An active suspension control method

Abstract

The present invention provides an active suspension control method, which includes the following steps: constructing a state space equation of the model according to the established dynamic model of the multi-variable non-linear active suspension to obtain an active suspension system model; linearizing the multi-variable non-linear links in the active suspension system model to obtain a corresponding quasi-linear system model of the active suspension; optimizing the quasi-linear system model of the active suspension by the Lagrange multiplier method, and solving by the bisection method to obtain the feedback gain K of the multi-variable non-linear active suspension and the feedback control law of the multi-variable non-linear active suspension. By adopting the above method, not only the non-linear problem of the inherent components is solved, but also the network non-linear problem is considered, improving the control accuracy and the stability of the system. At the same time, because the method is simple to reproduce, it is easy to implement in actual work.

Description

Technical Field

[0001] This application relates to the technical field of automotive dynamic control, and particularly to an active suspension control method. Background Art

[0002] The suspension connects the wheels and the vehicle body, directly affecting the ride comfort and driving safety of the vehicle. With the gradual improvement of vehicle performance requirements and the development of vehicle intelligence, active suspensions that can perform real-time parameter adjustment through additional controllable force devices have emerged.

[0003] The controllable force device consists of a measurement system, a feedback control system, an actuator, and an energy system. In actual engineering, the inherent components of the system have non-linear characteristics, such as saturation, dead zone, etc. On the other hand, the controllable force device needs to connect to the control closed-loop through a communication network, which belongs to a network control system. Network non-linearities such as packet loss and time delay will also pose challenges to the control of active suspensions. Therefore, the active suspension control system will be affected by multiple non-linearities caused by inherent components and communication networks.

[0004] Current active suspension control methods mainly focus on considering single non-linear characteristics. For example, function description methods, smooth functions, neural networks, and sliding mode control are used to handle the problem of input saturation in the control system, or methods such as phase lead compensation are used to solve non-linear problems. However, active suspension control methods that only consider single non-linearities will affect the accuracy and stability of the control system. Summary of the Invention

[0005] Embodiments of this application provide an active suspension control method to solve the technical problem that only considering single non-linear characteristics in current active suspension control affects the accuracy and stability of the control system.

[0006] In a first aspect, embodiments of this application provide an active suspension control method, which is characterized by including the following steps:

[0007] According to the established dynamic model of the active suspension considering multiple non-linearities, construct the state space equation of the model to obtain the active suspension system model;

[0008] Linearize the multiple non-linear links in the active suspension system model to obtain the corresponding active suspension quasi-linear system model;

[0009] Optimize the active suspension quasi-linear system model by the Lagrange multiplier method, and solve by the bisection method to obtain the feedback gain K of the active suspension considering multiple non-linearities and the feedback control law of the active suspension considering multiple non-linearities.

[0010] Further, the steps of constructing the spatial equation of the model state based on the established dynamic model of the multi - variable non - linear active suspension to obtain the active suspension system model include:

[0011] According to Newton's second law, list the dynamic model of the non - linear active suspension at any time t;

[0012] Select the state variable x and the road surface input w, and rewrite the dynamic model of the non - linear active suspension as the spatial equation of the model state according to the state variable x and the road surface input w;

[0013] The dynamic model of the non - linear active suspension is:

[0014] Equation (1):

[0015] In Equation (1): z r , z us , z s are the vertical displacements of the ground, tire and vehicle body respectively, and the origin of the vertical displacement coordinate is taken at the static equilibrium position; k s , k us are the suspension spring stiffness and tire stiffness; m s , m us are the sprung mass and unsprung mass respectively; c s , c us are the inherent damping coefficients of the suspension and tire respectively; F c represents the power output of the active suspension considering the multi - variable non - linear link;

[0016] The spatial equation of the model state is:

[0017] Equation (2):

[0018] In the equation:

[0019] C = I4,

[0020] Further, the steps of linearizing the multi - variable non - linear link in the active suspension system model to obtain the corresponding active suspension quasi - linear system model include:

[0021] Use the integral state transformation to construct the active suspension system model into an active suspension system model with implicit time delay;

[0022] Adopt the stochastic linearization method, and use a constant gain to replace the saturation non - linear link in the active suspension system model with implicit time delay to construct an active suspension quasi - linear system model.

