CN104651909B - Synchronous coordinated control method of series-parallel automobile electrophoretic painting conveying mechanism - Google Patents

Abstract

The invention discloses a synchronous and coordinated control method for a hybrid automobile electrophoretic coating conveying mechanism. First, the hybrid automobile electrophoretic coating conveying mechanism is used as a controlled object to establish a dynamic model of the conveying mechanism in a Cartesian space , and according to the control requirements of the conveying mechanism, a distributed structure is used to establish the synchronous coordination control hardware system of the conveying mechanism, and then according to the structural characteristics and motion characteristics of the lifting and turning mechanism of the conveying mechanism, a synchronization error is proposed, and the synchronization error is compared with Sliding mode control is combined to further design a dynamic synchronous coordination control law based on sliding mode control. Finally, software programming is carried out by VC++ to realize the synchronous coordination control of the hybrid automobile electrophoretic coating delivery mechanism. The present invention can not only The system has high tracking precision and fast response speed, and can realize the synchronization between each joint and the mechanisms on both sides, thereby improving the synchronous and coordinated motion control performance of the conveying mechanism.

Description

A synchronous and coordinated control method for a hybrid automobile electrophoretic coating conveying mechanism

technical field

The invention relates to the technical field of automobile electrophoretic coating, in particular to a synchronous and coordinated control method for a hybrid automobile electrophoretic coating conveying mechanism.

Background technique

For a hybrid automobile electrophoretic coating conveying mechanism, see Figure 1. There are multiple actuators in this mechanism, and the synchronization and coordination among the actuators directly affect the overall performance of the system.

The document "Synchronous Control of Planar Two-DOF Redundant Parallel Robots" (Mi Jianwei et al., Mechanical Science and Technology. February 2011, Volume 30, Issue 2, Pages 279-282+285) combines cross-coupling control technology with Combined with PD control technology, a synchronous control scheme is obtained, and this method is used to realize the motion control of the planar two-degree-of-freedom redundant parallel robot. influence, and ensure the synchronization of each control joint.

The document "Cross-Coupled Synchronous Control of Robotic Hand Base Joints" (Lan Tian et al., Robotics. March 2010, Vol. 32, No. 2, Pages 150-156+165) proposed to include synchronization error and position feedback items and smoothing A cross-coupling synchronous control strategy for robust nonlinear feedback compensation items is proposed, and this scheme is applied to the motion control of the base joints of the dexterous hand of the DLR/HITⅡ five-fingered robot to achieve synchronous and coordinated motion between the two drive motors.

However, the above-mentioned related control technologies all combine the cross-coupling control technology with the traditional PD control technology. They all require accurate model information of the system and all states can be measured. It is difficult to obtain the dynamic parameters of the multi-input multi-output system with characteristics of non-linearity, nonlinear dynamics and uncertain parameters, such as the position of the center of mass and the moment of inertia that changes with the movement of the mechanism. If the above technology is used, it will be difficult to obtain better control effect; in addition, the synchronization errors proposed by the above-mentioned related control technologies are all based on the definition of conventional synchronization errors. When placing the vehicle body fixing frame and the vehicle body, if the traditional conventional synchronization error setting method is used, only the synchronization error between the active joints in the mechanisms on both sides will be considered, and the synchronization error at both ends of the connecting rod will not be eliminated. Therefore, the above method is not suitable for the hybrid automobile electrophoretic coating conveying mechanism involved in the present invention, or it is difficult to obtain a better control effect after being applied to the conveying mechanism.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art above, to propose a synchronization error, and on this basis, to propose a dynamic synchronization coordination control method based on sliding mode control. The synchronous error between the two ends of the connecting rod of the mechanism is considered, and the combination of the cross-coupling control technology and the sliding mode control technology can not only realize the synchronous control between the active joints of the conveying mechanism and the mechanisms on both sides, but also improve the efficiency of the hybrid type. The synchronous coordination of the automobile electrophoretic coating conveying mechanism can effectively solve the uncertainty problem existing in the control system of the hybrid automobile electrophoretic coating conveying mechanism without the need for an accurate model of the system and the entire state of the system.

