CN107505844A - Synchronous coordination sliding-mode control of the series parallel type automobile electrophoretic coating conveyor structure based on composition error - Google Patents
Synchronous coordination sliding-mode control of the series parallel type automobile electrophoretic coating conveyor structure based on composition error Download PDFInfo
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Abstract
The invention discloses a kind of synchronous coordination sliding-mode control of series parallel type automobile electrophoretic coating conveyor structure based on composition error.First, the kinetic model of the mechanism is established using Lagrangian method, and Motion trajectory is carried out to the mechanism；To improve the tracking accuracy that automobile body-in-white is loaded in conveying mechanism running and carries out the mechanism end of application conveying, for its architectural characteristic and movement characteristic, a kind of combining mechanism end tracking error and the composition error of profile errors are proposed, designs the synchronous coordination sliding mode controller based on composition error；Finally, by software programming, synchronous coordination sliding formwork control of the conveying mechanism based on composition error is realized.The present invention is controlled by being realized based on composition error, can effectively improve the motion control accuracy of conveying mechanism end, realizes high-precision automobile electrophoretic painting conveying.
Description
Technical Field
The invention relates to the technical field of automobile electrophoretic coating conveying, in particular to a synchronous coordination sliding mode control method of a novel series-parallel automobile electrophoretic coating conveying mechanism.
Background
At present, advanced automobile electrophoretic coating conveyors, such as RoDip conveyors and multifunctional shuttles, have the defects of poor capability of bearing large load and heavy load, low flexibility level and the like due to the adoption of a cantilever beam structure. Therefore, a novel series-parallel type automobile electrophoretic coating conveying mechanism is developed to make up for the defects of the conveying equipment.
The hybrid mechanism is a complex system comprising a plurality of moving branched chains, the moving branched chains have a coupling effect, and the synchronous coordination among the active joints directly influences the reliability, safety and control precision of the system, so that the problem of synchronous coordination control of the hybrid mechanism needs to be solved.
The document 'double-lifting-bridge-crane double-lifting-appliance synchronous coordination control' (creep and the like, control theory and application, 10 months in 2013, 10 th in volume 30, 10 th in pages 1300-1308) provides a double-lifting-appliance synchronous coordination control method combining time-varying layered incremental sliding mode control and adaptive compensation based on a nonlinear induction motor dynamic mathematical model of double lifting appliances and a coupling dynamics model thereof.
A neuron PID controller and a speed compensator based on fuzzy control are designed in the document 'fuzzy control-based multi-motor neuron PID synchronous control' (urging all things, combined machine tool and automatic processing technology, 2.2013, 2 nd, page 81-83+ 87), and the defects that the conventional coupled multi-motor conventional PID synchronous control cannot be adjusted on line in real time once being determined in the dynamic load disturbance control process, the anti-interference capability is poor and the like are overcome by combining the neuron PID controller and the speed compensator.
However, the related synchronous coordination control technologies combine the cross-coupling control technology and the robust control technology, and only can ensure the synchronous coordination between the active joints. In the novel series-parallel automobile electrophoresis coating conveying mechanism, two groups of parallel lifting turnover mechanisms are connected through a connecting rod, an automobile body fixing frame and a white automobile body to be coated and conveyed are placed on the connecting rod, if the existing cross-coupling synchronous error design synchronous coordination controller is adopted, synchronous coordination among active joints in mechanisms on two sides can only be realized, and the tail end of the mechanism is difficult to ensure that the track tracking movement precision of automobile body conveying is finally realized. Therefore, the method cannot be well applied to the series-parallel automobile electrophoretic coating conveying mechanism, or a good motion control effect is difficult to obtain after the method is applied to the conveying mechanism.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention defines a comprehensive error combining a mechanism tail end tracking error and a tail end contour error aiming at a novel series-parallel automobile electrophoretic coating conveying mechanism, and further provides a synchronous coordination sliding mode control method based on the comprehensive error so as to effectively improve the motion control precision of the tail end of the conveying mechanism and realize high-precision automobile electrophoretic coating conveying.
The synchronous coordination sliding mode control method of the series-parallel automobile electrophoretic coating conveying mechanism based on the comprehensive error comprises the following steps:
1) The method comprises the following steps of (1) establishing a conveying mechanism dynamic model containing unmodeled dynamics, frictional force and external random interference by using a series-parallel automobile electrophoretic coating conveying mechanism as a controlled object by adopting a Lagrange method;
2) Determining an expected motion track of the tail end of the conveying mechanism according to the automobile electrophoretic coating process requirement and mechanism mechanical design parameters, and obtaining the expected motion track of each active joint through inverse kinematics solution;
3) Calculating the actual motion state of each active joint by using the position and speed information of each motor fed back by the encoder, obtaining the actual motion track of the tail end of the conveying mechanism through kinematics positive solution, and calculating the tracking error of the tail end track of the conveying mechanism based on the step 2);
4) In order to improve the synchronous coordination performance of the series-parallel automobile electrophoretic coating conveying mechanism and the motion control precision of the tail end of the mechanism, a contour error is defined, and a method for estimating the contour error of the tail end of the mechanism is provided;
5) Based on the step 3) and the step 4), defining a comprehensive error combining a mechanism end tracking error and a contour error;
6) Based on the step 1) and the step 5), a novel synchronous coordination sliding mode controller based on comprehensive errors is further designed;
7) And 6) based on the step 6), realizing synchronous coordination sliding mode control of the series-parallel automobile electrophoretic coating conveying mechanism based on comprehensive errors through software programming.
Further, in the step 1), establishing a joint space dynamics model of the lifting turnover mechanism by adopting a Lagrange method comprises the following steps:
in the formula, x is a group,respectively represent the actual motion pose, speed and acceleration vector of each active joint, and has(x i The unit is m, and the unit is,unit rad); m (x) is a linear chain,g (x) is respectively an inertia matrix, a Coud force and centrifugal force term and a gravity term when unmodeled dynamics are not considered; tau is a joint axial driving force vector, namely the control input (with the unit of N.m) of the system; d (t) is a friction force term,wherein F c Is a Coulomb friction matrix (unit is N.m), B c Is a viscosity coefficient matrix (in n.s); f (t) is an external disturbance term (with the unit of N.m).
Further, in the step 2), according to the requirements of the automobile electrophoretic coating process and in order to eliminate a roof air pocket, the automobile body-in-white needs to do small vertical lifting motion in an electrophoresis tank and turn over for 360 degrees. Carrying out track planning on the mechanism to obtain a pose component X of the P point expected motion track at the tail end of the conveying mechanism d (unit is m), Z d (unit is m) and beta d (unit is rad), wherein X d Desired trajectory of the end of the mechanism in the X direction, Z d For the desired trajectory of the end of the mechanism in the Z direction, β d Is the desired trajectory of the rotation of the end of the mechanism about the Y-axis. Determining each initiative of the mechanism according to the expected motion trail of the tail end of the mechanism and based on the inverse solution of the kinematics of the mechanismDesired motion trajectory x of joint d ＝[x 1d ,x 2d ,x 3d ,x 4d ,φ 1d ,φ 2d ] T (x id Unit is m, phi jd In rad), desired speed of movement(The unit is m/s, and the unit is,in rad/s), desired acceleration of motion(Unit is m/s 2 ，φ jd Unit is rad/s 2 )。
Further, in the step 3), the actual motion state of each active joint of the series-parallel automobile electrophoretic coating conveying mechanism is calculated by using the detection result of the absolute position encoder:
absolute position encoders equipped for driving motors (Mitsubishi servo motors) of active joints of the series-parallel automobile electrophoretic coating conveying mechanism detect actual motion states of the motors to obtain actual motion angular displacement sigma (unit is rad) and actual motion angular velocity of the driving motors(unit is rad/s). Then, the actual motion state of each active joint can be obtained from the lead screw s (unit is m), the mechanical efficiency η of the lead screw, and the reduction ratio 1: slider displacement x i (i =1.. 4) (unit is m), capstan angular displacement(in rad); speed of slide(unit is m/s), drive wheel angular velocity(unit is rad/s).
