An electromechanical brake system clamping force multi-loop anti-interference control method

Abstract

The application belongs to the technical field of automobiles, and particularly relates to a multi-closed-loop control method for clamping force of an electromechanical brake system considering nonlinear disturbance. The method comprises the following steps: step one, building an electromechanical brake actuator model; step two, designing a clamping force loop controller considering the variable stiffness characteristics of the system; step three, designing a position loop controller based on friction model compensation by using an inversion sliding mode control method; and step four, designing a current loop controller based on current decoupling, so as to finally realize multi-closed-loop control of the clamping force. The application has higher control precision, faster response speed and stronger robustness, can effectively improve the braking performance of the electromechanical brake system, and provides a feasible solution for high-precision control of braking force of an intelligent automobile.

Description

Technical Field

[0001] This invention belongs to the field of automotive technology, specifically a multi-closed-loop disturbance rejection control method for clamping force in an electromechanical braking system. Background Technology

[0002] The development of intelligent automotive technology has placed higher demands on the response speed, control precision, and stability of brakes. Electromechanical braking eliminates the hydraulic unit in traditional braking systems, using an electric motor to output clamping force, resulting in a simpler mechanism and a smaller overall mass of the braking unit. Furthermore, electromechanical braking offers more accurate clamping force control, aligning with the current trend in vehicle control development and conforming to the direction of modular and integrated control. Therefore, the study of clamping force control in electromechanical braking systems is particularly important.

[0003] To achieve clamping force control, a control architecture consisting of three loops—clamping force loop, position loop, and current loop—is commonly used. Different control methods are often employed in each loop to ensure effective tracking of the actual clamping force. Currently, methods such as proportional-integral-derivative (PI-DI) control, model predictive control, and sliding mode control are applied to electromechanical braking clamping force control. However, these control methods largely ignore the influence of system variable stiffness characteristics, frictional characteristics, and external disturbances on clamping force control, relying solely on controller error adjustment to achieve target clamping force tracking. This results in weak system robustness, making it difficult to achieve accurate clamping force control output in the presence of external disturbances. Furthermore, due to the significant differences in the control bandwidths of the clamping force loop, position loop, and current loop, multi-loop control methods are used to address the mismatch in characteristics among these three loops.

[0004] To address the aforementioned problems, this invention proposes an electromechanical braking clamping force control strategy that considers the system's variable stiffness characteristics, frictional characteristics, and external disturbances. First, a motor model including a motor, transmission reduction mechanism, and friction model is constructed. The clamping force loop consists of feedforward compensation for variable stiffness characteristics and a proportional-integral-derivative closed-loop feedback regulator. Second, the position loop overcomes the system's frictional loss problem by designing an inverse sliding mode controller and friction model compensation. Finally, current decoupling control is introduced into the current controller to reduce the impact of current coupling effects on the motor's response speed. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a multi-closed-loop disturbance rejection control method for clamping force in an electromechanical braking system. This method offers higher control precision, faster response speed, and stronger robustness, effectively improving the braking performance of the electromechanical braking system and providing a feasible solution for high-precision control of braking force in intelligent vehicles.

[0006] The technical solution of this invention is described below in conjunction with the accompanying drawings:

[0007] A multi-closed-loop disturbance rejection control method for clamping force in an electromechanical braking system includes the following steps:

[0008] Step 1: Build a model of the electromechanical brake actuator;

[0009] Step 2: Design a clamping force ring controller that takes into account the variable stiffness characteristics of the system;

[0010] Step 3: Design a position loop controller based on friction model compensation using the inversion sliding mode control method;

[0011] Step 4: Design a current loop controller based on current decoupling to ultimately achieve multi-closed-loop control of clamping force.