A synchronous and coordinated control method for a hybrid automobile electrophoretic coating conveying mechanism, comprising the following steps:

1) Taking the hybrid automobile electrophoretic coating conveying mechanism as the controlled object and the conveyed automobile body as the load, the kinematic inverse solution of the conveying mechanism is carried out by analytical method, and the Jacobian matrix of the mechanism is obtained;

2) The dynamic model of the conveying mechanism in the Cartesian space is established by using the Lagrangian method;

3) A distributed structure is adopted to establish a synchronous coordination control hardware system of the conveying mechanism;

4) According to the structural characteristics and motion characteristics of the lifting and turning mechanism of the hybrid automobile electrophoretic coating conveying mechanism, a synchronization error is proposed;

5) Combining synchronous error with sliding mode control, design a dynamic synchronous coordination control law based on sliding mode control;

6) Software programming is carried out through VC++ to realize the synchronous coordination control of the hybrid automobile electrophoretic coating conveying mechanism.

Further, in the step 1), the Jacobian matrix of the lifting and flipping mechanism is solved by using the differential transformation method based on symbolic operation to obtain:

In the formula, J is the Jacobian matrix; z is the z-axis position of the middle point of the connecting rod in the static coordinate system, and the unit is m; L ₁ is the length of the first connecting rod; r ₂ and r ₁ are the radius of the driving wheel and the Wheel radius.

Further, in said step 2), adopt Lagrange method to obtain the dynamic model of conveying mechanism in Cartesian space as:

In the formula, q=(z,β) ^T is the output pose vector; is the output velocity vector; is the output acceleration vector; M(q) is the inertia matrix; G(q) is the gravity item; D(t) is the friction item, the unit is N; F(t) is the external disturbance item, the unit is N.

Further, the conveying mechanism synchronous coordination control hardware system of the step 3) takes the UMAC multi-axis motion controller as the core control unit, and the CPU board TURBO PAMC2CPU module of the UMAC realizes the human-computer interaction with the upper computer IPC through the Ethernet network port protocol Interface communication, UMAC multi-axis motion controller axis channel expansion card ACC-24E2A communicates with the underlying servo drive through differential forms.

Further, in said step 4), a kind of synchronization error is proposed as: In the formula, is the synchronization error in the z direction, in m, is the synchronization error of counterclockwise rotation around the y-axis, in rad; λ is the diagonal positive definite coupling parameter matrix; e(t)=(e _z (t),e _β (t)) ^T is the position of the midpoint of the connecting rod Error, e _z (t) is the position error of the midpoint of the connecting rod in the z direction, the unit is m, e _β (t) is the error of the counterclockwise rotation angle of the midpoint of the connecting rod around the y axis, the unit is rad; ε(t )=(ε _z (t),ε _β (t)) ^T is the synchronization error at both ends of the connecting rod, ε _z (t) is the synchronization error in the z direction, the unit is m, ε _β (t) is the Synchronization error of the angle of counterclockwise rotation of the axis direction, in rad.

Further, in the step 5), the synchronous error is combined with the sliding mode control, and the sliding mode surface is first designed as:

The dynamic synchronous coordination control law based on sliding mode control is designed as:

Determine the driving force or driving torque required by each active joint through the above formula; where: is the synchronization error in the z direction, in m, is the synchronization error of anticlockwise rotation around the y-axis, in rad; J is the Jacobian matrix; M(q) is the inertia matrix; is the item of Coriolis force and centrifugal force; G(q) is the gravity item; D(t) is the friction item, the unit is N; F(t) is the external disturbance item, the unit is N; τ is the drive required by the active joint Force, unit is N; B=diag(b ₁ ,b ₂ ), and B is reversible, b ₁ , b ₂ are adjustable parameters and satisfy the Holwoods stability condition; is the speed synchronization error at both ends of the connecting rod, is the speed synchronization error in the z direction, the unit is m/s, is the synchronous speed error of the angle of counterclockwise rotation around the y-axis, the unit is rad/s; K=diag(k ₁ ,k ₂ …k _i ), k _i >0, the constant matrix K indicates that the moving point of the system is approaching The rate of switching surface S=0; sgn (S) is sign function; is the desired acceleration at the midpoint of the connecting rod, is the acceleration in the z direction, the unit is m/s ² , is the acceleration of counterclockwise rotation angle around the y-axis, the unit is rad/m ² ; is the actual velocity at the midpoint of the connecting rod

The present invention combines the sliding mode control technology with the cross-coupling control technology based on the dynamic model for the first time, and proposes a synchronization error. On this basis, a dynamic synchronous coordination control law based on sliding mode control is designed, It can realize the synchronous and coordinated motion control of the hybrid automobile electrophoretic coating conveying mechanism, and its characteristics and beneficial effects are:

1. Due to the design of the synchronous coordination controller based on the dynamic model, the dynamic characteristics of the hybrid automobile electrophoretic coating conveying mechanism are fully considered, so it has better control performance.

