Nonlinear tracking control method and device based on automobile air active suspension system
By designing a nonlinear tracking control method and device, the problem of traditional control methods being unable to adjust the active air suspension system was solved, achieving rapid response and stable control of the suspension system, and improving the ride comfort and handling stability of the vehicle.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- GUANGZHOU UNIVERSITY
- Filing Date
- 2023-07-12
- Publication Date
- 2026-05-19
AI Technical Summary
Traditional control methods such as PID control are difficult to effectively adjust the nonlinear characteristics of automotive active air suspension systems, making it difficult for the suspension performance to simultaneously meet the requirements of ride comfort and safety.
A nonlinear tracking control method based on an active air suspension system for automobiles is designed. By acquiring the suspension model, a vehicle height tracking controller is designed, and stability and zero-dynamic analysis are performed. Lyapunov functions and virtual control inputs are used to achieve fast response and stable control of vehicle height.
It achieves good tracking control of the suspension system, overcomes the problem of parameter uncertainty, and improves the ride comfort and handling stability of the suspension system. Compared with the traditional fuzzy PID control algorithm, it has a faster response and greater stability.
Smart Images
Figure CN116787983B_ABST
Abstract
Description
Technical Field
[0001] This document relates to the field of vehicle tracking control technology, and in particular to a nonlinear tracking control method and device based on an active air suspension system for automobiles. Background Technology
[0002] The suspension system of a car plays a decisive role in improving vehicle handling safety and ride comfort. However, a contradictory problem exists in traditional suspension design: the suspension effect needs to simultaneously satisfy both ride comfort and safety. Therefore, new controllable active suspension systems are the main means to resolve this contradiction.
[0003] New controllable active suspension systems require intelligent control systems to effectively adjust parameters such as stiffness, damping, and height, thereby improving ride comfort and smoothness, and ensuring high handling stability during steering and braking to guarantee driving safety. However, due to the complex structure and nonlinear characteristics of automotive air active suspensions, traditional PID control methods are difficult to achieve satisfactory results. Therefore, designing nonlinear tracking control algorithms specifically for active suspension systems is essential. Summary of the Invention
[0004] This invention provides a nonlinear tracking control method and device based on an automotive active air suspension system, aiming to solve the above-mentioned problems.
[0005] This invention provides a nonlinear tracking control method based on an automotive active air suspension system, comprising:
[0006] Obtain an active air suspension model, and design a vehicle height tracking controller for the suspension system based on the active air suspension model;
[0007] Stability analysis of the vehicle height tracking controller;
[0008] Zero-dynamic analysis was performed on the vehicle height tracking controller.
[0009] This invention provides a nonlinear tracking control device based on an automotive active air suspension system, comprising:
[0010] The vehicle height tracking controller module is used to acquire the air active suspension model and design the vehicle height tracking controller of the suspension system based on the air active suspension model.
[0011] The stability module is used for stability analysis of the vehicle height tracking controller;
[0012] The zero-dynamic module is used to perform zero-dynamic analysis on the vehicle height tracking controller.
[0013] By employing the nonlinear tracking control method and system based on an active air suspension system of this invention, a good tracking control effect can be achieved, while overcoming the parameter uncertainty problem in the tracking control of nonlinear systems. Compared with traditional PID control, the fuzzy PID control algorithm can more effectively achieve rapid response and stable control of the active air suspension vehicle height adjustment, thereby improving ride comfort. Attached Figure Description
[0014] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0015] Figure 1 This is a flowchart of a nonlinear tracking control method based on an active air suspension system for automobiles, according to an embodiment of the present invention.
[0016] Figure 2 This is a schematic diagram of a nonlinear tracking control device based on an active air suspension system for automobiles, according to an embodiment of the present invention.
