Clamping force constraint backstepping sliding mode control method for electronic mechanical braking system

Abstract

The invention relates to a clamping force constraint backstepping sliding mode control method for an electronic mechanical braking system, and belongs to the related technical field of new energy automobile control. The method comprises the following steps of: establishing a state space model of the system by considering the nonlinear characteristic of the electronic mechanical braking system, and reasonably simplifying the state space model into a strict feedback form; a time-varying tangent barrier Lyapunov function (BLF) containing an error integral term is constructed, an exponentially decayed time-varying function is used as a constraint boundary of a clamping force tracking error, the integral term is introduced to eliminate a steady-state error caused by unmodeled dynamics, and the output constraint performance and tracking precision of a system are ensured; on the basis, a control law is designed by combining a backstepping method and non-singular fast terminal sliding mode control, and fast and accurate tracking of the braking clamping force is achieved; and proving the system stability based on the Lyapunov stability theorem. According to the invention, the braking response time and the clamping force control precision of the electronic mechanical braking system can be effectively improved.

Description

Technical Field

[0001] The present invention mainly relates to control-related technical fields, in particular to the field of wire-controlled braking technology for new energy vehicles, and specifically to a clamping force constrained backstepping sliding mode control method for an electronic mechanical braking system. Background Art

[0002] With the rapid development of highly autonomous vehicles, automotive brake-by-wire technology has become a hot topic within the intelligent chassis sector. Brake-by-wire systems are primarily categorized as electronic hydraulic brakes (EHB) and electromechanical brakes (EMB). EMB completely eliminates hydraulic components, making it more suitable for the future development of braking systems for highly autonomous vehicles.

[0003] Clamping force control is a crucial factor in the safety performance of electromechanical braking systems (EMBs). Accurate and rapid control of the EMB clamping force, while ensuring accurate braking commands, is crucial for achieving coordinated regenerative braking and active braking control. Classical control theories such as PID control and fuzzy control have been widely used in electromechanical braking systems, but these methods struggle to achieve high-quality control under complex nonlinear conditions. Modern control methods have improved their adaptability to nonlinear variables, developing methods such as model predictive control, robust control, and sliding mode control. However, model predictive control is a continuous dynamic optimization process, which is computationally intensive. Robust clamping force control enhances robustness to model variations, but also exhibits significant conservatism. Sliding mode control is widely used to address parameter uncertainty in electromechanical systems. However, traditional sliding mode controllers suffer from slow convergence and inevitably suffer from singularity problems. The Lyapunov method has long been considered a powerful tool for stability analysis of nonlinear systems, and has spawned a variety of nonlinear control methods. Backstepping control has attracted considerable research attention due to its ability to handle mismatched uncertainties and its flexible design of virtual control variables to ensure the motion quality of each subsystem. However, conventional backstepping control can only guarantee system stability and cannot address output constraints. The barrier Lyapunov function is a commonly used output constraint method. This method has been applied to control mechatronic systems such as spacecraft, anti-skid brake systems, robotic arms, and electric motors.

[0004] Currently, the most common barrier Lyapunov functions are logarithmic and tangent. When the constraint bounds approach infinity, the logarithmic barrier Lyapunov function approaches zero, making it unsuitable for unconstrained situations. The tangent barrier Lyapunov function, on the other hand, has a wider range of applications. If the system's initial error is large, constant constraint bounds for both types of barrier Lyapunov functions will not guarantee system performance, and the presence of unmodeled dynamics will also affect overall control performance. Summary of the Invention

[0005] To address the shortcomings of current technologies, the present invention combines existing technologies with practical applications to provide a clamping force constrained backstepping sliding mode control method for an electronic mechanical brake system, which is applied to the clamping force control of an EMB. The present invention constructs a time-varying tangent barrier Lyapunov function containing an error integral term to eliminate the steady-state error caused by unmodeled dynamics and achieve time-varying constraints on the clamping force tracking error. An integral term is introduced into the design of the barrier Lyapunov function to eliminate the steady-state error caused by unmodeled dynamics and improve the clamping force control accuracy. The current loop is combined with non-singular fast terminal sliding mode control to avoid the problems of singularity and slow convergence speed. Combined with backstepping control, the conservatism of the sliding mode control is reduced, thereby improving system performance.