[0023] Further, the step of constructing the active suspension system model into an active suspension system model with implicit time delay by using integral state transformation includes:

[0024] At time t, for the active suspension system model with a time delay of τ, when only considering the time delay link, the F c is constructed as:

[0025] Equation (3A): F c = u(t - τ);

[0026] When w(t) = 0, the active suspension system model can be written as:

[0027] Equation (4):

[0028] Select the feedback rate with control memory as:

[0029] Equation (5):

[0030] The control gain K in Equation (5) makes the active suspension system asymptotically stable;

[0031] Introduce integral state transformation to transform the active suspension system model with time delay into the active suspension system model with implicit time delay:

[0032] Equation (7):

[0033] In Equation (7): x0 is x(0), that is, the initial value.

[0034] Further, the step of using the stochastic linearization method to replace the saturation nonlinear link in the active suspension system model with implicit time delay with a constant gain to construct an active suspension quasi-linear system model includes:

[0035] Construct the saturation nonlinear link in the active suspension system model with implicit time delay as:

[0036] Equation (9A):

[0037] In Equation (9A), ±a is the saturation limit critical point, β is the slope of the linear range, and u is the theoretical output of the actuator as power;

[0038] Use the stochastic linearization method to replace the saturation nonlinear link with the first linear constant element, and the first linear constant element is constructed as:

[0039] Equation (10A):

[0040] In Equation (10A), σ uis the standard deviation of the active suspension power u; erf(·) is the error function;

[0041] Combining Equation (7) and Equation (10A), the active suspension system model with implicit time delay is simplified to the active suspension quasi-linear system model:

[0042] Equation (11):

[0043] Furthermore, the step of linearizing the multi-variable non-linear link in the active suspension system model to obtain the corresponding active suspension quasi-linear system model includes:

[0044] Based on the variable time-delay system method, dealing with the packet loss non-linearity, and using the integral state transformation, the active suspension system model is constructed into an active suspension system model with implicit time delay;

[0045] Adopting the stochastic linearization method, replacing the saturation non-linear link and the dead zone non-linear link in the active suspension system model with implicit time delay with a constant gain to construct an active suspension quasi-linear system model.

[0046] Furthermore, the step of constructing the active suspension system model into an active suspension system model with implicit time delay based on the variable time-delay system method, dealing with the packet loss non-linearity, and using the integral state transformation includes:

[0047] Simplifying the active suspension system model into a system model with a certain continuous packet loss rate;

[0048] Based on the variable time-delay method, processing the system model with a certain continuous packet loss rate into an active suspension system model with time delay;

[0049] At time t, replacing the packet loss non-linearity with an equivalent time-delay quantity Replacing the F c Constructed as:

[0050] Equation (3B):

[0051] When w(t) = 0, the active suspension system model can be written as:

[0052] Equation (4):

[0053] Select the feedback rate with control memory as:

[0054] Equation (5):

[0055] The control gain K in Equation (5) makes the active suspension system asymptotically stable;

[0056] Introduce the integral state transformation to transform the active suspension system model with time delay into the active suspension system model with implicit time delay:

[0057] Equation (7):

[0058] In Equation (7): x0 is x(0), that is, the initial value.

[0059] Furthermore, the steps of using the stochastic linearization method to replace the saturation nonlinear link and the dead zone nonlinear link in the active suspension system model with implicit time delay with a constant gain to construct the active suspension quasi-linear system model include:

[0060] Construct the saturation nonlinear link in the active suspension system model with implicit time delay as:

[0061] Equation (9B):

[0062] In Equation (9B), ±a is the saturation limit critical point, β is the slope of the linear range, b is the symmetric dead zone bandwidth, and u is the theoretical output of the actuator driving force;

[0063] Using the stochastic linearization method, replace the saturation nonlinear link and the dead zone nonlinear link with a second linear time-invariant element, and the second linear time-invariant element is constructed as:

[0064] Equation (10B):

[0065] In Equation (10B), σ u is the standard deviation of the active suspension driving force u; erf(·) is the error function;

[0066] Combining Equation (7) and Equation (10B), simplify the active suspension system model with implicit time delay to the active suspension quasi-linear system model:

[0067] Equation (11):

[0068] Furthermore, the steps of optimizing the active suspension quasi-linear system model by the Lagrange multiplier method and obtaining the feedback gain K of the multi-variable nonlinear active suspension and the feedback control rate of the multi-variable nonlinear active suspension by the bisection method include:

[0069] Adopt optimal control to construct the optimization problem with constraints in the active suspension quasi-linear system model, and solve the optimization problem with constraints by the Lagrange multiplier method;

[0070] Obtain the feedback gain K of the multi-variable nonlinear active suspension and the feedback control rate of the multi-variable nonlinear active suspension by the bisection method.