[0017] Figure 3 This is a schematic diagram of an active air suspension model;
[0018] Figure 4 A schematic diagram of the vehicle height tracking process under the action of the designed controller when tracking a sinusoidal signal;
[0019] Figure 5 To track the control input change curve during the vehicle height adjustment process under the action of the designed controller when tracking a sinusoidal signal;
[0020] Figure 6 To track a sinusoidal signal, the error e1 variation curve during the vehicle height adjustment process under the action of the designed controller;
[0021] Figure 7 To track a sinusoidal signal, the error e2 variation curve during the vehicle height adjustment process under the action of the designed controller;
[0022] Figure 8 To track a sinusoidal signal, the error e3 variation curve during the vehicle height adjustment process under the action of the designed controller;
[0023] Figure 9 When the vehicle height is adjusted under the action of the designed controller to track a sinusoidal signal, the vehicle height tracking process is as follows: when the three uncertain external disturbances F1, F2, and F3 change abruptly at t=25.
[0024] Figure 10 The vehicle height tracking process under the action of the designed controller when tracking a constant signal;
[0025] Figure 11 To track the error e1 variation curve during the vehicle height adjustment process under the action of the designed controller when tracking a constant signal;
[0026] Figure 12 To track the error e2 variation curve during the vehicle height adjustment process under the action of the designed controller when tracking a constant signal;
[0027] Figure 13 To track the error e3 variation curve during the vehicle height adjustment process under the action of the designed controller when tracking a constant signal;
[0028] Figure 14 To track the vehicle speed change curve during the vehicle height adjustment process under the action of the designed controller when a constant signal is applied;
[0029] Figure 15 To track the vehicle body acceleration change curve during the vehicle height adjustment process under the action of the designed controller when a constant signal is applied;
[0030] Figure 16 This example illustrates the vehicle height tracking process under different controllers when tracking a constant signal, as mentioned in the implementation example.
[0031] Figure 17 To track the vehicle speed change curve during the vehicle height adjustment process under different controllers when the signal is constant;
[0032] Figure 18 To track the vehicle body acceleration change curve during the vehicle height adjustment process under different controllers when the signal is constant. Detailed Implementation
[0033] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.
[0034] Method Implementation Examples
[0035] According to an embodiment of the present invention, a nonlinear tracking control method based on an automotive active air suspension system is provided. Figure 1 This is a flowchart of a nonlinear tracking control method based on an active air suspension system for automobiles, according to an embodiment of the present invention. Figure 1 As shown, the nonlinear tracking control method based on an active air suspension system for automobiles according to an embodiment of the present invention includes:
[0036] S1. Obtain the air active suspension model, and design the vehicle height tracking controller of the suspension system based on the air active suspension model;
[0037] Specifically, Figure 3 The diagram shows the active air suspension model, which is obtained using formula (1):
[0038]
[0039]
[0040]
[0041]
[0042]
[0043] Formula (1) is the state equation of the air active suspension model referenced in the controller design, where x1 = z s This represents the vertical displacement of the vehicle body. F1, F2, and F3 are three uncertain parameters, z r The vertical input signal is u = Q, representing the air mass flow rate through the solenoid valve, which determines the inflation and deflation process of the air spring and serves as the control input for the controller. Therefore, the control problem can be described as: designing a controller u such that x1 tracks its reference value x. 1d .
[0044] Based on the active air suspension model described by formula (1), the specific design of the suspension height adjustment control algorithm is carried out. The design process is divided into the following 4 sub-steps:
[0045] Step 1
[0046] Define the error variable as Among them, F i Due to uncertain external disturbances, These are estimated values, i = 1, 2, 3;
[0047] Let e1 = x1 - x 1d e2 = x2 - x 2d , where x 2d For virtual control input, x 1d Using the reference value tracked by x1, the dynamic vehicle height tracking error is obtained as follows:
[0048]
[0049] Virtual control input x 2d for:
[0050]
[0051] Then the error dynamics of e1 can be obtained as follows:
[0052]
[0053] Figure 6 To track the error e1 variation curve during the vehicle height adjustment process under the action of the designed controller when a sinusoidal signal is applied, Figure 11 The error e1 variation curve during the vehicle height adjustment process under the action of the designed controller is used to track a constant signal.
