A control method for anti-time-varying interference of automobile electrophoretic coating conveying hybrid mechanism

Abstract

The present invention discloses a method for controlling a hybrid mechanism for electrophoretic coating conveying of an automobile against time-varying interference. First, a Lagrangian method is used to establish a dynamic model of a hybrid mechanism with time-varying interference that takes into account time-varying matching interference and time-varying non-matching interference factors; then, based on the dynamic model of the hybrid mechanism with time-varying interference, a generalized proportional integral observer with a unified bandwidth parameter is designed to estimate the time-varying non-matching interference and its derivative, and to simplify the parameter tuning process; then, a sliding mode variable and a control law containing a time-varying exponential power term are designed to achieve system stability within a fixed time, and the sliding mode surface is segmented to eliminate the singularity of the sliding mode control, thereby designing a control algorithm for controlling a hybrid mechanism against time-varying interference; finally, it is implemented through software programming. The present invention can simultaneously suppress time-varying matching / non-matching interference, improve system robustness, and accelerate system convergence speed, thereby achieving rapid stability of the system within a fixed time, thereby improving the tracking performance of the hybrid mechanism.

Description

Technical Field

[0001] The invention belongs to the technical field of automobile electrophoretic coating, and relates to a method for controlling an automobile electrophoretic coating conveying hybrid mechanism against time-varying interference. Background Art

[0002] In order to solve the problems of poor heavy load bearing capacity and low flexibility of the existing electrophoretic coating conveying equipment based on cantilever beam series structure, a hybrid mechanism for automobile electrophoretic coating conveying was developed by combining the advantages of series and parallel mechanisms. The mechanism has the characteristics of large working space, high flexibility, precision and rigidity. However, the actual operation of the hybrid mechanism system is not only affected by time-varying matching interference factors, which are specifically manifested as mechanism joint friction and modeling errors, but also by time-varying non-matching interference factors, which are specifically manifested as liquid resistance interference on the end load of the mechanism. These complex interferences affect the motion control accuracy of the hybrid mechanism, and even cause tilting or subversion, destroying the stability of the system, making the high-performance operation of the hybrid mechanism a difficulty in the field of control research.

[0003] In the article "Zhang Wenjie, Gao Guoqin. Adaptive backstepping sliding mode control of sandblasting and rust removal parallel mechanism against non-matching interference" (Zhang Wenjie, Gao Guoqin, Software Guide, 2023, Issue 11, Pages 110-117), an adaptive backstepping sliding mode control method combined with an extended state observer is designed to address the problem of non-matching interference of the jet reaction force in the sandblasting and rust removal parallel mechanism system. In this article, the state equation with non-matching interference is reconstructed into a state equation containing only matching interference by introducing auxiliary variables, and then the total matching interference is estimated by ESO, and an adaptive backstepping sliding mode controller is designed based on the interference estimation information to suppress non-matching interference. However, its extended state observer cannot estimate the interference derivative, so it cannot solve the time-varying interference problem of the hybrid mechanism system, and the system state can only converge to the equilibrium point in a finite time, and there is a problem of dependence on the initial value of the system state. Summary of the invention

[0004] In order to overcome the deficiencies of the prior art, the present invention proposes a time-varying interference resistant control method for a hybrid mechanism of automobile electrophoretic coating conveying. Aiming at the problem that the hybrid mechanism system is affected by complex interference during actual operation, the present invention firstly adopts the Lagrangian method to establish a dynamic model of a hybrid mechanism with time-varying interference in the joint space, which considers the time-varying matching interference and the time-varying non-matching interference factors; secondly, on the basis of the dynamic model of the hybrid mechanism with time-varying interference, the time-varying non-matching interference and its derivatives are respectively expanded into system states to obtain the dynamic extended state space equation, and a generalized proportional integral observer with a unified bandwidth parameter is designed based on the extended state space equation to estimate the time-varying non-matching interference and its derivatives, and simplify the parameter tuning process; then, the estimated value of the time-varying non-matching interference is introduced into the sliding mode variable design to construct a sliding surface of anti-time-varying interference control; finally, based on the dynamic model of the hybrid mechanism with time-varying interference, the sliding surface of the anti-time-varying interference control, and the estimated value of the derivative of the time-varying non-matching interference, the hybrid mechanism anti-time-varying interference controller is designed, and then a hybrid mechanism anti-time interference control method is proposed to simultaneously suppress the time-varying matching / non-matching interference, improve the system robustness, and accelerate the system convergence speed, so as to achieve rapid stability of the system within a fixed time.