2. On the basis of conventional synchronous error, combined with the concept of error transfer function, a synchronous error is established, which not only fully considers the synchronous error between the active joints, but also considers the synchronous error at both ends of the connecting rod, and improves the transmission mechanism. synchronization performance.

3. By combining the sliding mode control technology with the cross-coupling control technology, not only the introduction of the cross-coupling control technology fully considers the coupling relationship between the actuators in the process of mechanism control, so the stable tracking control of the mechanism is realized, At the same time, the synchronous movement of the active joints and the mechanisms on both sides is realized, thereby improving the synchronous and coordinated motion control performance of the mechanism, and due to the adoption of sliding mode control technology, the uncertainty problem existing in the system is effectively solved, and the lifting and turning execution is weakened. The fast-changing dynamic characteristics of the mechanism have adverse effects on the control performance of the system, so the control performance of the mechanism can be further improved.

Description of drawings

The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

Figure 1 is a hybrid automobile electrophoretic coating conveying mechanism.

Fig. 2 is a schematic structural diagram of the lifting and turning mechanism in Fig. 1 .

Figure 3 is the hardware system of the hybrid automobile electrophoretic coating conveying mechanism.

Fig. 4 is a diagram of the expected motion and the actual motion trajectory of each component of the motion pose of the midpoint of the connecting rod in Fig. 1, wherein: Fig. 4a is a trace tracking curve of the pose component trajectory of the midpoint of the connecting rod in the z direction, and Fig. 4b is the Trajectory tracking graph of the center point of the rod moving in the counterclockwise direction around the y-axis.

Fig. 5 is a trajectory tracking error diagram of the midpoint of the connecting rod in the z direction and counterclockwise around the y axis in Fig. 1, wherein: Fig. 5a is a trajectory tracking error diagram of the pose component of the midpoint of the connecting rod in the z direction, Fig. 5b is a trajectory tracking error graph of the midpoint of the connecting rod moving counterclockwise around the y-axis.

Fig. 6 is a trajectory tracking error diagram of the active joint of a single lifting and turning mechanism in Fig. 1, wherein: Fig. 6a is a trajectory tracking error diagram of the first slider in Fig. 1, and Fig. 6b is a trajectory tracking error diagram of the second slider in Fig. 1 Fig. 6c is the trajectory tracking error map of the driving wheel.

Figure 7 is a graph of the error of the two ends of the connecting rod in the z direction and the counterclockwise movement around the y axis in Figure 1, that is, the synchronous error curve, wherein: Figure 7a is the movement position of the two ends of the connecting rod in the z direction in Figure 1 The attitude component synchronization error curve, Fig. 7b is the synchronization error curve of the two ends of the connecting rod moving counterclockwise around the y-axis.

Fig. 8 is a structural diagram of the control software of the hybrid automobile electrophoretic coating conveying mechanism.

Fig. 9 is a schematic diagram of the control system of the hybrid automobile electrophoretic coating conveying mechanism.

In the figure, 1. The first driver 2. The first screw 3. The second screw 4. The guide rail 5. The first slider 6. The first rotating pair 7. The first connecting rod 8. The second rotating pair 9. The first Two sliders 10. The third rotating pair 11. The second connecting rod 12. The second driver 13. Driving wheel 14. Belt 15. Driven wheel 16. Connecting rod 17. Car body fixing frame 18. Car body 19. Walking drive 20 . Walking base 21. Guide wheel 22. First traveling wheel 23. Second traveling wheel 24. Guide rail.

detailed description

The specific implementation manner of the present invention will be further described below in conjunction with the accompanying drawings.

