Loading force control method based on active disturbance rejection control

Abstract

The invention discloses a loading force control method based on active disturbance rejection control, which comprises the following steps of: firstly, establishing a robot kinematics model, namely establishing a dynamic and static platform coordinate system, solving a loading structure kinematics inverse solution and deducing a static mapping relation between an air cylinder output force and a loading force; secondly, a driver model is established, mathematical modeling is conducted on a metal gap sealing air cylinder system driven by a proportional flow valve, and an approximate second-order model is deduced; an active disturbance rejection controller is designed and comprises a transition process module and a non-linear feedback module. In the transition process, a steepest discrete tracking differentiator is arranged, so that the overshoot problem caused by an overlarge initial error is avoided. A nonlinear feedback control law is adopted in the nonlinear feedback design, an error signal, an error differential signal and an error integral signal are combined, and an efficient nonlinear combined feedback law is designed to improve the control efficiency.

Description

Technical Field

[0001] The present invention relates to the field of robots, and in particular to a loading force control method based on active disturbance rejection control. Background Art

[0002] In today's industrial production and technological development, the application of robotics technology is becoming more and more extensive. The precise control and efficient operation of robots are of vital importance to improving production efficiency, ensuring product quality and expanding application areas. Traditional robot control methods often have some obvious shortcomings when facing complex working conditions and high-precision requirements. For example, in the establishment of kinematic models, previous methods may not be able to accurately describe the position and posture of the robot's end effector, resulting in limited accuracy of motion control. There is also a lack of in-depth research on the analysis of loading structures, and it is difficult to accurately calculate the relationship between the cylinder output force and the loading force, which affects the performance of the robot when it is under load.

[0003] In the construction of the driver model, the mathematical modeling of the cylinder system driven by the proportional flow valve was not perfect in the past, and it was unable to fully consider the interaction of multiple factors such as flow, pressure, and dynamics, making it difficult for the driver's control accuracy and response speed to meet actual needs. In terms of controller design, traditional control strategies such as PID control often have difficulty in achieving ideal control effects for complex nonlinear systems, and are prone to problems such as overshoot and oscillation, which affect the stable operation and work efficiency of the robot.

[0004] With the continuous improvement of industrial automation level, the performance requirements for robots are getting higher and higher. They are not only required to be able to complete simple repetitive actions, but also to be able to adapt to complex and changing working environments and high-precision tasks. Therefore, the development of a more accurate, efficient and stable robot control system has become an urgent problem to be solved in the current technical field. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a loading force control method based on active disturbance rejection control, and the specific steps are as follows: Step 1: Establish the robot kinematic model; by establishing the dynamic and static platform coordinate system, solve the inverse kinematic solution of the loading structure, and derive the static mapping relationship between the cylinder output force and the loading force; Step 2: Establish a driver model; mathematically model the metal gap seal cylinder system driven by the proportional flow valve and derive an approximate second-order model; Step 3: Design an auto-disturbance rejection controller. According to the drive model, design an auto-disturbance rejection controller, including two modules: transition process and nonlinear feedback. Step 4: Transition process design: Arrange the transition process through the fastest discrete tracking differentiator to ensure that the controller can quickly track the input signal and obtain its differential signal to avoid overshoot caused by excessive initial error; Step 5: Nonlinear feedback design: Use nonlinear feedback control law, combine error signal, error differential signal and error integral signal, design efficient nonlinear combined feedback law, and improve the control efficiency of the controller.