According to the obtained actual motion state of each active joint and by means of kinematics positive solution, obtaining the actual motion trail of the tail end P point of the conveying mechanism as follows:
wherein X is the displacement of the end of the conveying mechanism in the X direction (unit is m); z is the displacement of the end of the transport mechanism in the Z direction (in m); l is a radical of an alcohol 1 Is the first link length (in m); l is 3 Is the third link length (in m); beta is the rotation angle (in rad) of the end of the conveying mechanism around the Y axis.
The tracking error e of the P point at the tail end of the conveying mechanism can be obtained t (t) is:
e tx (t)＝x-X d
e tz (t)＝z-Z d
e tβ (t)＝β-β d
in the formula, e tx (t)、e tz (t) and e tβ (t) respectively representing the tracking errors of a P point at the tail end of the conveying mechanism in the X direction, the Z direction and the rotation angle around the Y axis (the unit is m, m and rad respectively); x d 、Z d And beta d Respectively represent expected motion track pose components (m, m and rad respectively) of a point P at the tail end of the conveying mechanism in the X direction, the Z direction and the rotation angle around the Y axis.
Further, in the step 4), as shown in fig. 4, a profile error e is defined c (t) is the error of the actual pose of the P point at the tail end of the conveying mechanism and the nearest point of the expected track:
e c (t)＝[e cx (t),e cz (t),e cβ (t)] T
in the formula, e cx (t)、e cz (t) and e cβ (t) represents the profile errors (in units of m, and rad, respectively) of the point P at the end of the transport mechanism in the X direction, the Z direction, and the rotation angle about the Y axis. Here, e cβ And (t) adopting the tracking error of the rotation angle of the tail end P point of the conveying mechanism around the Y axis. In addition to direct calculation or measurement of e cx (t) and e cz (t) is very difficult, and for this reason, the invention proposes to carry out e by using the tangential distance corresponding to the actual position of the end of the conveying mechanism in the X and Z planes to the desired position cx (t) and e cz (t) estimation. The method comprises the following steps:
in the formula (I), the compound is shown in the specification,is a profile error e c (t) estimated values in the X, Z plane (in m); e.g. of a cylinder tx (t)、e tz (t) respectively representing the tracking errors (in m) of the tail end P point of the conveying mechanism in the X direction and the Z direction; theta is the positive included angle (unit is rad) between the tangent of the expected motion track of the tail end of the conveying mechanism and the X axis.
Thereby further obtaining the contour error e of the tail end of the series-parallel automobile electrophoretic coating conveying mechanism in the X and Z directions cx (t) and e cz The estimated value of (t) is:
wherein e is tx (t)、e tz (t) respectively representing the tracking errors (in m) of the tail end P point of the conveying mechanism in the X direction and the Z direction; theta is the positive included angle (unit is rad) between the tangent of the expected motion track at the tail end of the conveying mechanism and the X axis.
Based on the above, the estimated value of the profile error of the end point P of the conveying mechanism is obtained as follows:
wherein the content of the first and second substances,representing the estimated error value (in m) of the end profile of the conveying mechanism;respectively representing estimated values (in m) of profile errors in X and Z directions of a P point at the tail end of the conveying mechanism; e.g. of the type cβ (t) is the tracking error (unit is rad) of the rotating angle of the tail end P point of the conveying mechanism around the Y axis; e.g. of the type t (t) is the tracking error of the end of the transport mechanism (e) tx (t)、e tz (t) units are m, e tβ (t) unit is rad), and the tracking error can be obtained by calculating the actual motion state of each active joint by using the detection result of the absolute position encoder and performing positive solution of kinematics; δ = R 3×3 Is a constant gain matrix expressed as follows:
wherein θ is the angle (in rad) between the tangent of the expected motion trajectory of the end of the conveying mechanism and the X axis, and can be represented by the following formula:
in the formula, P XZ To obtain the expected track of the tail end P point of the conveying mechanism on the X and Z planes,is P XZ The derivative of (c).
Further, in the step 5), a combined error vector e combining the mechanism end tracking error and the contour error is defined cc Comprises the following steps:
in the formula, e t (t) is the tracking error (in m) of the P point at the tail end of the conveying mechanism;an estimated value (in m) of the P point profile error at the tail end of the conveying mechanism; r L ＝diag(R 1 ,R 2 ,R 3 ) The coupling parameter matrix can be determined according to the established mechanism dynamic model.
Further, in the step 6), designing the sliding mode surface based on the comprehensive error is as follows:
in the formula B L ＝diag(b 1 ,b 2 ,b 3 ) And B is L Reversible, b i (i =1,2,3) satisfies the Hurwitz condition.
Taking a constant velocity approach law:
in the formula K L ＝diag(k 1 ,k 2 ,k 3 )，k i >0(i＝1,2,3)。
The control law of the formed novel synchronous coordination sliding mode controller based on the comprehensive error is as follows:
wherein τ = [ τ ] 1 ,τ 2 ,τ 3 ,τ 4 ,τ 5 ,τ 6 ]Outputting for a synchronous coordination sliding mode controller (the unit is N.m); m (q), C e G (q) is respectively an inertia matrix, a Cogowski force and centrifugal force term and a gravity term when the unmodeled dynamics are not considered; k is L ＝diag(k 1 ,k 2 ,k 3 ) Gain for sliding mode switching term, and k i (i＝1,2,3)>0；e cc Is a cross-coupled error vector (in m);an estimated value (in m) of the end contour error of the conveying mechanism;for each active joint actual velocity vector, and(x i the unit is m, and the unit is,unit rad);an acceleration vector (in m/s) is expected for each active joint 2 ) (ii) a D (t) is a friction force term,wherein F c Is a Coulomb friction matrix (unit is N.m), B c Is a viscosity coefficient matrix (in n.s). F (t) is an external disturbance term (with the unit of N.m).
The invention provides a synchronous coordination sliding mode control method based on comprehensive errors for the first time, which is applied to realizing the motion control of a series-parallel automobile electrophoretic coating conveying mechanism and has the characteristics and beneficial effects that:
1. the comprehensive error combining the tail end tracking error and the contour error of the mechanism is designed for realizing the motion control of the series-parallel automobile electrophoretic coating conveying mechanism, the utilization of the comprehensive error can effectively improve the motion control precision of the tail end of the conveying mechanism and is beneficial to realizing the high-precision automobile electrophoretic coating conveying.
2. A synchronous coordination sliding mode controller based on the comprehensive error is designed, the sliding mode control technology and the synchronous coordination technology based on the comprehensive error are combined, the problem of uncertainty of the system can be further effectively solved, the adverse effect of the quick change dynamic characteristic of the conveying mechanism on the control performance of the system is weakened, and therefore the control performance of the mechanism can be further improved.