The technical scheme that the present invention adopts is to adopt following steps:

1) Carry out kinematic inverse solution to the mechanism by analytical method, and obtain the Jacobian matrix of the mechanism;

2) The dynamic model of the mechanism in the Cartesian space is established by using the Lagrangian method;

3) A distributed structure is adopted to establish a synchronous coordination control hardware system of the conveying mechanism;

4) According to the structural characteristics and motion characteristics of the lifting and turning mechanism of the hybrid automobile electrophoretic coating conveying mechanism, a synchronization error is proposed;

5) Combining the synchronous error with sliding mode control, a dynamic synchronous coordination control law based on sliding mode control is designed;

6) Software programming is carried out through VC++ to realize the synchronous coordination control of the hybrid automobile electrophoretic coating conveying mechanism.

Firstly, the kinematics inverse analysis of the conveying mechanism is carried out, and the Jacobian matrix J of the mechanism is obtained; secondly, the dynamic model of the mechanism in the Cartesian space is deduced by using the Lagrangian method; then, according to the structural characteristics and motion characteristics of the mechanism , combining the synchronization error ε(t) at both ends of the connecting rod with the tracking error e(t) of each active joint to obtain a synchronization error e ^* (t); secondly, according to the existence and arrival conditions of the sliding mode, the definition is based on The sliding mode surface s of the synchronous error, by combining the synchronous error with the sliding mode control, designs a dynamic synchronous coordination control law based on the sliding mode control; finally, based on the constructed synchronous coordination control hardware system of the conveying mechanism, the software is implemented through VC++ Programming to realize the synchronous and coordinated control of the hybrid automobile electrophoretic coating conveying mechanism. The specific method is as follows:

1. Solve the Jacobian matrix

Select the pose parameter q=(z,β) ^T of the midpoint of the connecting rod as the generalized coordinates of the system, where z is the displacement of the midpoint of the connecting rod in the z-axis direction, m; β is the counterclockwise rotation of the midpoint of the connecting rod around the y-axis angle, rad. Analytical method is used to analyze the kinematic inverse solution of the mechanism to obtain its position inverse solution equation, and the derivative of the equation is the corresponding velocity inverse solution, and the inverse solution coefficient matrix is the Jacobian matrix, which is expressed as:

In the formula, is the output velocity vector, The unit is m/s, The unit is rad/s; is the input velocity vector, The unit is m/s, The unit is rad/s; J is the Jacobian matrix.

2. Using the Lagrangian method to derive the dynamic model of the mechanism in the Cartesian space

The Lagrangian function L is defined as the difference between the kinetic energy T and the potential energy P of the system, that is, L=T-P, where T and P can be expressed by any convenient coordinate system, and the system dynamics equation, namely the Lagrange equation is:

In the formula, Q is the generalized driving force, and the unit is N.

Organize and establish standard kinetic equations:

In the formula, M(q) is the inertia matrix, by the formula obtain; are the terms of Coriolis force and centrifugal force, by the formula Obtained; G(q) is the gravitational term, by the formula Get it.

In order to make the dynamic model more accurate, external disturbance and friction are added to the established dynamic model to obtain the dynamic model of the lifting and turning mechanism in the following form:

In the formula, D(t) is the friction term, the unit is N, In the formula, F _c is the Coulomb friction matrix, B _c is the viscosity coefficient matrix, x is the pose of the active joint; F(t) is the external disturbance item, the unit is N, such as noise, etc.

In order to transform the generalized force into joint driving force, the following transformation is required:

Q＝J ^T τ (3)

3. Adopt a distributed structure to establish a synchronous coordination control hardware system for the conveying mechanism

With UMAC multi-axis motion controller as the core control unit, a hybrid automotive electrophoretic coating conveying mechanism control system is designed. The control system adopts a distributed structure of "upper computer + lower UMAC multi-axis motion controller".

4. Set the synchronization error ε(t)

According to the structural characteristics and motion characteristics of the mechanism, in the joint space, considering the relationship between the active joints, a synchronization error ε(t)=(ε _z (t),ε _β (t)) at both ends of the connecting rod is proposed ^T , where ε _z (t) is the synchronization error of the two ends of the connecting rod in the z direction, the unit is m; ε _β (t) is the synchronization error of the counterclockwise rotation angle of the two ends of the connecting rod around the y-axis, the unit is rad . Based on the traditional synchronization error, the synchronization error combines the concept of error transmission, not only considering the synchronization between the active joints, but also considering the synchronization between the two ends of the connecting rod.