[0006] The technical solutions of the present invention are as follows: A clamping force constrained backstepping sliding mode control method for an electromechanical brake system comprises the following steps: S1. Establish a state space model of the electromechanical brake system and simplify it into a strict feedback form; S2. Construct a time-varying tangent barrier Lyapunov function with an error integral term. Use the exponentially decaying time-varying function as the constraint boundary for the clamping force tracking error of the electromechanical brake system. In addition, introduce an integral term to eliminate the steady-state error caused by unmodeled dynamics, thereby ensuring the output constraint performance and tracking accuracy of the system. S3. Based on the obstacle Lyapunova function in step S2, a backstepping control method is designed to obtain the virtual control rates of the outer clamping force loop and the speed loop; S4. Design a current controller based on the combination of fast terminal sliding mode control and backstepping control to obtain the feedback control rate of the inner current loop and achieve fast and accurate tracking of the clamping force of the electronic mechanical brake system.

[0007] Furthermore, in step S1, the electronic mechanical braking system includes a drive motor, a transmission mechanism, a brake caliper, a brake disc, a force sensor, and a control system, wherein the drive motor adopts a surface-mounted permanent magnet synchronous motor, and the transmission mechanism includes a reduction mechanism and a ball screw mechanism.

[0008] Furthermore, in step S1, the state space model expression of the electronic mechanical braking system is as follows: ; Among them, the state variable , is the clamping force, is the rotor mechanical angular velocity, 、 is the stator current vector 、 Axis component, is the clamping force coefficient, which represents the relationship between the reducer rotation angle and the clamping force The relationship between , is the stiffness coefficient of the brake disc, is the proportionality coefficient, and , is the ball screw mechanical efficiency, is the mechanical efficiency of the planetary gear mechanism, is the ball screw lead, is the reduction ratio, To convert the equivalent moment of inertia to the motor shaft, is the viscous friction coefficient, is the number of magnetic pole pairs, is the coupling flux of the rotor permanent magnet on the stator, is the load torque at the initial state, is the winding inductance, 、 is the stator voltage vector 、 Axis component, is the winding resistance.

[0009] Furthermore, in step S2, the expression of the time-varying tangent barrier Lyapunov function including the error integral term is as follows: ; Where, is the system dynamic tracking error, is the integral term of the system dynamic tracking error, is the designed error integral coefficient. The error integral term is introduced into the time-varying tangent barrier Lyapunov function. The steady-state error can be eliminated by the integral action, which is recorded as: ; Where, is the actual value of the clamping force at any time, is the reference value of clamping force at any time, is the dynamic tracking error at any time; is the time-varying error constraint boundary exponential decay function, and its expression is as follows: ; Where, for The initial value is set according to the initial error of the clamping force. for hour The steady-state value of ; In the steady-state phase, the parameter The size of determines the steady-state error boundary, The smaller the system steady-state error, for The convergence speed of .

[0010] Furthermore, in step S3, the virtual control rate of the outer ring clamping force ring is The expression is as follows: ; Where, is the clamping force coefficient, which represents the relationship between the reducer rotation angle and the clamping force. is the target clamping force, is a proportional coefficient greater than zero.

[0011] Furthermore, in step S3, the virtual control rate of the speed loop The expression is as follows: ; Where, , is the number of magnetic pole pairs, is the coupling flux of the rotor permanent magnet on the stator, is the error variable defined, , is a constant greater than zero, is the proportionality coefficient, and , is the ball screw mechanical efficiency, is the mechanical efficiency of the planetary gear mechanism, is the ball screw lead, is the reduction ratio, is the viscous friction coefficient, is the load torque at the initial state, To convert the equivalent moment of inertia to the motor shaft, the state variable , is the clamping force, is the rotor mechanical angular velocity, 、 is the stator current vector 、 Axis component.

[0012] Furthermore, in step S4, the quadrature axis and direct axis current controllers are designed respectively, wherein the quadrature axis ( The design expression of the current controller of axis is as follows: ; Where, , , are sliding surface coefficients; and is an odd number and satisfies , is the stator voltage vector Axis component, for Equivalent control item of axis sliding mode control, for Axis sliding mode control switching control item, is the winding resistance, is the winding inductance, for Axis reference current, , which means the definition Shaft current error variable, for Shaft sliding surface, 、 Both Reaching law coefficient of the switching control term of axis sliding mode control.