[0071] Furthermore, the steps of adopting optimal control to construct the optimization problem with constraints in the active suspension quasi-linear system model and solving the optimization problem with constraints by the Lagrange multiplier method include:

[0072] For any given ρ > 0, find the optimal gain K to minimize Equation (12):

[0073] Equation (12):

[0074] In Equation (12), ρ represents the weight considering energy consumption, and σ z is the standard deviation of the output variable z of the active suspension control system;

[0075] For all cases of the optimal gain K, take the minimum value to make A + BNK a Hurwitz matrix, and transform Equation (12) into the optimization problem with constraints:

[0076] Equation (13):

[0077] where (N, Q) satisfies the following constraint formula:

[0078] Equation (14): (A + BNK)Q + Q(A + BNK) T + LL T = 0;

[0079] Equation (15):

[0080] Use the Lagrange multiplier method to solve the optimization problem with constraints in Equations (13) to (15). For any symmetric matrix R and real number λ, (N, Q, R, λ) satisfies the following requirements:

[0081] Equation (16):

[0082] Compared with the related art, the beneficial effects of the present invention are as follows: By establishing a 1 / 4 two-degree-of-freedom active suspension system model considering multiple non-linear links, processing it into an active suspension system model with time delay, using integral state variation to handle the time-delay characteristics, and describing the saturation non-linear characteristics by the stochastic linearization method, the active suspension system model with time delay is processed into the active suspension quasi-linear system model. Combining the Lagrange multiplier method, the constrained optimization problem composed of the Riccati equation, the Lyapunov equation and the transcendental equation is derived, and the feedback gain K and the feedback control rate are obtained by using the bisection method. It not only solves the non-linear problem of the inherent components, but also considers the network non-linear problem, improves the control accuracy and the stability of the system. At the same time, because this method is simple to reproduce, it is easy to implement in actual work.

[0083] Details of one or more embodiments of the present application are set forth in the following drawings and description to make other features, objects, and advantages of the present application more concise and understandable. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments and descriptions thereof of the present application are used to explain the present application and do not constitute an improper limitation of the present application. In the drawings:

[0085] Figure 1 is a flowchart of the active suspension control method in the first embodiment of the present invention;

[0086] Figure 2 is a schematic diagram of the active suspension system model in the active suspension control method in the first embodiment of the present invention;

[0087] Figure 3 is a schematic diagram of the simulation result of the active suspension control method in the first embodiment of the present invention;

[0088] Figure 4 is a schematic diagram of the active suspension system model in the active suspension control method in the second embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0089] In order to make the purpose, technical solutions and advantages of the present application more clear and understandable, the present application will be described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application. Based on the embodiments provided in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present application.

[0090] Obviously, the accompanying drawings in the following description are only some examples or embodiments of the present application. For those of ordinary skill in the art, without creative efforts, the present application can also be applied to other similar scenarios based on these drawings. In addition, it can also be understood that although the efforts made in such a development process may be complex and lengthy, for those of ordinary skill in the art related to the content disclosed in the present application, some definitions, manufacturing or production changes based on the technical content disclosed in the present application are only conventional technical means and should not be understood as the content disclosed in the present application being insufficient.

[0091] As used in this application, the mention of "embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the present application. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It is explicitly and implicitly understood by those of ordinary skill in the art that the embodiments described in the present application can be combined with other embodiments without conflict.

[0092] Unless otherwise defined, the technical terms or scientific terms involved in this application should have the ordinary meaning understood by those of ordinary skill in the technical field to which this application belongs. The words such as "a", "an", "one", "the" and the like involved in this application do not indicate a quantity limitation and can represent a singular or plural number. The terms "including", "comprising", "having" and any variations thereof involved in this application are intended to cover non-exclusive inclusion; for example, a process, method, system, product or device including a series of steps or modules (units) is not limited to the listed steps or units, but may further include unlisted steps or units, or may further include other steps or units inherent to these processes, methods, products or devices. The terms "connected", "coupled" and the like involved in this application are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The "plurality" involved in this application means two or more. "And / or" describes the association relationship of associated objects and indicates that three relationships can exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally represents an "or" relationship between the associated objects before and after. The terms "first", "second", "third", etc. involved in this application are only used to distinguish similar objects and do not represent a specific order for the objects.

