An EMB system clamping force control method based on hierarchical model predictive control

Abstract

This invention discloses a clamping force control method for an EMB system based on hierarchical model predictive control. The method includes the following steps: establishing an EMB dynamic model, introducing displacement-related nonlinear stiffness and temperature effects to obtain a nonlinear contact stiffness model; designing an upper-level multi-objective real-time predictive controller for clamping force, converting it into a piecewise affine function and solving it; designing a self-disturbance rejection lower-level tracking controller, converting the upper-level reference trajectory into a motor current command control law; designing an inter-layer coordination mechanism to adjust the tracking error weights of the upper-level MPC, correcting equivalent damping parameters online, and updating the basic stiffness coefficients of the nonlinear contact model in real time; identifying the contact point position online, identifying the contact point position between the brake pad and the brake disc in real time, and compensating for physical zero-point drift; and driving the motor to achieve closed-loop control of the clamping force based on the bi-layer control cycle multiple relationship. This invention solves the problems of traditional MPC multi-objective optimization and rapid disturbance suppression being difficult to balance, and the controller's insufficient real-time performance.

Description

Technical Field

[0001] This invention belongs to the field of electric vehicle brake-by-wire technology, specifically relating to a clamping force control method for an EMB system based on hierarchical model predictive control. Background Technology

[0002] With the rapid development of automotive electrification and intelligentization technologies, electromechanical braking systems (EMB), as a new generation of brake-by-wire technology, are in urgent demand in the field of intelligent driving. EMB systems achieve braking force output through motor drive, and have advantages such as fast response speed and high control precision. However, the complex operating conditions during braking, such as high temperature and high pressure, brake pad wear, and changes in friction, pose severe challenges to clamping force control, and there is an urgent need for high-performance control methods that meet real-time requirements.

[0003] Existing methods mainly employ traditional feedback control strategies such as PID control, fuzzy control, or sliding mode control, but they have significant limitations: First, a single control objective cannot simultaneously address multiple performance indicators such as braking accuracy, energy efficiency, and comfort; second, they have weak constraint handling capabilities, making it difficult to systematically handle physical constraints such as current saturation, mechanical travel, and temperature limitations; and third, they lack predictability, as current error adjustment cannot predict future states, resulting in lag in response under dynamic operating conditions.

[0004] Although some studies have introduced model predictive control (MPC) into braking systems to achieve multi-objective control and constraint handling, they are still limited to a single-layer control structure. They have failed to resolve the contradiction between the high computational complexity of MPC and the requirement for rapid disturbance suppression, making it difficult to guarantee real-time performance and high robustness. Moreover, the control performance degrades when faced with uncertainties such as frictional changes and temperature effects.

[0005] Furthermore, the traditional MPC uses online optimization solutions, which results in long computation times and makes it difficult to meet the real-time requirements of vehicle controllers for millisecond-level response, thus restricting the practical application of MPC in EMB systems. Summary of the Invention

[0006] The purpose of this invention is to provide a clamping force control method for EMB systems based on hierarchical model predictive control, which solves the problems in the prior art where the high computational complexity of MPC leads to insufficient real-time performance of the on-board controller, and the difficulty in simultaneously achieving multi-objective optimization and rapid disturbance suppression.

[0007] The technical solution to achieve the objective of this invention is: a clamping force control method for an EMB system based on hierarchical model predictive control, comprising the following steps:

[0008] Step (1): Establish the mechanical dynamics model of the EMB brake actuator, introduce the displacement-related nonlinear stiffness and temperature influence to obtain the nonlinear contact stiffness model, and discretize the nonlinear contact stiffness model into a state-space model.

[0009] Step (2): Design a multi-objective real-time predictive controller for upper clamping force. The clamping force error, control increment and control amplitude are the optimization objectives, and the current saturation and mechanical stroke are the constraints. The controller is converted offline into a piecewise affine function using a multi-parameter quadratic programming method and solved online by a lookup table method.

