Multi-closed-loop anti-interference control method for clamping force of electronic mechanical braking system

Abstract

The invention belongs to the technical field of automobiles, and particularly relates to an electromechanical braking system clamping force multi-closed-loop control method considering nonlinear disturbance. Comprising the following steps of 1, building an electronic mechanical brake actuator model; 2, designing a clamping force ring controller considering the variable stiffness characteristic of the system; 3, designing a position loop controller based on friction model compensation by adopting an inversion sliding mode control method; and 4, designing a current loop controller based on current decoupling, and finally realizing clamping force multi-closed-loop control. The method has higher control precision, faster response speed and stronger robustness, can effectively improve the braking performance of an electronic mechanical braking system, and provides a feasible solution for high-precision control of the braking force of an intelligent automobile.

Description

Technical Field

[0001] The present invention belongs to the technical field of automobiles, and specifically relates to a multi-closed-loop disturbance rejection control method for the clamping force of an electro-mechanical braking system. Background Art

[0002] The development of automotive intelligent technologies has put forward higher requirements for the response speed, control accuracy, and stability of brakes. Electro-mechanical braking eliminates the hydraulic unit in the traditional braking system and uses an electric motor to output the clamping force, making its mechanism composition simpler and the total mass of the braking unit smaller. In addition, the clamping force control of electro-mechanical braking is more accurate, conforming to the general trend of current vehicle control development and following the development direction of control modularization and integration. Therefore, the clamping force control of the electro-mechanical braking system is particularly important for the research of the braking system.

[0003] To achieve clamping force control, a control architecture consisting of a clamping force loop, a position loop, and a current loop is commonly selected at present. Different control methods are often selected in each loop to ensure the following effect of the actual clamping force. At present, methods such as proportional-integral-derivative control, model predictive control, and sliding mode control have been applied to the clamping force control of electro-mechanical braking. However, most of these control methods ignore the influence of system variable stiffness characteristics, friction characteristics, and external disturbances on clamping force control, and only rely on the error adjustment of the controller to achieve the follow-up of the target clamping force, resulting in weak robustness of the system. Therefore, it is difficult for the system to achieve accurate clamping force control output in the presence of external disturbances. In addition, due to the significant differences in the control bandwidths of the clamping force loop, the position loop, and the current loop, a multi-closed-loop control method is selected to solve the problem of the mismatch of the characteristics of the three.

[0004] To address the above problems, the present invention proposes a clamping force control strategy for electro-mechanical braking considering system variable stiffness characteristics, friction characteristics, and external disturbances. First, a motor model including a motor, a transmission reduction mechanism, and a friction model is built. The clamping force loop consists of a feedforward compensation with variable stiffness characteristics and a proportional-integral-derivative closed-loop feedback regulator. Secondly, the position loop overcomes the friction loss problem of the system by designing an inverse sliding mode controller and a friction model compensation. Finally, current decoupling control is introduced into the current controller to reduce the influence of the current coupling effect on the response speed of the motor. Summary of the Invention

[0005] To solve the above problems, the present invention provides a multi-closed-loop disturbance rejection control method for the clamping force of an electro-mechanical braking system, which has higher control accuracy, faster response speed, and stronger robustness, can effectively improve the braking performance of the electro-mechanical braking system, and provides a feasible solution for the high-precision control of the braking force of intelligent vehicles.

[0006] The technical solution of the present invention is described in conjunction with the accompanying drawings as follows:

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

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

[0009] Step 2: Design a clamping force loop controller considering the variable stiffness characteristics of the system;

[0010] Step 3: Use the backstepping sliding mode control method to design a position loop controller based on friction model compensation;

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

[0012] Further, the specific method of Step 1 is as follows:

[0013] Build a model of an electromechanical brake actuator; the electromechanical brake actuator includes a motor, a reduction mechanism, and a brake caliper; specifically as follows:

[0014] Model the motor, and establish the stator voltage equation on the torque axis and the excitation axis without considering eddy current and hysteresis losses, as shown below:

[0015]

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

[0017] Establish a torque balance equation at the output shaft of the motor, as shown below:

[0018]

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

[0020] Based on the force balance relationship of the brake piston, an equation is established as follows:

[0021]

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

[0023] The mass and moment of inertia of all mechanism components are converted into an equivalent mass m eq , as follows:

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

[0025] Where J is the equivalent moment of inertia of the motor component; N is the transmission ratio of the entire transmission mechanism; m sc is the equivalent mass of the brake piston;

[0026] Integrating Equation (4) and Equation (5), the partial model of the electromechanical brake transmission mechanism is as follows:

[0027]

[0028] Where m eq is the equivalent mass; x is the displacement of the brake piston; N is the transmission ratio of the entire transmission mechanism; T e is the motor electromagnetic torque; F cl is the braking pressure output by the brake piston; F f is the frictional force on the brake piston;

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

[0030]

[0031] Where i is the planetary gear reduction ratio; s is the lead of the ball screw;

[0032] The friction in the electromechanical brake actuator during operation is divided into two categories, specifically: static friction related to speed and dynamic friction related to speed 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 force, as follows:

[0033]

[0034] In the formula, is the angular velocity of the motor;; F cl is the clamping force of the electromechanical brake actuator; T e is the difference between the motor torque and the load torque, T e = T m - N·F l ; D is the viscous friction coefficient in the system; C is the Coulomb friction torque of the electromechanical brake actuator without load; G is the system Coulomb friction coefficient; T s is the static friction torque of the electromechanical brake actuator; ε is infinitesimal.

[0035] Further, the specific method of the second step is as follows:

[0036] 21) Design the stiffness characteristic feedforward compensation based on the variable stiffness characteristic of the system, and obtain the expected piston displacement according to the relationship between the clamping force and the piston displacement

[0037]

[0038] In the formula, k d is the proportional coefficient, d dis-target (F * ) is 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 fitting curve parameters;

[0041] 22) Introduce a proportional-integral-derivative feedback controller, and use the difference between the expected clamping force F * and the actual clamping force F as the controller input to obtain the expected feedback piston displacement

[0042]

[0043] In the formula, F * is the target clamping force; F is the actual clamping force; k p1 is the proportional gain; k i1 is the integral gain; k d1 is the derivative gain;

[0044] Integrate Equation (9) and Equation (11) to obtain the final output expected piston displacement y * as:

[0045]

[0046] In the formula, is the piston displacement calculated according to the stiffness curve; is the piston displacement output by the proportional-integral-derivative controller according to the clamping force difference.

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

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

[0049] z1 = y - y * (13)

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

[0051] Take the derivative of the output error value z1, as follows:

[0052]

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

[0054]

[0055] 33) Introduce the virtual control quantity α1, as follows:

[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 formula (16) and formula (17), the following formula is obtained:

[0061]

[0062] 34) Perform a derivative operation on formula (17) to calculate the derivative of the control output error value z2, as follows:

[0063]

[0064] Combined with formula (6), the following formula is obtained:

[0065]

[0066] In the formula, m eq is the equivalent inertia mass of the friction plate; F lThe clamping force input to the system; F cl The clamping force output by the system; F f The friction force in the electromechanical braking mechanism; α1 is the virtual control variable;

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

[0068]

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

[0070] s = k1z1 + z2 (22)

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

[0072] Derive the sliding mode surface function as follows:

[0073]

[0074] Then derive Equation (21) as follows:

[0075]

[0076] 36) Combine Equation (16) and Equation (19) to obtain the following equation:

[0077]

[0078] 37) Design the reaching law as follows:

[0079]

[0080] In the formula, η > 0;

[0081] 38) Combine Equation (26), (20) and (23) to obtain the following equation:

[0082]

[0083] 39) Substitute the motor torque expression F l = k t i q into Equation (27) to obtain the target current as follows:

[0084]

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

[0086] Furthermore, the specific method of step 4 is as follows:

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

[0088]

[0089] Take the derivative of the error as follows:

[0090]

