CN111168682A - Limited time convergence sliding mode control method of parallel robot combined with robust precise differentiator for conveying - Google Patents

Limited time convergence sliding mode control method of parallel robot combined with robust precise differentiator for conveying Download PDF

Info

Publication number
CN111168682A
CN111168682A CN202010056924.9A CN202010056924A CN111168682A CN 111168682 A CN111168682 A CN 111168682A CN 202010056924 A CN202010056924 A CN 202010056924A CN 111168682 A CN111168682 A CN 111168682A
Authority
CN
China
Prior art keywords
conveying
parallel robot
sliding mode
differentiator
model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010056924.9A
Other languages
Chinese (zh)
Other versions
CN111168682B (en
Inventor
高国琴
叶梦阳
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Jiangsu University
Original Assignee
Jiangsu University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Jiangsu University filed Critical Jiangsu University
Priority to CN202010056924.9A priority Critical patent/CN111168682B/en
Publication of CN111168682A publication Critical patent/CN111168682A/en
Application granted granted Critical
Publication of CN111168682B publication Critical patent/CN111168682B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/003—Programme-controlled manipulators having parallel kinematics
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1679—Programme controls characterised by the tasks executed

Abstract

The invention discloses a finite time convergence sliding mode control method of a parallel robot for conveying combined with a robust accurate differentiator. Performing kinematic analysis on the parallel conveying robots and giving an expected motion track; a time delay estimation technology is adopted to obtain a dynamics model containing uncertain factors such as unknown dynamics, external interference and friction of the parallel robot for conveying on line in real time; aiming at a time delay estimation error generated by a time delay estimation technology, a finite time convergence robust accurate differentiator of a parallel robot system for conveying is designed for observation; further, a finite time convergence sliding mode controller is designed based on a feedforward compensation effect of a time delay estimation error observation value. And the limited time convergence sliding mode control of the parallel robot for conveying combined with the robust accurate differentiator feedforward compensation technology is realized through software programming. The method has obvious suppression effect on the sliding mode control buffeting, and the sliding mode variables and derivatives thereof are both limited in time and converged to the original point, so that the motion tracking precision is improved.