[0013] Furthermore, the straight axis ( The design expression of the current controller of axis is as follows: ; Where, , , are sliding surface coefficients, for Axis reference current, , which means the definition Shaft current error variable, for Shaft sliding surface, for Equivalent control item of axis sliding mode control, for Axis sliding mode control switching control item, 、 for Reaching law coefficient of the switching control term of axis sliding mode control.

[0014] Furthermore, the method further comprises: Step S5: Prove the stability of the system based on Lyapunov's stability theorem.

[0015] Beneficial effects of the present invention: The present invention designs a time-varying tangent barrier Lyapunov function, which solves the problem that the constant constraint boundary of the traditional barrier Lyapunov function is difficult to ensure the system control effect when the initial error is large. It can achieve time-varying constraints on the brake clamping force tracking error. In addition, the integral term is introduced into the design of the barrier Lyapunov function, which effectively reduces the steady-state error caused by the unmodeled dynamics of the electronic mechanical brake system and improves the clamping force control accuracy. In the present invention, the current loop is combined with non-singular fast terminal sliding mode control, which is combined with backstepping control to reduce the conservatism of the sliding mode control, avoid the problems of singularity and slow convergence, and improve system performance; Verification results show that the control method proposed in the present invention can improve the response time and control accuracy of the EMB clamping force compared with the traditional control method, and will bring certain economic benefits after being put into industrial application. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a principle block diagram of the present invention; Figure 2 The comparison diagram of sinusoidal clamping force and error of the obstacle Lyapunov function control method with and without integral term; Figure 3 Comparison chart of clamping force response time between the control method of the present invention and the constrained backstepping control method; Figure 4 Comparison chart of sinusoidal clamping force tracking between the control method of the present invention and the constrained backstepping control method; Figure 5 Comparison chart of sinusoidal clamping force tracking error between the control method of the present invention and the constrained backstepping control method. DETAILED DESCRIPTION

[0017] The present invention will be further described with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are intended only to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the contents of the present invention, those skilled in the art may make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the present application.

[0018] This embodiment provides a backstepping sliding mode control method for clamping force constraints of an electronic mechanical brake system (EMB), which belongs to the technical field related to wire control of new energy vehicles.

[0019] The main steps of the present invention are as follows: S1. Establish a mathematical model of the electromechanical brake system. The electromechanical brake system mainly consists of a drive motor, EMB transmission mechanism, brake caliper, brake disc, force sensor, control system, etc. The drive motor adopts a surface-mounted permanent magnet synchronous motor; S2. A time-varying constrained tangent type improved barrier Lyapunova function with error integral term is designed; S3. Based on the obstacle Lyapunova function in S2, a backstepping control method is designed to obtain the virtual control rates of the outer clamping force loop and the speed loop; S4. A fast terminal sliding mode control is designed to improve the convergence speed, which is combined with the backstepping control to obtain the feedback control rate of the inner current loop; S5. Use Lyapunov function to prove the stability of the system.

[0020] The above steps are described in detail below.

[0021] The electromechanical brake system primarily consists of a drive motor, EMB transmission mechanism, brake caliper, brake disc, force sensor, and control system. The drive motor is the core component of the EMB actuator. In this embodiment, the EMB drive motor uses a surface-mounted permanent magnet synchronous motor (SPMSM). The mathematical model is as follows: (1); Where, is the rotor mechanical angular displacement, is the rotor mechanical angular velocity, is the number of magnetic pole pairs, is the coupling flux of the rotor permanent magnet on the stator, To convert the equivalent moment of inertia to the motor shaft, 、 is the stator current vector Axis component, is the viscous friction coefficient, is the load torque, is the winding resistance, is the winding inductance, 、 is the stator voltage vector Axis component.