[0054] Take Lyapunov function Then there is
[0055]
[0056] Step 2
[0057] Let e3 = x6 - x 6d , where x 6d If the input is a virtual control input, then the dynamic error of e2 is:
[0058]
[0059] Virtual control input x 6d for:
[0060]
[0061] Then the error dynamics of e2 can be obtained as follows:
[0062]
[0063] Figure 7 To track the error e2 variation curve during the vehicle height adjustment process under the action of the designed controller when a sinusoidal signal is applied, Figure 12 To track the error e2 variation curve during the vehicle height adjustment process under the action of the designed controller when tracking a constant signal;
[0064] Take Lyapunov function Then there is
[0065]
[0066] Step 3
[0067] The dynamic representation of e3 is:
[0068]
[0069] set up
[0070]
[0071]
[0072]
[0073] The vehicle height tracking controller is designed as follows:
[0074]
[0075] Then the error dynamics of e3 can be obtained as follows:
[0076]
[0077] Figure 8 To track the error e3 variation curve during the vehicle height adjustment process under the action of the designed controller when a sinusoidal signal is applied, Figure 13 To track the error e3 variation curve during the vehicle height adjustment process under the action of the designed controller when tracking a constant signal;
[0078] Take Lyapunov function Then there is
[0079]
[0080] Step 4
[0081] make We can obtain:
[0082]
[0083]
[0084]
[0085] Right now:
[0086]
[0087]
[0088]
[0089] Formula (12) is the designed vehicle height tracking controller.
[0090] Figure 9When the vehicle height is adjusted under the control of the designed controller to track a sinusoidal signal, the vehicle height tracking process is as follows: when the three uncertain external disturbances F1, F2, and F3 change abruptly at t=25.
[0091] S2. Perform stability analysis on the vehicle height tracking controller;
[0092] Step S2 specifically includes: For the final Lyapunov function of the controller, we have:
[0093]
[0094]
[0095] This shows that V3 is positive definite. It is semi-negative definite, which shows that the equilibrium state is stable in the Lyapunov sense, so e1, e2, e3, They are all bounded.
[0096] set up
[0097] W(t) = e1 2 +e2 2 +e3 2 ≥0 (23)
[0098] Then there is
[0099]
[0100] Because e1, e2, e3, They are all bounded, therefore Since it is bounded, W(t) is uniformly continuous.
[0101] According to the Lyapunov class lemma, it can be proved that when t→∞, W(t)→0, and at this time e1,e2,e3→0. Thus, it can be seen that the controller can meet the requirements and realize the vehicle height tracking function.
[0102] S3. Perform zero-dynamic analysis on the vehicle height tracking controller.
[0103] Step S3 specifically includes:
[0104] As t→∞, e1, e2, e3→0, therefore x1→x 1d x2→x 2d (x6→) 6d Therefore, from formulas (3), (7), and (18), it can be seen that when the reference signal x 1d , When bounded, x1, x2, x6 are bounded.
[0105]
[0106]
[0107]
[0108]
[0109] Next, we analyze x3 and x4. From formula (25), we can derive formula (26). When e1, e2, e3 → 0, formula (26) can be transformed into formula (27), and its characteristic equation is:
[0110]
[0111] By c w >0,m w >0,k w >0 can be obtained and That is, all coefficients of the characteristic equation of the second-order zero-dynamic system are positive, therefore the zero-dynamic system is stable. When the road surface vertical input z... r , Reference signal And when the uncertainty F3 is bounded, x3 and x4 are bounded.
[0112] This embodiment designs simulation operation parameters and corresponding controller control parameters based on a reference air active suspension model. The effectiveness of the algorithm is verified through simulations under sinusoidal and constant signal conditions. Furthermore, the superiority of the controller is verified through comparative simulations. The designed simulation operation parameters and controller control parameters are shown in Table 1.