[0005] The technical solution of the present invention is: a method for controlling a hybrid mechanism for conveying electrophoretic coating of an automobile against time-varying interference, comprising the following steps:

[0006] 1) Aiming at the hybrid mechanism of automobile electrophoretic coating conveying, the inverse kinematics analysis of the hybrid mechanism is carried out by using analytical method, and the Jacobian matrix is ​​further obtained;

[0007] 2) The Lagrangian method is used to establish a dynamic model of a hybrid mechanism with time-varying interference in the joint space, taking into account the time-varying matching and time-varying non-matching interference factors;

[0008] 3) Based on the dynamic model of the hybrid mechanism with time-varying interference established in step 2), an extended state space model of the dynamics of the hybrid mechanism is established by expanding the time-varying non-matching interference and its derivative into system states respectively, and a generalized proportional integral observer with a uniform bandwidth parameter is designed to estimate the time-varying non-matching interference and its derivative;

[0009] 4) Based on the time-varying non-matching disturbance estimation information in step 3), the time-varying non-matching disturbance estimation value is introduced into the sliding mode variable design to construct a sliding mode surface for anti-time-varying disturbance control;

[0010] 5) Based on the dynamic model of the hybrid mechanism with time-varying interference designed in steps 2, 3, and 4), the sliding surface of the anti-time-varying interference control, and the estimated value of the derivative of the time-varying non-matching interference, the anti-time-varying interference controller of the hybrid mechanism is designed;

[0011] 6) Through software programming, an anti-time-varying interference control of the automobile electrophoretic coating conveying hybrid mechanism is realized.

[0012] Furthermore, in step 2), according to the definition of Lagrangian function, considering that the hybrid mechanism system is affected by time-varying matching interference including friction and modeling error during operation, a dynamic model of the hybrid mechanism with time-varying interference in the joint space is established:

[0013]

[0014] Where M(x) is the nominal inertia matrix; are the nominal Coriolis force and centrifugal force terms; G(x) is the nominal gravity term; DM(x), DG(x) is the modeling error; represents the friction term (in N·m); x, and are the active joint posture, velocity, and acceleration vector respectively; τ is the driving torque of the motor corresponding to the active joint (in N·m);

[0015] In addition, considering that the time-varying non-matching disturbance of the hydraulic resistance directly acts on the end of the hybrid mechanism, affecting the end posture velocity and not being in the same channel as the control input, it is easy to cause load decoupling, tilting or overturning problems; therefore, a dynamic model of the hybrid mechanism with time-varying disturbance considering time-varying matching disturbance and time-varying non-matching disturbance in the joint space is further established:

[0016]

[0017] Where x1 is the active joint pose vector; is the derivative of the active joint pose vector; x2 is the active joint velocity vector; is the active joint acceleration vector; f(x1,x2)=-M(x1) -1 (C(x1,x2)x2+G(x1)) is the nonlinear intrinsic dynamics of the system; b=M(x1) -1 is the inverse matrix of the inertia matrix; u = τ is the motor driving torque (in N·m); d1 is the time-varying non-matching disturbance, which directly affects the derivative relationship between the active joint posture vector and the velocity vector, and is in a different channel from the control input u; is the lumped time-varying matching disturbance term including joint friction and modeling error.

[0018] Furthermore, the step 4) further includes expanding the 0th and 1st order derivatives of the time-varying non-matching disturbance d1 into system states x3 and x4 respectively based on the designed dynamic model of the hybrid mechanism with time-varying interference, and obtaining the hybrid mechanism dynamics expanded state space model as follows:

[0019]

[0020] Where x3 is the time-varying non-matching interference, that is, x3 = d1; x4 is the derivative of the time-varying non-matching interference, that is,

[0021] Design of a generalized proportional-integral observer with uniform bandwidth parameter to estimate the time-varying mismatched disturbance d1 and its derivative

[0022]

[0023] In the formula, are the estimated values ​​of x1, x3, and x4 respectively; is the observation error; w o is the observer bandwidth; l1, l2, l3 are observer gain parameters and l1=3w o , l2=3w o 2 , l3=w o 3 .