Drawings
Fig. 1 is a series-parallel automobile electrophoretic coating conveying mechanism and a structural diagram thereof.
FIG. 2 is a control system schematic diagram of a novel synchronous coordinated sliding mode controller based on synthetic error.
Fig. 3 is a schematic structure diagram of the lifting turnover mechanism.
FIG. 4 is a schematic illustration of the end profile error of the transport mechanism.
Fig. 5 is a general structure diagram of a control system of a series-parallel automobile electrophoretic coating conveying mechanism.
FIG. 6 is a graph of synchronization error between the active joints of the mechanism. FIG. 6 (a) is a graph of the synchronization error between the first and third sliders; FIG. 6 (b) is a synchronization error curve between the second and fourth sliders; fig. 6 (c) is a graph of synchronization error between the first and second drive wheels.
Fig. 7 is a graph of the trajectory tracking of the tail end (the middle point of the connecting rod) of the lifting turnover mechanism. Fig. 7 (a) is a pose component trajectory tracking curve of the midpoint of the connecting rod in the Z direction when the mechanism performs lifting and overturning motion, and fig. 7 (b) is a pose component trajectory tracking curve of the midpoint of the connecting rod rotating counterclockwise around the Y axis when the mechanism performs lifting and overturning motion.
In the figure: 1-a first driver, 2-a first lead screw, 3-a second lead screw, 4-a guide rail, 5-a first sliding block, 6-a first rotating pair, 7-a first connecting rod, 8-a second rotating pair, 9-a second sliding block, 10-a third rotating pair, 11-a second connecting rod, 12-a second driver, 13-a driving wheel, 14-a belt, 15-a driven wheel, 16-a connecting rod, 17-a vehicle body fixing frame, 18-a vehicle body, 19-a walking driver, 20-a walking base, 21-a guide wheel, 22, 23-a walking wheel and 24-a guide rail.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
The technical scheme adopted by the invention comprises the following steps:
1) The method comprises the following steps of (1) establishing a conveying mechanism dynamic model containing unmodeled dynamics, frictional force and external random interference by using a series-parallel automobile electrophoretic coating conveying mechanism as a controlled object by adopting a Lagrange method;
2) Determining an expected motion track of the tail end of the conveying mechanism according to the automobile electrophoretic coating process requirement and mechanism mechanical design parameters, and obtaining the expected motion track of each active joint through inverse kinematics solution;
3) Calculating to obtain the actual motion state of each active joint by utilizing the position and speed information of each motor fed back by the encoder, obtaining the actual motion track of the tail end of the conveying mechanism through kinematics positive solution, and calculating the tail end tracking error of the conveying mechanism based on the step 2);
4) In order to improve the synchronous coordination performance of the series-parallel automobile electrophoretic coating conveying mechanism and the motion control precision of the tail end of the mechanism, a contour error is defined, and a method for estimating the contour error of the tail end of the mechanism is provided;
5) Based on the step 3) and the step 4), defining a comprehensive error combining a mechanism tail end tracking error and a contour error;
6) Based on the step 1) and the step 5), further designing a novel synchronous coordination sliding mode controller based on the comprehensive error;
7) And 6) based on the step 6), realizing synchronous coordination sliding mode control of the series-parallel automobile electrophoretic coating conveying mechanism based on comprehensive errors through software programming.
Firstly, establishing a mechanism dynamics model containing unmodeled dynamics, frictional force and external random interference by adopting a Lagrange method; secondly, according to the car electrophoretic coatingPlanning the tail end motion of the series-parallel automobile electrophoretic coating conveying mechanism according to the process requirements, and determining the expected motion track x of each active joint of the mechanism in the process of realizing the expected motion of the tail end of the mechanism through inverse kinematics d (ii) a Then, detecting the actual motion state of each driving joint driving motor by using an absolute position encoder, calculating to obtain the actual motion state of each driving joint, obtaining the actual motion track of the tail end of the conveying mechanism through kinematic forward solution, and calculating a track tracking error; in order to improve the synchronous coordination among all the moving branch chains in the operation process of the conveying mechanism and the track tracking precision of the tail end of a mechanism for loading a white automobile body of an automobile to carry out coating conveying, a contour error of the tail end track of the mechanism is defined aiming at the structural characteristics and the movement characteristics of the conveying mechanism, a comprehensive error combining the tail end tracking error and the contour error of the conveying mechanism is further provided, and a synchronous coordination sliding mode controller based on the comprehensive error is designed; and finally, realizing synchronous coordination sliding mode control of the series-parallel automobile electrophoretic coating conveying mechanism based on comprehensive errors through software programming. The specific method comprises the following steps:
1. establishing a mechanism dynamic model containing unmodeled dynamics, frictional force and external random interference
The structure diagram of the series-parallel automobile electrophoretic coating conveying mechanism is shown in fig. 1, and the mechanism consists of two relatively independent parts, namely a travelling mechanism and a lifting turnover mechanism. The walking mechanism comprises a walking driving motor, a speed reducer, walking wheels, a guide rail, a walking base and other components, and the walking driving motor drives the walking wheels to roll on the guide rail so as to drive the walking base to realize one-dimensional movement; the lifting turnover mechanism comprises a turnover driving motor, a speed reducer, a lifting driving motor, an electric lead screw, a sliding block, a connecting rod, a driving wheel, a driven wheel, a belt and other components, the lifting turnover mechanism is fixed on the walking base, and the lifting turnover mechanism is driven to move together when the walking mechanism moves in the horizontal direction. When the mechanism works, the vehicle body is fixed on the vehicle body fixing frame, and the two walking driving motors synchronously drive the walking mechanism to move forwards; each pair of slide blocks on the two sides of the lifting turnover mechanism are driven by a lifting driving motor to synchronously translate in the same direction or in opposite directions so as to drive a connecting rod corresponding to the slide block to move and further drive a vehicle body fixing frame provided with a vehicle body to carry out lifting motion through the connecting rod; the turnover motors on the two sides of the lifting turnover mechanism synchronously operate to drive the driving wheel to rotate and drive the driven wheel to rotate through the belt, so that the connecting rod fixed on the driven wheel is driven to rotate, and the turnover movement of the vehicle body fixing frame of the loaded vehicle body is realized. The series-parallel automobile electrophoretic coating conveying mechanism takes the lifting turnover mechanism as a main body, has large influence on the overall performance of the mechanism and has high control requirement, and therefore, the specific implementation mode of the invention focuses on the explanation of the control of the lifting turnover mechanism.
The joint space dynamics model of the lifting turnover mechanism is established by adopting a Lagrange method and comprises the following steps:
in the formula, x is a group,respectively represent the actual motion pose, speed and acceleration vector of each active joint, and haveWherein x i (i =1 \ 82304; 4) is the actual displacement of four sliders (in m),actual angular displacement (unit is rad) for two driving wheels; m (x) is a linear chain structure,g (x) is respectively an inertia matrix, a Coud force and centrifugal force term and a gravity term when unmodeled dynamics are not considered; τ is the joint axial driving force vector, i.e. the control input of the system (in n.m); d (t) is a friction force term,wherein F c Is a Coulomb friction matrix (unit is N.m), B c Is stickyThe degree coefficient matrix unit is (N.s); f (t) is an external disturbance term (with the unit of N.m).
