A fixed-time sliding mode control method for intelligent vehicle steering system

Abstract

A fixed-time sliding mode control method for intelligent vehicle steering system is proposed to solve the fixed-time tracking control problem of steer-by-wire steering system with motor actuator dead zone and output saturation. Firstly, interval type-2 fuzzy logic system is used to online approximate the nonlinearities of steer-by-wire steering system, including unknown model such as friction torque and return torque. The adaptive law of interval type-2 fuzzy logic system parameter vector is derived from Lyapunov function, which ensures the approximation accuracy of unknown nonlinearities. Then, according to the robustness of sliding mode controller, dynamic gain robust term is used to compensate the influence of unknown control gain and dead zone on the control performance of steer-by-wire steering system, and reference auxiliary variable is used to eliminate the influence of actuator output saturation on steer-by-wire steering system. The proposed method can significantly suppress high-frequency chattering, effectively improve the control accuracy, stability and robustness of intelligent vehicle steering system under rough road conditions, and improve the dynamic response performance of the system.

Description

Technical Field

[0001] This invention belongs to the field of steering angle tracking control of intelligent vehicle steering systems, and specifically relates to a fixed-time tracking control method based on an interval type II fuzzy logic system for a steer-by-wire system that considers the influence of motor actuator dead zone and output saturation on the steer-by-wire system with model uncertainty. Background Technology

[0002] With the rapid iteration of intelligent vehicle technology, steer-by-wire systems, as a core component of intelligent vehicle chassis, completely eliminate the physical connection of traditional mechanical steering. They receive steering commands from the electronic control unit and drive the steering motor to adjust the front wheel steering, ensuring the vehicle accurately tracks the planned path. This is a key technological support for ensuring driving safety in complex road conditions and improving steering maneuverability. This is especially important for vehicles operating in complex or rugged terrain.

[0003] In steer-by-wire vehicles operating on rough terrain, the frictional torque and rotational torque generated between the tires and the ground increase significantly. When the output torque of the steering motor is within a small range, it is often difficult to overcome the aforementioned resistance torque, causing the system to fail to respond to steering commands. This phenomenon is known as the input dead zone phenomenon of steer-by-wire systems.

[0004] Input dead zone, a typical nonlinear element in steer-by-wire systems, reduces system control accuracy, causes lag in small-signal response, and in severe cases, can induce limit cycle oscillations, significantly impacting vehicle steering performance and driving safety. Theoretically, for steer-by-wire systems with input dead zone, the controller needs to output a relatively large control command when the dead zone occurs to overcome its effects and restore system response. However, in practical engineering applications, the steering motor, limited by its structure and power, has a defined range of output torque, meaning it exhibits output saturation. This saturation characteristic limits the maximum output torque of the motor, preventing it from responding to excessively large torque commands from the controller. Consequently, it cannot effectively overcome the input dead zone, leading to decreased vehicle steering accuracy, response delays, and even the risk of loss of steering control.

[0005] Actuator output saturation, also known as controlled system input saturation, is a common phenomenon in practical control systems.

[0006] Physical constraints, which can lead to a decline in the performance of closed-loop systems and even cause system instability in severe cases, have become a research hotspot in the field of nonlinear system control in recent years. Currently, scholars at home and abroad have conducted a large number of studies on the input saturation problem of nonlinear systems. Most of the related control methods attempt to eliminate the influence of saturation characteristics through various compensation or transformation methods. However, when dealing with nonlinear systems that cannot be modeled, they often have application limitations and are difficult to adapt to the complex operating conditions of steer-by-wire systems.

[0007] In current research on steer-by-wire system control methods, actuator dead zone and output saturation are two types of nonlinear...

[0008] The comprehensive impact of performance factors on the control performance of steer-by-wire systems has not received sufficient attention, making it difficult for existing control methods to address this issue.

[0009] Simply taking into account the constraints of both factors cannot meet the steering precision and driving safety requirements of steer-by-wire vehicles under complex road conditions. Therefore, it is urgent to design a highly adaptable and robust control strategy that fully considers the effects of motor actuator dead zone and output saturation, while also addressing system model uncertainties, to ensure the control performance and driving safety of the steer-by-wire system. Summary of the Invention

[0010] This invention focuses on two typical nonlinear constraints in steer-by-wire systems: actuator input dead zone and output saturation. By constructing a system dynamics model incorporating dead zone and saturation characteristics, its comprehensive impact on steering control accuracy, response speed, and stability is analyzed. Based on this, a fixed-time sliding surface is designed to ensure that the system state converges to the sliding surface within a fixed time and maintains the sliding mode. Simultaneously, an interval type-II fuzzy logic system is introduced to approximate and compensate for unknown nonlinear terms in the model in real time. Then, based on the robustness of the sliding mode controller, a dynamic gain robust term is used to compensate for the impact of unknown control gain and dead zone phenomena on the control performance of the steer-by-wire system. Finally, auxiliary variables are used to eliminate the influence of actuator output saturation on the steer-by-wire system, thus completing the controller design.