[0010] Step (3): Design an active disturbance rejection lower-level tracking controller. Based on the equivalent single-degree-of-freedom dynamic model, use a second-order extended state observer to estimate the total disturbance value of the system in real time. Combine PD feedback control and disturbance feedforward compensation to convert the upper-level reference trajectory into motor current command.

[0011] Step (4): Design an interlayer coordination mechanism, adaptively adjust the tracking error weight of the upper MPC according to the clamping force tracking error, correct the equivalent damping parameters of the equivalent single-degree-of-freedom dynamic model online according to the disturbance estimate, and update the basic stiffness coefficient of the nonlinear contact model in real time in combination with the temperature sensor signal.

[0012] Step (5): Identify the contact point position online. Use the recursive least squares algorithm to identify the contact point position between the brake pad and the brake disc in real time to compensate for the physical zero-point drift caused by brake pad wear.

[0013] Step (6): Based on the double-layer control cycle multiple relationship, the clamping force reference trajectory is output by step (2), and the ESO status is updated and the motor current command is output by step (3). During the execution process, the model parameters and physical zero points corrected by steps (4) and (5) are called in real time to drive the motor to realize the clamping force closed-loop control.

[0014] Compared with the prior art, the significant advantages of this invention are:

[0015] This application presents a clamping force control method for EMB systems based on hierarchical model predictive control. The control task is divided into two layers: the upper layer optimizes clamping force tracking accuracy, energy consumption, and comfort as multiple objectives, completing complex optimization calculations offline and storing them as a lookup table. During braking, the optimal clamping force control command can be obtained simply by quickly looking up the table, improving braking response speed. The lower layer is responsible for rapid response to disturbances and execution. The two layers work together to achieve multi-objective coordinated optimization of clamping force accuracy, response speed, and energy consumption. A dynamic coordination mechanism between layers is designed to automatically adjust the control focus based on real-time clamping force errors and continuously correct the control model using temperature signals and disturbance information, ensuring stable and reliable clamping force control performance even under complex conditions such as high temperatures and frictional changes. Simultaneously, by identifying the brake pad contact position online, the physical zero-point offset caused by long-term wear is automatically compensated, guaranteeing clamping force control accuracy throughout the entire lifespan. Attached Figure Description

[0016] Figure 1This is a flowchart of the clamping force control method for the EMB system based on hierarchical model predictive control according to the present invention.

[0017] Figure 2 This is a flowchart of the upper-layer explicit model prediction controller of the present invention.

[0018] Figure 3 This is a flowchart of the inter-layer coordination mechanism of the present invention. Detailed Implementation

[0019] The technical solution of this application will be described in detail below with reference to the accompanying drawings.

[0020] Figure 1 The clamping force control method for an EMB system based on hierarchical model predictive control described in this application, such as... Figure 1 As shown, a clamping force control method for an EMB system based on hierarchical model predictive control includes:

[0021] S1: Establish a mechanical dynamics model of the EMB brake actuator, introduce displacement-related nonlinear stiffness and temperature effects to obtain a nonlinear contact stiffness model, and discretize the nonlinear contact stiffness model into a state-space model.

[0022] S2: Design a multi-objective real-time predictive controller for upper clamping force. The clamping force error, control increment, and control amplitude are optimized as objectives, and current saturation and mechanical stroke are constrained. The controller is converted offline into a piecewise affine function using a multi-parameter quadratic programming method and then solved online using a lookup table method.

[0023] S3: Design an active disturbance rejection lower-level tracking controller. Based on an equivalent single-degree-of-freedom dynamic model, it uses a second-order extended state observer to estimate the total disturbance value of the system in real time. Combined with PD feedback control and disturbance feedforward compensation, it converts the upper-level reference trajectory into motor current commands.