2. Determining the expected motion trail of the tail end of the conveying mechanism according to the requirements of the automobile electrophoretic coating process and the mechanical design parameters of the mechanism, and obtaining the expected motion trail of each active joint through inverse kinematics
According to the requirements of the automobile electrophoretic coating process and in order to eliminate a roof air bag, the white automobile body of the automobile needs to do vertical lifting motion in an electrophoresis tank and turn over by 360 degrees. Planning the mechanism to obtain the expected track X of the P point at the tail end of the conveying mechanism d (unit is m), Z d (unit is m) and beta d (unit is rad), wherein X d For desired trajectory of the end of the mechanism in the X direction, Z d For the desired trajectory of the end of the mechanism in the Z direction, β d Is the desired trajectory of the rotation of the mechanism tip about the Y axis. Determining the expected motion trail x of each active joint in the process of realizing the expected motion of the tail end of the mechanism according to the expected track of the P point at the tail end of the conveying mechanism and based on the inverse kinematics of the mechanism d ＝[x 1d ,x 2d ,x 3d ,x 4d ,φ 1d ,φ 2d ] T (x id Unit is m, phi jd Rad), desired speed of movement(The unit is m/s, and the unit is,in rad/s), desired acceleration of motion(Unit is m/s 2 ，φ jd Unit is rad/s 2 )。
3. Calculating the actual motion state of each active joint of the series-parallel automobile electrophoretic coating conveying mechanism by using the detection result of the absolute position encoder, obtaining the actual motion track of the tail end of the conveying mechanism by kinematics positive solution, and calculating the tail end tracking error of the conveying mechanism
Absolute position encoders equipped for driving motors (Mitsubishi servo motors) of active joints of the series-parallel automobile electrophoretic coating conveying mechanism detect actual motion states of the motors to obtain actual motion angular displacement sigma (unit is rad) and actual motion angular velocity of the driving motors(unit is rad/s). Then, the actual motion state of each active joint can be obtained from the lead screw s (unit is m), the mechanical efficiency η of the lead screw, and the reduction ratio 1: slider displacement x i (i =1.. 4) (unit is m), capstan angular displacement(in rad); speed of slide(unit is m/s), drive wheel angular velocity(unit is rad/s).
According to the obtained actual motion state of each active joint, obtaining the actual motion trail of the tail end P point of the conveying mechanism through kinematics positive solution, wherein the actual motion trail comprises the following steps:
wherein X is the displacement of the end of the conveying mechanism in the X direction (unit is m); z is the displacement of the end of the conveying mechanism in the Z direction (in m); l is 1 Is the first link length (in m); l is a radical of an alcohol 3 Is the third link length (in m); beta is the rotation angle (in rad) of the end of the transport mechanism about the Y axis.
Thereby can beObtaining the tracking error e of the P point at the tail end of the conveying mechanism t (t) is:
e tx (t)＝x-x d
e tz (t)＝z-z d (3)
e tβ (t)＝β-β d
in the formula, e tx (t)、e tz (t) and e tβ (t) respectively representing the tracking errors of the P point at the tail end of the conveying mechanism in the X direction, the Z direction and the rotation angle around the Y axis (the units are m, m and rad respectively); x is the number of d 、z d And beta d Respectively representing the desired motion trajectories (in m, m and rad, respectively) of the point P of the conveyor end in the X direction, the Z direction and the rotation angle about the Y axis.
4. Defining contour error
As shown in fig. 4, a profile error e is defined c (t) is the error between the actual position of the tail end P point of the conveying mechanism and the nearest point of the expected track:
e c (t)＝[e cx (t),e cz (t),e cβ (t)] T (4)
in the formula, e cx (t)、e cz (t) and e cβ (t) represents the profile errors (in units of m, and rad, respectively) of the point P at the end of the transport mechanism in the X direction, the Z direction, and the rotation angle about the Y axis. Here, e cβ And (t) adopting the tracking error of the rotation angle of the tail end P point of the conveying mechanism around the Y axis. In addition to direct calculation or measurement of e cx (t) and e cz (t) is very difficult, and for this reason, the invention proposes to carry out e by using the tangential distance corresponding to the actual position of the end of the conveying mechanism in the X and Z planes to the desired position cx (t) and e cz (t) estimation. The method comprises the following steps:
in the formula (I), the compound is shown in the specification,is a profile error e c (t) estimation in the X, Z planeA value (in m); e.g. of the type tx (t)、e tz (t) respectively representing the tracking errors (in m) of the P point at the tail end of the conveying mechanism in the X direction and the Z direction; theta is the positive included angle (unit is rad) between the tangent of the expected motion track of the tail end of the conveying mechanism and the X axis.
Thereby further obtaining the contour error e of the tail end of the series-parallel automobile electrophoretic coating conveying mechanism in the X and Z directions cx (t) and e cz The estimated value of (t) is:
wherein e is tx (t)、e tz (t) represents the tracking error (in m) of the tail end of the conveying mechanism in the X direction and the Z direction respectively; θ is the positive angle (in rad) between the tangent to the desired track and the X-axis.
Based on the above, the estimated value of the profile error of the end point P of the conveying mechanism is obtained as follows:
wherein, the first and the second end of the pipe are connected with each other,representing the estimated error value (in m) of the end profile of the conveying mechanism;respectively representing estimated values (in m) of profile errors in X and Z directions of a P point at the tail end of the conveying mechanism; e.g. of the type cβ (t) is the tracking error (unit is rad) of the rotating angle of the tail end P point of the conveying mechanism around the Y axis; e.g. of the type t (t) is the tracking error of the end of the transport mechanism (e) tx (t)、e tz (t) units are m, e tβ (t) in rad), the tracking error can be determined by using the absolute value ofCalculating the actual motion state of each active joint obtained by the detection result of the position encoder and obtaining the actual motion state through a kinematics positive solution; δ = R 3×3 Is a constant gain matrix, expressed as follows:
wherein θ is the forward angle (in rad) between the tangent of the expected motion trajectory at the end of the conveying mechanism and the X axis, and can be represented by the following formula:
in the formula, P XZ To obtain the expected track of the tail end P point of the conveying mechanism on the X and Z planes,is P XZ The derivative of (c).
5. Defining composite error
Defining a combined error vector e combining tracking error and contour error cc Comprises the following steps:
in the formula, e t (t) is the tracking error (in m) of the P point at the tail end of the conveying mechanism;an estimated value (in m) of the P point profile error at the tail end of the conveying mechanism; r L ＝diag(R 1 ,R 2 ,R 3 ) The coupling parameter matrix can be determined according to the established mechanism dynamic model.
6. Design is based on novel synchronous coordination sliding mode controller of combined error
The design slip form surface based on the comprehensive error is as follows:
in the formula B L ＝diag(b 1 ,b 2 ,b 3 ) And B is L Reversible, b i (i =1,2,3) satisfies the Hurwitz condition.
Derivation is performed on S in equation (19), and equation (18) is substituted to obtain:
from formula (1):
taking a constant velocity approach law:
in the formula K L ＝diag(k 1 ,k 2 ,k 3 )，k i >0(i＝1,2,3)。
The formulas (13) to (14) are substituted into the formula (12) to obtain a novel synchronous coordination sliding mode control law based on the comprehensive error, wherein the novel synchronous coordination sliding mode control law is as follows:
wherein τ is the output of the novel synchronous coordination sliding mode controller based on the designed comprehensive error, and τ (i =1,2,3,4,5, 6) acts on each branch component (unit is n.m) for the output of the controller.