Assuming that the actual trajectory of the two ends of the connecting rod 16 in Fig. 1 is respectively q _i (t) = (z _i (t), β _i (t)) ^T , (i = 1, 2), where z _i (t) is the actual trajectory of the two ends of the connecting rod in the z direction, in m; β _i (t) is the actual trajectory of the counterclockwise movement of the two ends of the connecting rod around the y-axis, in rad. The desired trajectory is In the formula is the expected motion trajectory of the two ends of the connecting rod in the z direction, the unit is m; is the actual trajectory of the counterclockwise movement of the two ends of the connecting rod around the y-axis, in rad. Then its position error e _i (t) = (e _xi (t), e _βi (t)) ^T (i = 1, 2) as shown in the formula (4), where the unit of e _xi (t) is m, The unit of e _βi (t) is rad.

For the synchronous coordinated motion of the two ends of the connecting rod, its control objective can be defined as:

f(q ₁ (t),q ₂ (t))=q ₁ (t)-q ₂ (t)=0 (5)

Subtract formula (5) and formula (6) to get:

Therefore, according to formula (7), the synchronization error ε(t) can be defined as:

ε(t)＝e ₁ (t)-e ₂ (t) (8)

When e ₁ (t)→0, e ₂ (t)→0, it means that both ends of the connecting rod can move along the desired trajectory; if ε(t)→0, it means that the two ends of the connecting rod have realized synchronous motion.

The relationship between the two ends of the connecting rod and its corresponding active joints is as follows:

e _i (t) = V _i e _x (t) (i = 1,2) (9)

Where e _x (t) = (e _x1 (t), e _x2 (t), e _x3 (t), e _x4 (t), e _φ1 (t), e _φ2 (t)) is the active joint error, In the formula, the unit of e _xi (i=1,2,3,4) is m, the unit of e _φj ( _j =1,2) is rad; Active joint relation.

Substituting formula (9) into formula (8), the synchronization error can be obtained as:

ε(t)＝H _x (t) (10)

Let the actual trajectory of the midpoint of the connecting rod be q(t)=(z(t),β(t)) ^T , where the unit of z(t) is m, and the unit of β(t) is rad; the desired trajectory Respectively q ^d (t)=(z ^d (t),β ^d (t)) ^T , where the unit of z ^d (t) is m, and the unit of β ^d (t) is rad; then its position tracking error e( t)=(e _z (t), e _β (t)) ^T is shown in the following formula, where the unit of e _z (t) is m, and the unit of e _β (t) is rad.

^e (t)=qd(t)-q(t) (11)

Combined with the position tracking error e(t), the synchronization error can be obtained as:

where λ is a diagonal positive definite coupling parameter matrix.

Substituting the synchronous error formula (12) into the sliding surface, that is:

In the formula, B=diag(b ₁ ,b ₂ ), and B is reversible, b ₁ , b ₂ are both adjustable parameters and satisfy the Holwoods stability condition.

5. Design of dynamic synchronous coordination control law based on sliding mode control

Derivation of S in formula (13), and substituting formula (11) and formula (12):

From formula (2) can get

Take the constant velocity approach law:

In the formula, K=diag(k ₁ , k ₂ ...k _i ), _ki >0, and the constant matrix K represents the speed at which the moving point of the system approaches the switching surface S=0. When k _i is small, the approaching speed is slow; when k _i is large, the moving point arrives and the screen will have a greater speed, causing chattering is also greater.

Substituting Equation (15) and Equation (16) into Equation (14), the dynamic synchronous coordination control law based on sliding mode control can be obtained as follows:

In the formula, M(q) is the inertia matrix, are the Coriolis force and centrifugal force items, G(q) is the gravity item, D(t) is the friction item, F(t) is the external disturbance item, and sgn(S) is a sign function.

Substituting Equation (17) into Equation (3), the driving force of each joint can be obtained as:

6. Software programming through VC++ to realize the synchronous coordination control system of the hybrid automobile electrophoretic coating conveying mechanism.

Choose VC++ as the software development platform, use the basic class library MFC (Microsoft Foundation Class) provided by Microsoft as the system interface development software package, create a project based on dialog window according to MFC AppWizard, and complete the development of the application program.