[0012] Furthermore, the specific method for step one is as follows:

[0013] An electromechanical brake actuator model is established; the electromechanical brake actuator includes a motor, a reduction mechanism, and a brake caliper; specifically as follows:

[0014] The motor is modeled, and the stator voltage equations are established on the torque axis and excitation axis without considering eddy current and hysteresis losses, as shown below:

[0015]

[0016] In the formula, u d u q These are the voltage components along the d-axis and q-axis of the stator voltage, respectively; i d i q These represent the stator current components along the d-axis and q-axis, respectively; L d L q These are the d-axis and q-axis components of the inductance, respectively; R is the stator resistance. ψ is the electric angular velocity. f For permanent magnet flux linkage;

[0017] The torque balance equation is established at the motor output shaft as follows:

[0018]

[0019] In the formula, J is the equivalent moment of inertia; w m T is the angular velocity of the motor. l T represents the motor load torque. f T is the frictional torque; e p is the electromagnetic torque of the motor. n i is the number of pole pairs of the motor; q For torque shaft current; ψ f For permanent magnet flux linkage;

[0020] The equations for the force balance relationship on the brake piston are established as follows:

[0021]

[0022] In the formula, m sc The equivalent mass of the brake piston is x; the displacement of the brake piston is F. l F is the pressure exerted by the actuator on the brake piston. cl F is the braking pressure output by the brake piston. f The frictional force acting on the brake piston;

[0023] Convert the mass and moment of inertia of all mechanism components into an equivalent mass m eq As shown below:

[0024] m eq =JN 2 +m sc (5)

[0025] In the formula, J is the equivalent moment of inertia of the motor assembly; N is the transmission ratio of the entire transmission mechanism; m sc The equivalent mass of the brake piston;

[0026] Integrating equations (4) and (5), we arrive at the electromechanical braking transmission mechanism part model, as shown below:

[0027]

[0028] In the formula, m eq For equivalent mass; x is the brake piston displacement; N is the transmission ratio of the entire transmission mechanism; T e F represents the electromagnetic torque of the motor. cl F is the braking pressure output by the brake piston. f The frictional force acting on the brake piston;

[0029] The friction loss of the system mechanism is calculated using a concentrated friction model. Therefore, the reduction mechanism and transmission mechanism are simplified to the transmission ratio. The calculation method is as follows:

[0030]

[0031] In the formula, i is the planetary gear reduction ratio; s is the ball screw lead;

[0032] Friction in electromechanical brake actuators during operation is classified into two categories: static friction, which is related to velocity, and dynamic friction, which is related to both velocity and displacement. The static friction model consists of static friction, Coulomb friction, and viscous friction. A coupled friction model is designed to model the frictional forces, as shown below:

[0033]

[0034] In the formula, F is the angular velocity of the motor. cl T is the clamping force of the electromechanical brake actuator; e T is the difference between the motor torque and the load torque. e =T m -N·F l D is the viscous friction coefficient of the system; C is the Coulomb friction torque of the electromechanical brake actuator under no-load conditions; G is the Coulomb friction coefficient of the system; T s ε represents the static friction torque of the electromechanical brake actuator; ε is infinitesimal.

[0035] Furthermore, the specific method for step two is as follows:

[0036] 21) Based on the variable stiffness characteristics of the system, design stiffness characteristic feedforward compensation, and obtain the desired piston displacement according to the relationship between clamping force and piston displacement.

[0037]

[0038] In the formula, k d d is the proportionality constant. dis-target (F * Let ) be the stiffness characteristic function of the system, expressed as:

[0039] F = a·x 3 +b·x 2 +c·x+d (10)

[0040] In the formula, x is the piston displacement; a, b, c and d are the parameters of the fitted curve;

[0041] 22) Introduce a proportional-integral-derivative feedback controller to control the desired clamping force F in the clamping force loop feedback control. * The difference between the actual clamping force F and the actual clamping force F is used as the controller input to obtain the desired feedback piston displacement.

[0042]

[0043] In the formula, F * Target clamping force; F is the actual clamping force; k p1 For proportional gain; k i1 For integral gain; k d1 This is the differential gain;

[0044] Integrating equations (9) and (11), we obtain the final output desired piston displacement y. * for:

[0045]

[0046] In the formula, The piston displacement is calculated based on the stiffness curve; The proportional-integral-derivative controller outputs the piston displacement based on the clamping force difference.