[0093] Please refer to Figure 1 , the main control suspension control method provided by the first embodiment of the present invention. In this embodiment, the active suspension control method takes into account time-delay nonlinearity and saturation nonlinearity. The method includes steps S10 to S30:

[0094] Step S10: According to the established dynamic model considering the multi - variable non - linear active suspension, construct the state - space equation of the model state to obtain the active suspension system model;

[0095] Please refer to Figure 2 , specifically, the step S10 includes:

[0096] Step S11: According to Newton's second law, list the dynamic equation of the non - linear active suspension at any time t:

[0097] Equation (1):

[0098] In Equation (1): z r , z us , z s are the vertical displacements of the ground, tire, and vehicle body respectively, and the origin of the vertical displacement coordinate is taken at the static equilibrium position; k s , k us are the suspension spring stiffness and tire stiffness; m s , m us are the sprung mass and unsprung mass respectively; c s , c us are the inherent damping coefficients of the suspension and tire respectively; F c represents the power output of the active suspension considering multi - variable non - linear links;

[0099] Step S12: Select the state variable x as: Take the road surface input z as the system output variable. Therefore, rewrite Equation (1) into the following state - space expression:

[0100] Equation (2):

[0101] In the formula:

[0102] C = I4,

[0103] Step S20: Linearize the multi - variable non - linear links in the active suspension system model to obtain the corresponding quasi - linear active suspension system model;

[0104] Specifically, the step 20 includes:

[0105] Step S21: Use the integral state transformation to construct the active suspension system model with implicit time - delay;

[0106] At time t, for the active suspension system model with a time - delay of τ, only considering the time - delay link, the Fc Constructed as:

[0107] Equation (3A): F c = u(t - τ);

[0108] Substitute Equation (3A) into Equation (2). Assuming there is no interference, that is, when w(t) = 0, the active suspension system model can be written as:

[0109] Equation (4):

[0110] Select the feedback rate with control memory as:

[0111] Equation (5):

[0112] where r represents the integral variable of the feedback control rate of the active suspension system model with the implicit time delay.

[0113] The control gain K in Equation (5) makes the active suspension system asymptotically stable;

[0114] Introduce the integral state transformation:

[0115] Equation (6):

[0116] Therefore, transform the active suspension system model with the time delay quantity into the active suspension system model with the implicit time delay:

[0117] Equation (7):

[0118] In Equation (7): x0 is x(0), that is, the initial value.

[0119] Substitute Equation (6) into Equation (5), and it can be found that there is an equivalent relationship between the selected feedback rate with control memory Equation (5) of the active suspension system model Equation (4) and the control rate of the active suspension system model with the implicit time delay Equation (7):

[0120] Equation (8): u(+) = Ky(t);

[0121] Therefore, the undetermined control gain K in Equation (5) can be determined by Equation (7).

[0122] Step S22: Adopt the stochastic linearization method, and replace the saturation nonlinear link in the active suspension system model with the implicit time delay with a constant gain to construct an active suspension quasi-linear system model.

[0123] Construct the saturation nonlinear link in the active suspension system model with the implicit time delay as:

[0124] Equation (9A):

[0125] In Equation (9A), ±a is the saturation limit critical point, β is the slope of the linear range, and u is the theoretical output of the actuator as power.

[0126] Using the stochastic linearization method, the saturated nonlinear link is replaced with the first linear time-invariant element to minimize the mean square error between the outputs of the two systems. The power u of the nonlinear active suspension is a zero-mean wide-sense stationary Gaussian process with a variance of The first linear time-invariant element can be represented by a constant gain value N, that is, the first linear time-invariant element is constructed as:

[0127] Equation (10A):

[0128] In Equation (10A), σ u is the standard deviation of the power u of the active suspension; erf(·) is the error function, defined as;

[0129]

[0130] where m represents the integration range of the error function; exp represents the exponential function with the natural constant e as the base.