[0011] The objective of this invention can be achieved through the following technical solutions:

[0012] This invention discloses a fixed-time sliding mode control method for an intelligent vehicle steering system, comprising the following steps:

[0013] S1. Establish a mathematical model of the steer-by-wire system, considering input dead zone and actuator saturation characteristics;

[0014] S2. An interval-type fuzzy logic system is used to approximate the unknown nonlinearity of the steer-by-wire system online.

[0015] S3. Define the tracking error between the front wheel steering angle of the steer-by-wire system and the desired signal, and design a sliding surface that converges over a fixed time.

[0016] S4. Construct the Lyapunov function;

[0017] S5. Combining a first-order filter to suppress sliding mode chattering, a suitable filter was designed for the steer-by-wire system of intelligent vehicles.

[0018] Find a fixed-time sliding mode controller.

[0019] As a preferred technical solution, in step S1, the mathematical model of the steer-by-wire system is:

[0020] The mathematical model of the steering motor in a steer-by-wire system is expressed as follows:

[0021] (1)

[0022] in, This indicates the rotation angle of the motor output shaft. The moment of inertia of the steering motor. For the steering motor adhesive

[0023] coefficient of friction, This indicates the load torque of the motor. For motor output torque and This is the disturbance torque.

[0024] The steering front wheel rotates about a vertical axis intersecting the wheel center based on the received torque. (Mathematical model)

[0025] The type can be described as:

[0026] (2)

[0027] in, The moment of inertia of the front wheels, This is the steering angle of the front wheels. and These represent the frictional torque between the front wheel and the ground, and the self-aligning torque, respectively. This refers to the steering torque transmitted from the steering motor to the front wheels via a mechanical connection.

[0028] Furthermore, the gear ratio between the steering motor and the front wheels can be expressed as:

[0029] (3)

[0030] in, This is the total transmission ratio between the steering motor and the front wheels.

[0031] Combining equations (1)-(3), the mathematical model of the steer-by-wire system can be expressed as the following state equations:

[0032] (4)

[0033] in, This is the equivalent moment of inertia of the steer-by-wire system.

[0034] The mathematical model of a steer-by-wire system considering actuator output saturation and dead zone can be expressed as:

[0035] (5)

[0036] in, For state variables, Including nonlinear terms for aligning torque and friction torque, To control the gain, For time-varying external

[0037] Disturbance For the system output, This refers to a steer-by-wire system that considers input saturation and dead zone phenomena.

[0038] The input of the system For the control signals designed.

[0039] System input saturation can be expressed as:

[0040] (6)

[0041] in, and This is a positive constant. The actuator dead-time model can be represented as:

[0042] (7)

[0043] in, , , and It is an unknown positive variable.

[0044] The control input of a steer-by-wire system exhibiting input saturation and dead zone phenomena can be expressed as:

[0045] (8)

[0046] function It can be represented as:

[0047] (9)

[0048] in, and They are defined as follows:

[0049] (10)

[0050] (11)

[0051] Additionally, input saturation can be expressed as:

[0052] (12)

[0053] in, For the positive constants of the design. Substituting equation (12) into equation (9) yields:

[0054] (13)

[0055] in, For a bounded function, it is represented as:

[0056] (14)

[0057] Substituting equation (14) into equation (5) yields:

[0058] (15)

[0059] As a preferred technical solution, in step S2...

[0060] For any continuous function In compact Therefore, there must exist an optimal parameter vector. And a zero-order interval type II fuzzy logic system, satisfying

[0061] (16)

[0062] in, For a type-two fuzzy logic system, the membership function is... This is the upper bound of the approximation error of the type II fuzzy logic system.

[0063] As a preferred technical solution, in step S3, the sliding mode variable of the steer-by-wire system is defined as follows:

[0064] (17)

[0065] Define the sliding surface of the system as:

[0066] (18)

[0067] in, , and For the design of positive constants, For signal The filtering result, i.e.

[0068] (19)

[0069] in, For the design of positive constants, Designed as follows:

[0070] (20)

[0071] in, For the design of positive constants, Designed as follows:

[0072] (twenty one)

[0073] in, For the designed positive constant, time... It can be obtained through the following mechanisms:

[0074] (twenty two)

[0075] As a preferred technical solution, in step S4, the following barrier Lyapunov function is constructed.