[0047] Furthermore, the specific method for step three is as follows:

[0048] 31) Define the difference z1 between the actual piston displacement and the target displacement as the system input value, as shown below:

[0049] z1=yy * (13)

[0050] In the formula, y is the actual displacement of the piston; * For the target displacement of the piston;

[0051] The derivative of the output error value z1 is shown below:

[0052]

[0053] 32) Define the Lyapunov function as follows:

[0054]

[0055] 33) Introduce a virtual control variable α1, as shown below:

[0056] α1=c1z1 (16)

[0057] In the formula, c1 is a positive constant;

[0058] Define the control error variable z2 as follows:

[0059]

[0060] From equations (16) and (17), we obtain the following equation:

[0061]

[0062] 34) Take the derivative of equation (17) to calculate the derivative of the control output error value z2, as shown below:

[0063]

[0064] Combining equation (6), we get the following equation:

[0065]

[0066] In the formula, m eq F is the equivalent inertial mass of the friction plate; lF is the clamping force input to the system. cl F is the clamping force output by the system. f α1 represents the frictional force in the electromechanical braking mechanism; α2 is the virtual control quantity.

[0067] 35) Define the Lyapunov function as follows:

[0068]

[0069] In the formula, s is the sliding surface function, defined as follows:

[0070] s=k1z1+z2 (22)

[0071] In the formula, k1 is a positive constant;

[0072] The derivative of the sliding surface function is shown below:

[0073]

[0074] The derivative of equation (21) is then taken as follows:

[0075]

[0076] 36) Combining equations (16) and (19), we obtain the following equation:

[0077]

[0078] 37) The design convergence law is as follows:

[0079]

[0080] In the formula, η>0;

[0081] 38) Combining equations (26), (20), and (23), we obtain the following equation:

[0082]

[0083] 39) Transform the motor torque expression F l =k t i q Substituting into equation (27) yields the target current. As shown below:

[0084]

[0085] In the formula, k t m is the motor torque coefficient. eq The equivalent inertial mass of the friction plate; k1, k2 are positive constants; c1 is a positive constant; F clF is the clamping force output by the system. f Friction force in electromechanical braking mechanisms; y * The target displacement.

[0086] Furthermore, the specific method for step four is as follows:

[0087] 41) Define the current tracking error as follows:

[0088]

[0089] The derivative of the error is as follows:

[0090]

[0091] In the formula, u d u q These are the voltage components along the d-axis and q-axis of the stator voltage, respectively; i d i q These are the components of the stator current along the d-axis and q-axis, respectively. These are the target values ​​for the stator current along the d-axis and q-axis, respectively; L d L q These represent the d-axis and q-axis components of the inductance, respectively; R is the stator resistance; w e ψ is the electric angular velocity. f For permanent magnet flux linkage;

[0092] 42) The current control law is designed using the Lyapunov direct method, as shown below:

[0093]

[0094] The beneficial effects of this invention are as follows:

[0095] 1) This invention uses system stiffness characteristic feedforward compensation and proportional-integral-derivative control method to design clamping force loop controller, which can effectively improve the clamping force following hysteresis problem caused by the variable stiffness characteristics of electromechanical braking system;

[0096] 2) This invention designs a position loop controller based on friction compensation and inversion sliding mode controller, which simplifies the complex nonlinear system control problem into a low-order system control, reduces the difficulty of controller design, and improves system robustness. It also introduces a coupled friction model that considers Coulomb friction, viscous friction and static friction to compensate for friction loss in the mechanism and correct the target current value.

[0097] 3) The present invention introduces current decoupling control in the design of the current loop controller, which can reduce the impact of the coupling between the excitation shaft current and the torque shaft current of the PMSM motor and improve the voltage build-up speed of the system during emergency braking. Attached Figure Description

[0098] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0099] Figure 1 This is a schematic diagram of the process of the present invention;

[0100] Figure 2 This is a schematic diagram of an electromechanical brake actuator.