An embodiment of the invention is provided below:

Example

The Fangming control method mainly focuses on solving the synchronous coordination control problem of the hybrid automobile electrophoretic coating conveying mechanism with a synchronous coordination control technology, and realizes high-performance control of the mechanism. The specific implementation of this control method is as follows:

1. Solve the Jacobian matrix

In Figure 2, using the rod length constraint equation, according to the structure of the lifting and turning mechanism, the inverse kinematics equation of the mechanism can be obtained:

In the formula, z _i (i=1,2), β _i (i=1,2) are respectively the z-axis position of the two ends of the connecting rod 16 in Fig. 1 under the static coordinate system and the counterclockwise rotation around the y-axis direction Angle, the units are m and rad; x _i (i=1,2,3,4) are the positions of the four sliders in the x-axis direction in Figure 1, the unit is m; φ _i (i=1,2) are respectively the counterclockwise rotation angles of the two drive wheels around the y-axis in Figure 1, and the unit is rad.

The Jacobian matrix of the lifting and turning mechanism is solved by using the differential transformation method based on symbolic operations, that is, the two ends of formula (19) are differentiated with respect to time respectively and can be obtained:

Equation (20) is abbreviated as Then the Jacobian matrix of the lifting and turning mechanism is:

In the formula, J is the Jacobian matrix; z and β are the z-axis position of the midpoint of the connecting rod in the static coordinate system and the counterclockwise rotation angle around the y-axis direction, and the units are m and rad respectively; L ₁ is the first The length of the connecting rod; r ₂ and r ₁ are the radius of the driving wheel and the radius of the driven wheel respectively.

2. Using the Lagrangian method to deduce the dynamic model of the lifting and turning mechanism in Cartesian space

The system kinetic energy T of the lifting and turning mechanism includes vehicle body kinetic energy T _P , branch chain kinetic energy T _L , transmission kinetic energy T _T and slider kinetic energy T _S . That is, the kinetic energy T of the system is:

T＝T _P +T _L +T _T +T _S (21)

The system potential energy P of the lifting and turning mechanism includes the vehicle body potential energy _{P P} , the branch chain potential energy _PL , the transmission potential energy PT and the slider potential energy PS _. That is, the potential energy P of the system is:

P＝P _P +P _L +P _T +P _S (22)

Substituting formula (21) and formula (22) into formula (2) and sorting out the dynamic equation of the lifting and turning mechanism is:

The final result available is:

G ₁₁ ＝(m _p +4m _l4 +m _l1 +m _l2 +m _l3 +2m _b )g

According to the size of the mechanism, the parameters in the formula can be obtained as follows: m _p =17kg, m _l1 =3.5kg, m _l2 =1.5kg, m _l3 =3kg, m _l4 =0.5kg, m ₁ =m ₂ =2kg, m _a = 0.5kg, m _b = 0.25kg, a = 0.65m, b = 0.56m, c = 1.125m, r _l3 = 0.015m, r ₁ = 0.05m, r ₂ = 0.03m, L ₁ = 0.311m, L ₄ =0.65m, θ=120°.

3. Adopt a distributed structure to establish a synchronous coordination control hardware system for the conveying mechanism

The control system hardware of the hybrid automobile electrophoretic coating conveying mechanism adopts a distributed structure of "upper computer IPC + lower computer UMAC multi-axis motion controller", and its hardware system is shown in Figure 3. With UMAC multi-axis motion controller as the core control unit, UMAC's CPU board TURBO PAMC2CPU module realizes the human-computer interaction interface communication with the upper computer IPC through the Ethernet network port protocol, and the UMAC multi-axis motion controller axis channel expansion card ACC-24E2A Communicate with the underlying servo drive in a differential manner. The control system uses an absolute position detection system to solve the control problem that the incremental system cannot mark the mechanical position caused by mechanical redundancy. The upper computer realizes the serial communication with the servo driver through the RS232/RS422 converter to read the absolute position information.

4. Set up synchronization error

According to kinematic analysis, it can be known that:

Differentiate the active joint motion parameters on both sides of formula (24) and rewrite it in matrix form to get:

δY ₁ =R ₁ δX ₁ (25)

In the formula, δY ₁ =[δz ₁ ,δβ ₁ ] ^T , δX ₁ =[δx ₁ ,δx ₂ ,δφ ₁ ] ^T . δY, δX ₁ are the pose errors of one end of the connecting rod and its corresponding input end respectively.