[0131] Combining Equation (7) and Equation (10A), the active suspension system model with implicit time delay is simplified to the active suspension quasi-linear system model:

[0132] Equation (11):

[0133] In Equation (11), is the estimated value of y(t0, z, u) in Equations (7) and (8).

[0134] Step S30: Optimize the active suspension quasi-linear system model by the Lagrange multiplier method, and solve it by the bisection method to obtain the feedback gain K considering the multi-variable nonlinear active suspension and the feedback control rate considering the multi-variable nonlinear active suspension;

[0135] Specifically, Step S30 includes:

[0136] Step S31: Adopt optimal control to construct an optimization problem with constraints in the active suspension quasi-linear system model, and solve the optimization problem with constraints by the Lagrange multiplier method.

[0137] For Equation (11), the active suspension not only considers the output index but also needs to consider the energy consumption problem.

[0138] For any given ρ > 0, find the optimal gain K to minimize Equation (12):

[0139] Equation (12):

[0140] In Equation (12), it means finding the optimal gain K to minimize the above index, ρ represents the weight considering energy consumption, and σ z is the standard deviation of the output variable z of the active suspension control system;

[0141] For all cases of the optimal gain K, take the minimum value to make A + BNK a Hurwitz matrix. Therefore, Equation (12) is transformed into the optimization problem with constraints:

[0142] Equation (13):

[0143] where (N, Q) satisfies the following constraint formula:

[0144] Equation (14): (A + BNK)Q + Q(A + BNK) T + LL T = 0;

[0145] Equation (15):

[0146] In Equation (13), Q is the positive definite solution of the Riccati equation in Equation (14); and N should satisfy Equation (15); R is a positive definite matrix satisfying the Lyapunov equation.

[0147] Using the Lagrange multiplier method, introducing a new parameter λ (λ is the Lagrange multiplier), the constraint condition function and the optimization equation in the optimization problem with constraints are related together to form an equation equal to the number of variables, so as to find the solutions of each variable in the optimal problem with constraints.

[0148] Using the Lagrange multiplier method to solve the optimization problem with constraints in Equations (13) to (15), for any symmetric matrix R and real number λ, (N, Q, R, λ) satisfies the following requirements:

[0149] Equation (16):

[0150] Step S32: Solve through the bisection method to obtain the feedback gain K considering the multi - variable non - linear active suspension and the feedback control rate considering the multi - variable non - linear active suspension.

[0151] Adopt the bisection method algorithm to solve Equation (16) to obtain the optimal gain K;

[0152] Equation (17):

[0153] If R is non - singular, then the state - feedback control gain K is unique.

[0154] Substitute the obtained optimal gain K into Equation (5) to obtain the feedback control law.

[0155] Please refer to Figure 3 , set the optimal controller that completely ignores the non - linear link (i.e., uses a linear - quadratic optimal controller) as Controller I, and set the optimal controller designed in the present invention that comprehensively considers the non - linear link as Controller II. The time - delay τ = 0.1 s, the saturation is taken as 100%, and other non - linearities are not considered. By establishing a 1 / 4 two - degree - of - freedom active suspension system model considering multiple non - linear links, it is processed into an active suspension system model with time - delay. The integral state change is used to process the time - delay characteristics, and the stochastic linearization method is used to describe the saturation non - linear characteristics. The active suspension system model with time - delay is processed into the active suspension quasi - linear system model. Combining the Lagrange multiplier method, the constrained optimization problem composed of the Riccati equation, Lyapunov equation, and transcendental equation is derived. The feedback gain K and the feedback control law are obtained by using the bisection method. It not only solves the non - linear problem of the inherent components but also considers the network non - linear problem, improves the control accuracy and system stability. At the same time, because this method is simple to reproduce, it is easy to implement in actual work.