[0101] Figure 3 A schematic diagram showing the current following results of the controller designed for this invention under slope conditions;

[0102] Figure 4 A schematic diagram showing the displacement following results of the controller designed in this invention under slope conditions;

[0103] Figure 5 This is a schematic diagram showing the clamping force following result of the controller designed for this invention under slope conditions. Detailed Implementation

[0104] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0105] Example 1

[0106] This embodiment provides a multi-closed-loop disturbance rejection control method for clamping force in an electromechanical braking system, including the following steps:

[0107] Step 1: To achieve accurate control of the electromechanical braking clamping force, it is first necessary to build an electromechanical braking actuator model; the schematic diagram of the electromechanical braking actuator is shown below. Figure 2 As shown, it mainly includes a motor, a reduction mechanism, brake friction pads, a brake disc, and a brake caliper.

[0108] This invention first models the motor and establishes stator voltage equations on the torque axis and excitation axis without considering eddy current and hysteresis losses, as shown below:

[0109]

[0110] In the formula, u d u q These are the voltage components along the d-axis and q-axis of the stator voltage, respectively; id i q These represent the stator current components along the d-axis and q-axis, respectively; L d L q These are the d-axis and q-axis components of the inductance, respectively; R is the stator resistance. ψ is the electric angular velocity. f For permanent magnet flux linkage;

[0111] The torque balance equation is established at the motor output shaft as follows:

[0112]

[0113] In the formula, J is the equivalent moment of inertia; w m T is the angular velocity of the motor. l T represents the motor load torque. f T is the frictional torque. e For the electromagnetic torque of the motor, xn i is the number of pole pairs of the motor; q For torque shaft current; ψ f For permanent magnet flux linkage;

[0114] The equations for the force balance relationship on the brake piston are established as follows:

[0115]

[0116] In the formula, m sc The equivalent mass of the brake piston is x; the displacement of the brake piston is F. l F is the pressure exerted by the actuator on the brake piston. cl F is the braking pressure output by the brake piston. f The frictional force acting on the brake piston;

[0117] To simplify the analysis process, this invention converts the mass and moment of inertia of all mechanism components into an equivalent mass m. eq As shown below:

[0118] m eq =JN 2 +m sc (5)

[0119] In the formula, J is the equivalent moment of inertia of the motor assembly; N is the transmission ratio of the entire transmission mechanism; m se The equivalent mass of the brake piston;

[0120] Integrating equations (4) and (5), we arrive at the electromechanical braking transmission mechanism part model, as shown below:

[0121]

[0122] In the formula, m eq For equivalent mass; x is the brake piston displacement; N is the transmission ratio of the entire transmission mechanism; T e F represents the electromagnetic torque of the motor. cl F is the braking pressure output by the brake piston. f The frictional force acting on the brake piston;

[0123] To reduce friction complexity and simplify analysis, this invention employs a lumped friction model to calculate the friction loss of the system mechanism. Therefore, the reduction mechanism and transmission mechanism are simplified to transmission ratios, and the calculation method is as follows:

[0124]

[0125] In the formula, i is the planetary gear reduction ratio; s is the ball screw lead;

[0126] Friction in electromechanical brake actuators during operation is classified into two categories: static friction, which is related to speed, and dynamic friction, which is related to both speed and displacement. The static friction model consists of static friction, Coulomb friction, and viscous friction. Therefore, this invention designs a coupled friction model to model the frictional force, as shown below:

[0127]

[0128] In the formula, F is the angular velocity of the motor. cl T is the clamping force of the electromechanical brake actuator. e T is the difference between the motor torque and the load torque. e =T m -N·F l D is the viscous friction coefficient of the system; C is the Coulomb friction torque of the electromechanical brake actuator under no-load conditions; G is the Coulomb friction coefficient of the system; T s ε represents the static friction torque of the electromechanical brake actuator; ε is infinitesimal.

[0129] Step 2: Design a clamping force ring controller that considers the variable stiffness characteristics of the system, as follows:

[0130] 21) Based on the variable stiffness characteristics of the system, design stiffness characteristic feedforward compensation, and obtain the desired piston displacement according to the relationship between clamping force and piston displacement.