[0024] Further, in step 4), the time-varying non-matching interference estimation value is combined Right now Design sliding mode variables S = [S1, S2, S3, S4, S5, S6] for time-varying disturbance resistance control T for:

[0025]

[0026] In the formula, m1, m2, α s , β s is an adjustable parameter and m1>1, 0 <m2<1、α s >0, β s >0; e is a small normal number; are all variable gain parameters; x1 is the active joint pose vector, x d is the desired pose vector of the active joint, e = x1-x d is the active joint tracking error vector; is the active joint velocity error vector; l1(e) and l2(e) are the switching term segment expressions designed based on the active joint tracking error vector;

[0027] Furthermore, in step 5), based on the designed dynamic model of the hybrid mechanism with time-varying interference and the sliding surface of the anti-time-varying interference control, combined with the estimated value of the time-varying non-matching interference derivative Right now Design the hybrid mechanism anti-time-varying interference controller as follows:

[0028]

[0029] In the formula, m3, m4, α r , β r is an adjustable parameter and m3>1, 0 <m4<1、α r >0, β r >0; H>0 is the switching gain parameter; is the variable gain parameter;

[0030] Then, under the action of the designed anti-time-varying disturbance control method, the system state reaches the sliding surface within a fixed time T1, and then converges to the residual set ∑ along the sliding surface within a fixed time T2, so the system is stable within a fixed time T, T￡T max =T1+T2;

[0031]

[0032]

[0033]

[0034] Among them, the residual set ∑ is the specific area where the system state converges to the equilibrium point, T1 is the upper bound of the time required for the system state to reach the sliding surface, T2 is the upper bound of the time required for the system state to converge to the residual set ∑ along the sliding surface, and T is the upper bound of the time required for the system to stabilize.

[0035] The present invention proposes for the first time a time-varying interference control method for a hybrid mechanism for conveying electrophoretic coating of an automobile, so as to realize high-precision trajectory tracking control of the hybrid mechanism for conveying electrophoretic coating of an automobile, and its characteristics and beneficial effects are:

[0036] 1. Considering that the hybrid mechanism system is affected by complex interference during actual operation, the Lagrange method is used to establish a dynamic model of the hybrid mechanism with time-varying interference in the joint space, which takes into account the time-varying interference and time-varying non-matching interference factors;

[0037] 2. Based on the established dynamic model of the hybrid mechanism with time-varying interference, the time-varying non-matching interference and its derivatives are expanded into system states respectively, and the extended state space model of the dynamics of the hybrid mechanism is established. A generalized proportional integral observer with a unified bandwidth parameter is designed to estimate the time-varying non-matching interference and its derivatives, simplify the parameter tuning process, and introduce the interference estimation information into the sliding surface design to suppress the time-varying non-matching interference;

[0038] 3. Based on the dynamic model of the hybrid mechanism with time-varying interference, combined with the time-varying non-matching interference and its derivative estimation information, a time-varying interference control algorithm is designed to simultaneously suppress the time-varying matching / non-matching interference, improve the system robustness and accelerate the system convergence speed, and achieve rapid stability of the system within a fixed time. Therefore, this method can effectively improve the motion tracking control performance of the hybrid mechanism for automobile electrophoretic coating conveying in practical application. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a structural diagram of the hybrid mechanism for conveying automobile electrophoretic coating. In the figure: 1. Guide rail 2. Base 3. Travel drive motor 4. Reducer 5. Moving slide block 6. Lifting drive motor 7. Connecting rod 8. Driven wheel 9. Driving wheel 10. Connecting rod 11. Car body 12. Flipping drive motor 13. Electric cylinder.

[0040] Figure 2 It is the principle diagram of the anti-time-varying interference control method.

[0041] Figure 3 It is a simplified diagram of the lifting and flipping mechanism structure.

[0042] Figure 4 It is the distributed structure diagram of the control system of the automobile electrophoretic coating conveying hybrid mechanism.

[0043] Figure 5 The expected motion pose and actual motion pose of each component of the terminal pose of the hybrid mechanism. (a) is the trajectory tracking curve of the pose component of the midpoint of the connecting rod in the z direction; (b) is the trajectory tracking curve of the midpoint of the connecting rod flipped counterclockwise around the y axis.

[0044] Figure 6 The following are the trajectory tracking error curves of the terminal posture components of the hybrid mechanism. (a) is the trajectory tracking error curve of the posture component of the midpoint of the connecting rod in the z direction; (b) is the trajectory tracking error curve of the midpoint of the connecting rod flipped counterclockwise around the y axis. DETAILED DESCRIPTION

[0045] The specific implementation manner of the present invention is further described below with reference to the accompanying drawings.