[0022] The EMB's transmission mechanism consists of a reduction gear and a ball screw mechanism. The ball screw converts the reduction gear's rotational motion into linear motion, thereby pushing the friction plate to apply clamping force. The linear displacement of the ball screw can be expressed as: (2); Where, is the output angle of the reducer, is the reduction ratio, is the ball screw lead. To facilitate the design of the controller, this embodiment performs data fitting based on the bench test, and the relationship between them can be approximately expressed as a linear relationship: (3); Where, is the clamping force, is the stiffness coefficient of the brake disc, is the displacement of the screw nut, is the initial gap, Indicates the angular position when contacting the friction plate. Indicates the angular position when the target clamping force is reached.

[0023] Assuming that the friction plate and brake disc are in contact at the initial moment, , combining (2) and (3) to get the variable ,definition is the clamping force coefficient, which represents the reducer rotation angle and clamping force The relationship between them. It is converted from the superposition of inertia torque and friction torque. For the sake of simplicity, it can be considered that within the small displacement range and It is a linear relationship, that is, it satisfies the elastic load property: (4); Where, is the load torque at the initial state, is the proportionality coefficient, and , is the ball screw mechanical efficiency, is the mechanical efficiency of the planetary gear mechanism.

[0024] Get state variables , combining (1)(3)(4), we can get the state space equation of the EMB braking system as: (5); Control objective: For the electromechanical brake system shown in formula (5), the controller is designed by constructing the obstacle Lyapunov function to achieve the desired clamping force Accurate tracking requires dynamic tracking error Bounded and constrained to the interval within, among them is the exponential decay function of the time-varying error constraint boundary. To achieve the target control, the following assumptions are made.

[0025] Assumption 1: Continuous, the derivative is uniformly continuous and bounded; Assumption 2: State variables in the model All can be measured.

[0026] The obstacle Lyapunova function designed for step S2 is as follows: Conventional backstepping control can only guarantee system stability but cannot address the output constraints of the system. Currently, a backstepping method combined with a barrier Lyapunova function is used to design a controller, which can effectively solve this problem and has a systematic and superior design.

[0027] The traditional logarithmic barrier Lyapunov function (BLF) expression is: (6); Where, is the natural logarithm, is the constraint boundary, the initial value of the error satisfy .when Sometimes, there are , so it has limitations for unconstrained situations. The expression of the tangent barrier Lyapunov function is: (7); when Sometimes, there are , which is applicable to unconstrained situations and has a wider range of applications than the logarithmic BLF. The system error constraints of the above two BLFs are constants. To ensure the control accuracy of the system, the constant constraint boundary needs to be set to a smaller value as much as possible. If the constant constraint boundary is large, it is difficult to ensure the system control effect. Considering the unmodeled dynamics of the EMB system, a time-varying tangent BLF with an error integral term is constructed for the clamping force control of the electronic mechanical brake (EMB) system. The expression is: (8); Where, is the system dynamic tracking error, is the integral term of the system dynamic tracking error. By introducing the integral term of the error into the time-varying tangent BLF, the steady-state error can be eliminated by the integral action, which is recorded as: (9); is the time-varying error constraint boundary exponential decay function, and its expression is shown in formula (10): (10); Where, for The initial value is set according to the initial error of the clamping force and must meet . for hour The steady-state value of In the steady state phase, the parameter The size of determines the steady-state error boundary, The smaller it is, the smaller the steady-state error of the system. for The convergence speed of .

[0028] In this embodiment, the virtual control rates of the outer ring clamping force ring and the speed ring in step S3 are designed as follows: For the nonlinear system in equation (5), a clamping force backstepping control method based on improved BLF is proposed. The design steps are as follows: 1) Clamping force ring control design: set up is the target clamping force, and the allowable error range of the clamping force is , define the dynamic tracking error of the clamping force as: (11); right Taking the derivative, we can get: (12); Select the constructed time-varying tangent BLF function with error integral term: (13); From the definition, we can see that For BLF, take the derivative of the above formula and get: (14); Where, , is the virtual control law, and the above formula can be obtained Virtual control law for: (15); Substituting formula (15) into formula (14), we can obtain: (16); Where, is a constant greater than zero.

[0029] 2) Speed loop control design: Define the error variable as: (17); right Taking the derivative, we can get: (18); Where, , , Design a virtual control law for the virtual control law for: (19); Where, is a constant greater than zero.