Description

Limited time convergence sliding mode control method of parallel robot combined with robust precise differentiator for conveying
Technical Field
The invention relates to a parallel robot for conveying, in particular to a finite time convergence sliding-mode control method of a parallel robot for conveying by combining a model-free robust precise differentiator.
Background
In order to meet the engineering application requirements of automobile coating conveying equipment, a parallel robot for conveying is developed based on a parallel mechanism so as to overcome the structural defects of insufficient bearing capacity and low flexibility level of the existing automobile electrophoretic coating conveying equipment adopting a cantilever beam series structure. The parallel robot for conveying has the advantages of strong bearing capacity, wide applicability of vehicle types, high positioning precision, small motion inertia of end members, no accumulated error, high response speed and the like. However, the structural characteristics of the multi-branch closed chain of the parallel robot for conveying and the coupling relationship among joints also make the parallel robot become a typical complex nonlinear system with multiple inputs, multiple outputs and strong coupling. The actual system is difficult to establish an accurate dynamic model, and uncertain factors such as external interference, friction and the like exist in actual operation, so that the motion control problem becomes a difficult point in the control research field, and the operation stability and the electrophoretic coating quality of the parallel robot for conveying are directly concerned.
In the literature, "dynamics modeling and control research of compliant joint parallel robot" (tianhao et al, volume 45 of agricultural mechanics journal, 5 th 2014, pages 278-283), a dynamics model is established by adopting a Lagrange method for the compliant joint parallel robot, and uncertain factors of a system are designed by an approximation law sliding mode controller. This method has two disadvantages: (1) the control method comprises the steps of firstly establishing a dynamic model of the parallel robot, and the calculation amount is large; (2) a discontinuous sign function exists in the control law of the approximation law sliding mode control, and therefore the sliding mode control buffeting is caused.
The document "delay estimation adaptive sliding mode control for series-parallel automobile electrophoretic coating conveying mechanism" (gao national organ, 40 th volume of automotive engineering, 12 th 2018, p. 1405-1412) designs a delay estimation adaptive sliding mode control method for series-parallel automobile electrophoretic coating conveying mechanism. The method has the following defects: (1) the control method directly adopts sliding mode control to overcome the influence of uncertain factors such as delay estimation errors and the like, so that the required control quantity is large, and large switching gain is easy to aggravate the buffeting of the sliding mode control; (2) according to the control method, the self-adaptive rule is introduced to adjust the control switching gain, but the obtained sliding mode control law is still discontinuous, so that the suppression capability of the sliding mode control buffeting is limited, and the self-adaptive parameters are not easy to adjust in practical application. (3) The control method belongs to first-order sliding mode control, and can only ensure the convergence of sliding mode variables.
Disclosure of Invention
Aiming at overcoming the defects of the prior art, the invention provides a finite time convergence sliding mode control method combining a robust accurate differentiator feedforward compensation technology by establishing a time delay estimation dynamic model aiming at a parallel robot for conveying. According to the control method, on the premise of not needing a system dynamics model and uncertain information, firstly, a robust accurate differentiator of the parallel robot system for conveying is designed to carry out limited-time accurate observation and feedforward compensation on a delay estimation error, then a limited-time convergence smooth second-order sliding mode control law of the parallel robot system for conveying is designed, sliding mode control buffeting can be obviously weakened, sliding mode variables and derivatives thereof are limited-time converged to an original point, robustness of the parallel robot control system for conveying is effectively improved, and high-precision track tracking control of the parallel robot control system for conveying is facilitated.
The technical scheme of the invention is as follows: a finite time convergence sliding mode control method for a parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying comprises the following steps:
1) the parallel robot for conveying is used as a controlled object, the inverse kinematics solution analysis is carried out on the parallel robot for conveying by adopting an analytical method, and the positive kinematics solution and the Jacobian matrix are further obtained;
2) according to the requirements of the automobile electrophoretic coating process, an expected motion track of the midpoint of the connecting rods of the parallel robots for conveying is designed, and the expected motion track of the active joint is obtained by combining with inverse kinematics;
3) a time delay estimation technology is adopted to obtain a dynamics model of the parallel robot for conveying, which contains uncertain factors such as unknown dynamics, external interference and friction on line in real time;
4) aiming at the time delay estimation error generated by the time delay estimation technology in the step 3), a robust accurate differentiator of the parallel robot system for conveying is designed to observe the time delay estimation error within a limited time:
5) based on the step 3) and the step 4), performing feedforward compensation by using an observed value obtained by the robust accurate differentiator, and designing a finite time convergence sliding mode controller for the parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying;
6) constructing a finite time convergence sliding mode control system of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying by adopting a distributed structure;
7) and sending the control quantity of each active joint of the parallel robot for conveying obtained by calculation to each motor driver so as to enable the parallel robot to move according to the expected track.
Further, in the step 1), two ends of the inverse kinematics solution equation are subjected to derivation, so that:
Figure BDA0002371879910000021
in the formula, J is a Jacobian matrix of the parallel robot system for conveying;
Figure BDA0002371879910000022