[0046] Firstly, the inverse kinematics analysis of the automobile electrophoretic coating hybrid mechanism is carried out by analytical method, and the Jacobian matrix J is further obtained; secondly, the Lagrangian method is used to establish the dynamic model of the hybrid mechanism with time-varying interference in the joint space, considering the time-varying matching and time-varying non-matching interference factors; then, based on the dynamic model of the hybrid mechanism with time-varying interference, the time-varying non-matching interference and its derivatives are respectively expanded into the system state, and the hybrid mechanism dynamics extended state space model is established, and a generalized proportional integral observer with a unified bandwidth parameter is designed to estimate the time-varying non-matching interference and its derivative; then, combined with the time-varying non-matching interference estimation information, the time-varying non-matching interference estimation value is introduced into the sliding mode variable design; further, the hybrid mechanism anti-time-varying interference controller is designed in combination with the time-varying non-matching interference derivative estimation value, and then a hybrid mechanism anti-time-varying interference control method is proposed; finally, the anti-time-varying interference control of the automobile electrophoretic coating conveying hybrid mechanism is realized through software programming. The specific method is as follows:

[0047] 1) The inverse kinematics analysis of the hybrid mechanism of automobile electrophoretic coating conveying is carried out by analytical method to obtain the Jacobian matrix

[0048] The motion coordinate system is established with the midpoint of the connecting rod as the origin. The position parameters of the end effector of the hybrid mechanism in generalized coordinates are defined as q = (z, b) T , where z represents the lifting displacement of the midpoint of the connecting rod along the z-axis (in m); b represents the counterclockwise flip angle of the midpoint of the connecting rod around the y-axis (in rad). The analytical method is used to perform inverse kinematics analysis on the hybrid mechanism to obtain the position inverse solution equation. By taking the derivative of the two ends of the position inverse solution equation, we get:

[0049]

[0050] In the formula, is the speed of the connecting rod midpoint in the z-axis direction (in m / s), is the angular velocity of the connecting rod midpoint flipping counterclockwise around the y-axis (in rad / s), is the active joint velocity vector, are the speed variables of the four sliders, are the speed variables of the two driving wheels, and J is the Jacobian matrix.

[0051] 2) The Lagrangian method is used to establish a dynamic model of a hybrid mechanism with time-varying interference, considering time-varying matching and time-varying non-matching interference factors.

[0052] According to the definition of Lagrangian function, the standard dynamic equation of the hybrid mechanism is established:

[0053]

[0054] Where M(q) is the positive definite inertia matrix, are the Coriolis force and centrifugal force, G(q) is the gravity term, Q is the generalized force (unit: N·m); q, They are respectively the end position vector, velocity vector and acceleration vector of the hybrid mechanism.

[0055] In order to realize the actual control of the mechanism by controlling the motor, the generalized force is converted into the driving force of each active joint. For this purpose, the task space dynamics model is converted into the joint space dynamics model. The conversion relationship is as follows:

[0056]

[0057] Where M(x) is the nominal inertia matrix; are the nominal Coriolis force and centrifugal force; G(x) is the gravity term; J + is the generalized inverse matrix of the Jacobian matrix J; τ is the motor driving torque (in N·m).

[0058] Considering that the hybrid mechanism system is affected by time-varying matching interference including friction and modeling error during operation, a dynamic model of the hybrid mechanism with time-varying matching interference in joint space is established:

[0059]

[0060] In the formula, DM(x), DG(x) is the modeling error; represents the friction term (in N·m); x, and are the active joint pose, velocity, and acceleration vector respectively.

[0061] In addition, considering that the time-varying non-matching disturbance of the hydraulic resistance directly acts on the end of the hybrid mechanism, affecting the end posture velocity and not in the same channel as the control input, it is easy to cause load decoupling, tilting or overturning problems. To this end, a dynamic model of the hybrid mechanism with time-varying disturbance considering time-varying matching disturbance and time-varying non-matching disturbance is further established:

[0062]

[0063] Where x1 is the active joint pose vector; is the derivative of the active joint posture vector; x2 is the active joint velocity vector; is the active joint acceleration vector; f(x1,x2)=-M(x1) -1 (C(x1,x2)x2+G(x1)) is the nonlinear intrinsic dynamics of the system; b=M(x1) -1is the inverse matrix of the inertia matrix; u = τ is the motor driving torque (in N·m); d1 is the time-varying non-matching disturbance, which directly affects the derivative relationship between the active joint posture vector and the velocity vector, and is in a different channel from the control input u; is the lumped time-varying matching disturbance term including joint friction and modeling error.

[0064] 3) Based on the designed dynamic model of the hybrid mechanism with time-varying disturbance, the 0th and 1st order derivatives of the time-varying non-matching disturbance d1 are expanded into the state x3 and x4 of the system, that is, x3 = d1. The extended state space model of the hybrid mechanism dynamics is obtained as follows:

[0065]

[0066] Design a generalized proportional-integral observer with uniform bandwidth parameter to estimate d1 and its derivative:

[0067]

[0068] In the formula, are the estimated values ​​of x1, x3, and x4 respectively; is the observation error; l1, l2, l3 are the observer gain parameters.