[0030] Substituting formula (19) into formula (18), we can obtain: (20); Constructing Lyapunov functions for: (twenty one); right Taking the derivative we get: (twenty two); To prove the stability of the system, we first substitute Equation (16) and Equation (20) into Equation (22), and we can get: (twenty three).

[0031] In this embodiment, the feedback control rate design in step S4 is specifically as follows: The main goal of the current controller is to make the error variable , Converges to zero. Fast terminal sliding mode improves the convergence speed of conventional terminal sliding mode. Combined with backstepping control, it effectively reduces the conservatism of sliding mode control and improves system performance. For ease of design, this embodiment designs the quadrature-axis and direct-axis current controllers separately.

[0032] The quadrature-axis current error variable is defined as: (twenty four); right Taking the derivative, we can get: (25); Based on the basic principle of fast terminal sliding mode control, the sliding surface can be selected: (26); Where, , , and is an odd number and satisfies .

[0033] Therefore, the quadrature-axis current sliding mode controller of the electrical subsystem is designed as follows: (27); Constructing Lyapunov functions for: (28); right Taking the derivative we get: (29); Combining equations (23)(25)(26)(27)(29) we can get: (30).

[0034] In order to achieve the decoupling of current and speed and make the torque not affected by the flux current, the The control strategy is defined as follows: (31); right Taking the derivative, we can get: (32); Define the sliding surface: (33); Where, , , the direct-axis current sliding mode controller is designed as: (34).

[0035] In this embodiment, step S5 is specifically as follows: Lemma 1: For a system with bounded initial conditions, if there exists a Continuous and positive definite Lyapunov function ,satisfy ,like ,in 、 : Class function and 、 If it is a positive constant, then the solution of the system Consistently eventually bounded.

[0036] Theorem 1: For the electronic mechanical brake system shown in equation (5), using the virtual control law shown in equations (15) (19) and the feedback control law shown in equations (27) (34), the controller tends to be stable and the tracking error can be constrained to the boundary (- R 1, R Within 1).

[0037] Proof: The control Lyapunov function of the entire system is selected as: (35); right Taking the derivative, we can get: (36); Substituting the virtual control rate (15)(19) and the control rate (27)(34) into formula (36), we can obtain: (37); Select 、 、 is a positive real number, and is an odd number and satisfies .but , the controller tends to be stable. Where, It can be expressed as: (38); Formula (38) can be further expressed as: (39); ,and and The expressions are: (40), (41); Integrating both sides of formula (39) simultaneously, we can obtain: (42); Where, (43); From formula (35) and formula (39), we can get: (44); Solving the inequality, we can get: (45).

[0038] From the above formula, we can get the system tracking error Constrained at the boundary This proves the stability of the system.

[0039] In an embodiment provided by the present invention, the main parameters of the system are shown in Table 1, and the main parameters of the controller are shown in Table 2.

[0040] Table 1 Main system parameters .

[0041] Table 2 Controller parameters parameter Numerical <![CDATA[ α 1 α 2]]> 20 <![CDATA[ β 1 β 2]]> 0.1 37 35 220 <![CDATA[ δ 1]]> 600 <![CDATA[ δ 2]]> 50 <![CDATA[ k 3= k 4]]> 120 <![CDATA[ η 1= η 2]]> 5

[0042] In this embodiment, the following comparison is made to demonstrate the advantages of the method proposed in this embodiment.

[0043] The sinusoidal braking condition simulates a relatively mild braking process. The sinusoidal clamping force condition designed for simulation has a frequency of 1 Hz, an amplitude of 500 N, and a sine wave offset of 700 N. That is, there is a large error of 200 N at the initial moment. The specific expression of the time-varying error constraint boundary function is: While verifying the effectiveness of the control method of this application, the simulation also compared a group of control methods without integral feedback, with the rest of the control parts being the same, such as Figure 2 As shown. Figure 2From (a), we can see that the two control methods have good control effects, can effectively track the target clamping force, and are always constrained within the error range, which proves the effectiveness of the designed controller. Figure 2 The tracking error comparison results in (b) show the role of integral feedback. Due to the time-varying characteristics of parameters and unmodeled dynamics in the braking system, the introduction of the integral term can improve the clamping force tracking accuracy, accelerate the convergence speed of the error signal, and achieve better control effect.