[0076] (twenty three)

[0077] As a preferred technical solution, in step S5, the control method designed for a steer-by-wire system with model and parameter uncertainties, external disturbances, actuator dead zones, and input saturation is as follows.

[0078] (twenty four)

[0079] The actual control quantity can be expressed as:

[0080] (25)

[0081] in, , and For the design of positive constants, It can be represented as:

[0082] (26)

[0083] in, For the design of positive constants. For function The first-order filtering result. Designed as follows:

[0084] (27)

[0085] in, For unknown vectors

[0086] The estimation results , and For the design of positive constants, unknown parameters , ,

[0087] , , and satisfy , , , where the function Designed as follows:

[0088] (28)

[0089] in, and For the design of positive constants, and These are the parameter vector and basis vector of the type-II fuzzy logic system, respectively. Additionally, auxiliary variables are defined. for:

[0090] (29)

[0091] and The adaptive laws are designed as follows:

[0092] (30)

[0093] (31)

[0094] in, , , , , and For the design of positive constants.

[0095] Compared with the prior art, the present invention has the following beneficial effects:

[0096] 1. This invention proposes a fixed-time sliding mode control method for the steer-by-wire system of intelligent vehicles, combining obstacle Lyapunov function technology. This method addresses input nonlinearity issues such as input dead zone and actuator saturation.

[0097] The steer-by-wire system with model uncertainty converges to the neighborhood of the origin within a fixed time and can effectively suppress sliding mode chatter, thereby improving the tracking accuracy and handling smoothness of the steering system.

[0098] 2. This invention applies an interval-type fuzzy logic system to approximate the unknown nonlinearity of the steer-by-wire system online, combines dynamic gain technology to compensate for the impact of the input dead zone on the system control performance, and eliminates actuator saturation constraints through auxiliary variables, thereby enhancing the robustness and engineering practicality of the control system. Attached Figure Description

[0099] Figure 1 This is a block diagram of a steer-by-wire system with input saturation and dead zone.

[0100] Figure 2 For input saturation and dead zone models.

[0101] Figure 3 This is a dead-zone model exhibiting input saturation.

[0102] Figure 4 The tracking performance of the invented steer-by-wire system.

[0103] Figure 5 The tracking error of the steer-by-wire system of the invention A schematic diagram.

[0104] Figure 6 The sliding mode variable trajectory diagram of the steer-by-wire system of the invention.

[0105] Figure 7 This is a schematic diagram of the control signals and control inputs of the steer-by-wire system of the invention.

[0106] Figure 8 Signal for the invention of the steer-by-wire system With registered results A schematic diagram.

[0107] Figure 9 Signal for the invention of the steer-by-wire system First-order filtering results A schematic diagram.

[0108] Figure 10 In the radial basis function neural network of the invention A schematic diagram of the adaptive result of the vector.

[0109] Figure 11 In the controller of the steer-by-wire system of the invention A schematic diagram of the vector estimation results. Detailed Implementation

[0110] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0111] Example

[0112] In the tracking control of intelligent vehicle steering systems, the effects of actuator output saturation and dead zone on the steer-by-wire system are considered.

[0113] To address the impact of traditional methods, a fixed-time sliding mode control method for intelligent vehicle steering systems is proposed, the detailed implementation of which includes:

[0114] S1. Establish a mathematical model of the steer-by-wire system;

[0115] The mathematical model of the steering motor in a steer-by-wire system is expressed as follows:

[0116] (1)

[0117] in, This indicates the rotation angle of the motor output shaft. The moment of inertia of the steering motor. For the steering motor adhesive

[0118] coefficient of friction, This indicates the load torque of the motor. For motor output torque and This is the disturbance torque.

[0119] The steering front wheel rotates about a vertical axis intersecting the wheel center based on the received torque. (Mathematical model)

[0120] The type can be described as:

[0121] (2)

[0122] in, The moment of inertia of the front wheels, This is the steering angle of the front wheels. and These represent the frictional torque between the front wheel and the ground, and the self-aligning torque, respectively. This refers to the steering torque transmitted from the steering motor to the front wheels via a mechanical connection.

[0123] Furthermore, the gear ratio between the steering motor and the front wheels can be expressed as:

[0124] (3)

[0125] in, This is the total transmission ratio between the steering motor and the front wheels.

[0126] Combining equations (1)-(3), the mathematical model of the steer-by-wire system can be expressed as the following state equations:

[0127] (4)

[0128] in, This is the equivalent moment of inertia of the steer-by-wire system.