[0091] In the formula, u d , u q are the voltage components of the stator voltage on the d-axis and q-axis respectively; i d , i q are the components of the stator current on the d-axis and q-axis respectively; are the target values of the stator current on the d-axis and q-axis respectively; L d , L q are the components of the inductance on the d-axis and q-axis respectively; R is the stator resistance; w e is the electrical angular velocity; ψ f is the permanent magnet flux linkage;

[0092] 42) Design the current control law by Lyapunov direct method as follows:

[0093]

[0094] The beneficial effects of the present invention are:

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

[0096] 2) The present invention designs the position loop controller based on friction compensation and backstepping sliding mode controller, simplifies the complex nonlinear system control problem to the control of a low-order system, can reduce the difficulty of controller design, and improve the system robustness, and introduces a coupled friction model considering Coulomb friction, viscous friction and static friction to compensate for the friction loss in the mechanism and correct the target current value;

[0097] 3) The present invention introduces current decoupling control in the process of designing the current loop controller, which can reduce the influence caused by the coupling of the excitation axis current and the torque axis current of the PMSM motor and improve the voltage building speed of the system during emergency braking. Description of the Drawings

[0098] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following accompanying drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other relevant accompanying drawings can also be obtained based on these drawings.

[0099] Figure 1 is a schematic flow chart of the present invention;

[0100] Figure 2 is a schematic structural diagram of an electromechanical brake actuator;

[0101] Figure 3 is a schematic diagram of the current following result of the controller designed by the present invention under a ramp condition;

[0102] Figure 4 is a schematic diagram of the displacement following result of the controller designed by the present invention under a ramp condition;

[0103] Figure 5 is a schematic diagram of the clamping force following result of the controller designed by the present invention under a ramp condition. Specific Embodiments

[0104] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the present invention and not to limit the present invention. Additionally, it should be noted that for the sake of description, only parts related to the present invention rather than all structures are shown in the accompanying drawings.

[0105] Embodiment 1

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

[0107] Step 1. To accurately control the clamping force of the electromechanical brake, an electromechanical brake actuator model needs to be built first; the schematic diagram of the actuator of the electromechanical brake is as Figure 2 shown, mainly including a motor, a reduction mechanism, a brake friction plate, a brake disc, a brake caliper, etc.

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

[0109]

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

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

[0112]

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

[0114] For the balance relationship of the forces acting on the brake piston, an equation is established as follows:

[0115]

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

[0117] To simplify the analysis process, the present invention converts the mass and moment of inertia of all mechanism components into an equivalent mass m eq as follows:

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

[0119] where J is the equivalent moment of inertia of the motor components; N is the transmission ratio of the entire transmission mechanism; m se is the equivalent mass of the brake piston;

[0120] Integrating Equation (4) and Equation (5), the partial model of the electromechanical brake transmission mechanism is as follows:

[0121]

[0122] where m eq is the equivalent mass; x is the displacement of the brake piston; N is the transmission ratio of the entire transmission mechanism; T e is the electromagnetic torque of the motor; F cl is the braking pressure output by the brake piston; F f is the friction force received by the brake piston;

[0123] In order to reduce the friction complexity and lower the analysis difficulty, the present invention adopts a concentrated friction model to calculate the friction loss of the system mechanism. Therefore, when simplifying the reduction mechanism and the transmission mechanism into a transmission ratio, the calculation method is as follows:

[0124]

[0125] where i is the planetary gear reduction ratio; s is the lead of the ball screw;

[0126] The friction during the operation of the electromechanical brake actuator is divided into two categories, specifically: static friction related to speed and dynamic friction related to speed and displacement. The static friction model consists of static friction, Coulomb friction, and viscous friction. Therefore, the present invention designs a coupled friction model to model the friction force, as follows:

[0127]

[0128] where is the angular velocity of the motor;; F cl is the clamping force of the electromechanical brake actuator; T e is the difference between the motor torque and the load torque, T e = T m - N·F l ; D is the viscous friction coefficient in the system; C is the Coulomb friction torque of the electromechanical brake actuator without load; G is the system Coulomb friction coefficient; T s is the static friction torque of the electromechanical brake actuator; ε is infinitesimal.

