vertical speed of the vehicle body, is the vertical acceleration of the vehicle body, z u represents the unsprung mass displacement, is the unsprung mass velocity, is the unsprung mass acceleration, z r Indicates road roughness, represents the road disturbance velocity, and u(t-τ) is the control input of the suspension system with time delay at time t.

[0119] Select the system state variable: x1(t)=z s (t)-z u (t) is the dynamic deflection of the suspension, x2(t)=z u (t)-z r (t) is the tire dynamic displacement, represents the velocity of the sprung mass; represents the velocity of the unsprung mass; is the road disturbance input; u(t-τ) is the control input of the vehicle active suspension system with time delay at time t, and the system state variables are defined as:

[0120] x(t)=[x1(t)x2(t)x3(t)x4(t)] T (2)

[0121] In order to measure the ride comfort, the vertical acceleration of the vehicle body is selected as the control output of the system, namely:

[0122]

[0123] Finally, the state equation of the vehicle active suspension system with time delay is described in the following form:

[0124]

[0125] where the matrices A, B, B1, C1, and D1 are defined as:

[0126]

[0127] Among them, A is the system matrix, B is the input matrix, B1 is the perturbation matrix, C1 is the state-output matrix, and D1 is the input-output matrix.

[0128] (2) The method for discretizing to obtain the discrete model of the vehicle active suspension system with time delay is as follows:

[0129] Describe the time delay in the state equation of the vehicle active suspension system with time delay as τ=(d - 1)T+τ', where d (integer)≥0, 0<=τ'<T. Since the solution of this equation is:

[0130]

[0131] In the formula, t0 is the initial sampling time; σ is the sampling time.

[0132] Take the sampling values at adjacent sampling times kT (integer k≥0) and (k + 1)T for observation. Let t0 = kT, t=(k + 1)T, and take

[0133]

[0134] Substitute equation (7) into (6), take s=(k + 1)T - σ, and simplify the sampling time kT to k. When τ'≠0 and d = 1, the discrete-time model of the system can be obtained as:

[0135]

[0136] where G1 is the system matrix, H1 and H2 are the input matrices, V1 is the perturbation matrix, C1 is the state-output matrix, and D1 is the input-output matrix.

[0137] Consider the following augmented matrix of state variables

[0138]

[0139] Then the discrete model of the vehicle active suspension system with time delay can be described as:

[0140]

[0141] The matrices G, H, V, and C are defined as:

[0142]

[0143] 2. For the discrete model of the automobile active suspension system with time delay, a memory output controller is designed to obtain the automobile active suspension closed-loop control system, and the disturbance suppression performance index is designed.

[0144] (1) The method for designing a memory output feedback controller to obtain a closed-loop control system for an active suspension of an automobile with time lag is as follows:

[0145] The memory output feedback controller is:

[0146] u(k)=k0y(k)+k1y(k-1)+k2y(k-2) (12)

[0147] in, is the controller gain matrix;

[0148] Define state variables:

[0149]

[0150] Substituting formula (12) into formula (10), the closed-loop control system of the vehicle active suspension with time delay is obtained as follows:

[0151]

[0152] Among them, the matrix E, They are:

[0153]

[0154] Where diag{} represents a diagonal block matrix, where I (ny+ny+nx) represents the ny+ny+nx dimensional identity matrix, 0 (nu×nu) Represents a nu×nu-dimensional rank-0 matrix.

[0155] (2) The method for designing disturbance suppression performance indicators is as follows:

[0156] The designed controller must ensure the asymptotic stability of the closed-loop system and improve the ride comfort of the system. It should be noted that the control output y(t) of the closed-loop system represents the vertical acceleration of the vehicle body.

[0157] The ride comfort of a car can be described by the following equation: under the influence of the disturbance w(t) input, the output of the closed-loop suspension system satisfies the following disturbance rejection performance index:

[0158]

[0159] Among them, γ represents the disturbance suppression performance index, γ>0, the smaller its value is, the stronger the anti-disturbance ability of the vehicle active suspension closed-loop control system with time delay is, y T (t), w T (t) are the transposed matrices of y(t) and w(t) respectively.

[0160] 3. Based on the closed-loop control system of the active suspension of an automobile with time delay, nonlinear matrix inequality constraints that meet its asymptotic stability requirements are designed. The Lyapunov function is selected to prove that the nonlinear matrix inequality constraints can ensure the asymptotic stability of the closed-loop control system of the active suspension of an automobile with time delay and meet the disturbance suppression performance indicators.