[0024] S4: Design an interlayer coordination mechanism to adaptively adjust the tracking error weight of the upper MPC based on the clamping force tracking error, correct the equivalent damping parameters of the equivalent single-degree-of-freedom dynamic model online based on the disturbance estimate, and update the basic stiffness coefficient of the nonlinear contact model in real time in conjunction with the temperature sensor signal.

[0025] S5: Online identification of contact point position. The recursive least squares algorithm is used to identify the contact point position between the brake pad and the brake disc in real time, and to compensate for the physical zero-point drift caused by brake pad wear.

[0026] S6: Based on the double-layer control cycle multiple relationship, S2 outputs the clamping force reference trajectory, S3 updates the ESO status and outputs the motor current command. During the execution process, the model parameters and physical zero points corrected by steps S4 and S5 are called in real time to drive the motor to realize the clamping force closed-loop control.

[0027] In step S1, a mechanical dynamics model of the EMB brake actuator is established, and the effects of displacement-related nonlinear stiffness and temperature are introduced to obtain a nonlinear contact stiffness model. The nonlinear contact stiffness model is then discretized into a state-space model.

[0028] S11: The equation of motion for the motor rotor is established as follows:

[0029]

[0030] In the formula, The moment of inertia of the motor. For the motor rotation angle, For electromagnetic torque, For the torsional stiffness of the motor shaft, For the rotation angle of the pinion, For the torsional damping of the motor shaft, This is the motor damping coefficient;

[0031] S12: The equation for the rotation of the pinion is established as follows:

[0032] S13: The equation for the rotation of the pinion is established as follows:

[0033]

[0034] In the formula, Let the moment of inertia of the pinion be _____. This refers to the gear meshing torque;

[0035] S14: The equation for the rotation of the ball screw is established as follows:

[0036]

[0037] In the formula, The moment of inertia of the leadscrew. This is the gear ratio. For transmission efficiency, This is the damping coefficient of the leadscrew. For load reaction torque, For the lead screw angle;

[0038] S15: The motion of the lead screw and nut is converted into the linear displacement of the nut. With lead screw angle The relationship is as follows:

[0039]

[0040] In the formula, For the ball screw lead;

[0041] S16: Establish the nonlinear stiffness model as follows:

[0042]

[0043] In the formula, For clamping force, This refers to the temperature-dependent basic stiffness coefficient. Location of the contact point The power exponent, It is the exponential growth coefficient. It is an exponential growth rate;

[0044] The temperature-dependent stiffness coefficient is:

[0045]

[0046] In the formula, , , For temperature coefficient, This refers to the brake disc temperature.

[0047] S17: Select an eleven-dimensional state vector for:

[0048]

[0049] In the formula, and These are the motor rotation angle and angular velocity, respectively. and These are the pinion's rotation angle and angular velocity, respectively. and These are the lead screw rotation angle and angular velocity, respectively. and These represent the linear displacement and linear velocity of the nut, respectively. Use the target reference clamping force;

[0050] S18: Discretize the nonlinear contact stiffness model into a state-space model:

[0051]

[0052] In the formula, It is an eleven-dimensional state vector. For including nonlinear contact stiffness parameters , , The discrete state transition matrix of linearized information. For discrete control input matrix, For control input, the physical meaning is the desired q-axis current command of the motor at time k. This is the prediction time step index, used to represent discrete time nodes extrapolated from the current time k into the future.

[0053] In step S2, a multi-objective real-time predictive controller for the upper clamping force is designed. The clamping force error, control increment, and control amplitude are optimized as objectives, with current saturation and mechanical stroke as constraints. The controller is offline transformed into a piecewise affine function using a multi-parameter quadratic programming method, and then solved online using a lookup table method.