[0113] Table 1. Simulation operation parameters and controller control parameters
[0114]
[0115] The selection of control parameters is shown in Table 2:
[0116] Table 2 Selection of Control Parameters
[0117]
[0118] Figures 3 to 18All figures are simulation curves. According to the simulation curves, the nonlinear tracking control algorithm designed in this embodiment can achieve good trajectory tracking, enabling the suspension system to perform vehicle height adjustment, and overcoming a certain degree of parameter uncertainty. Furthermore, compared with the traditional fuzzy PID control algorithm, the nonlinear controller designed in this embodiment tracks more quickly, ensures the error stabilizes to zero, and allows the vehicle body to maintain lower acceleration and speed during tracking, which helps ensure superior vehicle ride comfort. Therefore, our designed controller has superior performance.
[0119] Device Examples
[0120] According to an embodiment of the present invention, a nonlinear tracking control device based on an automotive active air suspension system is provided. Figure 2 This is a schematic diagram of a nonlinear tracking control device based on an active air suspension system for automobiles, according to an embodiment of the present invention. Figure 2 As shown, the nonlinear tracking control device based on an active air suspension system for automobiles according to an embodiment of the present invention includes:
[0121] The vehicle height tracking controller module 20 is used to acquire the air active suspension model and design the vehicle height tracking controller of the suspension system based on the air active suspension model.
[0122] Stability module 22 is used to perform stability analysis on the vehicle height tracking controller;
[0123] Zero-dynamic module 24 is used to perform zero-dynamic analysis on the vehicle height tracking controller.
[0124] Specifically, the vehicle height control tracking controller module 20, used to acquire the air active suspension model, includes:
[0125]
[0126]
[0127]
[0128]
[0129]
[0130] Where, x1=z s This represents the vertical displacement of the vehicle body. F1, F2, and F3 are three uncertain parameters, z r The vertical input signal is u = Q, which represents the mass flow rate of air passing through the solenoid valve. This determines the inflation and deflation process of the air spring and serves as the control input for the controller.
[0131] Specifically, the vehicle height tracking controller module 20, designed based on the air active suspension model, includes the following vehicle height tracking controller for the suspension system:
[0132] Define the error variable as Among them, F i Due to uncertain external disturbances, These are estimated values, i = 1, 2, 3;
[0133] Let e1 = x1 - x 1d e2 = x2 - x 2d , where x 2d For virtual control input, x 1d Using the reference value tracked by x1, the dynamic vehicle height tracking error is obtained as follows:
[0134]
[0135] Virtual control input x 2d for:
[0136]
[0137] Then the error dynamics of e1 can be obtained as follows:
[0138]
[0139] Take Lyapunov function Then there is
[0140]
[0141] Let e3 = x6 - x 6d , where x 6d If the input is a virtual control input, then the dynamic error of e2 is:
[0142]
[0143] Virtual control input x 6d for:
[0144]
[0145] Then the error dynamics of e2 can be obtained as follows:
[0146]
[0147] Take Lyapunov function Then there is
[0148]
[0149] The dynamic representation of e3 is:
[0150]
[0151] set up
[0152]
[0153]
[0154]
[0155] The vehicle height tracking controller is designed as follows:
[0156]
[0157] Then the error dynamics of e3 can be obtained as follows:
[0158]
[0159] Take Lyapunov function Then there is
[0160]
[0161] make We can obtain:
[0162]
[0163]
[0164]
[0165] Right now:
[0166]
[0167]
[0168]
[0169] Specifically, stability module 22 is used for:
[0170] Obtain the final Lyapunov function of the controller:
[0171]
[0172]
[0173] Among them, V3 is positive definite. It is semi-negative definite, therefore the equilibrium state is stable in the Lyapunov sense, so e1, e2, e3, They are all bounded.