[0069] definition Subtracting equation (17) from equation (16) yields the observation error system equation:

[0070]

[0071] If the selection of l1, l2, l3 satisfies the polynomial P(s) = s (3) +l1s (2) +l2s (1) +l3 root loci all fall in the left half plane of the complex plane s, then the closed-loop system (18) is asymptotically stable, that is,

[0072] To this end, define the observer bandwidth w o ,satisfy:

[0073]

[0074] Where l1 = 3w o , l2=3w o 2 , l3=w o 3 are observer gain parameters with uniform observer bandwidth parameters.

[0075] 4) Combined with time-varying non-matching interference estimates Right now Design sliding mode variables S = [S1, S2, S3, S4, S5, S6] for time-varying disturbance resistance control T for:

[0076]

[0077]

[0078] In the formula, m1, m2, α s , β s is an adjustable parameter and m1>1, 0 <m2<1、α s >0, β s >0; e is a small normal number; are all variable gain parameters; x1 is the active joint pose vector, x d is the desired pose vector of the active joint, e = x1-x d is the active joint tracking error vector; is the active joint velocity error vector; l1(e) and l2(e) are the switching term segment expressions designed based on the active joint tracking error vector;

[0079] 5) Based on the designed dynamic model of the hybrid mechanism with time-varying disturbance and the sliding surface of the anti-time-varying disturbance control, combined with the estimated value of the time-varying non-matching disturbance derivative Right now Design the hybrid mechanism anti-time-varying interference controller as:

[0080]

[0081] In the formula, m3, m4, α r , β r is an adjustable parameter and m3>1, 0 <m4<1、α r >0, β r >0; H>0 is the switching gain parameter; is the variable gain parameter;

[0082] Then, under the action of the designed anti-time-varying interference control method, the system state reaches the sliding surface within a fixed time T1, and then converges to the residual set ∑ along the sliding surface within a fixed time T2. Therefore, the system is stable within a fixed time T, T <T max =T1+T2.

[0083]

[0084]

[0085]

[0086] Among them, the residual set ∑ is the specific area where the system state converges to the equilibrium point, T1 is the upper bound of the time required for the system state to reach the sliding surface, T2 is the upper bound of the time required for the system state to converge to the residual set ∑ along the sliding surface, and T is the upper bound of the time required for the system to stabilize.

[0087] 6) Through software programming, the anti-time-varying interference control of the automobile electrophoretic coating conveying hybrid mechanism is realized.

[0088] According to formula (22), the motor drive control quantity of each active joint of the automobile electrophoretic coating conveying hybrid mechanism is calculated, and the analog quantity obtained by digital-to-analog conversion of the control quantity is sent to the servo driver corresponding to the motor to drive the end effector of the hybrid mechanism to move according to the desired trajectory.

[0089] The following provides embodiments of the present invention:

[0090] Example 1

[0091] like Figure 1 As shown, 1-guide rail 2-base 3-travel drive motor 4-reducer 5-moving slider 6-lifting drive motor 7-connecting rod 8-driven wheel 9-driving wheel 10-connecting rod 11-car body in white 12-flipping drive motor 13-electric screw.

[0092] The present invention mainly focuses on using a time-varying interference-resistant control technology to achieve high-performance operation of the automobile electrophoretic coating conveying hybrid mechanism. The principle block diagram of the time-varying interference-resistant control system of the automobile electrophoretic coating conveying hybrid mechanism is as follows: Figure 2 As shown, the specific implementation of the control method is as follows:

[0093] 1) The inverse kinematics analysis of the hybrid mechanism of automobile electrophoretic coating conveying is carried out by analytical method to obtain the Jacobian matrix J

[0094] according to Figure 3 The lifting and flipping mechanism diagram is shown, and the inverse kinematics equation is obtained:

[0095]

[0096] Where, L1 is the length of the connecting rod (in meters); z i (i=1,2)(unit is m) Figure 1 The lifting displacement of the middle point of the middle connecting rod along the z-axis direction, b i (i=1,2) (unit: rad) is the angle of the connecting rod midpoint flipping counterclockwise around the y-axis; x i (i=1,2,3,4) respectively Figure 1 The positions of the four sliders in the x-axis direction (in meters); (unit: rad) are Figure 1The angle of the middle driving wheel turning counterclockwise around the y-axis; R and r (both in m) are Figure 1 The radius of the driving wheel and the radius of the driven wheel.