[0054] S21: Construct a multi-objective optimization problem:

[0055] ,

[0056] In the formula, Let cost function be To predict the time domain, To control the time domain, To track error weights, To predict the clamping force, To control the incremental weight, To control the weight of quantities;

[0057] S22: The constraints on current and mechanical stroke are as follows:

[0058]

[0059] In the formula, and These are the upper and lower limits of the current. and These are the upper and lower limits of displacement;

[0060] S23: Solved offline using multi-parameter quadratic programming, specifically:

[0061]

[0062] In the formula, This is the optimal control sequence. This is a parameter vector containing the current state and the target clamping force. Let j be the gain matrix of the j-th key region. For the j-th bias vector, This is the j-th critical region;

[0063] S24: Online KD-tree search for the key region to which the current parameter vector belongs to extract optimal control, specifically:

[0064]

[0065] In the formula, Index the key regions found in the search. Let j be the center point of the critical region. This represents the optimal control at the current moment, with the subscript 1 indicating the first element of the vector.

[0066] In step S3, a self-disturbance rejection lower-level tracking controller is designed. Based on an equivalent single-degree-of-freedom dynamic model, a second-order extended state observer is used to estimate the total disturbance value of the system in real time. Combined with PD feedback control and disturbance feedforward compensation, the upper-level reference trajectory is converted into motor current commands.

[0067] S31: The mechanical dynamics model of the actuator described in S1 is simplified into the following equivalent single-degree-of-freedom model according to the principle of rotational energy equivalence:

[0068]

[0069] In the formula, To incorporate the equivalent moment of inertia of the motor, gears, lead screw, and load, This is the motor torque coefficient. For q-axis current, For load torque, For equivalent damping;

[0070] S32: Design a second-order extended state observer, defining the extended state as:

[0071]

[0072] In the formula, This is the first expansion state. This is the second expanded state, which includes the total disturbance. External disturbance;

[0073] The observer equation is:

[0074]

[0075] In the formula, and This is the state estimate. and For the observer gain, satisfying , , For observer bandwidth;

[0076] S33: Design of motor current command control law:

[0077]

[0078] In the formula, For proportional gain, For differential gain, This is a reference value for the turning angle. Used for disturbance feedforward compensation.

[0079] In step S4, an inter-layer coordination mechanism is designed to adaptively adjust the tracking error weight of the upper-layer MPC based on the clamping force tracking error, correct the equivalent damping parameters of the equivalent single-degree-of-freedom dynamic model online based on the disturbance estimate, and update the basic stiffness coefficient of the nonlinear contact model in real time in conjunction with the temperature sensor signal.

[0080] S41: Adaptively adjust the tracking error weight of the upper-layer MPC based on the clamping force tracking error.

[0081]

[0082] In the formula, For the adjusted weights, As the benchmark weight, This represents the deviation between the actual value of the clamping force at the current moment and the reference trajectory. This is the normalization constant;

[0083] S42: Correct the equivalent damping parameters of the equivalent single-degree-of-freedom dynamic model online based on the disturbance estimate:

[0084]

[0085] In the formula, This is the updated equivalent damping coefficient used for calculating the S3 control law. γ is the nominal damping, and γ is the corrected gain. This refers to the total disturbance term observed in real time by ESO in S3. The angular velocity of the motor. To prevent zero constant;

[0086] S43: Real-time update of the fundamental stiffness coefficients of the nonlinear contact model based on temperature sensor signals:

[0087]

[0088] In the formula, These are the fundamental stiffness parameters of the nonlinear contact stiffness model in S1. This represents the current brake disc temperature.

[0089] In step S5, the contact point position is identified online. A recursive least squares algorithm is used to identify the contact point position between the brake pad and the brake disc in real time, compensating for the physical zero-point drift caused by brake pad wear.