[0129] The mathematical model of a steer-by-wire system considering actuator output saturation and dead zone can be expressed as:

[0130] (5)

[0131] in, For state variables, Including the righting force

[0132] Nonlinear terms of torque and friction torque, To control the gain, For time-varying external disturbances, For the system output, This represents the input of a steer-by-wire system considering system input saturation and dead zone phenomena. For the control signals designed.

[0133] System input saturation can be expressed as:

[0134] (6)

[0135] in, and This is a positive constant. The actuator dead-time model can be represented as:

[0136] (7)

[0137] in, , , and It is an unknown positive variable.

[0138] The control input of a steer-by-wire system exhibiting input saturation and dead zone phenomena can be expressed as:

[0139] (8)

[0140] function It can be represented as:

[0141] (9)

[0142] in, and They are defined as follows:

[0143] (10)

[0144] (11)

[0145] In this example, the model parameters of the selected steer-by-wire system are as follows:

[0146] Friction torque of steer-by-wire system and the restoring torque The simulation models selected are as follows:

[0147] (12)

[0148] (13)

[0149] in, and This can be obtained through the following two-degree-of-freedom model, namely...

[0150] (14)

[0151] The parameters for the steer-by-wire system are selected as follows:

[0152] , , , , , , , , , , , , , , , , , The initial values ​​of the state variables are chosen as follows: , The simulation step size was selected as 0.001s. A time-varying perturbation was set in the simulation. for:

[0153] (15)

[0154] S2. An interval-type fuzzy logic system is used to approximate the unknown nonlinearity of the steer-by-wire system online.

[0155] For any continuous function In compact Therefore, there must exist an optimal parameter vector. And a zero-order interval type II fuzzy logic system, satisfying

[0156] (16)

[0157] in, For a type-two fuzzy logic system, the membership function is... This is the upper bound of the approximation error of the type II fuzzy logic system.

[0158] S3. Define the tracking error between the front wheel steering angle of the steer-by-wire system and the desired signal, and design a sliding surface that converges over a fixed time.

[0159] The sliding mode variable of the steer-by-wire system is defined as:

[0160] (17)

[0161] Define the sliding surface of the system as:

[0162] (18)

[0163] in, , and For the design of positive constants, , , , For signal The filtering result, i.e.

[0164] (19)

[0165] in, For the design of positive constants, , Designed as follows:

[0166] (20)

[0167] in, For the design of positive constants, , Designed as follows:

[0168] (twenty one)

[0169] in, For the design of positive constants, ,time It can be obtained through the following mechanisms:

[0170] (twenty two)

[0171] S4. Construct the Lyapunov function;

[0172] (twenty three)

[0173] S5. Combining a first-order filter to suppress sliding mode chattering, a suitable filter was designed for the steer-by-wire system of intelligent vehicles.

[0174] Find a fixed-time sliding mode controller.

[0175] The control method designed is as follows:

[0176] (twenty four)

[0177] The actual control quantity can be expressed as:

[0178] (25)

[0179] in, , and For the design of positive constants, , , , It can be represented as:

[0180] (26)

[0181] in, For the design of positive constants, . For function The first-order filtering result. Designed as follows:

[0182] (27)

[0183] in, For unknown vectors

[0184] The estimation results. , and For the design of positive constants, , Unknown parameters , , , , and satisfy , , , where the function Designed as follows:

[0185] (28)

[0186] in, and For the design of positive constants, , , and These are the parameter vector and basis vector of the type-II fuzzy logic system, respectively. Additionally, auxiliary variables are defined. for:

[0187] (29)

[0188] and The adaptive laws are designed as follows:

[0189] (30)

[0190] (31)

[0191] Among them, among them, , , , , and For the design of positive constants. , , , , , , , .

[0192] Figure 4 The control performance of the invented steer-by-wire system shows that the front wheel steering angle of the steer-by-wire system can track its reference signal very well. Figure 5 The results of tracking the reference signal for the front wheel steering angle of the invention show that the tracking error of the front wheel steering angle can quickly converge to the neighborhood of the origin in the initial state of non-origin. Figure 6 The trajectory of the sliding mode variable of the invented steer-by-wire system shows that the sliding mode variable and its derivative can converge to the vicinity of the origin, thus forming the actual sliding mode. Figure 7 By comparing the designed control signal with the actual control input of the steer-by-wire system, it can be seen that the designed control quantity is different from the actual input of the steer-by-wire system. Furthermore, the designed signal can quickly pass through the dead zone, thereby reducing the impact of the dead zone phenomenon on the control performance. Figure 8 For signal and its registration result . Figure 9 For signal and its first-order filtering result . Figure 10 For vectors estimation results . Figure 11 The adaptive result of the parameter vector of the type II fuzzy logic system shows that all these signals are bounded.