[0129] Step 2: Design a clamping force loop controller considering the variable stiffness characteristic of the system, specifically as follows:

[0130] 21) Design a stiffness characteristic feedforward compensation based on the variable stiffness characteristic of the system. According to the relationship between the clamping force and the displacement of the piston, obtain the expected piston displacement

[0131]

[0132] where k d is the proportional coefficient, d dis-target (F * ) is the stiffness characteristic function of the system, expressed as:

[0133] F = a·x 3 + b·x 2 + c·x + d (10)

[0134] Where x is the piston displacement; a, b, c, and d are fitting curve parameters;

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

[0136] Where F * is the target clamping force; F is the actual clamping force; k p1 is the proportional gain; k i1 is the integral gain; k d1 is the derivative gain;

[0137] Integrate Equation (9) and Equation (11) to obtain the final output desired piston displacement y * as follows:

[0138]

[0139] Where is the piston displacement calculated according to the stiffness curve; is the piston displacement output by the proportional-integral-derivative controller according to the clamping force difference.

[0140] Step 3: Design a position loop controller using the inverse sliding mode control method, and compensate the output current with a friction model to reduce the influence of non-linear friction on the clamping force control accuracy, specifically as follows:

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

[0142] z1 = y - y * (13)

[0143] Where y is the actual piston displacement; y * is the piston target displacement;

[0144] Take the derivative of the output error value z1, as follows:

[0145]

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

[0147]

[0148] 33) Introduce the virtual control quantity α1 as follows:

[0149] α1 = c1z1 (16)

[0150] where c1 is a positive constant;

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

[0152]

[0153] From equations (16) and (17), the following equation is obtained:

[0154]

[0155] When z2 = 0 above, the derivative of the Lyapunov function is a quadratic function of the control output error value z1 of the system, and it can be seen that However, in the actual control process, z2 ≠ 0, so the next design is needed.

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

[0157]

[0158] Combined with equation (6), the following equation is obtained:

[0159]

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

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

[0162]

[0163] where s is the sliding mode surface function, defined as follows:

[0164] s = k1z1 + z2 (22)

[0165] where k1 is a positive constant;

[0166] Take the derivative of the sliding mode surface function as follows:

[0167]

[0168] Derive Equation (21) again as follows:

[0169]

[0170] 36) Combine Equation (16) and Equation (19) to obtain the following equation:

[0171]

[0172] 37) Design the reaching law as follows:

[0173]

[0174] where η > 0;

[0175] 38) Combine Equation (26), (20) and (23) to obtain the following equation:

[0176]

[0177] 39) Substitute the motor torque expression F l = k t i q into Equation (27) to obtain the target current as follows:

[0178]

[0179] where k t is the motor torque coefficient; m eq is the equivalent inertia mass of the friction plate; k1, k2 are positive constants; c1 is a positive constant; F cl is the clamping force output by the system; F f is the friction force in the electromechanical braking mechanism; y * is the target displacement;

[0180] Substitute Equation (26) into Equation (24) to obtain the following equation:

[0181]

[0182] Substitute into Equation (22) to obtain the following equation:

[0183]

[0184] From Young's inequality obtain the following equation:

[0185]

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

[0187] Step 4: When designing the current loop controller, consider the coupling of the field-axis current i d and the torque-axis current i q The coupling will cause the two-axis currents to affect each other, and as the electrical angular velocity increases, the coupling effect will become more obvious, resulting in a decrease in the current control accuracy and the dynamic response speed of the system. Therefore, current decoupling control is introduced in the current loop control, as follows:

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

[0189]

[0190] Take the derivative of the error as follows:

[0191]

[0192] In the formula, u d , u q are the voltage components of the stator voltage on the d-axis and q-axis respectively; i d , i q are the components of the stator current on the d-axis and q-axis respectively; are the target values of the stator current on the d-axis and q-axis respectively; L d , L q are the components of the inductance on the d-axis and q-axis respectively; R is the stator resistance; w e is the electrical angular velocity; ψ f is the permanent magnet flux linkage;

[0193] 42) Design the current control law by Lyapunov direct method as follows:

[0194]

[0195] So far, the control law of the multi-closed-loop disturbance rejection control of the clamping force of the electromechanical braking system has been obtained.