[0006] Furthermore, the process of establishing the robot kinematic model in step 1 can be expressed as: Step 1.1 Establish the coordinate system of the dynamic and static platform Step 1.1.1 Static platform coordinate system: Establish the base coordinate system Static platform coordinate system It is a fixed reference coordinate system, taking the robot base as the coordinate system ;make The origin is , the basis vectors are ; in, Perpendicular to the base plane, and In the plane of the base; Step 1.1.2 Moving platform coordinate system: Establish the end coordinate system Moving platform coordinate system is the coordinate system that moves with the robot end effector; The origin is , the basis vectors are ;in, Perpendicular to the end effector plane, and In the plane of the end effector; Step 1.1.3 Coordinate transformation Moving platform coordinate system Relative to the stationary platform coordinate system The position and attitude are transformed by the homogeneous matrix express:

[0007] in: is a 3×3 rotation matrix, representing Relative to posture; is a 3×1 translation vector, indicating Relative to location; Step 1.1.4 Derive the rotation matrix : The rotation matrix is ​​calculated using the Euler angles, which are , then the rotation matrix is:

[0008] in, is the rotation matrix around the z-axis, is the rotation matrix around the y-axis, is the rotation matrix around the x-axis:

[0009]

[0010]

[0011] Step 1.2: Obtain the inverse kinematic solution of the loaded structure Step 1.2.1 The goal of inverse kinematics solution is: The position of the end effector is known and posture , solve the displacement variable vector of each joint , is the displacement variable of the nth joint; Step 1.2.2 Numerical solution For complex robot structures, the nonlinear equations are solved by numerical methods; the kinematic equation is assumed to be , solved by iteration:

[0012] in, yes The displacement variables of the joints, yes The displacement variables of the joints, is the Jacobian matrix, defined as:

[0013] in, is the partial derivative; Step 1.3 Derive the static mapping relationship between cylinder output force and loading force Step 1.3.1 Loading force analysis The loading force on the end effector is , yes The component in the x-axis direction, yes The component in the y-axis direction, yes The component in the z-axis direction establishes the relationship between the cylinder output force and the loading force through the static equilibrium condition; Step 1.3.2 Static mapping relationship The force vector of the cylinder is , is the output force of the nth cylinder, and the loading force vector is , through the static equilibrium equation, establish the mapping relationship:

[0014] in is the Jacobian matrix, which represents the geometric relationship between the cylinder force and the loading force; Step 1.3.3 Derivation of the Jacobian matrix Jacobian matrix Calculated by the position vector of the platform hinge point and the cylinder direction vector; The cylinder direction vector is , the hinge point position vector is , then the Jacobian matrix Columns:

[0015] in Represents vector product.

[0016] Furthermore, the driver model established in step 2 can be expressed as follows: Step 2.1: Establish the relationship between flow and pressure: The proportional flow valve adjusts the output flow by controlling the input electrical signal. For the proportional flow valve, its flow With input control signal And the pressure difference before and after the valve Related, expressed as:

[0017] in, is the flow coefficient; is the valve port area, which is related to the input signal Directly proportional relationship; is the fluid density; Let the pressure of the cylinder rodless chamber be , the rod cavity pressure is , when the proportional flow valve controls the flow into the rodless chamber of the cylinder:

[0018] in, is the pressure difference before and after the valve port, is the oil supply pressure; Step 2.2: Cylinder dynamics analysis: In a cylinder system, the net force acting on the piston is Output force of the cylinder With load force The difference; from step 1, we can know that the cylinder output force is:

[0019] in, is the rodless piston area, is the piston area of ​​the rod chamber; Acceleration of the piston With displacement The second derivative of The relationship is expressed as:

[0020] Load capacity Including friction , inertial force And external loading force, etc., the friction It is approximately the sum of Coulomb friction and viscous friction, that is:

[0021] in, is the Coulomb friction force, is the viscous friction coefficient, For displacement The first derivative of ; Step 2.3: Establish the gas state equation: The gas in the cylinder is regarded as an ideal gas and follows the ideal gas state equation. During the movement of the cylinder, the gas volume With piston displacement Changes, for the rodless cavity volume :

[0022] in, is the initial volume, and the volume of the rod cavity :

[0023] in, is the initial volume, we can get:

[0024] in, is the adiabatic index, , is a constant; Step 2.4: Derive an approximate second-order model: Solving the flow equation, cylinder dynamics equation, and gas state equation simultaneously, we can finally get a formula for piston displacement: Approximate second-order linear differential equation for :

[0025] in, is the equivalent mass of the piston and load, is the viscous friction coefficient, is the equivalent spring stiffness of the cylinder, is the proportional flow valve control coefficient, is the external loading coefficient, Input control signal for proportional flow valve, is the external loading force; this equation is an approximate second-order model of the metal gap sealing cylinder system driven by the proportional flow valve.