7. Novel synchronous coordination sliding mode control based on comprehensive error of series-parallel automobile electrophoretic coating conveying mechanism through software programming
Due to the series-parallel automobile electrophoretic coating conveyingIn the mechanism, a first branch chain, a second branch chain, a third branch chain and a fourth branch chain are directly connected with a ball screw by an alternating current servo motor to realize the axial movement of a sliding block (a driving pair), and a first driving wheel and a second driving wheel are driven by the alternating current servo motor through a speed reducer. Therefore, the output component [ tau ] of each branch controller determined in step 6 needs to be determined 1 τ 2 τ 3 τ 4 τ 5 τ 6 ] T The actual driving torque of each driving joint driving motor can be obtained after certain conversion.
Specifically, the torques of the driving motors of the first, second, third and fourth sliders are respectively:
wherein s is a lead screw lead (in m); eta is the mechanical efficiency of the screw rod.
The driving motor torques of the first driving wheel and the second driving wheel are respectively as follows:
τ j ＝nτ j (N.m)(j＝5,6)(16)
in the formula, n is a reduction gear ratio of the reduction gear.
And writing a synchronous coordination sliding mode control algorithm software program based on comprehensive errors, sending a voltage analog quantity obtained by performing digital/analog conversion on a calculation result (namely the torque required by each driving motor) through a numerical control system to a servo driver corresponding to the motor, and controlling each motor to drive a corresponding active joint so as to drive a connecting rod (loaded with a body-in-white to be coated) at the tail end of the series-parallel automobile electrophoretic coating conveying mechanism to realize expected motion.
Examples of the invention are provided below:
example 1
The invention mainly aims to improve the tracking precision of the tail end track of the mechanism by using a synchronous coordination sliding mode control method based on comprehensive errors so as to realize high-precision automobile electrophoretic coating conveying. A schematic block diagram of a synchronous coordination sliding mode control principle of a series-parallel automobile electrophoretic coating conveying mechanism based on comprehensive errors is shown in fig. 2, taking a developed prototype as an example, the control method has the following specific implementation mode:
1. establishing a dynamic model of a lifting turnover mechanism containing unmodeled dynamics, frictional force and external random interference
Based on FIG. 3 with S 1 And S 2 Has a base coordinate system { B } = { O-XYZ } with X-axis along S 1 S 2 Direction, Y axis parallel to P 2 P 1 The Z axis is vertically downward, and the pose parameter q = (x, Z, beta) of the P point is selected T Is a system generalized coordinate. Wherein X is the displacement (unit is m) of the connecting rod midpoint in the X direction, Z is the displacement (unit is m) of the connecting rod midpoint in the Z direction, and β is the counterclockwise rotation angle (unit is rad) of the connecting rod midpoint around the Y axis, and the dynamic model of the lifting turnover mechanism is established as follows:
wherein M (q) is an inertia matrix;are terms of Copenforces and centrifugal forces; g (q) is a gravity term; q is a generalized driving force or torque;the first and second derivatives of q, respectively. And is provided with
M 11 ＝m p +4m l1 +m l5 +m T1 +2m a +2m b +4m s1 ,
G 1 ＝0,G 2 ＝(m p +2m l1 +m l5 +4m T1 +m b )g,G 3 ＝Δ 4 g,
In the formula, the mechanism-related parameters are: m is a unit of p =22kg mass of vehicle body, m l1 ＝m l2 =5kg mass of the first and second connecting rods, m l5 =7kg connecting rod mass, m T1 =6kg for inclined bracket mass of vehicle body fixing bracket, m s1 ＝m s2 =4kg mass of the first and second sliders, m a =0.5kg as the mass of the driving wheel, m b =0.5kg isDriven wheel mass, a =0.58m for vehicle body length, b =0.23m for vehicle body width, c =0.2m for vehicle body height, r l3 =0.0125m is the radius of the connecting rod, r 1 =0.075m for driven wheel radius, r 2 =0.025m is the radius of the driving wheel,/ 1 ＝l 2 =0.495m is the length of the first and second connecting rods, l 8 =0.6m is the length of the inclined bracket of the car body fixing frame l 7 =0.72m connecting rod length, and θ =60 ° is the angle between two diagonal rods of the car body fixing frame.
And (3) obtaining the axial driving force/moment of each active joint by converting the generalized driving force/moment Q obtained by the dynamic model established by the Lagrange method through a Jacobian matrix. Based on the static coordinates { B } = { O-XYZ }, which are established as shown in fig. 3, a connecting rod length constraint equation is adopted, so that a mechanism kinematics inverse solution equation can be obtained:
in the formula, x i (i =1,2,3,4) are respectively the position of the i-th slider in the X-axis direction (unit is m);respectively the angle (unit is rad) of the counterclockwise rotation of the jth driving wheel around the Y axis; beta is a j (i =1, 2) respectively rotating the two ends of the connecting rod anticlockwise around the Y axis (unit is rad); l 1 ＝l 2 ＝l 3 ＝l 4 =0.5m is the corresponding connecting rod length respectively; n =2 is the ratio of the radius of the driven wheel to the radius of the driving wheel.
The two ends of the formula are respectively subjected to time derivation and arrangement to obtain a Jacobian matrix:
the kinematics analysis shows that the speed and the acceleration of the position and the attitude of the middle point of the connecting rod have the following relations with the speed and the acceleration of each active joint:in the formula (I), the compound is shown in the specification,velocity and acceleration vectors of each active joint, respectively, and havingWherein x is i (i =1 \ 82304): 4) is the actual displacement (unit is m) of the four sliders in the X-axis direction;for the two drive wheels, in real angular displacement (in rad) counterclockwise about the Y axis.
The dynamic equation of the lifting turnover mechanism in the joint space obtained by the Jacobian matrix is as follows:
considering unmodeled dynamics and mechanism friction, and in the actual working process, many unknown environment random disturbances such as motion resistance change, rounding error, sampling delay, sensor noise and the like exist, so that a complete mechanism dynamic model is further obtained:
in the formula, x is a linear or branched alkyl group,respectively represent the actual motion pose, speed and acceleration vector of each active joint, and hasM(x)，G (x) is independentlyThe inertia matrix, the coriolis and centrifugal force terms, and the gravity terms in the dynamic state are modeled. τ is the joint axial drive force vector, i.e., the control input to the system (in n.m). D (t) is a friction force term,wherein F c Is a Coulomb friction matrix (unit is N.m), B c The viscosity coefficient matrix unit is (n.s). F (t) is an external disturbance term (with the unit of N.m).