[0044] In order to verify the superiority of the algorithm performance of this application combined with sliding mode control, the constrained backstepping sliding mode control method constructed in this application is recorded as M1, where the virtual control law and feedback control law are expressed as (15)(19), (27)(34); M2 is not combined with sliding mode control, where the clamping force loop and speed loop are the same as the control method of this application, and the current loop adopts the traditional constrained backstepping method to design the control law, which is expressed as formula (46). Among them, the controller parameters .

[0045] (46).

[0046] Braking response time is a crucial indicator of vehicle safety, so a dual-step test was designed to simulate emergency braking of a small vehicle. The target maximum brake clamping forces for the dual-step test were 1000N and 500N, representing emergency braking at higher and lower speeds, respectively. Figure 3 The clamping force following test results of the two control methods under double-step working conditions are shown. From the partially enlarged diagram, it can be seen that the two control methods under the double-step target of 1000N begin to generate braking clamping force at 0.5s. The M1 and M2 control methods reach the target clamping force at 0.55s and 0.63s respectively. Therefore, the clamping force response time of the two control methods is approximately 0.05s and 0.13s respectively. Compared with the M2 method, the response time of the M1 control method of this application is improved by 61%, which proves that the backstepping control method based on BLF combined with non-singular fast terminal sliding mode control of this application has relatively better rapid response performance. It is worth noting that compared with Figure 2 The simulation results show that there are small fluctuations in the experimental result curves, which is mainly due to the inevitable mechanical vibration and external noise interference around the force sensor.

[0047] The triangular wave braking condition represents the driver's regular application of the brake pedal in certain specific situations. The triangular wave braking target clamping force frequency designed for the experiment is 1Hz, amplitude 500N, offset 700N, and there is also a 200N clamping force error at the initial moment, so the limited boundary parameters are also set to The experimental results of the two control methods under triangular wave conditions are as follows: Figure 4 、 Figure 5 As shown. Figure 4 It can be seen from the clamping force diagram that both control methods can effectively track the target clamping force, proving the practical feasibility of the two control methods under the triangular wave target clamping force. However, it can be seen from the enlarged diagram that the M1 control method of the present application is more effective, especially near the turning point of the clamping force. Figure 5 The error diagram of the two control methods under the triangular wave working condition is shown in Figure 2. The standard deviations of the M1 control method and the M2 control method of the present application are 20.10N and 28.14N respectively. The standard deviation of the method of the present application under the triangular wave working condition is effectively reduced by 28.57%. It can also be seen from the figure that the M1 control method of the present application can basically keep the error bounded within the boundary. The constraint effect is better than that of the M2 control method.

[0048] According to the research results, the control method of the present invention can improve the response time and control accuracy of the EMB clamping force compared with the control method before the improvement. It will bring certain economic benefits after being put into industrial application, which shows great engineering application prospects.

Claims

1. A clamping force constrained backstepping sliding mode control method for an electromechanical brake system, characterized in that: The steps include: S1. Establish a state space model of the electromechanical brake system and simplify it into a strict feedback form; S2. Construct a time-varying tangent barrier Lyapunov function with an error integral term. Use the exponentially decaying time-varying function as the constraint boundary for the clamping force tracking error of the electromechanical brake system. In addition, introduce an integral term to eliminate the steady-state error caused by unmodeled dynamics, thereby ensuring the output constraint performance and tracking accuracy of the system. S3. Based on the obstacle Lyapunova function in step S2, a backstepping control method is designed to obtain the virtual control rates of the outer clamping force loop and the speed loop; S4. Design a current controller based on the combination of fast terminal sliding mode control and backstepping control to obtain the feedback control rate of the inner current loop and achieve fast and accurate tracking of the clamping force of the electronic mechanical brake system.

2. The clamping force constrained backstepping sliding mode control method for an electronic mechanical brake system according to claim 1, characterized in that: In step S1, the electronic mechanical braking system includes a drive motor, a transmission mechanism, a brake caliper, a brake disc, a force sensor, and a control system. The drive motor adopts a surface-mounted permanent magnet synchronous motor, and the transmission mechanism includes a reduction mechanism and a ball screw mechanism.