[0161] According to the dynamic equation of the automobile active suspension system given by formula (1), if there exists a positive definite matrix P>0 and γ>0, then the memory output feedback controller of formula (12) can make the automobile active suspension closed-loop control system with time delay of formula (14) asymptotically stable and meet the disturbance suppression performance index γ>0;

[0162] That is, the nonlinear matrix inequality constraint condition is:

[0163]

[0164] in, Represent the state matrix and disturbances The transposed matrix of .

[0165] Select the Lyapunov function as:

[0166]

[0167] Where P is a positive definite matrix, denote the state vector and its transposed vector respectively.

[0168] The forward difference of V(k) is:

[0169] ΔV(k)=V(k+1)-V(k)<0 (19)

[0170] Where ΔV(k) is the forward difference of V(k).

[0171] Further we can get:

[0172]

[0173] Where W(k) is the perturbation vector after discretization.

[0174] We further obtain the following inequality:

[0175]

[0176] Consider the disturbance suppression performance index, as shown in the following formula:

[0177] y T (t)y(t)-γ 2 w T (t)w(t)<0 (22)

[0178] Among them, y T (t), w T (t) represents the transposed vector of the output and perturbation vectors, respectively.

[0179] Then, by adding formula (21) and formula (22), we can get the following inequality:

[0180]

[0181] If formula (17) holds true, it can be guaranteed that ΔV(t)<0, that is, the closed-loop control system of the active suspension of the vehicle with time delay is asymptotically stable.

[0182] Fourth, the projection theorem is used to transform the nonlinear matrix inequality constraints into linear matrix inequality constraints. By solving the minimum value of the disturbance rejection performance index in the linear matrix inequality constraints, the gain matrix of the output feedback controller with memory is obtained.

[0183] In the case of asymptotic stability of the closed-loop system of active suspension of automobile, if there is a matrix Then the memory output feedback controller gain matrix can be obtained by the following inequality:

[0184]

[0185] in:

[0186]

[0187] Sym{} represents a symbolic function.

[0188] The memory output feedback controller matrix can be obtained by the following formula:

[0189]

[0190] Proof: To facilitate the solution, the projection theorem is used to transform the nonlinear matrix inequality (17) into a linear matrix inequality, which can be written as follows:

[0191]

[0192] Among them, the matrix X i Defined as:

[0193] X i =[X1 X2 X3 MN] (28)

[0194] in, Define new variables:

[0195]

[0196] Substituting equations (28) and (29) into equation (27), we can obtain the linear matrix inequality (24).

[0197] The disturbance rejection performance index γ of the suspension system and its corresponding controller gain matrix are obtained by the following method:

[0198] Solve the disturbance rejection performance index γ 2 The constraints on the minimum value of are as follows:

[0199] P>0

[0200] γ>0

[0201]

[0202] The above formula can be used to obtain the minimum disturbance suppression performance index γ, thereby maximizing the ride comfort of the car. At the same time, the above algorithm can be used to obtain the matrices P and K, and then the controller gain matrix can be obtained using the following formula:

[0203]

[0204] For Figure 2 The active suspension system of the car shown in the figure selects the parameter k s =16000N / m,k t =160000N / m,c s =980N s / m,m s =500kg,m u =45kg,c t =0, w(t)=5e (-0.03t) cos(0.5t). Selecting a sampling period of 1s and a time-delay input of 0.03s, the controller gains obtained through the above optimization algorithm are as follows: k0 = 0.2934, k1 = -0.8086, k2 = -0.8762.

[0205] Figure 3 The curve of the input force of the automobile active suspension system changing with time. From the simulation results, it can be seen that the input force of the memory control method has a smaller input fluctuation amplitude than that of the memoryless method.

[0206] Figure 4The vertical acceleration of the car changes with time. From the simulation results, it can be seen that the control effects of the memory control method and the memoryless control method are not much different, but the memory output feedback only requires a smaller actuator input to achieve better results, and the vertical vibration amplitude is relatively small. The memory output feedback controller designed in this invention has a smaller control output than the memoryless controller and has a stronger ability to suppress disturbances, which verifies the effectiveness of the designed controller and achieves the expected purpose.

[0207] This paper examines a discrete model of an active suspension with time lag, addressing the problem of existing design models that fail to account for the effects of time lag. It proposes a method for output feedback control with memory, incorporating time lag into the controller design. This method ensures that even in the presence of time lag, the system output gradually approaches zero, leading to a stable state. Simulation results demonstrate the feasibility and effectiveness of the controller design, reducing the negative impact of road disturbances on the suspension system and achieving the intended design goal.