[0097] The differential transformation method is used to solve the Jacobian matrix of the lifting and flipping mechanism, and the two ends of equation (26) are differentiated with respect to time to obtain:

[0098]

[0099] Formula (27) can be simplified as Then the Jacobian matrix J of the lifting and flipping mechanism is

[0100]

[0101] 2) The Lagrangian method is used to establish a dynamic model of a hybrid mechanism with time-varying interference, considering time-varying matching and time-varying non-matching interference factors.

[0102] According to the definition of Lagrangian function, the standard dynamic equation of the hybrid mechanism is established:

[0103]

[0104] Where, M(q) is the inertia matrix; are the Coriolis force and centrifugal force; G(q) is the gravity term; Q is the generalized force (unit: N·m); q, They are respectively the end position vector, velocity vector and acceleration vector of the hybrid mechanism.

[0105] In order to realize the actual control of the mechanism by controlling the motor, the generalized driving force is converted into the driving force of each active joint. For this purpose, the Cartesian space dynamics model is converted into the joint space dynamics model. The conversion relationship is as follows:

[0106]

[0107] Where M(x) is the nominal inertia matrix; are the nominal Coriolis force and centrifugal force; G(x) is the gravity term; J + is the generalized inverse matrix of the Jacobian matrix J; τ is the motor driving torque (in N·m).

[0108] Considering that the hybrid mechanism system is affected by time-varying matching interference including friction and modeling error during operation, a dynamic model of the hybrid mechanism with time-varying matching interference in joint space is established:

[0109]

[0110] In the formula, DM(x), DG(x) is the modeling error; represents the friction term (in N·m); x, and They are the active joint pose, velocity, and acceleration vectors respectively;

[0111] In addition, considering that the time-varying non-matching disturbance of the hydraulic resistance directly acts on the end of the hybrid mechanism, affecting the end posture velocity and not in the same channel as the control input, it is easy to cause problems such as load decoupling, tilting or overturning. To this end, a dynamic model of the hybrid mechanism with time-varying disturbance considering time-varying matching disturbance and time-varying non-matching disturbance is further established:

[0112]

[0113] Where x1 is the active joint pose vector; is the derivative of the active joint posture vector; x2 is the active joint velocity vector; is the active joint acceleration vector; f(x1,x2)=-M(x1) -1 (C(x1,x2)x2+G(x1)) is the nonlinear intrinsic dynamics of the system; b=M(x1) -1 is the inverse matrix of the inertia matrix; u = τ is the motor driving torque (in N·m); d1 is the time-varying non-matching disturbance, which directly affects the derivative relationship between the active joint posture vector and the velocity vector, and is in a different channel from the control input u; is the lumped time-varying matching disturbance term including joint friction and modeling error.

[0114] 3) Based on the designed dynamic model of the hybrid mechanism with time-varying interference, the 0th and 1st order derivatives of the time-varying non-matching interference d1 are expanded into the states x3 and x4 of the system respectively, and the dynamic expanded state space model of the hybrid mechanism is obtained as follows:

[0115]

[0116] Where x3 is the time-varying non-matching interference, that is, x3 = d1; x4 is the derivative of the time-varying non-matching interference, that is,

[0117] Design of a generalized proportional-integral observer with uniform bandwidth parameter to estimate the time-varying mismatched disturbance d1 and its derivative

[0118]

[0119] In the formula, are the estimated values ​​of x1, x3, and x4 respectively; is the observation error; l1, l2, l3 are the observer gain parameters.

[0120] definition Subtracting equation (34) from equation (33) yields the observation error system equation:

[0121]

[0122] If the selection of l1, l2, l3 satisfies the polynomial P(s) = s (3) +l1s (2) +l2s (1) +l3 root loci all fall in the left half plane of the complex plane s, then the closed-loop system (35) is asymptotically stable, that is,

[0123] To this end, define the observer bandwidth w o ,satisfy:

[0124] (s+w o ) 3 =s (3) +l1s (2) +l2s (1) +l3 (36)

[0125] Where l1 = 3w o , l2=3w o 2 , l3=w o 3 are observer gain parameters with uniform observer bandwidth parameters.