[0156] Please refer to Figure 4 , the active suspension control method provided by the second embodiment of the present invention. The active suspension control method in this embodiment considers time - delay non - linearity, packet - loss non - linearity, dead - zone non - linearity, and saturation non - linearity, and includes the following steps:

[0157] Step S100: According to the established dynamic model of the multi - non - linear active suspension, construct the state - space equation of the model to obtain the active suspension system model;

[0158] Specifically, step S100 includes:

[0159] Step S101: According to Newton's second law, list the dynamic equation of the non - linear active suspension at any time t:

[0160] Equation (1):

[0161] In Equation (1): z r , z us , z s are the vertical displacements of the ground, tire, and vehicle body respectively, and the origin of the vertical displacement coordinate is taken at the static equilibrium position; k s , k us are the suspension spring stiffness and tire stiffness; m s , m usThey are the sprung mass and the unsprung mass respectively; c s 、c us They are the natural damping coefficients of the suspension and the tire respectively; F c It represents the power output of the active suspension considering the multi - variable non - linear link;

[0162] Step S102: Select the state variable x as: Take the road surface input z as the system output variable. Therefore, rewrite Equation (1) into the following state - space expression:

[0163] Equation (2):

[0164] In the formula:

[0165] C = I4,

[0166] Step S200: Linearize the multi - variable non - linear link in the active suspension system model to obtain the corresponding quasi - linear system model of the active suspension;

[0167] Specifically, the step S200 includes:

[0168] Step S201: Based on the variable - time - delay system method, deal with the packet - loss non - linearity. Using the integral state transformation, construct the active suspension system model into an active suspension system model with implicit time - delay;

[0169] Network congestion, network access competition, and network transmission errors cause data packet loss, making the active control system unable to receive network transmission information in time. For the packet - loss and time - delay processing methods, simplify the active suspension system model into a system model with a certain continuous packet - loss rate;

[0170] Based on the variable - time - delay method, process the system model with a certain continuous packet - loss rate into an active suspension system model with time - delay;

[0171] At time t, replace the packet - loss non - linearity with an equivalent time - delay quantity Construct the F c as:

[0172] Equation (3B):

[0173] Assume that under the condition of no interference, that is, when w(t)=0, the active suspension system model can be written as:

[0174] Equation (4):

[0175] Select the feedback rate with control memory as:

[0176] Equation (5):

[0177] In Equation (5), the control gain K makes the active suspension system asymptotically stable;

[0178] Introduce an integral state transformation to transform the active suspension system model with time delay into the active suspension system model with implicit time delay:

[0179] Equation (7):

[0180] In Equation (7): x0 is x(0), that is, the initial value.

[0181] Step S202: Adopt the stochastic linearization method, and replace the saturation nonlinear link and the dead zone nonlinear link in the active suspension system model with implicit time delay with a constant gain to construct an active suspension quasi-linear system model

[0182] Considering the saturation and dead zone characteristics, construct the saturation nonlinear link in the active suspension system model with implicit time delay as:

[0183] Equation (9B):

[0184] In Equation (9B), ±a is the saturation limit critical point, β is the slope of the linear range, b is the symmetric dead zone bandwidth, and u is the theoretical output of the actuator driving force;

[0185] Adopt the stochastic linearization method, and replace the saturation nonlinear link and the dead zone nonlinear link with a second linear constant element, and the second linear constant element is constructed as:

[0186] Equation (10B):

[0187] In Equation (10B), σ u is the standard deviation of the active suspension driving force u; erf(·) is the error function, defined as:

[0188]

[0189] where m represents the integration range of the error function; exp represents the exponential function with the natural constant e as the base.

[0190] Combining Equation (7) and Equation (10B), simplify the active suspension system model with implicit time delay to the active suspension quasi-linear system model:

[0191] Equation (11):

[0192] Step S300: Optimize the quasi-linear system model of the active suspension by the Lagrange multiplier method, and solve it by the bisection method to obtain the feedback gain K considering the multi-variable non-linear active suspension and the feedback control rate considering the multi-variable non-linear active suspension;

[0193] Step S301: Adopt optimal control to construct an optimization problem with constraints in the quasi-linear system model of the active suspension, and solve the optimization problem with constraints by the Lagrange multiplier method.

[0194] For Equation (11), the active suspension not only considers the output index but also the energy consumption problem.

[0195] For any given ρ > 0, find the optimal gain K to minimize Equation (12):

[0196] Equation (12):

[0197] In Equation (12), means finding the optimal gain K to minimize the above index, ρ represents the weight considering energy consumption, and σ z is the standard deviation of the output variable z of the active suspension control system;

[0198] For all cases of the optimal gain K, take the minimum value to make A + BNK a Hurwitz matrix. Therefore, Equation (12) is transformed into the optimization problem with constraints:

[0199] Equation (13):

[0200] Among them, (N, Q) satisfies the following constraint formula:

[0201] Equation (14): (A + BNK)Q + Q(A + BNK) T + LL T = 0;

[0202] Equation (15):

[0203] Using the Lagrange multiplier method, introduce a new parameter λ (λ is the Lagrange multiplier), connect the constraint condition function and the optimization equation in the optimization problem with constraints, so that an equation equal to the number of variables can be formed, and then find the solutions of each variable in the optimal problem with constraints.