[0131]

[0132] In the formula, k d d is the proportionality constant. dis-target (F * Let ) be the stiffness characteristic function of the system, expressed as:

[0133] F = a·x 3 +b·x 2 +c·x+d (10)

[0134] In the formula, x is the piston displacement; a, b, c and d are the parameters of the fitted curve;

[0135] 22) Introduce a proportional-integral-derivative feedback controller to control the desired clamping force F in the clamping force loop feedback control. * The difference between the actual clamping force F and the actual clamping force F is used as the controller input to obtain the desired feedback piston displacement.

[0136] In the formula, F * Target clamping force; F is the actual clamping force; k p1 For proportional gain; k i1 For integral gain; k d1 This is the differential gain;

[0137] Integrating equations (9) and (11), we obtain the final output desired piston displacement y. * for:

[0138]

[0139] In the formula, The piston displacement is calculated based on the stiffness curve; The proportional-integral-derivative controller outputs the piston displacement based on the clamping force difference.

[0140] Step 3: Design a position loop controller using the inverse sliding mode control method, and compensate the output current using a friction model to reduce the impact of nonlinear friction on the clamping force control accuracy, as detailed below:

[0141] 31) Define the difference z1 between the actual piston displacement and the target displacement as the system input value, as shown below:

[0142] z1=yy * (13)

[0143] In the formula, y is the actual displacement of the piston; * For the target displacement of the piston;

[0144] The derivative of the output error value z1 is shown below:

[0145]

[0146] 32) Define the Lyapunov function as follows:

[0147]

[0148] 33) Introduce a virtual control quantity α1, as shown below:

[0149] α1=c1z1 (16)

[0150] In the formula, c1 is a positive constant;

[0151] Define the control error variable z2 as follows:

[0152]

[0153] From equations (16) and (17), we obtain the following equation:

[0154]

[0155] When z2 = 0, the derivative of the Lyapunov function is... Let z1 be a quadratic function of the system's control output error value, then we know However, in actual control, z2≠0, so further design is required.

[0156] 34) Take the derivative of equation (17) to calculate the derivative of the control output error value z2, as shown below:

[0157]

[0158] Combining equation (6), we get the following equation:

[0159]

[0160] In the formula, m eq F is the equivalent inertial mass of the friction plate; l F is the clamping force input to the system. cl F is the clamping force output by the system. f α1 represents the frictional force in the electromechanical braking mechanism; α2 is the virtual control quantity.

[0161] 35) Define the Lyapunov function as follows:

[0162]

[0163] In the formula, s is the sliding surface function, defined as follows:

[0164] s=k1z1+z2 (22)

[0165] In the formula, k1 is a positive constant;

[0166] The derivative of the sliding surface function is shown below:

[0167]

[0168] The derivative of equation (21) is then taken as follows:

[0169]

[0170] 36) Combining equations (16) and (19), we obtain the following equation:

[0171]

[0172] 37) The design convergence law is as follows:

[0173]

[0174] In the formula, η>0;

[0175] 38) Combining equations (26), (20), and (23), we obtain the following equation:

[0176]

[0177] 39) Transform the motor torque expression F l =k t i q Substituting into equation (27) yields the target current. As shown below:

[0178]

[0179] In the formula, k t m is the motor torque coefficient. eq The equivalent inertial mass of the friction plate; k1, k2 are positive constants; c1 is a positive constant; F cl F is the clamping force output by the system. f Friction force in electromechanical braking mechanisms; y * For the target displacement;

[0180] Substituting equation (26) into equation (24), we obtain the following equation:

[0181]

[0182] Substituting into equation (22), we get the following equation:

[0183]

[0184] By Young's inequality We obtain the following formula:

[0185]

[0186] when When η>0, The system is asymptotically stable, which proves that the design of equation (28) is reasonable.