Therefore, from formula (25), we can get:

e ₁ (t) = R ₁ e ₁ '(t) (26)

Similarly on the other side of the connecting rod:

e ₂ (t) = R ₂ e′ ₂ (t) (27)

In the formula, e _i ′(t)(i=1, 2) are the unilateral input pose errors at both ends of the connecting rod, respectively. R _i (i=1,2) are the transfer matrices between the unilateral input pose error and the end pose error at both ends of the connecting rod, respectively:

And because:

e _i '(t)=V _i e _x (t)(i=1,2) (28)

In the formula, V _i (i=1, 2) are the relationship expressions between the unilateral input pose error at both ends of the connecting rod and the active joint position tracking error, respectively:

Substituting equations (25)-(28) into equation (13), the synchronization error of the mechanism can be obtained as follows:

ε(t) = He _x (t) (29)

In the formula

Let the expected pose of the midpoint of the connecting rod 16 in Fig. 1 be q ^d (t) (q ^d (t) = [z ^d , β ^d ] ^T ), and the pose error e(t ) and speed error As a state variable, that is:

Then the synchronization error is set up as:

where λ is a diagonal positive definite coupling parameter matrix.

5. Design of dynamic synchronous coordination controller based on sliding mode control

The design sliding surface is:

In the formula, B=diag(b ₁ ,b ₂ ), and B is reversible, b ₁ , b ₂ are both adjustable parameters and satisfy the Holwoods stability condition.

The dynamic synchronous coordinated control law based on sliding mode control, which is verified to meet the system stability conditions, is:

6. Software programming through UMAC to realize the synchronous coordination control system of the hybrid automobile electrophoretic coating conveying mechanism

Based on VC++, the software programming of the hybrid automobile electrophoretic coating conveying mechanism is carried out, and its control software structure diagram is shown in Figure 8. The main functions of this software are: connect to UAMC and disconnect from UMAC, program editing and downloading, real-time monitoring of motion, kinematics inversion, online command input and feedback, manual control, movement back to parking position, control method selection, emergency stop , exit, etc. By combining the software platform with the hardware platform of the hybrid automobile electrophoretic coating conveying mechanism completed in step 3, the synchronous and coordinated control of the conveying mechanism is completed, and the conveying mechanism is driven to complete the desired movement. The schematic diagram of the control system is shown in Figure 9 Show.

The actual trajectories of the midpoint of the connecting rod of the conveying mechanism in the z direction and counterclockwise around the y axis are shown in dotted lines in the sub-figures of Figure 4, respectively, and the trajectory tracking error curves are shown in the sub-figures of Figure 5, respectively. The trajectory tracking error curves of the active joints are shown in the sub-figures in Figure 6, and the synchronization error curves are shown in the sub-figures in Figure 7 respectively.

Figures 4 to 7 show that the synchronous coordination control method of the hybrid automobile electrophoretic coating conveying mechanism proposed by the present invention can not only make the system have higher tracking accuracy and faster response speed, but also realize the Synchronization between mechanisms, thereby improving the synchronous and coordinated motion control performance of the conveying mechanism.

It should be understood that the above-mentioned embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. After reading the present invention, those skilled in the art all fall into the appended claims of the present application to the amendments of various equivalent forms of the present invention limited range.

Claims (5)