[0196] Example 2

[0197] Verify the effectiveness and superiority of the method proposed in the present invention. Based on MATLAB / Simulink, a simulation test environment is built, and the control strategy designed in the present invention is compared with the traditional three-closed-loop PID controller. Select the ramp condition, set the pressurization speed of 2000 N / s, and the simulation time is 9 s. The obtained current following curve, displacement following curve, and clamping force following curve are as Figure 3 , Figure 4 , Figure 5As shown. It can be seen that in terms of response speed, the controller designed by the present invention can reach the target clamping force more quickly and can achieve clamping force following more accurately. In terms of overshoot, there is almost no overshoot phenomenon in the actual clamping force of the controller designed by the present invention. Therefore, the controller designed by the present invention can effectively avoid system instability or mechanical damage caused by overshoot.

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

Claims

1. A multi-closed-loop control method for the clamping force of an electro-mechanical braking system considering non-linear disturbances, characterized in that, It includes the following steps: Step 1: Build an electro-mechanical brake actuator model; Step 2: Design a clamping force loop controller considering the system's variable stiffness characteristics; Step 3: Use the backstepping sliding mode control method to design a position loop controller based on friction model compensation; Step 4: Design a current loop controller based on current decoupling, and finally achieve multi-closed-loop control of the clamping force.

2. The multi-closed-loop control method for the clamping force of an electromechanical braking system considering non-linear disturbances according to claim 1, wherein, The specific method of Step 1 is as follows: Build an electro-mechanical brake actuator model; the electro-mechanical brake actuator includes a motor, a reduction mechanism, and a brake caliper; specifically as follows: Model the motor, and establish the stator voltage equation on the torque axis and the excitation axis without considering eddy current and hysteresis losses, as shown below: where, u d , u q are the voltage components of the stator voltage on the d-axis and q-axis respectively; i d , i q are the components of the stator current on the d-axis and q-axis respectively; L d , L q are the components of the inductance on the d-axis and q-axis respectively; R is the stator resistance; is the electrical angular velocity; ψ f is the permanent magnet flux linkage; Establish a torque balance equation at the output shaft of the motor, as shown below: Where, J is the equivalent moment of inertia; w m is the angular velocity of the motor; T l is the load torque of the motor; T f is the frictional torque; T e is the electromagnetic torque of the motor, p n is the number of pole pairs of the motor; i q is the torque axis current; ψ f is the magnetic flux linkage of the permanent magnet; Establish an equation for the force balance relationship of the brake piston, specifically as follows: where m sc is the equivalent mass of the brake piston; x is the displacement of the brake piston; F l is the pressure exerted by the actuator on the brake piston; F cl is the braking pressure output by the brake piston; F f is the frictional force acting on the brake piston; Convert the mass and moment of inertia of all mechanism components into an equivalent mass m eq , as follows: m eq = JN 2 + m sc (5) Where J is the equivalent rotational inertia of the motor assembly; N is the transmission ratio of the entire transmission mechanism; m sc is the equivalent mass of the brake piston; Integrate Equation (4) and Equation (5) to obtain the model of the electro-mechanical brake transmission mechanism part, as shown below: where m eq is the equivalent mass; x is the displacement of the brake piston; N is the transmission ratio of the entire transmission mechanism; T e is the electromagnetic torque of the motor; F cl is the braking pressure output by the brake piston; F f is the frictional force on the brake piston; Adopt a concentrated friction model to calculate the friction loss of the system mechanism, so simplify the reduction mechanism and the transmission mechanism into a transmission ratio, and the calculation method is as shown below: In the formula, i is the planetary gear reduction ratio; s is the lead of the ball screw; The friction during the operation of the electro-mechanical brake actuator is divided into two categories, specifically: static friction related to speed and dynamic friction related to speed and displacement. The static friction model consists of static friction, Coulomb friction, and viscous friction; design a coupled friction model to model the friction force, as shown below: In the formula, is the angular velocity of the motor;; F cl is the clamping force of the electromechanical brake actuator; T e is the difference between the motor torque and the load torque, T e = T m - N·F l ; D is the viscous friction coefficient in the system; C is the Coulomb friction torque of the electromechanical brake actuator without load; G is the system Coulomb friction coefficient; T s is the static friction torque of the electromechanical brake actuator; ε is infinitesimal.