[0187] Step 4: Consider the excitation shaft current i when designing the current loop controller. d and torque shaft current i q The coupling between the two axes causes the currents to affect each other, and the coupling effect becomes more pronounced as the electric angular velocity increases, thus reducing the control accuracy of the current and the dynamic response speed of the system. Therefore, current decoupling control is introduced into the current loop control, as follows:

[0188] 41) Define the current tracking error as follows:

[0189]

[0190] The derivative of the error is as follows:

[0191]

[0192] In the formula, u d u q These are the voltage components along the d-axis and q-axis of the stator voltage, respectively; i d i q These are the components of the stator current along the d-axis and q-axis, respectively. These are the target values ​​for the stator current along the d-axis and q-axis, respectively; L d L q These represent the d-axis and q-axis components of the inductance, respectively; R is the stator resistance; w e ψ is the electric angular velocity. f For permanent magnet flux linkage;

[0193] 42) The current control law is designed using the Lyapunov direct method, as shown below:

[0194]

[0195] Thus, the control law for multi-closed-loop disturbance rejection control of clamping force in electromechanical braking system was obtained.

[0196] Example 2

[0197] To verify the effectiveness and superiority of the method proposed in this invention, a simulation test environment was built based on MATLAB / Simulink. The control strategy designed in this invention was compared with a traditional three-closed-loop PID controller. A ramp condition was selected, with a boost rate of 2000 N / s and a simulation time of 9 seconds. The obtained current following curve, displacement following curve, and clamping force following curve are shown below. Figure 3 , Figure 4 , Figure 5As shown in the figure, in terms of response speed, the controller designed in this invention can reach the target clamping force more quickly and achieve clamping force tracking more accurately. Regarding overshoot, the actual clamping force of the controller designed in this invention exhibits almost no overshoot; therefore, the controller designed in this invention can effectively avoid system instability or mechanical damage caused by overshoot.

[0198] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-closed-loop disturbance rejection control method for clamping force in an electromechanical braking system, characterized in that, Includes the following steps: Step 1: Build a model of the electromechanical brake actuator; Step 2: Design a clamping force ring controller that takes into account the variable stiffness characteristics of the system; Step 3: Design a position loop controller based on friction model compensation using the inversion sliding mode control method; Step 4: Design a current loop controller based on current decoupling to ultimately achieve multi-closed-loop control of clamping force; The specific method for step one is as follows: An electromechanical brake actuator model is established; the electromechanical brake actuator includes a motor, a reduction mechanism, brake friction pads, a brake disc, and a brake caliper; specifically as follows: The motor is modeled, and the stator voltage equations are established on the torque axis and excitation axis without considering eddy current and hysteresis losses, as shown below: （1） In the formula, , Stator voltages shaft and Voltage components of the axis; , The stator currents are respectively shaft and The components of the axis; , Inductance respectively shaft and The components of the axis; Stator resistance; Electric angular velocity; For permanent magnet flux linkage; The torque balance equation is established at the motor output shaft as follows: （2） （3） In the formula, It is the equivalent moment of inertia; The angular velocity of the motor; This represents the motor load torque. Friction torque; This refers to the electromagnetic torque of the motor. This represents the number of pole pairs of the motor. For torque shaft current; For permanent magnet flux linkage; The equations for the force balance relationship on the brake piston are established as follows: （4） In the formula, The equivalent mass of the brake piston; For the displacement of the braking piston; The pressure exerted by the actuator on the brake piston; The braking pressure output by the brake piston; The frictional force acting on the brake piston; Convert the mass and moment of inertia of all mechanism components into equivalent mass As shown below: （5） In the formula, This is the equivalent rotational inertia of the motor assembly. This refers to the transmission ratio of the entire transmission mechanism; The equivalent mass of the brake piston; Integrating equations (4) and (5), we arrive at the electromechanical braking transmission mechanism part model, as shown below: （6） In the formula, For equivalent quality; For the displacement of the braking piston; This refers to the transmission ratio of the entire transmission mechanism; This refers to the electromagnetic torque of the motor. The braking pressure output by the brake piston; The frictional force acting on the brake piston; The friction loss of the system mechanism is calculated using a concentrated friction model. Therefore, the reduction mechanism and transmission mechanism are simplified to the transmission ratio. The calculation method is as follows: （7） In the formula, This refers to the planetary gear reduction ratio; For the ball screw lead; Friction in electromechanical brake actuators during operation is classified into two categories: static friction, which is related to velocity, and dynamic friction, which is related to both velocity and displacement. The static friction model consists of static friction, Coulomb friction, and viscous friction. A coupled friction model is designed to model the frictional forces, as shown below: （8） In the formula, This refers to the angular velocity of the motor. The clamping force of the electromechanical brake actuator; This is the difference between the motor torque and the load torque. ; The viscous friction coefficient in the system The Coulomb friction torque of the electromechanical brake actuator under no-load conditions; Let be the system's Coulomb friction coefficient; The static friction torque of the electromechanical brake actuator; It is infinitesimal.