[0026] Furthermore, the transition process design in step 4 can be expressed as follows: Step 4.1: Build the fastest discrete tracking differentiator Assume that the system's expected input signal is , is a time variable, which becomes , is a discrete time variable, and two sequences are obtained through the fastest discrete tracking differentiator and ;in For fast tracking of input signals ,and Approximately The differential signal of Step 4.2: The iterative formula of the fastest discrete tracking differentiator is as follows:

[0027] in, Indicates Fast tracking input signal, Indicates of differential signal, represents the discrete time step; is the tracking speed parameter; The bigger, track The faster the speed, the more likely it is that the system will respond too drastically or even overshoot. The smaller the value, the slower the tracking speed, but the system response will be smoother. The tracking speed parameter of the differentiator and discrete time steps Can be adjusted according to the dynamic characteristics of the system:

[0028] in, is the equivalent mass of the piston and load in the approximate second-order model, is the equivalent spring stiffness of the cylinder, is the system damping ratio:

[0029] in, is the viscous friction coefficient in the approximate second-order model, and the function It is the core part of the fastest discrete tracking differentiator, which is defined as: in, , yes variable, , is a symbolic function.

[0030] Furthermore, the nonlinear feedback design in step 5 is expressed as follows: Step 5.1: Define the error signal Input signal Generate a smooth reference signal through the fastest discrete tracking differentiator and its derivative signal ; The actual output of the system is , then the error signal Defined as:

[0031] For error signal Derivative, get the error differential signal :

[0032] For error signal Integrate to get the error integral signal ; Step 5.2: Nonlinear feedback control law design The nonlinear feedback control law takes the following form:

[0033] in, is the output of the controller, i.e. the control quantity; , , They are proportional coefficient, differential coefficient and integral coefficient respectively; , , It is a nonlinear function of the error signal, the error differential signal and the error integral signal; Step 5.3: Nonlinear function description The nonlinear functions of the error signal, the error differential signal, and the error integral signal all use saturation functions, which are defined as:

[0034] in, is the saturation value, It is a nonlinear function variable; when the error signal or its derivative or integral is large, the saturation function can limit the size of the control amount to avoid excessive overshoot or oscillation in the system. The loading force control method based on the self-disturbance rejection control of the present invention has the following beneficial effects: 1. The perfect driver model of the present invention provides a solid foundation for precise driver control. The in-depth mathematical modeling of the metal gap seal cylinder system driven by the proportional flow valve makes the driver control more precise and the response speed faster, effectively reducing the delay and error of the system.

[0035] 2. The design of the active disturbance rejection controller of the present invention, especially the combination of the transition process and the nonlinear feedback module, can effectively avoid the overshoot problem caused by excessive initial error and enhance the stability and robustness of the system.

[0036] 3. The application of the nonlinear feedback control law of the present invention, combined with the error signal, the error differential signal and the error integral signal, significantly improves the control efficiency of the controller, enabling the robot to respond quickly and accurately when facing complex and changeable working environments and tasks, thereby improving work efficiency and quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flow chart of the present invention.

[0038] Figure 2 A schematic diagram is established for the coordinate system of the present invention. DETAILED DESCRIPTION

[0039] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments: The present invention relates to robot control technology, including establishing a robot kinematic model, a driver model and an anti-disturbance controller. Through precise modeling and innovative control strategies, the shortcomings of traditional control are solved. The control accuracy, response speed and stability are improved, the work efficiency and quality are improved, and the requirements of complex working conditions and high-precision tasks are met. The invention flow chart is as follows Figure 1 As shown, the steps of the present invention are described in detail below.