[0204] Using the Lagrange multiplier method to solve the optimization problem with constraints in Equations (13) to (15), for any symmetric matrix R and real number λ, (N, Q, R, λ) satisfy the following requirements:

[0205] Equation (16):

[0206] Step S302: Solve through the bisection method to obtain the feedback gain K considering the multi-variable non-linear active suspension and the feedback control law considering the multi-variable non-linear active suspension.

[0207] Use the bisection algorithm to solve Equation (16) to obtain the optimal gain K.

[0208] Equation (17):

[0209] If R is non-singular, the state feedback control gain K is unique.

[0210] Substitute the obtained optimal gain K into Equation (5) to obtain the feedback control law.

[0211] The present invention also provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements the active suspension control method described in the above technical solution.

[0212] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the active suspension control method described in the above technical solution.

[0213] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0214] The above embodiments only represent several implementation manners of the present application. The description is relatively specific and detailed, but it cannot be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. An active suspension control method, characterized in that, It includes the following steps: According to the established dynamic model considering the multi - variable non - linear active suspension, construct the state - space equation of the model state to obtain the active suspension system model; The step of constructing the state - space equation of the model state according to the established dynamic model considering the multi - variable non - linear active suspension to obtain the active suspension system model includes: According to Newton's second law, list the dynamic model of the non - linear active suspension at any time t; Select the state variable x and the road surface input w, and rewrite the dynamic model of the non - linear active suspension as the state - space equation of the model state according to the state variable x and the road surface input w; The dynamic model of the non - linear active suspension is: Equation (1): In Equation (1): z r , z us , z s are the vertical displacements of the ground, the tire, and the vehicle body, respectively, and the origin of the vertical displacement coordinate is taken at the static equilibrium position; k s , k us are the suspension spring stiffness and the tire stiffness; m s , m us are the sprung mass and the unsprung mass, respectively; c s , c us are the natural damping coefficients of the suspension and the tire, respectively; F c represents the active suspension power output considering the multi-element non-linear link; The state - space equation of the model state is: Equation (2): In the formula: C = I4, Linearize the multi - variable non - linear link in the active suspension system model to obtain the corresponding quasi - linear active suspension system model; The step of linearizing the multi - variable non - linear link in the active suspension system model to obtain the corresponding quasi - linear active suspension system model includes: Use integral state transformation to construct the active suspension system model into an active suspension system model with implicit time - delay; The step of using integral state transformation to construct the active suspension system model into an active suspension system model with implicit time - delay includes: At time t, for the active suspension system model with a time delay of τ, when only considering the time delay link, the F c is constructed as: Equation (3A): F c = u(t - τ); When w(t)=0, the active suspension system model can be written as: Equation (4): Select the feedback rate with control memory as: Equation (5): The control gain K in formula (5) makes the active suspension system asymptotically stable; Introduce integral state transformation to transform the active suspension system model with time - delay into the active suspension system model with implicit time - delay: Equation (7): In formula (7): x0 is x(0), that is, the initial value; Adopt the stochastic linearization method, replace the saturation non - linear link in the active suspension system model with implicit time - delay with a constant gain to construct a quasi - linear active suspension system model; Optimize the quasi - linear active suspension system model by the Lagrange multiplier method, and solve by the bisection method to obtain the feedback gain K considering the multi - variable non - linear active suspension and the feedback control rate considering the multi - variable non - linear active suspension.