3. The clamping force constrained backstepping sliding mode control method for an electromechanical brake system according to claim 2, characterized in that: In step S1, the state space model expression of the electronic mechanical brake system is as follows: ； Among them, the state variable , is the clamping force, is the rotor mechanical angular velocity, 、 is the stator current vector 、 Axis component, is the clamping force coefficient, which represents the relationship between the reducer rotation angle and the clamping force The relationship between , is the stiffness coefficient of the brake disc, is the proportionality coefficient, and , is the ball screw mechanical efficiency, is the mechanical efficiency of the planetary gear mechanism, is the ball screw lead, is the reduction ratio, To convert the equivalent moment of inertia to the motor shaft, is the viscous friction coefficient, is the number of magnetic pole pairs, is the coupling flux of the rotor permanent magnet on the stator, is the load torque at the initial state, is the winding inductance, 、 is the stator voltage vector 、 Axis component, is the winding resistance.

4. The clamping force constrained backstepping sliding mode control method for an electromechanical brake system according to claim 1, characterized in that: In step S2, the expression of the time-varying tangent barrier Lyapunov function including the error integral term is as follows: ； Where, is the system dynamic tracking error, is the integral term of the system dynamic tracking error, is the designed error integral coefficient. The error integral term is introduced into the time-varying tangent barrier Lyapunov function. The steady-state error can be eliminated by the integral action, which is recorded as: ； Where, is the actual value of the clamping force at any time, is the reference value of clamping force at any time, is the dynamic tracking error at any time; is the time-varying error constraint boundary exponential decay function, and its expression is as follows: ； Where, for The initial value is set according to the initial error of the clamping force. for hour The steady-state value of ; In the steady-state phase, the parameter The size of determines the steady-state error boundary, The smaller the system steady-state error, The convergence speed of .

5. The clamping force constrained backstepping sliding mode control method for an electronic mechanical brake system according to claim 4, characterized in that: In step S3, the virtual control rate of the outer ring clamping force ring is The expression is as follows: ； Where, is the clamping force coefficient, which represents the relationship between the reducer rotation angle and the clamping force. is the target clamping force, is a proportional coefficient greater than zero.

6. The clamping force constrained backstepping sliding mode control method for an electromechanical brake system according to claim 5, characterized in that: In step S3, the virtual control rate of the speed loop The expression is as follows: ； Where, , is the number of magnetic pole pairs, is the coupling flux of the rotor permanent magnet on the stator, is the error variable defined, , is a constant greater than zero, is the proportionality coefficient, and , is the ball screw mechanical efficiency, is the mechanical efficiency of the planetary gear mechanism, is the ball screw lead, is the reduction ratio, is the viscous friction coefficient, is the load torque at the initial state, To convert the equivalent moment of inertia to the motor shaft, the state variable , is the clamping force, is the rotor mechanical angular velocity, 、 is the stator current vector 、 Axis component.

7. The clamping force constrained backstepping sliding mode control method for an electromechanical brake system according to claim 6, characterized in that: In step S4, the quadrature axis and direct axis current controllers are designed respectively, wherein the quadrature axis ( The design expression of the current controller of axis is as follows: ； Where, , , are sliding surface coefficients; and is an odd number and satisfies , is the stator voltage vector Axis component, for Equivalent control item of axis sliding mode control, for Axis sliding mode control switching control item, is the winding resistance, is the winding inductance, for Axis reference current, , which means the definition Shaft current error variable, for Shaft sliding surface, 、 Both Reaching law coefficient of the switching control term of axis sliding mode control.

8. The clamping force constrained backstepping sliding mode control method for an electronic mechanical brake system according to claim 7, characterized in that: Straight shaft ( The design expression of the current controller of axis is as follows: ； Where, , , are sliding surface coefficients, for Axis reference current, , which means the definition Shaft current error variable, for Shaft sliding surface, for Equivalent control item of axis sliding mode control, for Axis sliding mode control switching control item, 、 for Reaching law coefficient of the switching control term of axis sliding mode control.

9. The clamping force constrained backstepping sliding mode control method for an electronic mechanical brake system according to claim 1, characterized in that: The method also includes: Step S5: Prove the stability of the system based on Lyapunov's stability theorem.

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