[0174] set up
[0175] W(t) = e1 2 +e2 2 +e3 2 ≥0 (23)
[0176] Then there is
[0177]
[0178] Because e1, e2, e3, They are all bounded, therefore Since it is bounded, W(t) is uniformly continuous. According to the Lyapunov class lemma, it can be proved that when t→∞, W(t)→0, and at this time e1,e2,e3→0. Therefore, the vehicle height tracking controller can realize the vehicle height tracking function.
[0179] Specifically, the zero dynamic module 24 is used for:
[0180] Therefore, from formulas (3), (7), and (18), it can be seen that when the reference signal x 1d , When bounded, x1, x2, x6 are bounded;
[0181]
[0182]
[0183]
[0184]
[0185] Formula (26) is derived from formula (25). When e1, e2, e3 → 0, formula (26) becomes formula (27), and its characteristic equation is:
[0186]
[0187] By c w >0, m w >0, k w >0 can be obtained and That is, all coefficients of the characteristic equation of the second-order zero-dynamic system are positive, therefore the zero-dynamic system is stable when the vertical input z of the road surface is positive. r , Reference signal And when the uncertainty F3 is bounded, x3 and x4 are bounded.
[0188] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A nonlinear tracking control method based on an active air suspension system for automobiles, comprising: Obtain an active air suspension model, and design a vehicle height tracking controller for the suspension system based on the active air suspension model; The acquisition of the active air suspension model specifically includes: （1）； Where K is the polytropic index, R is the ideal gas constant, and T is the gas temperature. For the sprung mass, For unsprung mass, This refers to the damping coefficient of the suspension shock absorber. For the vertical stiffness of the tire, For tire vertical damping, This is the initial height of the air spring. x1 represents the vertical displacement of the vehicle body, x2 represents the vertical velocity of the vehicle body, x3 represents the vertical displacement of the wheels, x4 represents the vertical velocity of the wheels, and x6 represents the overall state variable of the suspension system. There are three uncertain parameters. For the vertical input signal of the road surface, This indicates the mass flow rate of air passing through the solenoid valve, which determines the inflation and deflation process of the air spring and serves as the control input for the controller. Stability analysis of the vehicle height tracking controller; Zero-dynamic analysis of the vehicle height tracking controller; The vehicle height tracking controller for the suspension system designed based on the air active suspension model specifically includes: Define the error variable as ,in, Due to uncertain external disturbances, , ; make , ,in For virtual control input, for Based on the tracked reference value, the dynamic vehicle height tracking error is obtained as follows: （2）； Virtual control input for: （3）； Then we can obtain The error dynamics are: （4）； Take Lyapunov function Then there is （5）； make ,in If it is a virtual control input, then The error dynamics are: （6）； Virtual control input for: （7）； Then we can obtain The error dynamics are: （8）； Take Lyapunov function Then there is （9）； The dynamic representation is as follows: （10）； set up ，（11）； Where f, y, and h are intermediate calculation functions of the model; The vehicle height tracking controller is designed as follows: （12）； Then we can obtain The error dynamics are: （13）； Take Lyapunov function Then there is （14）； make We can obtain: （15）； （16）； （17）； Right now: （18）； （19）； （20）。 2. The method according to claim 1, characterized in that, The stability analysis of the vehicle height tracking controller specifically includes: Obtain the final Lyapunov function of the controller: （21）； （22）； in, It is positive definite. It is semi-negative definite, therefore the equilibrium state is stable in the Lyapunov sense, so... They are all bounded. set up （23）； W(t) is the sum of squares of the total system error; Then there is （24）； because They are all bounded, therefore It is bounded, therefore It is uniformly continuous, and according to the Lyapunov class lemma, it can be proved that as t→∞, →0, at this time →0, thus we can conclude that the vehicle height tracking controller can achieve the vehicle height tracking function.