2. Determining the expected motion trail of the tail end of the conveying mechanism according to the requirements of the automobile electrophoretic coating process and the mechanical design parameters of the mechanism, and obtaining the expected motion trail of each active joint through inverse kinematics
Finally determining the overall operation time of a prototype of the conveying mechanism to be 16s according to the requirements of the automobile electrophoretic coating process and the mechanical design parameters of the prototype mechanism: at 0s-2s, the conveying mechanism moves to the electrophoresis tank opening, and the turnover mechanism drives the vehicle body to turn over 180 degrees in the anticlockwise direction within 2s-6s ° The vehicle body enters the electrophoresis tank liquid downwards, and the turnover mechanism stops turnover at the 6 th time; along with the overturning motion, the lifting mechanism starts to do lifting motion in the tank liquor from 4s, wherein the lifting motion is performed in 4s-8s, the lifting motion is performed in 8s-12s, the overturning mechanism starts to continuously overturn for 180 degrees anticlockwise in 10s, and the overturning is completed when the automobile body is upwards; within 12s-16s, the lifting mechanism stops, and the 14 th conveying mechanism stops moving, so that the expected track of the midpoint P of the connecting rod at the end of the sample machine is obtained as follows:
X d ＝0(0s≤t≤16s)
the expected track of each active joint of the lifting turnover mechanism is obtained by inverse kinematics in the above formula:
in the formula, x di (i =1,2,3,4) is the i-th slider desired trajectory, φ dj (j =1, 2) is the j-th capstan desired trajectory.
3. Calculating the actual motion state of each active joint of the series-parallel automobile electrophoretic coating conveying mechanism by using the detection result of the absolute position encoder, obtaining the actual motion track of the tail end of the conveying mechanism by kinematics positive solution, and calculating the tail end tracking error of the conveying mechanism
Absolute position encoders equipped for driving motors (Mitsubishi servo motors) of active joints of the series-parallel automobile electrophoretic coating conveying mechanism detect actual motion states of the motors to obtain actual motion angular displacement sigma (unit is rad) and actual motion angular velocity of the driving motors(unit is rad/s). Then, the actual motion state of each active joint can be obtained from the lead screw s (unit is m), the mechanical efficiency η of the lead screw, and the reduction ratio 1: slider displacement x i (i =1.. 4) (unit is m), and the angular displacement of the driving wheel(in rad); speed of slide(unit is m/s), drive wheel angular velocity(unit is rad/s).
According to the obtained actual motion state of each active joint, and by means of kinematics positive solution, obtaining the actual motion track of the P point at the tail end of the conveying mechanism as follows:
wherein X is the displacement of the end of the conveying mechanism in the X direction (unit is m); z is the displacement of the end of the transport mechanism in the Z direction (in m); l is 1 Is the first link length (in m); l is 3 Is the third link length (in m); beta is the rotation angle (in rad) of the end of the conveying mechanism around the Y axis.
The tracking error e of the P point at the tail end of the conveying mechanism can be obtained t (t) is:
e tx (t)＝x-x d
e tz (t)＝z-z d
e tβ (t)＝β-β d
in the formula, e tx (t)、e tz (t) and e tβ (t) respectively representing the tracking errors of a P point at the tail end of the conveying mechanism in the X direction, the Z direction and the rotation angle around the Y axis (the unit is m, m and rad respectively); x is a radical of a fluorine atom d 、z d And beta d Respectively representing the desired motion trajectories (in m, m and rad, respectively) of the point P of the conveyor end in the X direction, the Z direction and the rotation angle about the Y axis.
4. Defining a contour error and providing a mechanism end contour error estimation method
Defining a profile error e c (t) is the error between the actual position of the tail end P point of the conveying mechanism and the nearest point of the expected track:
e c (t)＝[e cx (t),e cz (t),e cβ (t)] T
in the formula, e cx (t)、e cz (t) and e cβ (t) represents the profile error (in m, and rad, respectively) of the transport mechanism end point P in the X direction, Z direction, and rotation angle about the Y axis. Here, e cβ And (t) adopting the tracking error of the rotation angle of the tail end P point of the conveying mechanism around the Y axis. In addition to direct calculation or measurement of e cx (t) and e cz (t) is very difficult, and for this reason, the invention proposes to carry out e by using the tangential distance corresponding to the actual position of the end of the conveying mechanism in the X and Z planes to the desired position cx (t) and e cz (t) estimation. The method comprises the following steps:
in the formula (I), the compound is shown in the specification,is a profile error e c (t) estimated values in the X, Z plane (in m); e.g. of the type tx (t)、e tz (t) respectively representing the tracking errors (in m) of the P point at the tail end of the conveying mechanism in the X direction and the Z direction; theta is the positive included angle (unit is rad) between the tangent of the expected motion track at the tail end of the conveying mechanism and the X axis.
Thereby further obtaining the contour error e of the tail end of the series-parallel automobile electrophoretic coating conveying mechanism in the X and Z directions cx (t) and e cz The estimated value of (t) is:
wherein e is tx (t)、e tz (t) respectively representing the tracking errors (in m) of the P point at the tail end of the conveying mechanism in the X direction and the Z direction; theta is the positive included angle (unit is rad) between the tangent of the expected motion track at the tail end of the conveying mechanism and the X axis.
Based on the above, the estimated value of the profile error of the end point P of the conveying mechanism is obtained as follows:
wherein the content of the first and second substances,representing an estimated value of the end profile error of the conveying mechanism (in m);respectively representing estimated values (in m) of profile errors in X and Z directions of a P point at the tail end of the conveying mechanism; e.g. of the type cβ (t) is the tracking error (unit is rad) of the rotating angle of the tail end P point of the conveying mechanism around the Y axis; e.g. of the type t (t) is the tracking error of the end of the transport mechanism (e) tx (t)、e tz (t) units are m, e tβ (t) unit is rad), and the tracking error can be obtained by calculating the actual motion state of each active joint by using the detection result of the absolute position encoder and performing positive solution of kinematics; δ = R 3×3 Is a constant gain matrix, expressed as follows:
wherein θ is the angle (in rad) between the tangent of the expected motion trajectory of the end of the conveying mechanism and the X axis, and can be represented by the following formula:
in the formula, P XZ To obtain the expected track of the tail end P point of the conveying mechanism on the X and Z planes,is P XZ The derivative of (c).
5. Defining a composite error combining the end tracking error and the contour error of the mechanism
Defining a combined error vector e combining tracking error and contour error cc Comprises the following steps:
in the formula, e t (t) is the tracking error (in m) of the P point at the tail end of the conveying mechanism;an estimated value (in m) of the P point profile error at the tail end of the conveying mechanism; r L ＝diag(R 1 ,R 2 ,R 3 ) Is a coupling parameter matrix which can be determined according to the established mechanism dynamic model.
6. Design of novel synchronous coordination sliding mode control law based on comprehensive error
The design slip form surface based on the comprehensive error is as follows:
in the formula B L ＝diag(b 1 ,b 2 ,b 3 ) And B is L Reversible, b i (i =1,2,3) satisfies the Hurwitz condition.
Derivation is performed on S in equation (19), and equation (18) is substituted to obtain:
from formula (1):
taking a constant velocity approach law:
in the formula K L ＝diag(k 1 ,k 2 ,k 3 )，k i >0(i＝1,2,3)。
The formulas (13) to (14) are substituted into the formula (12) to obtain a novel synchronous coordination sliding mode control law based on the comprehensive error, wherein the novel synchronous coordination sliding mode control law is as follows:
wherein τ is the output of the novel synchronous coordination sliding mode control based on the comprehensive error, and τ (i =1,2,3,4,5, 6) acts on each branch component (unit is n.m) for the output of the controller.
7. Novel synchronous coordination sliding mode control based on comprehensive error of series-parallel automobile electrophoretic coating conveying mechanism through software programming
Because the first, second, third and fourth branched chains in the series-parallel automobile electrophoretic coating conveying mechanism adopt the direct connection of an alternating current servo motor and a ball screw to realize the axial movement of a sliding block (a driving pair), and the first driving wheel and the second driving wheel are driven by the alternating current servo motor and a speed reducer. Therefore, the output component [ tau ] of each branch controller determined in step 6 needs to be determined 1 τ 2 τ 3 τ 4 τ 5 τ 6 ] T The actual required torque of each driving joint driving motor is obtained through the following conversion.