[0193] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A fixed-time sliding mode control method for an intelligent vehicle steering system, characterized in that, It includes the following steps: S1. Establish a mathematical model of the steer-by-wire system, considering input dead zone and actuator saturation characteristics; S2. An interval-type fuzzy logic system is used to approximate the unknown nonlinearity of the steer-by-wire system online. S3. Define the tracking error between the front wheel steering angle of the steer-by-wire system and the desired signal, and design a sliding surface that converges over a fixed time. S4. Construct the Lyapunov function; S5. By combining a first-order filter to suppress sliding mode chatter, a fixed-time sliding mode controller that meets the requirements is designed for the steer-by-wire system of intelligent vehicles.

2. The fixed-time sliding mode control method for an intelligent vehicle steering system according to claim 1, characterized in that: In step S1, the mathematical model of the steer-by-wire system is: The mathematical model of the steering motor in a steer-by-wire system is expressed as follows: (1) in, This indicates the rotation angle of the motor output shaft. The moment of inertia of the steering motor. The coefficient of viscous friction of the steering motor. This indicates the load torque of the motor. For motor output torque and For disturbance torque; The steering front wheel rotates about a vertical axis intersecting the wheel center based on the received torque. The mathematical model can be described as follows: (2) in, The moment of inertia of the front wheels, This is the steering angle of the front wheels. and These represent the frictional torque between the front wheel and the ground, and the self-aligning torque, respectively. The steering torque is transmitted from the steering motor to the front wheels via a mechanical connection; Furthermore, the gear ratio between the steering motor and the front wheels can be expressed as: (3) in, This is the total gear ratio between the steering motor and the front wheels; Combining equations (1)-(3), the mathematical model of the steer-by-wire system can be expressed as the following state equations: (4) in, The equivalent moment of inertia of the steer-by-wire system; The mathematical model of a steer-by-wire system considering actuator output saturation and dead zone can be expressed as: (5) in, For state variables, Including nonlinear terms for aligning torque and friction torque, To control the gain, For time-varying external disturbances, For the system output, This represents the input of a steer-by-wire system considering system input saturation and dead zone phenomena. For the control signals designed; System input saturation can be expressed as: (6) in, and For positive constants; the actuator dead-time model can be represented as: (7) in, , , and For unknown positive variables; The control input of a steer-by-wire system exhibiting input saturation and dead zone phenomena can be expressed as: (8) function It can be represented as: (9) in, and They are defined as follows: (10) (11) Additionally, input saturation can be expressed as: (12) in, For the positive constants of the design; substituting equation (12) into equation (9) yields: (13) in, For a bounded function, it is represented as: (14) Substituting equation (14) into equation (5) yields the following result: (15) 。 3. The fixed-time sliding mode control method for an intelligent vehicle steering system according to claim 1, characterized in that: In step S2, For any continuous function In compact Therefore, there must exist an optimal parameter vector. And a zero-order interval type II fuzzy logic system, satisfying (16) in, For a type-two fuzzy logic system, the membership function is... This is the upper bound of the approximation error of the type II fuzzy logic system.

4. The fixed-time sliding mode control method for an intelligent vehicle steering system according to claim 1, characterized in that: In step S3, the sliding mode variable of the steer-by-wire system is defined as follows: (17) Define the sliding surface of the system as: (18) in, , and For the design of positive constants, For signal The filtering result, i.e. (19) in, For the design of positive constants, Designed as follows: (20) in, For the design of positive constants, Designed for (21) in, For the designed positive constant, time... It can be obtained through the following mechanisms (22)。 5. The fixed-time sliding mode control method for an intelligent vehicle steering system according to claim 1, characterized in that: In step S4, Construct the following barrier Lyapunov function: (23)。 6. The fixed-time sliding mode control method for an intelligent vehicle steering system according to claim 1, characterized in that: In step S5, the control method designed for a steer-by-wire system with model and parameter uncertainties, external disturbances, actuator dead zones, and input saturation is as follows: (24) The actual control quantity can be expressed as: (25) in, , and For the design of positive constants, It can be represented as: (26) in, For the design of positive constants; For function The first-order filtering result; Designed as follows: (27) in, For unknown vectors The estimation results , and For the design of positive constants, unknown parameters , , , , and satisfy , , , where the function Designed as follows: (28) in, and For the design of positive constants, and These are the parameter vector and basis vector of the type-II fuzzy logic system, respectively; additionally, auxiliary variables are defined. for: (29) and The adaptive laws are designed as follows: (30) (31) in, , , , , and For the design of positive constants.

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