3. The method according to claim 2, characterized in that, The zero-dynamic analysis of the vehicle height tracking controller specifically includes: Therefore, from formulas (3), (7), and (18), it can be seen that when the reference signal... When it is bounded, , , Bounded; （25）； + + + （26）； + + + （27）； Formula (26) is derived from formula (25), when When →0, formula (26) becomes formula (27), and its characteristic equation is: + （28）； Where s is the Laplace operator; Depend on >0, >0, >0 can be obtained >0 and >0, meaning all coefficients of the characteristic equation of the second-order zero-dynamic system are positive, therefore the zero-dynamic system is stable when the road surface vertical input... , Reference signal and uncertainty When it is bounded, , Bounded.
4. A nonlinear tracking control device based on an automotive active air suspension system, comprising: The vehicle height tracking controller module is used to acquire the air active suspension model and design the vehicle height tracking controller of the suspension system based on the air active suspension model. The vehicle height control tracking controller module is used to acquire the active air suspension model, specifically including: （1）； Where K is the polytropic index, R is the ideal gas constant, and T is the gas temperature. For the sprung mass, For unsprung mass, This refers to the damping coefficient of the suspension shock absorber. For the vertical stiffness of the tire, For tire vertical damping, This is the initial height of the air spring. x1 represents the vertical displacement of the vehicle body, x2 represents the vertical velocity of the vehicle body, x3 represents the vertical displacement of the wheels, x4 represents the vertical velocity of the wheels, and x6 represents the overall state variable of the suspension system. There are three uncertain parameters. For the vertical input signal of the road surface, This indicates the mass flow rate of air passing through the solenoid valve, which determines the inflation and deflation process of the air spring and serves as the control input for the controller. The stability module is used for stability analysis of the vehicle height tracking controller; The zero-dynamic module is used to perform zero-dynamic analysis on the vehicle height tracking controller. The vehicle height tracking controller module, designed based on the air active suspension model, specifically includes the following: Define the error variable as ,in, Due to uncertain external disturbances, , ; make , ,in For virtual control input, for Based on the tracked reference value, the dynamic vehicle height tracking error is obtained as follows: （2）； Virtual control input for: （3）； Then we can obtain The error dynamics are: （4）； Take Lyapunov function Then there is （5）； make ,in If it is a virtual control input, then The error dynamics are: （6）； Virtual control input for: （7）； Then we can obtain The error dynamics are: （8）； Take Lyapunov function Then there is （9）； The dynamic representation is as follows: （10）； set up ，（11）； Where f, y, and h are intermediate calculation functions of the model; The vehicle height tracking controller is designed as follows: （12）； Then we can obtain The error dynamics are: （13）； Take Lyapunov function Then there is （14）； make We can obtain: （15）； （16）； （17）； Right now: （18）； （19）； （20）。 5. The apparatus according to claim 4, characterized in that, The stability module is specifically used for: Obtain the final Lyapunov function of the controller: （21）； （22）； in, It is positive definite. It is semi-negative definite, therefore the equilibrium state is stable in the Lyapunov sense, so... They are all bounded. set up （23）； W(t) is the sum of squares of the total system error; Then there is （24）； because They are all bounded, therefore It is bounded, therefore It is uniformly continuous, and according to the Lyapunov class lemma, it can be proved that as t→∞, →0, at this time →0, thus we can conclude that the vehicle height tracking controller can achieve the vehicle height tracking function.
6. The apparatus according to claim 4, characterized in that, The zero-dynamic module is specifically used for: Therefore, from formulas (3), (7), and (18), it can be seen that when the reference signal... When it is bounded, , , Bounded; （25）； + + + （26）； + + + （27）； Formula (26) is derived from formula (25), when When →0, formula (26) becomes formula (27). Its characteristic equation is: + （28）； Where s is the Laplace operator; Depend on >0, >0, >0 can be obtained >0 and >0, meaning all coefficients of the characteristic equation of the second-order zero-dynamic system are positive, therefore the zero-dynamic system is stable when the road surface vertical input... , Reference signal and uncertainty When it is bounded, , Bounded.