[0090] S51: Define the parameter vector for the characteristics of the contact interface between the brake pads and the brake disc as follows:

[0091]

[0092] In the formula, The parameter vector to be identified, Location of the contact point Equivalent stiffness;

[0093] S52: Constructing a regression model:

[0094]

[0095] In the formula, This is the measured value of the clamping force. This is the measured value of the nut displacement. For measuring noise;

[0096] S53: Calculate the gain vector:

[0097]

[0098] In the formula, For the gain vector, Let be the covariance matrix of the previous time step. For the regression vector, This is the forgetting factor, with a value range of 0.95-0.99;

[0099] S54: Recursive parameter update:

[0100]

[0101] In the formula, These are the parameter estimates from the previous time step;

[0102] S55: Update the covariance matrix:

[0103]

[0104] In the formula, This is the updated covariance matrix;

[0105] S56: Extract the contact point location as follows:

[0106]

[0107] In the formula, This is an estimate of the contact point location. It is the first element of the parameter vector.

[0108] In step S6, based on the double-layer control cycle multiple relationship, S2 outputs the clamping force reference trajectory, S3 updates the ESO state and outputs the motor current command, and during the execution process, the model parameters and physical zero points corrected by S4 and S5 are called in real time to drive the motor to realize the clamping force closed-loop control.

[0109] S61: Set the two-layer control cycle relationship as follows:

[0110]

[0111] In the formula, For the upper-layer MPC cycle, For the lower-level control cycle, It is a positive integer;

[0112] At the start of each execution cycle, the basic stiffness coefficients modified by S4 are loaded synchronously. Equivalent damping And the physical zero point identified by S5 ,

[0113] S62: The clamping force reference trajectory is output by S2, specifically as follows:

[0114] S621: Constructing the parameter vector:

[0115]

[0116] In the formula, For parameter vectors, This is the current state vector;

[0117] S622: Calculate optimal control by looking up a table:

[0118]

[0119] In the formula, Let j be the gain matrix of the j-th key region. This is the bias vector corresponding to the j-th critical region, used to characterize the constant correction term in the optimal control law within that region;

[0120] S623: Calculate the reference clamping force trajectory:

[0121]

[0122] In the formula, The clamping force at time k+a is the reference clamping force. For the output matrix, Includes the stiffness coefficient at the current time. Discrete state transition matrix of linearized information;

[0123] S63: S3 updates the ESO status and outputs the motor current command, specifically:

[0124] S631: Update observer state:

[0125]

[0126] In the formula, This is the estimated value of the first expansion state at time k+a. This is the estimated value of the first expansion state at time k. The value of the second expanded state at time k is the total disturbance estimate. This is the motor torque coefficient. For the equivalent moment of inertia, Let k be the q-axis current of the motor. For the first-order observer gain, The measured value of the motor angular velocity at time k. This is the estimated value of the second expanded state at time k+a. For the second-order observer gain;

[0127] S632: Calculate and execute motor current commands including feedforward compensation:

[0128]

[0129] In the formula, The equivalent moment of inertia after including the S4 real-time corrected damping term. For proportional gain, Let k be the rotation angle error. For differential gain, The angular velocity error at time k is used to output the motor current command to the motor driver to achieve clamping force control.

Claims

1. A clamping force control method for an EMB system based on hierarchical model predictive control, characterized in that, Includes the following steps: Step (1): Establish the mechanical dynamics model of the EMB brake actuator, introduce the displacement-related nonlinear stiffness and temperature influence to obtain the nonlinear contact stiffness model, and discretize the nonlinear contact stiffness model into a state-space model. Step (2): Design a multi-objective real-time predictive controller for upper clamping force, with clamping force error, control increment and control amplitude as optimization objectives, current saturation and mechanical stroke as constraints, and use a multi-parameter quadratic programming method to convert it offline into a piecewise affine function, and solve it online by looking up a table; Step (3): Design an active disturbance rejection lower-level tracking controller. Based on the equivalent single-degree-of-freedom dynamic model, use a second-order extended state observer to estimate the total disturbance value of the system in real time. Combine PD feedback control and disturbance feedforward compensation to convert the upper-level reference trajectory into motor current command. Step (4): Design an interlayer coordination mechanism, adaptively adjust the tracking error weight of the upper MPC according to the clamping force tracking error, correct the equivalent damping parameters of the equivalent single-degree-of-freedom dynamic model online according to the disturbance estimate, and update the basic stiffness coefficient of the nonlinear contact model in real time in combination with the temperature sensor signal. Step (5): Identify the contact point position online. Use the recursive least squares algorithm to identify the contact point position between the brake pad and the brake disc in real time to compensate for the physical zero-point drift caused by brake pad wear. Step (6): Based on the double-layer control cycle multiple relationship, the clamping force reference trajectory is output by step (2), and the ESO status is updated and the motor current command is output by step (3). During the execution process, the model parameters and physical zero points corrected by steps (4) and (5) are called in real time to drive the motor to realize the clamping force closed-loop control.