2. The multi-closed-loop disturbance rejection control method for clamping force of an electromechanical braking system according to claim 1, characterized in that, The specific method for step two is as follows: 21) Based on the variable stiffness characteristics of the system, design stiffness characteristic feedforward compensation, and obtain the desired piston displacement according to the relationship between clamping force and piston displacement. : （9） In the formula, This is the proportionality coefficient. Let the stiffness characteristic function of the system be expressed as: （10） In the formula, This represents piston displacement; , , and These are the parameters for the fitted curve; 22) Introduce a proportional-integral-derivative feedback controller to control the desired clamping force in the clamping force loop feedback control. With actual clamping force The difference is used as the controller input to obtain the desired feedback piston displacement. : （11） In the formula, Clamping force for the target; This is the actual clamping force; For proportional gain; This is the integral gain; This is the differential gain; Integrating the above formula, we obtain the final desired piston displacement. for: （12） In the formula, The piston displacement is calculated based on the stiffness curve; The proportional-integral-derivative controller outputs the piston displacement based on the clamping force difference.

3. The multi-closed-loop disturbance rejection control method for clamping force of an electromechanical braking system according to claim 1, characterized in that, The specific method for step three is as follows: 31) Define the difference between the actual displacement and the target displacement of the piston. The system's input values ​​are as follows: （13） In the formula, This represents the actual displacement of the piston. For the target displacement of the piston; For output error value Differentiate as follows: （14） 32) Define the Lyapunov function as follows: （15） 33) Introduce virtual control variables As shown below: （16） In the formula, It is a positive number; Define control error variables As shown below: （17） From equations (16) and (17), we obtain the following equation: （18） 34) Take the derivative of equation (17) and calculate the control output error value. The derivative is shown below: （19） Combining equation (6), we get the following equation: （20） In the formula, This is the equivalent inertial mass of the friction plate; The clamping force input to the system; The clamping force output by the system; Friction force in electromechanical braking mechanisms; This is a virtual control variable; 35) Define the Lyapunov function as follows: （21） In the formula, The sliding surface function is defined as follows: （22） In the formula, It is a positive number; The derivative of the sliding surface function is shown below: （23） Then, taking the derivative of equation (21) is as follows: （24） 36) Combining equations (16) and (19), we obtain the following equation: （25） 37) The design convergence law is as follows: （26） In the formula, ; 38) Combining equations (26), (20), and (23), we obtain the following equation: （27） 39) Transform the motor torque expression Substituting into equation (27) yields the target current. As shown below: （28） In the formula, This is the motor torque coefficient; This is the equivalent inertial mass of the friction plate; , It is a positive number; It is a positive number; The clamping force output by the system; Friction force in electromechanical braking mechanisms; The target displacement.

4. The multi-closed-loop disturbance rejection control method for clamping force of an electromechanical braking system according to claim 1, characterized in that, The specific method for step four is as follows: 41) Define the current tracking error as follows: （32） （33） The derivative of the error is as follows: （34） （35） In the formula, , Stator voltages shaft and Voltage components of the axis; , These are the stator currents. shaft and The components of the axis; , These are the stator currents. shaft and The target value of the axis; , Inductance respectively shaft and The components of the axis; Stator resistance; Electric angular velocity; For permanent magnet flux linkage; 42) The current control law is designed using the Lyapunov direct method, as shown below: （36） （37）。

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