2. The active suspension control method according to claim 1, characterized in that, The step of adopting the stochastic linearization method, replacing the saturation non - linear link in the active suspension system model with implicit time - delay with a constant gain to construct a quasi - linear active suspension system model includes: Construct the saturation non - linear link in the active suspension system model with implicit time - delay as: Equation (9A): In formula (9A), ±a is the saturation limit critical point, β is the slope of the linear range, and u is the theoretical output of the actuator; Adopt the stochastic linearization method, replace the saturation non - linear link with the first linear constant element, and the first linear constant element is constructed as: Formula (10A): In formula (10A), σ u is the standard deviation of the active suspension actuation force u; erf(·) is the error function; Combined with formula (7) and formula (10A), simplify the active suspension system model with implicit time - delay into the quasi - linear active suspension system model: Equation (11):

3. The active suspension control method according to claim 1, wherein The step of linearizing the multi - variable non - linear link in the active suspension system model to obtain the corresponding quasi - linear active suspension system model includes: Based on the variable time-delay system method, deal with the packet loss non-linearity, and use the integral state transformation to construct the active suspension system model into an active suspension system model with implicit time-delay; Adopt the stochastic linearization method, and replace the saturation non-linear link and the dead zone non-linear link in the active suspension system model with implicit time-delay with a constant gain to construct an active suspension quasi-linear system model.

4. The active suspension control method according to claim 3, wherein The steps of the method based on the variable time-delay system, dealing with the packet loss non-linearity, and using the integral state transformation to construct the active suspension system model into an active suspension system model with implicit time-delay include: Simplify the active suspension system model into a system model with a certain continuous packet loss rate; Based on the variable time-delay method, process the system model with a certain continuous packet loss rate into an active suspension system model with time-delay; At time t, the packet loss is non-linearly replaced with an equivalent time delay The F c is constructed as: Formula (3B): When w(t)=0, the active suspension system model can be written as: Equation (4): Select the feedback rate with control memory as: Equation (5): The control gain K in Equation (5) makes the active suspension system asymptotically stable; Introduce the integral state transformation to transform the active suspension system model with time-delay into the active suspension system model with implicit time-delay: Equation (7): In Equation (7): x0 is x(0), that is, the initial value.

5. The active suspension control method according to claim 4, wherein The steps of the method of adopting the stochastic linearization method, replacing the saturation non-linear link and the dead zone non-linear link in the active suspension system model with implicit time-delay with a constant gain to construct an active suspension quasi-linear system model include: Construct the saturation non-linear link in the active suspension system model with implicit time-delay as: Formula (9B): In Equation (9B), ±a is the saturation limit critical point, β is the slope of the linear range, b is the symmetric dead zone bandwidth, and u is the theoretical output of the actuator driving force; Adopt the stochastic linearization method, and replace the saturation non-linear link and the dead zone non-linear link with a second linear time-invariant element, and the second linear time-invariant element is constructed as: Equation (10B): In Equation (10B), σ u is the standard deviation of the active suspension actuation force u; erf(·) is the error function; Combining Equation (7) and Equation (10B), simplify the active suspension system model with implicit time-delay into the active suspension quasi-linear system model: Equation (11):

6. The active suspension control method according to claim 2 or 5, wherein The steps of optimizing the active suspension quasi-linear system model by the Lagrange multiplier method and solving by the bisection method to obtain the feedback gain K of the multi-variable non-linear active suspension and the feedback control rate of the multi-variable non-linear active suspension include: Adopt optimal control to construct an optimization problem with constraints in the active suspension quasi-linear system model, and solve the optimization problem with constraints by the Lagrange multiplier method; Solve by the bisection method to obtain the feedback gain K of the multi-variable non-linear active suspension and the feedback control rate of the multi-variable non-linear active suspension.

7. The active suspension control method according to claim 6, wherein The steps of adopting optimal control to construct an optimization problem with constraints in the active suspension quasi-linear system model and solving the optimization problem with constraints by the Lagrange multiplier method include: For any given ρ>0, find the optimal feedback gain K to minimize Equation (12): Equation (12): In Equation (12), ρ represents the weight considering energy consumption, and σ z is the standard deviation of the output variable z of the active suspension control system; For all cases of the optimal feedback gain K, take the minimum value to make A + BNK a Hurwitz matrix, and transform Equation (12) into the optimization problem with constraints: Equation (13): Among them, (N, Q) satisfies the following constraint formula: Equation (14): (A + BNK)Q + Q(A + BNK) T + LL T = 0; Equation (15): Use the Lagrange multiplier method to solve the constrained optimization problem described by equations (13) to (15). For any symmetric matrix R and real number λ, (N, Q, R, λ) satisfies the following requirements: Equation (16):

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