Namely: the torque of the driving motor of the first, second, third and fourth sliders is determined by the lead screw s =0.004m and the mechanical efficiency η =0.9 of the lead screw:(i =1,2,3,4) (unit n.m).
The torque of the driving motors of the first driving wheel and the second driving wheel is determined by the reduction ratio n of the speed reducer and the mechanical efficiency of the speed reducer, wherein n =20. Because the series-parallel automobile electrophoretic coating conveying mechanism adopts the planetary speed reducer, the transmission efficiency is very high, and the mechanical efficiency of the speed reducer can be approximate to 100 percent. Therefore, the torque of the driving motor of the first driving wheel and the torque of the driving motor of the second driving wheel are as follows: tau. j ＝20τ j (j =5,6) (unit is n.m).
The series-parallel automobile electrophoretic coating conveying mechanism adopts a distributed control system of an upper computer (PC) and a lower computer (UMAC multi-axis motion controller), and the general structural schematic diagram of the control system is shown in FIG. 4.
The upper computer application program takes VC + +6.0 software as a development platform, and realizes system initialization, data management, code compilation and real-time monitoring of mechanism states based on Pcomm32W.dll dynamic link libraries provided by MFC and Delta Tau companies.
And compiling a lower computer motion program, namely a novel synchronous coordination sliding mode control algorithm program based on comprehensive errors, wherein the control quantity output by the program operation is subjected to UMAC (unified modeling and control) digital-to-analog conversion to obtain corresponding voltage analog quantity (-10V to + 10V), and the analog quantity is used as a driving instruction and is sent to a servo driver corresponding to each motor to control each motor to drive a corresponding active joint, so that an end effector of the series-parallel automobile electrophoretic coating conveying mechanism is driven to realize expected motion.
When uncertain factors such as unmodeled dynamics, friction force, position environment interference and the like exist in the system, synchronous error curve graphs among all active joints of the series-parallel automobile electrophoretic coating conveying mechanism are respectively shown in all sub-graphs in FIG. 6; the actual motion trajectories of the middle point of the connecting rod moving in the Z direction and counterclockwise around the Y axis are shown by dashed lines in the respective sub-diagrams of fig. 7.
And in order to verify the synchronous coordination performance of the designed synchronous coordination sliding mode controller based on the comprehensive error, the synchronous coordination sliding mode controller is subjected to simulation comparison with the synchronous coordination sliding mode controller. Wherein, fig. 6 (a) is a synchronization error curve between the first and third sliders; FIG. 6 (b) is a graph showing the synchronization error between the second and fourth sliders; fig. 6 (c) is a graph of synchronization error between the first and second drive wheels.
In order to verify the tracking performance of the designed synchronous coordination sliding mode controller based on the comprehensive error, the simulation comparison is carried out on the lifting and overturning movement (no movement in the X direction) of the mechanism and the synchronous coordination sliding mode controller. Fig. 7 (a) is a pose component trajectory tracking curve of the midpoint of the connecting rod in the Z direction when the mechanism performs lifting and overturning motion, and fig. 7 (b) is a pose component trajectory tracking curve of the midpoint of the connecting rod rotating counterclockwise around the Y axis when the mechanism performs lifting and overturning motion.
As can be seen from fig. 6 and 7, when the system is affected by a plurality of uncertain factors, the novel synchronous coordination sliding mode control method based on the comprehensive error provided by the invention can not only realize the synchronous motion between each active joint, but also effectively improve the tracking precision of the tail end motion trail of the conveying mechanism, and is beneficial to realizing high-precision automobile electrophoretic coating conveying.
It should be understood that the above-described embodiments are illustrative only and are not limiting upon the scope of the invention, which is to be given the full breadth of the appended claims and any and all equivalent modifications thereto that may occur to those skilled in the art upon reading the present disclosure.
Claims (9)
1. A synchronous coordination sliding mode control method of a series-parallel automobile electrophoretic coating conveying mechanism based on comprehensive errors is characterized by comprising the following steps:
1) The method comprises the following steps of (1) establishing a conveying mechanism dynamic model containing unmodeled dynamics, frictional force and external random interference by taking a series-parallel automobile electrophoretic coating conveying mechanism as a controlled object by adopting a Lagrange method;
2) Determining an expected motion track of the tail end of the conveying mechanism according to the automobile electrophoretic coating process requirement and mechanism mechanical design parameters, and obtaining expected motion tracks of all active joints through inverse kinematics solution;
3) Calculating the actual motion state of each active joint by using the position and speed information of each motor fed back by the encoder, obtaining the actual motion track of the tail end of the conveying mechanism through kinematic positive solution, and calculating the tracking error of the tail end track of the conveying mechanism based on the step 2);
4) In order to improve the synchronous coordination performance of the series-parallel automobile electrophoretic coating conveying mechanism and the motion control precision of the tail end of the mechanism, a contour error is defined, and a mechanism tail end contour error estimation method is provided;
5) Based on the step 3) and the step 4), defining a comprehensive error combining a mechanism end tracking error and a contour error;
6) Based on the step 1) and the step 5), further designing a novel synchronous coordination sliding mode controller based on the comprehensive error;
7) Based on the step 6), synchronous coordination sliding mode control of the series-parallel automobile electrophoretic coating conveying mechanism based on comprehensive errors is realized through software programming.
2. The synchronous coordination sliding-mode control method based on the comprehensive error for the series-parallel automobile electrophoretic coating conveying mechanism according to claim 1, characterized in that: in the step 1), the joint space dynamics model of the lifting turnover mechanism is established by adopting a Lagrange method and comprises the following steps:
in the formula, x is a group,respectively represent the actual motion pose, speed and acceleration vector of each active joint, and hasWherein x i (i =1 \ 82304; 4) is the actual displacement of four sliders,actual angular displacement of the two driving wheels; m (x) is a linear chain,g (x) is an inertia matrix, a Cogowski force and centrifugal force term and a gravity term respectively when the unmodeled dynamics are not considered; tau is a joint axial driving force vector, namely the control input of the system; d (t) is a friction force term,wherein F c Is a Coulomb friction matrix, B c Is a viscosity coefficient matrix; f (t) is an external disturbance term.