[0208] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A memory output feedback control method for an automobile active suspension system, characterized in that: It includes the following steps: S1. According to the mechanical model of the automotive active suspension system, establish a model of the automotive active suspension system with time delay, and discretize it to obtain a discrete model of the automotive active suspension system with time delay; The state equation of the automotive active suspension system with time delay is: where the matrices A, B, B1, C1, D1 are defined as: Among them, A is the system matrix, B is the input matrix, B1 is the disturbance matrix, C1 is the state-output matrix, and D1 is the input-output matrix; m s Refers to the mass on the spring; m u Refers to the mass under the spring; c s ,k s ,c t and k t They represent the suspension damping coefficient, spring stiffness coefficient, tire damping coefficient and tire stiffness coefficient respectively; x(t) is the system state variable, is the first-order derivative of the system state variable, w(t) is the road disturbance input, u(t-τ) is the suspension system control input with time lag at time t; y(t) is the control output of the system; S2. For the discrete model of the automotive active suspension system with time delay described in step S1, design a memory output feedback controller to obtain a closed-loop control system of the automotive active suspension with time delay, and design a vehicle ride comfort disturbance rejection performance index; The closed-loop control system of the automotive active suspension with time delay is as follows: Among them, the matrix E, They are: Where diag{} represents a diagonal block matrix, where I (ny+ny+nx) represents the ny+ny+nx dimensional identity matrix, 0 (nu×nu) represents a nu×nu dimension 0-order matrix; k0, k1, k2 are controller gain matrices; is the state variable at time k; is the state variable at time k+1; G, H, V, C are all matrices; S3. According to the closed-loop control system of the automotive active suspension with time delay described in step S2, design a nonlinear matrix inequality constraint condition that meets its asymptotic stability requirements, select a Lyapunov function, and prove that the nonlinear matrix inequality constraint condition can ensure the asymptotic stability of the closed-loop control system of the automotive active suspension with time delay and meet the disturbance rejection performance index; S4. Use the projection theorem to transform the nonlinear matrix inequality constraint condition described in step S3 into a linear matrix inequality constraint condition, and obtain the gain matrix of the memory output feedback controller by solving the minimum value of the disturbance rejection performance index in the constraint condition of the linear matrix inequality.

2. The memory output feedback control method for an automobile active suspension system according to claim 1, characterized in that: The method for establishing the model of the automotive active suspension system with time delay described in step S1 is specifically as follows: Establish the dynamic equation of the automotive active suspension system as follows: Among them, m s Refers to the mass on the spring; m u refers to the unsprung mass; u(t) is the control input of the suspension system; c s ,k s ,c t and k t Respectively represent the suspension damping coefficient, spring stiffness coefficient, tire damping coefficient and tire stiffness coefficient; z s Indicates the vehicle distance. Indicates the vertical speed of the vehicle body, is the vertical acceleration of the vehicle body, z u represents the unsprung mass displacement, is the unsprung mass velocity, is the unsprung mass acceleration, z r Indicates road roughness, represents the road disturbance velocity, u(t-τ) is the control input of the suspension system with time delay at time t; Select the system state variable: x1(t)=z s (t)-z u (t) is the dynamic deflection of the suspension, x2(t)=z u (t)-z r (t) is the tire dynamic displacement, represents the velocity of the sprung mass; represents the velocity of the unsprung mass; is the road disturbance input; u(t-τ) is the control input of the vehicle active suspension system with time delay at time t, and the system state variables are defined as: x(t)=[x1(t)x2(t)x3(t)x4(t)] T (2) Select the vertical acceleration of the vehicle body as the control output of the system, that is: Obtain the state equation of the automotive active suspension system with time delay as: where the matrices A, B, B1, C1, D1 are defined as: where A is the system matrix, B is the input matrix, B1 is the disturbance matrix, C1 is the state-output matrix, and D1 is the input-output matrix.

3. The memory output feedback control method for an automobile active suspension system according to claim 2, characterized in that: The method for discretizing to obtain the discrete model of the automotive active suspension system with time delay described in step S1 is as follows: Let the time delay τ in the state equation of the automotive active suspension system with time delay be τ=(d - 1)T+τ', where d is an integer, d≥0, 0<=τ'<T. Since the solution of the state equation of the automotive active suspension system with time delay is: In the formula, t0 is the initial sampling time; σ is the sampling time; Take the sampling values at adjacent sampling times kT (integer k≥0) and (k + 1)T for observation, let t0 = kT, t=(k + 1)T, and take: Substitute equation (7) into (6), take s=(k + 1)T - σ, and simplify the sampling time kT to k. When τ'≠0, d = 1, obtain the discrete-time model of the system as: Where G1 = e AT , C1 = C, D1 = D Take the following state variable augmented matrix: Then the discrete model of the automotive active suspension system with time delay is: where the matrices G, H, V, C are respectively: C=(C1 D1) where G1 is the system matrix, H1, H2 are the input matrices, V1 is the disturbance matrix, C1 is the state-output matrix, and D1 is the input-output matrix.