[0040] Step 1: Establish the robot kinematic model, solve the inverse kinematic solution of the loading structure by establishing the dynamic and static platform coordinate system, and derive the static mapping relationship between the cylinder output force and the loading force.

[0041] Step 1.1 Establish the coordinate system of the dynamic and static platform Step 1.1.1 Static platform coordinate system: Establish the base coordinate system Static platform coordinate system It is a fixed reference coordinate system, taking the robot base as the coordinate system .make The origin is , the basis vectors are .

[0042] in, Perpendicular to the base plane, and In the base plane, the coordinate system is established as shown in the following figure: Figure 2 shown.

[0043] Step 1.1.2 Moving platform coordinate system: Establish the end coordinate system Moving platform coordinate system is the coordinate system that moves with the robot end effector. The origin is , the basis vectors are .in, Perpendicular to the end effector plane, and In the plane of the end effector.

[0044] Step 1.1.3 Coordinate transformation Moving platform coordinate system Relative to the static platform coordinate system The position and attitude are transformed by the homogeneous matrix express:

[0045] in: is a 3×3 rotation matrix, representing Relative to posture. is a 3×1 translation vector, indicating Relative to location.

[0046] Step 1.1.4 Derive the rotation matrix : The rotation matrix is ​​calculated using the Euler angles, which are , then the rotation matrix is:

[0047] in, is the rotation matrix around the z-axis, is the rotation matrix around the y-axis, is the rotation matrix around the x-axis:

[0048]

[0049]

[0050] Step 1.2: Obtain the inverse kinematic solution of the loaded structure Step 1.2.1 The goal of inverse kinematics solution is: The position of the end effector is known and posture , solve the displacement variable vector of each joint , is the displacement variable of the nth joint.

[0051] Step 1.2.2 Numerical solution For complex robot structures, the nonlinear equations are solved by numerical methods. Assume that the kinematic equation is , solved by iteration:

[0052] in, yes The displacement variables of the joints, yes The displacement variables of the joints, is the Jacobian matrix, defined as:

[0053] in, is the partial derivative.

[0054] Step 1.3 Derive the static mapping relationship between cylinder output force and loading force Step 1.3.1 Loading force analysis The loading force on the end effector is , yes The component in the x-axis direction, yes The component in the y-axis direction, yes The component in the z-axis direction establishes the relationship between the cylinder output force and the loading force through the static equilibrium condition.

[0055] Step 1.3.2 Static mapping relationship The force vector of the cylinder is , is the output force of the nth cylinder, and the loading force vector is , through the static equilibrium equation, establish the mapping relationship:

[0056] in is the Jacobian matrix, which represents the geometric relationship between the cylinder force and the loading force.

[0057] Step 1.3.3 Derivation of the Jacobian matrix Jacobian matrix Calculated by the position vector of the platform hinge point and the cylinder direction vector.

[0058] The cylinder direction vector is , the hinge point position vector is , then the Jacobian matrix Columns:

[0059] in Represents vector product.

[0060] Step 2: Establish the actuator model. Mathematically model the metal gap seal cylinder system driven by the proportional flow valve and derive an approximate second-order model.

[0061] Step 2.1: Establish the relationship between flow and pressure: The proportional flow valve adjusts the output flow by controlling the input electrical signal. For the proportional flow valve, its flow With input control signal And the pressure difference before and after the valve Related, expressed as:

[0062] in, is the flow coefficient; is the valve port area, which is related to the input signal Directly proportional relationship; is the fluid density.

[0063] Let the pressure of the cylinder rodless chamber be , the rod cavity pressure is , when the proportional flow valve controls the flow into the rodless chamber of the cylinder:

[0064] in, is the pressure difference before and after the valve port, The oil supply pressure.

[0065] Step 2.2: Cylinder dynamics analysis: In a cylinder system, the net force acting on the piston is Output force of the cylinder With load force From step 1, we can know that the cylinder output force is:

[0066] in, is the rodless piston area, is the piston area of ​​the rod chamber.