[0126] 4) Combined with time-varying non-matching interference estimates Right now Design sliding mode variables S = [S1, S2, S3, S4, S5, S6] for time-varying disturbance resistance control T for:

[0127]

[0128]

[0129] In the formula, m1, m2, α s , β s is an adjustable parameter and m1>1, 0 <m2<1、α s >0, β s >0; e is a small normal number; are all variable gain parameters; x1 is the active joint pose vector, x d is the desired pose vector of the active joint, e = x1-x d is the active joint tracking error vector; is the active joint velocity error vector; l1(e) and l2(e) are the switching term segment expressions designed based on the active joint tracking error vector;

[0130] 5) Based on the designed dynamic model of the hybrid mechanism with time-varying disturbance and the sliding surface of the anti-time-varying disturbance control, combined with the estimated value of the time-varying non-matching disturbance derivative Right now Design the hybrid mechanism anti-time-varying interference controller as:

[0131]

[0132] In the formula, m3, m4, α r , β r is an adjustable parameter and m3>1, 0 <m4<1、α r >0, β r >0; H>0 is the switching gain parameter; is the variable gain parameter;

[0133] Then, under the action of the designed anti-time-varying disturbance control method, the system state reaches the sliding surface within a fixed time T1, and then converges to the residual set ∑ along the sliding surface within a fixed time T2, so the system is stable within a fixed time T, T￡T max =T1+T2.

[0134]

[0135]

[0136] Among them, the residual set ∑ is the specific area where the system state converges to the equilibrium point, T1 is the upper bound of the time required for the system state to reach the sliding surface, T2 is the upper bound of the time required for the system state to converge to the residual set ∑ along the sliding surface, and T is the upper bound of the time required for the system to stabilize.

[0137] 6) Through software programming, the anti-time-varying interference control of the automobile electrophoretic coating conveying hybrid mechanism is realized.

[0138] The anti-time-varying interference control system of the hybrid mechanism of automobile electrophoretic coating conveying is based on the "host computer + slave computer" distributed control structure, which has high flexibility and reliability. It is suitable for large-scale and complex control systems and scenarios with high requirements for system response speed and real-time performance. The control system structure is as follows Figure 4As shown. The control system consists of four parts: the host computer, the multi-axis motion controller UMAC of the lower computer, the servo system and the hybrid mechanism prototype. Among them, the host computer is responsible for parameter configuration, data processing, program compilation and downloading; the multi-axis motion controller UMAC of the lower computer is mainly responsible for numerical calculation, motion control and analog-to-digital conversion and other functions. Its CPU board TURBO PMAC2 CPU module realizes Ethernet communication with the host computer through the Ethernet RJ45 network port, and the axis channel expansion card ACC-24E2A communicates with the servo driver to collect encoder information and output the drive control signal. The digital expansion I / O interface board ACC-65E transmits information with each servo driver and the automotive electrophoretic coating conveying hybrid mechanism to realize servo start, stop and alarm functions; the servo system is divided into three parts: servo driver, servo motor and reducer. The servo driver receives the torque analog signal from UMAC, and drives the servo motor through the signal to control the active joint corresponding to the motor, so that the end effector of the hybrid mechanism runs according to the expected trajectory. In addition, in order to detect the servo motor's position, speed and other parameters, a 22-bit high-resolution absolute position encoder (4194304 pulses / rev) is selected and directly connected to the above-mentioned servo motor to monitor the servo motor's current motion state in real time.

[0139] Through MATLAB simulation and hybrid mechanism prototype experiments, the proposed anti-time-varying disturbance control method (control method 1), finite time convergence anti-time-varying disturbance control method (control method 2) and anti-time-varying disturbance control method without generalized proportional integral observer (control method 3) are compared, and the results are respectively Figure 5 The trajectory tracking curve of each component of the midpoint of the connecting rod of the automobile electrophoretic coating conveying hybrid mechanism shown in the figure, Figure 6 The trajectory tracking error curves of each posture component at the midpoint of the connecting rod are shown.

[0140] Depend on Figure 5 and Figure 6 It can be seen that compared with the finite time convergence anti-time-varying interference control method and the anti-time-varying interference control method without generalized proportional integral observer, the hybrid mechanism system under the anti-time-varying interference control method proposed in the present invention can simultaneously suppress time-varying matching / non-matching interference, and has stronger robustness and faster convergence speed.

[0141] It should be understood that the above embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent modifications of the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