2. The method according to claim 1, characterized in that, Step (1) is as follows: The equation of motion for the motor rotor is established as follows: ， In the formula, The moment of inertia of the motor. For the motor rotation angle, For electromagnetic torque, For the torsional stiffness of the motor shaft, For the rotation angle of the pinion, For the torsional damping of the motor shaft, This is the motor damping coefficient; The equation for the rotation of the pinion is established as follows: ， In the formula, Let the moment of inertia of the pinion be _____. This refers to the gear meshing torque; The equation for the rotation of the ball screw is established as follows: ， In the formula, The moment of inertia of the leadscrew. This is the gear ratio. For transmission efficiency, This is the damping coefficient of the leadscrew. For load reaction torque, For the lead screw angle; The motion of the lead screw and nut is converted into the linear displacement of the nut. With lead screw angle The relationship is as follows: ， In the formula, For the ball screw lead; The nonlinear stiffness model is established as follows: ， In the formula, For clamping force, This refers to the temperature-dependent basic stiffness coefficient. Location of the contact point The power exponent, It is the exponential growth coefficient. It is an exponential growth rate; The temperature-dependent stiffness coefficient is: ， In the formula, , , For temperature coefficient, For brake disc temperature; Choose an eleven-dimensional state vector for: ， In the formula, and These are the motor rotation angle and angular velocity, respectively. and These are the pinion's rotation angle and angular velocity, respectively. and These are the lead screw rotation angle and angular velocity, respectively. and These represent the linear displacement and linear velocity of the nut, respectively. Use the target reference clamping force; Discretize the nonlinear contact stiffness model into a state-space model: ， In the formula, It is an eleven-dimensional state vector. For including nonlinear contact stiffness parameters , , The discrete state transition matrix of linearized information. For discrete control input matrix, For control input, the physical meaning is the desired q-axis current command of the motor at time k. This is the prediction time step index, used to represent discrete time nodes extrapolated from the current time k into the future.

3. The method according to claim 2, characterized in that, Step (2) specifically involves: Construct a multi-objective optimization problem: ， In the formula, Let cost function be To predict the time domain, To control the time domain, To track error weights, To predict the clamping force, To control the incremental weight, To control the weight of quantities; The constraints on the relationship between current and mechanical travel are: ， In the formula, and These are the upper and lower limits of the current. and These are the upper and lower limits of displacement; The solution is obtained offline using multi-parameter quadratic programming, specifically as follows: ， In the formula, This is the optimal control sequence. This is a parameter vector containing the current state and the target clamping force. Let j be the gain matrix of the j-th key region. For the j-th bias vector, This is the j-th critical region; The optimal control is extracted online by searching the key region to which the current parameter vector belongs using a KD-tree. Specifically: ， In the formula, Index the key regions found in the search. Let j be the center point of the critical region. This represents the optimal control at the current moment, with the subscript 1 indicating the first element of the vector.