3. The synchronous coordination sliding-mode control method based on the comprehensive error for the series-parallel automobile electrophoretic coating conveying mechanism according to claim 1, characterized in that: in the step 2), according to the requirements of the automobile electrophoretic coating process and in order to eliminate an air bag at the top of the automobile, the body-in-white of the automobile needs to vertically move in an electrophoresis tank and turn for 360 degrees; to pairThe mechanism carries out track planning to obtain an expected track X of a P point at the tail end of the conveying mechanism d 、Z d And beta d Wherein X is d Desired trajectory of the end of the mechanism in the X direction, Z d For the desired trajectory of the end of the mechanism in the Z direction, β d A desired trajectory for the rotation angle of the end of the mechanism about the Y axis; determining the expected motion trail x of each active joint in the process of realizing the expected motion of the tail end of the mechanism according to the expected track of the P point at the tail end of the conveying mechanism and based on the inverse kinematics of the mechanism d ＝[x 1d ,x 2d ,x 3d ,x 4d ,φ 1d ,φ 2d ] T ，x id Unit is m, phi jd Unit rad, desired speed of movement The unit is m/s, and the unit is,unit rad/s, desired acceleration of motion Unit is m/s 2 ，φ jd Unit is rad/s 2 。
4. The synchronous coordination sliding-mode control method based on the comprehensive error for the series-parallel automobile electrophoretic coating conveying mechanism according to claim 1, characterized in that: in the step 3), the actual motion state of each active joint of the series-parallel automobile electrophoretic coating conveying mechanism is calculated by using the detection result of the absolute position encoder:
the absolute position encoders equipped with driving motors of the driving joints of the series-parallel automobile electrophoretic coating conveying mechanism detect the actual position of each motorObtaining the actual motion angular displacement sigma and the actual motion angular velocity of each driving joint driving motor according to the motion stateThen, according to a lead screw lead s, a lead screw mechanical efficiency eta and a speed reducer reduction ratio 1 n, the actual motion state of each active joint can be obtained: slider displacement x i (i =1.. 4), capstan angular displacementSpeed of slideAngular velocity of driving wheel
5. The comprehensive error-based synchronous coordination sliding mode control method for the series-parallel automobile electrophoretic coating conveying mechanism according to claim 1, characterized in that: in the step 3), the actual motion trajectory of the tail end of the conveying mechanism is obtained through kinematics positive solution:
in the formula, X is the displacement of the tail end of the conveying mechanism in the X direction; z is the displacement of the tail end of the conveying mechanism in the Z direction; l is 1 Is a first link length; l is 3 Is the third link length; beta is the rotation angle of the tail end of the conveying mechanism around the Y axis;
the tracking error e of the P point at the tail end of the conveying mechanism can be obtained t (t) is:
e tx (t)＝x-x d
e tz (t)＝z-z d
e tβ (t)＝β-β d
in the formula, e tx (t)、e tz (t) and e tβ (t) respectively representing the tracking errors of the P point at the tail end of the conveying mechanism in the X direction, the Z direction and the rotation angle around the Y axis; x is the number of d 、z d And beta d Respectively representing the expected movement trajectories of the point P of the conveying mechanism in the X direction, the Z direction and the rotation angle around the Y axis.
6. The synchronous coordination sliding-mode control method based on the comprehensive error for the series-parallel automobile electrophoretic coating conveying mechanism according to claim 1, characterized in that: in the step 4), a contour error e is defined c (t) is the error between the actual position of the end point P of the conveying mechanism and the nearest point of the expected track:
e c (t)＝[e cx (t),e cz (t),e cβ (t)] T
in the formula, e cx (t)、e cz (t) and e cβ (t) profile errors of a point P at the tail end of the conveying mechanism in the X direction, the Z direction and the rotation angle around the Y axis are respectively represented; here, e cβ (t) tracking error by rotation angle of P point at tail end of conveying mechanism around Y axis, e cx (t)、e cz The estimation formula of (t) is:
wherein the content of the first and second substances,respectively representing estimated values of contour errors of a P point at the tail end of the conveying mechanism in the X direction and the Z direction; e.g. of the type tx (t)、e tz (t) respectively representing the tracking errors of the tail end P point of the conveying mechanism in the X direction and the Z direction; theta is a positive included angle between a tangent line of an expected motion track at the tail end of the conveying mechanism and the X axis;
based on the above, the estimated contour error of the end point P of the conveying mechanism is:
wherein the content of the first and second substances,representing an estimated value of the end profile error of the conveying mechanism;respectively representing estimated values of contour errors in X and Z directions of a P point at the tail end of the conveying mechanism; e.g. of the type cβ (t) is a tracking error of a rotating angle of a P point at the tail end of the conveying mechanism around the Y axis; e.g. of the type t (t) the tracking error of the tail end of the conveying mechanism can be obtained by calculating the actual motion state of each active joint by using the detection result of the absolute position encoder and performing positive solution of kinematics; δ = R 3×3 Is a constant gain matrix expressed as follows:
wherein θ is a forward angle between a tangent of a desired motion trajectory of the end of the conveying mechanism and the X axis, and can be represented by the following formula:
in the formula, P XZ To obtain the expected track of the tail end P point of the conveying mechanism on the X and Z planes,is P XZ The derivative of (c).
7. The synchronous coordination sliding-mode control method based on the comprehensive error for the series-parallel automobile electrophoretic coating conveying mechanism according to claim 1, characterized in that: in the step 5), a combined error combining the mechanism end tracking error and the contour error is defined:
in the formula, e t (t) is the tracking error (in m) of the P point at the tail end of the conveying mechanism;the P point contour error estimation value (in m) at the tail end of the conveying mechanism is obtained; r L ＝diag(R 1 ,R 2 ,R 3 ) The coupling parameter matrix can be determined according to the established mechanism dynamic model.
8. The synchronous coordination sliding-mode control method based on the comprehensive error for the series-parallel automobile electrophoretic coating conveying mechanism according to claim 1, characterized in that: in the step 6), the control law of the formed novel synchronous coordination sliding mode controller based on the comprehensive error is as follows:
wherein τ = [ τ ] 1 ,τ 2 ,τ 3 ,τ 4 ,τ 5 ,τ 6 ]Outputting for a synchronous coordination sliding mode controller; m (q), C e G (q) is respectively an inertia matrix, a Coud force and centrifugal force term and a gravity term when unmodeled dynamics are not considered; k is L ＝diag(k 1 ,k 2 ,k 3 ) Gain for sliding mode switching term, and k i (i＝1,2,3)>0；e cc Is a cross-coupling error vector;the end contour error estimation value of the conveying mechanism is obtained;for each active joint actual velocity vector, andx i the unit is m, and the unit is,unit is rad;expecting an acceleration vector for each active joint; b L ＝diag(b 1 ,b 2 ,b 3 ) And B is L Reversible, b i (i =1,2,3) satisfies the Hurwitz condition; r L ＝diag(R 1 ,R 2 ,R 3 ) Is a coupling parameter matrix; d (t) is a friction force term,wherein F c Is a Coulomb friction matrix, B c Is a viscosity coefficient matrix; f (t) is an external disturbance term; s is a sliding mode surface function.
9. The synchronous coordination sliding-mode control method based on the comprehensive error for the series-parallel automobile electrophoretic coating conveying mechanism according to claim 1, characterized in that: and 7), writing a synchronous coordination sliding mode control algorithm software program based on comprehensive errors, sending voltage analog quantities obtained by performing digital/analog conversion on the calculation results of the torques required by the driving motors through a numerical control system to a servo driver corresponding to the motors, and controlling the motors to drive corresponding active joints, so that the connecting rod at the tail end of the series-parallel automobile electrophoretic coating conveying mechanism is driven to realize expected movement.
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| CN109189112A (en) * | 2018-09-25 | 2019-01-11 | 辽宁工业大学 | A kind of idler roller strip tension sliding-mode control and control device |
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| CN117626384A (en) * | 2024-01-26 | 2024-03-01 | 艾森曼机械设备(中国)有限公司 | Turning device for automobile body electrophoresis application production line |
| CN117626384B (en) * | 2024-01-26 | 2024-05-03 | 艾森曼机械设备(中国)有限公司 | Turning device for automobile body electrophoresis application production line |
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