Claims

1. A method for controlling a hybrid mechanism for conveying electrophoretic coating of an automobile against time-varying interference, characterized in that: The steps include: 1) Aiming at the hybrid mechanism of automobile electrophoretic coating conveying, the inverse kinematics analysis of the hybrid mechanism is carried out by using analytical method, and the Jacobian matrix is ​​further obtained; 2) The Lagrangian method is used to establish a dynamic model of a hybrid mechanism with time-varying interference in the joint space, taking into account the time-varying matching and time-varying non-matching interference factors; 3) Based on the dynamic model of the hybrid mechanism with time-varying interference established in step 2), the time-varying non-matching interference and its derivative are expanded into system states respectively, and an extended state space model of the dynamics of the hybrid mechanism is established. A generalized proportional integral observer with a uniform bandwidth parameter is designed to estimate the time-varying non-matching interference and its derivative; 4) Based on the time-varying non-matching disturbance estimation information in step 3), the time-varying non-matching disturbance estimation value is introduced into the sliding mode variable design to construct a sliding mode surface for anti-time-varying disturbance control; 5) Based on the dynamic model of the hybrid mechanism with time-varying interference designed in steps 2, 3, and 4), the sliding surface of the anti-time-varying interference control, and the estimated value of the derivative of the time-varying non-matching interference, the anti-time-varying interference controller of the hybrid mechanism is designed; 6) Through software programming, a hybrid mechanism for automobile electrophoretic coating conveying is realized to resist time-varying interference control; In step 2), according to the definition of Lagrangian function, considering that the hybrid mechanism system is affected by time-varying matching interference including friction and modeling error during operation, a dynamic model of the hybrid mechanism with time-varying interference in the joint space is established: Where M(x) is the nominal inertia matrix; are the nominal Coriolis force and centrifugal force terms; G(x) is the nominal gravity term; ΔM(x), ΔG(x) is the modeling error; represents the friction term, with the unit of N·m; x, and are the active joint posture, velocity, and acceleration vector respectively; τ is the driving torque of the motor corresponding to the active joint, in N·m; In addition, considering that the time-varying non-matching disturbance of the hydraulic resistance directly acts on the end of the hybrid mechanism, affecting the end posture velocity and not being in the same channel as the control input, it is easy to cause load decoupling, tilting or overturning problems; therefore, a dynamic model of the hybrid mechanism with time-varying disturbance considering time-varying matching disturbance and time-varying non-matching disturbance in the joint space is further established: Where x1 is the active joint pose vector; is the derivative of the active joint pose vector; x2 is the active joint velocity vector; is the active joint acceleration vector; f(x1,x2)=-M(x1) -1 (C(x1,x2)x2+G(x1)) is the nonlinear intrinsic dynamics of the system; b=M(x1) -1 is the inverse matrix of the inertia matrix; u = τ is the motor driving torque, in N·m; d1 is the time-varying non-matching disturbance, which directly affects the derivative relationship between the active joint posture vector and the velocity vector, and is in a different channel from the control input u; is the lumped time-varying matching disturbance term including joint friction and modeling error; The step 4) further includes expanding the 0th and 1st order derivatives of the time-varying non-matching disturbance d1 into system states x3 and x4 respectively based on the designed dynamic model of the hybrid mechanism with time-varying interference, and obtaining the hybrid mechanism dynamics expanded state space model as follows: Where x3 is the time-varying non-matching interference, that is, x3 = d1; x4 is the derivative of the time-varying non-matching interference, that is, Design of a generalized proportional-integral observer with uniform bandwidth parameter to estimate the time-varying mismatched disturbance d1 and its derivative In the formula, are the estimated values ​​of x1, x3, and x4 respectively; is the observation error; w o is the observer bandwidth; l1, l2, l3 are observer gain parameters and l1=3w o , l2=3w o 2 , l3=w o 3 ; In step 4), the time-varying non-matching interference estimate is combined Right now Design sliding mode variables S = [S1, S2, S3, S4, S5, S6] for time-varying disturbance resistance control T for: In the formula, m1, m2, α s , β s is an adjustable parameter and m1>1, 0<m2<1, α s >0, β s >0; ε is a small normal number; are all variable gain parameters; x1 is the active joint pose vector, x d is the desired pose vector of the active joint, e = x1-x d is the active joint tracking error vector; is the active joint velocity error vector; λ1(e) and λ2(e) are the piecewise expressions of the switching terms designed based on the active joint tracking error vector; 2. The method according to claim 1, characterized in that: In the step 5), based on the designed dynamic model of the hybrid mechanism with time-varying interference and the sliding surface of the anti-time-varying interference control, combined with the estimated value of the time-varying non-matching interference derivative Right now Design the hybrid mechanism anti-time-varying interference controller as follows: In the formula, m3, m4, α r , β r is an adjustable parameter and m3>1, 0<m4<1, α r >0, β r >0; H>0 is the switching gain parameter; is the variable gain parameter; Then, under the action of the designed anti-time-varying interference control method, the system state reaches the sliding surface within a fixed time T1, and then converges to the residual set Σ along the sliding surface within a fixed time T2. Therefore, the system is stable within a fixed time T, T≤T max =T1+T2; Among them, the residual set Σ is the specific area where the system state converges to the equilibrium point, T1 is the upper bound of the time required for the system state to reach the sliding surface, T2 is the upper bound of the time required for the system state to converge to the residual set Σ along the sliding surface, and T is the upper bound of the time required for the system to stabilize.

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