[0067] Acceleration of the piston With displacement The second derivative of The relationship is expressed as:

[0068] Load capacity Including friction , inertial force And external loading force, etc., the friction It is approximately the sum of Coulomb friction and viscous friction, that is:

[0069] in, is the Coulomb friction force, is the viscous friction coefficient, For displacement The first derivative of .

[0070] Step 2.3: Establish the gas state equation: The gas in the cylinder is regarded as an ideal gas and follows the ideal gas state equation. During the movement of the cylinder, the gas volume With piston displacement Changes, for the rodless cavity volume :

[0071] in, is the initial volume, and the volume of the rod cavity :

[0072] in, is the initial volume, we can get:

[0073] in, is the adiabatic index, , is a constant.

[0074] Step 2.4: Derive an approximate second-order model: Solving the flow equation, cylinder dynamics equation, and gas state equation simultaneously, we can finally get a formula for piston displacement: Approximate second-order linear differential equation for :

[0075] in, is the equivalent mass of the piston and load, is the viscous friction coefficient, is the equivalent spring stiffness of the cylinder, is the proportional flow valve control coefficient, is the external loading coefficient, Input control signal for proportional flow valve, is the external loading force. This equation is an approximate second-order model of the metal gap seal cylinder system driven by the proportional flow valve.

[0076] Step 3: Design an auto-disturbance rejection controller. According to the drive model, an auto-disturbance rejection controller is designed, including two modules: transition process and nonlinear feedback.

[0077] Step 4: Transition process design. Arrange the transition process through the fastest discrete tracking differentiator to ensure that the controller can quickly track the input signal and obtain its differential signal, avoiding overshoot problems caused by excessive initial error.

[0078] Step 4.1: Build the fastest discrete tracking differentiator Assume that the system's expected input signal is , is a time variable, which becomes , is a discrete time variable, and two sequences are obtained through the fastest discrete tracking differentiator and .in For fast tracking of input signals ,and Approximately The differential signal.

[0079] Step 4.2: The iterative formula of the fastest discrete tracking differentiator is as follows:

[0080] in, Indicates Fast tracking input signal, Indicates of differential signal, Represents the discrete time step. is the tracking speed parameter. The bigger, track The faster the speed, the more likely it is that the system will respond too drastically or even overshoot. The smaller the value, the slower the tracking speed, but the system response will be smoother. The tracking speed parameter of the differentiator and discrete time steps Can be adjusted according to the dynamic characteristics of the system:

[0081] in, is the equivalent mass of the piston and load in the approximate second-order model, is the equivalent spring stiffness of the cylinder, is the system damping ratio:

[0082] in, is the viscous friction coefficient in the approximate second-order model, and the function It is the core part of the fastest discrete tracking differentiator, which is defined as: in, , yes variable, , is a symbolic function.

[0083] Step 5: Nonlinear feedback design: Adopt nonlinear feedback control law, combine error signal, error differential signal and error integral signal, design efficient nonlinear combined feedback law, and improve the control efficiency of the controller.

[0084] Step 5.1: Define the error signal Input signal Generate a smooth reference signal through the fastest discrete tracking differentiator and its derivative signal .

[0085] The actual output of the system is , then the error signal Defined as:

[0086] For error signal Derivative, get the error differential signal :

[0087] For error signal Integrate to get the error integral signal .

[0088] Step 5.2: Nonlinear feedback control law design The nonlinear feedback control law takes the following form:

[0089] in, is the output of the controller, i.e. the control quantity; , , They are proportional coefficient, differential coefficient and integral coefficient respectively; , , It is a nonlinear function of the error signal, the error differential signal and the error integral signal.

[0090] Step 5.3: Nonlinear function description The nonlinear functions of the error signal, the error differential signal, and the error integral signal all use saturation functions, which are defined as:

[0091] in, is the saturation value, It is a nonlinear function variable. When the error signal or its derivative or integral is large, the saturation function can limit the size of the control amount to avoid excessive overshoot or oscillation in the system.