3. A multi-closed-loop control method for the clamping force of an electro-mechanical braking system considering non-linear disturbances according to claim 1, characterized in that, The specific method of Step 2 is as follows: 21) Design the stiffness characteristic feedforward compensation based on the variable stiffness characteristic of the system. According to the relationship between the clamping force and the piston displacement, obtain the expected piston displacement where k d is the proportionality coefficient, d dis-target (F * ) is the stiffness characteristic function of the system, expressed as: F = a·x 3 + b·x 2 + c·x + d (10) In the formula, x is the piston displacement; a, b, c, and d are fitting curve parameters; 22) Introduce a proportional-integral-derivative feedback controller, and use the difference between the desired clamping force F * and the actual clamping force F as the input of the controller to obtain the desired feedback piston displacement Where, F * is the target clamping force; F is the actual clamping force; k p1 is the proportional gain; k i1 is the integral gain; k d1 is the derivative gain; Combining the above equation gives the final output desired piston displacement y * as follows: In the formula, is the piston displacement calculated according to the stiffness curve; is the piston displacement output by the proportional-integral-derivative controller according to the clamping force difference.

4. A multi-closed-loop control method for the clamping force of an electro-mechanical braking system considering non-linear disturbances according to claim 1, characterized in that, The specific method of Step 3 is as follows: 31) Define the difference z1 between the actual piston displacement and the target displacement as the input value of the system, as shown below: z1 = y - y * (13) where y is the actual displacement of the piston; y * is the target displacement of the piston; Take the derivative of the output error value z1, as shown below: 32) Define the Lyapunov function, as shown below: 33) Introduce the virtual control quantity α1, as shown below: α1 = c1z1 (16) In the formula, c1 is a positive constant; Define the control error variable z2, as shown below: Obtain the following formula from Equation (16) and Equation (17): 34) Perform a derivative operation on Equation (17) to calculate the derivative of the control output error value z2, as shown below: Combine with Equation (6) to obtain the following formula: where m eq is the equivalent inertial mass of the friction plate; F l is the clamping force input to the system; F cl is the clamping force output by the system; F f is the frictional force in the electromechanical braking mechanism; α1 is the virtual control variable; 35) Define the Lyapunov function, as shown below: In the formula, s is the sliding mode surface function, defined as shown below: s = k1z1 + z2 (22) In the formula, k1 is a positive constant; Take the derivative of the sliding mode surface function, as shown below: Take the derivative of Equation (21) again, as shown below: 36) Combine Equation (16) and Equation (19) to obtain the following formula: 37) Design the reaching law, as shown below: In the formula, 38) Combine Equation (26), (20), and (23) to obtain the following formula: (39) Substitute the motor torque expression F l = k t i q into Equation (27) to obtain the target current as follows: where k t is the motor torque coefficient; m eq is the equivalent inertia mass of the friction plate; k1 and k2 are positive constants; c1 is a positive constant; F cl is the clamping force output by the system; F f is the friction force in the electromechanical braking mechanism; y * is the target displacement.

5. A multi-closed-loop control method for the clamping force of an electromechanical braking system considering non-linear disturbances according to claim 1, characterized in that The specific method of Step 4 is as follows: 41) Define the current tracking error, as shown below: Take the derivative of the error, as shown below: where u d , u q are the voltage components of the stator voltage on the d-axis and q-axis respectively; i d , i q are the components of the stator current on the d-axis and q-axis respectively; are the target values of the stator current on the d-axis and q-axis respectively; L d , L q are the components of the inductance on the d-axis and q-axis respectively; R is the stator resistance; w e is the electrical angular velocity; ψ f is the permanent magnet flux linkage; 42) Design the current control law by the Lyapunov direct method, as shown below:

Images