1. A synchronous and coordinated control method of a hybrid automobile electrophoretic coating conveying mechanism, characterized in that, comprising the steps: 1) Taking the hybrid automobile electrophoretic coating conveying mechanism as the controlled object and the conveyed automobile body as the load, the kinematic inverse solution of the conveying mechanism is carried out by analytical method, and the Jacobian matrix of the mechanism is obtained; 2) The dynamic model of the conveying mechanism in the Cartesian space is established by using the Lagrangian method; 3) A distributed structure is adopted to establish a synchronous coordination control hardware system of the conveying mechanism; 4) Aiming at the structural characteristics and motion characteristics of the lifting and turning mechanism of the hybrid automobile electrophoretic coating conveying mechanism, a synchronization error is proposed; a synchronization error proposed in the step 4) is: In the formula, is the synchronization error in the z direction, in m, is the synchronization error of counterclockwise rotation around the y-axis, in rad; λ is the diagonal positive definite coupling parameter matrix; e(t)=(e _z (t),e _β (t)) ^T is the position of the midpoint of the connecting rod Error, e _z (t) is the position error of the midpoint of the connecting rod in the z direction, the unit is m, e _β (t) is the error of the counterclockwise rotation angle of the midpoint of the connecting rod around the y axis, the unit is rad; ε(t )=(ε _z (t),ε _β (t)) ^T is the synchronization error at both ends of the connecting rod, ε _z (t) is the synchronization error in the z direction, the unit is m, ε _β (t) is the The synchronous error of the angle of counterclockwise rotation of the shaft direction, the unit is rad; 5) Combining the synchronous error with sliding mode control, a dynamic synchronous coordination control law based on sliding mode control is designed; 6) Software programming is carried out through VC++ to realize the synchronous coordination control of the hybrid automobile electrophoretic coating conveying mechanism. 2. The synchronous coordination control method of a kind of hybrid automobile electrophoretic coating conveying mechanism according to claim 1, it is characterized in that: in described step 1), adopt the differential transformation method based on symbolic operation to solve the lifting and turning mechanism Jacobian matrix, get: $\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; =</span>{\left[\begin{array}{cccccc}\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}}{\sqrt{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}& \frac{\mathrm{<span\; class="notranslate">\; z</span>}}{\sqrt{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}& \frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}}{\sqrt{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}& \frac{\mathrm{<span\; class="notranslate">\; z</span>}}{\sqrt{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}$ In the formula, J is the Jacobian matrix; z is the z-axis position of the middle point of the connecting rod in the static coordinate system, and the unit is m; L ₁ is the length of the first connecting rod; r ₂ and r ₁ are the radius of the driving wheel and the Wheel radius. 3. The synchronous coordination control method of a kind of hybrid automobile electrophoretic coating conveying mechanism according to claim 1, it is characterized in that: in described step 2), adopt Lagrangian method to obtain conveying mechanism in Cartesian The dynamic model in space is: $\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;\&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; J</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; J</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Q</span>}$ In the formula, q=(z,β) ^T is the output pose vector; is the output velocity vector; is the output acceleration vector; M(q) is the inertia matrix; G(q) is the gravity item; D(t) is the friction item, the unit is N; F(t) is the external disturbance item, the unit is N. 4. The synchronous coordination control method of a kind of hybrid automobile electrophoretic coating conveying mechanism according to claim 1, it is characterized in that: the conveying mechanism synchronous coordination control hardware system of described step 3), with UMAC multi-axis motion control The CPU board TURBO PAMC2 CPU module of UMAC realizes the human-computer interaction interface communication with the upper computer IPC through the Ethernet network port protocol. Communication in differential form. 5. The synchronous coordination control method of a kind of hybrid automobile electrophoretic coating conveying mechanism according to claim 1, is characterized in that: in described step 5), synchronous error is combined with sliding mode control, at first design sliding mode face is: $\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; B</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>$ The dynamic synchronous coordination control law based on sliding mode control is designed as: $\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; J</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; B</span>}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Ksgn</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; )</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}}^{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; J</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$ Determine the driving force or driving torque required by each active joint through the above formula; where: is the synchronization error in the z direction, in m, is the synchronization error of anticlockwise rotation around the y-axis, in rad; J is the Jacobian matrix; M(q) is the inertia matrix; is the item of Coriolis force and centrifugal force; G(q) is the gravity item; D(t) is the friction item, the unit is N; F(t) is the external disturbance item, the unit is N; τ is the drive required by the active joint Force, unit is N; B=diag(b ₁ ,b ₂ ), and B is reversible, b ₁ , b ₂ are adjustable parameters and satisfy the Holwoods stability condition; is the speed synchronization error at both ends of the connecting rod, is the speed synchronization error in the z direction, the unit is m/s, is the synchronous speed error of the angle of counterclockwise rotation around the y-axis, the unit is rad/s; K=diag(k ₁ ,k ₂ …k _i ), k _i >0, the constant matrix K indicates that the moving point of the system is approaching The rate of switching surface S=0; sgn (S) is sign function; is the desired acceleration at the midpoint of the connecting rod, is the acceleration in the z direction, the unit is m/s ² , is the acceleration of counterclockwise rotation angle around the y-axis, the unit is rad/m ² ; is the actual velocity at the midpoint of the connecting rod.