[0092] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. The loading force control method based on active disturbance rejection control has the following specific steps, which are characterized by: Step 1: Establish the robot kinematic model; by establishing the dynamic and static platform coordinate system, solve the inverse kinematic solution of the loading structure, and derive the static mapping relationship between the cylinder output force and the loading force; Step 2: Establish a driver model; mathematically model the metal gap seal cylinder system driven by the proportional flow valve and derive an approximate second-order model; Step 3: Design an auto-disturbance rejection controller. According to the drive model, design an auto-disturbance rejection controller, including two modules: transition process and nonlinear feedback. Step 4: Transition process design: Arrange the transition process through the fastest discrete tracking differentiator to ensure that the controller can quickly track the input signal and obtain its differential signal to avoid overshoot caused by excessive initial error; Step 5: Nonlinear feedback design; By adopting the nonlinear feedback control law, combining the error signal, error differential signal and error integral signal, an efficient nonlinear combined feedback law is designed to improve the control efficiency of the controller.

2. The loading force control method based on active disturbance rejection control according to claim 1, characterized in that: The process of establishing the robot kinematic model in step 1 can be expressed as: Step 1.1 Establish the coordinate system of the dynamic and static platform Step 1.1.1 Static platform coordinate system: Establish the base coordinate system Static platform coordinate system It is a fixed reference coordinate system, taking the robot base as the coordinate system ;make The origin is , the basis vectors are ; in, Perpendicular to the base plane, and In the plane of the base; Step 1.1.2 Moving platform coordinate system: Establish the end coordinate system Moving platform coordinate system is the coordinate system that moves with the robot end effector; The origin is , the basis vectors are ;in, Perpendicular to the end effector plane, and In the plane of the end effector; Step 1.1.3 Coordinate transformation Moving platform coordinate system Relative to the static platform coordinate system The position and attitude are transformed by the homogeneous matrix express: in: is a 3×3 rotation matrix, representing Relative to posture; is a 3×1 translation vector, indicating Relative to location; Step 1.1.4 Derive the rotation matrix : The rotation matrix is ​​calculated using the Euler angles, which are , then the rotation matrix is: in, is the rotation matrix around the z-axis, is the rotation matrix around the y-axis, is the rotation matrix around the x-axis: Step 1.2: Obtain the inverse kinematic solution of the loaded structure Step 1.2.1 The goal of inverse kinematics solution is: The position of the end effector is known and posture , solve the displacement variable vector of each joint , is the displacement variable of the nth joint; Step 1.2.2 Numerical solution For complex robot structures, the nonlinear equations are solved by numerical methods; the kinematic equation is assumed to be , solved by iteration: in, yes The displacement variables of the joints, yes The displacement variables of the joints, is the Jacobian matrix, defined as: in, is the partial derivative; Step 1.3 Derive the static mapping relationship between cylinder output force and loading force Step 1.3.1 Loading force analysis The loading force on the end effector is , yes The component in the x-axis direction, yes The component in the y-axis direction, yes The component in the z-axis direction establishes the relationship between the cylinder output force and the loading force through the static equilibrium condition; Step 1.3.2 Static mapping relationship The force vector of the cylinder is , is the output force of the nth cylinder, and the loading force vector is , through the static equilibrium equation, establish the mapping relationship: in is the Jacobian matrix, which represents the geometric relationship between the cylinder force and the loading force; Step 1.3.3 Derivation of the Jacobian matrix Jacobian matrix Calculated by the position vector of the platform hinge point and the cylinder direction vector; The cylinder direction vector is , the hinge point position vector is , then the Jacobian matrix Columns: in Represents vector product.