4. The memory output feedback control method for an automobile active suspension system according to claim 3, characterized in that: The method for designing a memory output feedback controller to obtain a closed-loop control system of the automotive active suspension with time delay described in step S2 is as follows: The memory output feedback controller is: u(k)=k0y(k)+k1y(k-1)+k2y(k-2) (12) Among them, k0, k1, is the controller gain matrix; Define state variables: Substituting formula (12) into formula (10), the closed-loop control system of the vehicle active suspension with time delay is obtained as follows: Among them, the matrix E, They are: Where diag{} represents a diagonal block matrix, where I (ny+ny+nx) represents the ny+ny+nx dimensional identity matrix, 0 (nu×nu) Represents a nu×nu-dimensional rank-0 matrix.

5. The memory output feedback control method for an automobile active suspension system according to claim 4, characterized in that: The designed vehicle ride comfort disturbance suppression performance index described in step S2 is as follows: Among them, γ represents the disturbance suppression performance index, γ>0, the smaller its value is, the stronger the anti-disturbance ability of the vehicle active suspension closed-loop control system with time delay is, y T (t), w T (t) are the transposed matrices of y(t) and w(t) respectively.

6. The memory output feedback control method for an automobile active suspension system according to claim 5, characterized in that: The method for designing the nonlinear matrix inequality constraint condition that satisfies the asymptotic stability requirement described in step S3 is as follows: According to the dynamic equation of the automobile active suspension system given by formula (1), if there exists a positive definite matrix P>0 and γ>0, then the memory output feedback controller of formula (12) can make the automobile active suspension closed-loop control system with time delay of formula (14) asymptotically stable and meet the disturbance suppression performance index γ>0; That is, the nonlinear matrix inequality constraint condition is: in, Represent the state matrix and disturbances The transposed matrix of .

7. The memory output feedback control method for an automobile active suspension system according to claim 6, characterized in that: The method for selecting the Lyapunov function in step S3 and proving that the nonlinear matrix inequality constraint can ensure the asymptotic stability of the vehicle active suspension closed-loop control system with time delay and meet the disturbance suppression performance index is as follows: The Lyapunov function is: Where P is a positive definite matrix, Represent the state vector and its transposed vector respectively; The forward difference of V(k) is: ΔV(k)=V(k+1)-V(k)<0 (19) Where ΔV(k) is the forward difference of V(k); Further we can get: Where W(k) is the perturbation vector after discretization; We further obtain the following inequality: Consider the disturbance suppression performance index, as shown in the following formula: y T (t)y(t)-γ 2 w T (t)w(t)<0 (22) Among them, y T (t), w T (t) represents the transposed vector of the output and perturbation vectors respectively; Then, by adding formula (21) and formula (22), we can get the following inequality: If formula (17) holds true, it can be guaranteed that ΔV(t)<0, that is, the closed-loop control system of the active suspension of the vehicle with time delay is asymptotically stable.

8. The method for controlling an active suspension system of an automobile with memory output feedback according to claim 7, characterized in that: The method described in step S4 for converting the nonlinear matrix inequality constraint condition described in step S3 into a linear matrix inequality constraint condition by using the projection theorem is specifically as follows: In the case of asymptotic stability of the closed-loop system of active suspension of automobile, if there is a matrix Then the memory output feedback controller gain matrix can be obtained by the following linear matrix inequality constraints: in: Sym{} represents a symbolic function; According to formula (24), the gain matrix of the memory output feedback controller is: Using the projection theorem, the nonlinear matrix inequality constraint of formula (17) is transformed into a linear matrix inequality constraint, which can be written as follows: Among them, the matrix X i Defined as: X i [X1 X2 X3 MN] (28) in, Define new variables: Substituting formula (28) and formula (29) into formula (27), we can obtain the linear matrix inequality constraint condition of formula (24).

9. The method for controlling an automobile active suspension system with memory output feedback according to claim 8, characterized in that: The method described in step S4 for obtaining the gain matrix of the output feedback controller with memory by solving the minimum value of the disturbance rejection performance index in the constraints of the linear matrix inequality is as follows: Solve the disturbance rejection performance index γ 2 The constraints on the minimum value of are as follows: P>0 γ>0 The above formula can be used to obtain the minimum disturbance suppression performance index γ, thereby maximizing the ride comfort of the car. At the same time, the above algorithm can be used to obtain matrices P and K, thereby obtaining the memory output feedback controller gain matrix.

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