4. The method according to claim 3, characterized in that, Step (3) is as follows: The mechanical dynamics model of the EMB brake actuator in step (1) is simplified into the following equivalent single-degree-of-freedom dynamic model according to the principle of rotational energy equivalence: ， In the formula, To incorporate the equivalent moment of inertia of the motor, gears, lead screw, and load, This is the motor torque coefficient. For q-axis current, For load torque, For equivalent damping; Design a second-order extended state observer, defining the extended state as: ， In the formula, This is the first expansion state. This is the second expanded state, which includes the total disturbance. External disturbance; The observer equation is: ， In the formula, and This is the state estimate. and For the observer gain, satisfying , , For observer bandwidth; Design a motor current command control law: ， In the formula, For proportional gain, For differential gain, This is a reference value for the turning angle. Used for disturbance feedforward compensation.

5. The method according to claim 4, characterized in that, Step (4) is as follows: The tracking error weights of the upper-layer MPC are adaptively adjusted based on the clamping force tracking error. ， In the formula, For the adjusted weights, As the benchmark weight, This represents the deviation between the actual value of the clamping force at the current moment and the reference trajectory. This is the normalization constant; The equivalent damping parameters of the equivalent single-degree-of-freedom dynamic model are corrected online based on the disturbance estimate: ， In the formula, The updated equivalent damping coefficient is used for calculating the control law in step (3). γ is the nominal damping, and γ is the corrected gain. This refers to the total disturbance term observed by ESO in real time during step (3). The angular velocity of the motor. To prevent zero constant; The fundamental stiffness coefficients of the nonlinear contact model are updated in real time by incorporating temperature sensor signals. ， In the formula, These are the basic stiffness parameters of the nonlinear contact stiffness model in step (1). This represents the current brake disc temperature.

6. The method according to claim 5, characterized in that, Step (5) is as follows: The parameter vector defining the characteristics of the contact interface between the brake pads and the brake disc is as follows: ， In the formula, The parameter vector to be identified, Location of the contact point Equivalent stiffness; Constructing a regression model: ， In the formula, This is the measured value of the clamping force. This is the measured value of the nut displacement. For measuring noise; Calculate the gain vector: ， In the formula, For the gain vector, Let be the covariance matrix of the previous time step. For the regression vector, This is the forgetting factor, with a value range of 0.95-0.99; Recursive parameter update: ， In the formula, These are the parameter estimates from the previous time step; Update the covariance matrix: ， In the formula, This is the updated covariance matrix; The location of the contact point is extracted as follows: ， In the formula, This is an estimate of the contact point location. It is the first element of the parameter vector.

7. The method according to claim 6, characterized in that, Step (6) specifically involves: The two-layer control cycle relationship is set as follows: ， In the formula, For the upper-layer MPC cycle, For the lower-level control cycle, It is a positive integer; At the start of each execution cycle, the basic stiffness coefficients modified in step (4) are loaded synchronously. Equivalent damping and the physical zero point identified by step (5) , The clamping force reference trajectory is output from step (2), specifically as follows: Construct the parameter vector: ， In the formula, For parameter vectors, This is the current state vector; Optimal control is calculated by looking up a table: ， In the formula, Let j be the gain matrix of the j-th key region. This is the bias vector corresponding to the j-th critical region, used to characterize the constant correction term in the optimal control law within that region; Calculate the reference clamping force trajectory: ， In the formula, The clamping force at time k+a is the reference clamping force. For the output matrix, Includes the stiffness coefficient at the current time. Discrete state transition matrix of linearized information; Step (3) updates the ESO status and outputs the motor current command, specifically as follows: Update observer state: ， In the formula, This is the estimated value of the first expansion state at time k+a. This is the estimated value of the first expansion state at time k. The value of the second expanded state at time k is the total disturbance estimate. This is the motor torque coefficient. For the equivalent moment of inertia, Let k be the q-axis current of the motor. For the first-order observer gain, The measured value of the motor angular velocity at time k. This is the estimated value of the second expanded state at time k+a. For the second-order observer gain; Calculate and execute motor current commands including feedforward compensation: ， In the formula, The equivalent moment of inertia after real-time correction of the damping term in step (4), For proportional gain, Let k be the rotation angle error. For differential gain, The angular velocity error at time k is used to output the motor current command to the motor driver to achieve clamping force control.

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