3. The loading force control method based on active disturbance rejection control according to claim 1 is characterized in that: The driver model established in step 2 can be expressed as follows: Step 2.1: Establish the relationship between flow and pressure: The proportional flow valve adjusts the output flow by controlling the input electrical signal. For the proportional flow valve, its flow With input control signal And the pressure difference before and after the valve Related, expressed as: in, is the flow coefficient; is the valve port area, which is related to the input signal Directly proportional relationship; is the fluid density; Let the pressure of the cylinder rodless chamber be , the rod cavity pressure is , when the proportional flow valve controls the flow into the rodless chamber of the cylinder: in, is the pressure difference before and after the valve port, is the oil supply pressure; Step 2.2: Cylinder dynamics analysis: In a cylinder system, the net force acting on the piston is Output force of the cylinder With load force The difference; from step 1, we can know that the cylinder output force is: in, is the rodless piston area, is the piston area of ​​the rod chamber; Acceleration of the piston With displacement The second derivative of The relationship is expressed as: Load capacity Including friction , inertial force And external loading force, etc., the friction It is approximately the sum of Coulomb friction and viscous friction, that is: in, is the Coulomb friction force, is the viscous friction coefficient, For displacement The first derivative of ; Step 2.3: Establish the gas state equation: The gas in the cylinder is regarded as an ideal gas and follows the ideal gas state equation. During the movement of the cylinder, the gas volume With piston displacement Changes, for the rodless cavity volume : in, is the initial volume, and the volume of the rod cavity : in, is the initial volume, we can get: in, is the adiabatic index, , is a constant; Step 2.4: Derive an approximate second-order model: Solving the flow equation, cylinder dynamics equation, and gas state equation simultaneously, we can finally get a formula for piston displacement: Approximate second-order linear differential equation for : in, is the equivalent mass of the piston and load, is the viscous friction coefficient, is the equivalent spring stiffness of the cylinder, is the proportional flow valve control coefficient, is the external loading coefficient, Input control signal for proportional flow valve, is the external loading force; this equation is an approximate second-order model of the metal gap sealing cylinder system driven by the proportional flow valve.

4. The loading force control method based on active disturbance rejection control according to claim 1, characterized in that: The transition process design in step 4 can be expressed as follows: Step 4.1: Build the fastest discrete tracking differentiator Assume that the system's expected input signal is , is a time variable, which becomes , is a discrete time variable, and two sequences are obtained through the fastest discrete tracking differentiator and ;in For fast tracking of input signals ,and Approximately The differential signal of Step 4.2: The iterative formula of the fastest discrete tracking differentiator is as follows: in, Indicates Fast tracking input signal, Indicates of differential signal, represents the discrete time step; is the tracking speed parameter; The bigger, track The faster the speed, the more likely it is that the system will respond too drastically or even overshoot. The smaller the value, the slower the tracking speed, but the system response will be smoother. The tracking speed parameter of the differentiator and discrete time steps Can be adjusted according to the dynamic characteristics of the system: in, is the equivalent mass of the piston and load in the approximate second-order model, is the equivalent spring stiffness of the cylinder, is the system damping ratio: in, is the viscous friction coefficient in the approximate second-order model, and the function It is the core part of the fastest discrete tracking differentiator, which is defined as: in, , yes variable, , is a symbolic function.

5. The loading force control method based on active disturbance rejection control according to claim 1, characterized in that: The nonlinear feedback design in step 5 is expressed as follows: Step 5.1: Define the error signal Input signal Generate a smooth reference signal through the fastest discrete tracking differentiator and its derivative signal ; The actual output of the system is , then the error signal Defined as: For error signal Derivative, get the error differential signal : For error signal Integrate to get the error integral signal ; Step 5.2: Nonlinear feedback control law design The nonlinear feedback control law takes the following form: in, is the output of the controller, i.e. the control quantity; , , They are proportional coefficient, differential coefficient and integral coefficient respectively; , , It is a nonlinear function of the error signal, the error differential signal and the error integral signal; Step 5.3: Nonlinear function description The nonlinear functions of the error signal, the error differential signal, and the error integral signal all use saturation functions, which are defined as: in, is the saturation value, It is a nonlinear function variable; when the error signal or its derivative or integral is large, the saturation function can limit the size of the control amount to avoid excessive overshoot or oscillation in the system.

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