is an active joint pose vector of the parallel robot for conveying, wherein x1，x2，x3，x4Respectively showing the displacement of four slide blocks of the parallel robot for conveying,
Figure BDA0002371879910000023
respectively showing the rotation angles of two driving wheels of the parallel robot for conveying,
Figure BDA0002371879910000024
is the active joint velocity vector;
Figure BDA0002371879910000025
is the connecting rod midpoint velocity vector.
Further, in the step 2), according to the electrophoretic coating process requirements of the automobile body-in-white groove, the automobile body-in-white groove and the automobile body-out groove, the expected motion track of the middle point of the connecting rod of the parallel robot for conveying is determined to be xd＝(zd，βd)TWherein z isdfor the desired displacement of the midpoint of the connecting rod in the Z direction, betadThe expected motion trail of the active joint is further obtained for the expected angle of the end effector rotating around the Y axis in the anticlockwise direction by combining with the inverse solution equation of kinematics
Figure BDA0002371879910000031
Wherein xd1，xd2，xd3，xd4Respectively show the expected displacement of four sliding blocks of the parallel robot for conveying,
Figure BDA0002371879910000032
respectively showing the expected rotation angles of the two driving wheels of the parallel robot for conveying.
Further, the specific process of step 3) is as follows:
the general form of the kinetic model of the parallel robot for transportation is:
Figure BDA0002371879910000033
in the formula, M (q) is a symmetric positive definite inertia matrix;
Figure BDA0002371879910000034
are terms of Copenforces and centrifugal forces; g (q) is the gravity term (in N.m);
Figure BDA0002371879910000035
is the friction term (in n.m); tau isdIs an external interference term (unit n.m); τ is the control moment vector (in n.m);
introducing positive definite constant diagonal matrix for applying time delay estimation technique
Figure BDA0002371879910000036
The kinetic model (1) is abbreviated as:
Figure BDA0002371879910000037
in the formula (I), the compound is shown in the specification,
Figure BDA0002371879910000038
representing dynamics information items containing uncertain factors such as nonlinear unknown dynamics, external interference, friction and the like of the parallel robot for conveying;
the real-time online acquisition of the kinetic information of the parallel robot system for conveying by adopting the time delay estimation technology comprises the following steps:
Figure BDA0002371879910000039
in the formula (I), the compound is shown in the specification,
Figure BDA00023718799100000310
is that
Figure BDA00023718799100000311
the above variable with subscript t- η represents the value of the variable at that moment, i.e. the time lag value of the variable, where η is the delay time and the minimum value of η can be set as the sampling period.
Further, in the step 4), a robust accurate differentiator of the parallel robot system for conveying is designed to delay the estimation error when observed in a limited time:
when a time delay estimation technology is adopted to obtain a dynamic model of the parallel robot for conveying on line, because a sampling value at the previous moment is used to approximate the current values of a nonlinear term and an uncertain term of a parallel robot system for conveying, a time delay estimation error is generated, and the expression is as follows:
Figure BDA0002371879910000041
wherein the content of the first and second substances,
Figure BDA0002371879910000042
for a positive constant diagonal matrix, N ∈ R6Represents a dynamics information item containing uncertain factors such as nonlinear unknown dynamics, external interference, friction and the like of the parallel robot for conveying,
Figure BDA0002371879910000043
is the delay estimate of N;
is provided with
Figure BDA0002371879910000044
And
Figure BDA0002371879910000045
defining the track tracking error of the active joint of the parallel robot for conveying as follows:
e(t)＝q(t)-qd(t)
selecting sliding mode variables of the parallel robot model-free combined robust accurate differentiator finite time convergence sliding mode control for conveying as follows:
Figure BDA0002371879910000046
wherein A is a positive definite diagonal matrix;
in order to obtain a finite time observation value of a time delay estimation error epsilon of a nonlinear term and an uncertain term of the parallel robot for conveying, a robust accurate differentiator of the parallel robot system for conveying is designed as follows:
Figure BDA0002371879910000047
wherein u is a virtual control law, z0，z1，z2∈R6，z1Is an observed value of epsilon, z1Will converge to epsilon within a finite time; v. ofi∈R6(i＝1，2)；λi＝diag(λi1，λi2，…，λi6)，(i＝0，1，2)；L＝diag(l1，l2，…，l6) Is that
Figure BDA00023718799100000410
Lipshitz constant and li＞0，
Figure BDA0002371879910000048
Let x be (x)1，…，xn)TThe symbol sign (x) is defined as (sign (x)1)，…，sign(xn))T，|x|qsign(x)＝(|x1|qsign(x1)，…，|xn|qsign(xn))T。
Further, in the step 5), the finite time observation value z is obtained by using a robust accurate differentiator of the parallel robot system for conveying1Carrying out feedforward compensation, and designing a virtual control law u of model-free finite time convergence sliding mode control as follows:
Figure BDA0002371879910000049
wherein m is not less than 1, alpha1＝diag(α11，α12，…，α16)，α2＝diag(α21，α22，…，α26) And w is an intermediate variable introduced when designing the virtual control law u.
Further, still include:
virtual control law u under finite time convergence sliding mode control without model and observed value z obtained by robust accurate differentiator of parallel robot system for conveying1Under the feedforward compensation action on the delay estimation error epsilon, the dynamic of the sliding mode variable s is as follows:
Figure BDA0002371879910000051
because the sliding mode variable dynamic system controlled by the finite time convergence sliding mode of the model-free combined robust precise differentiator has stable finite time, the sliding mode variable and the derivative thereof both have finite time convergence to the origin, and because the sliding mode variable and the derivative thereof have finite time convergence to the origin
Figure BDA0002371879910000052
Is continuous, so the virtual control law u is not only continuous but also smooth.
Further, the step 5) further includes, in a situation that a parallel robot dynamics model for conveying and system uncertainty information are not needed, designing a finite time convergence sliding mode control law τ without a model and combining with a robust precise differentiator feed-forward compensation technology according to a virtual control law u of finite time convergence sliding mode control without a model based on a parallel robot time delay estimation dynamics model for conveying and a virtual control law u of finite time convergence sliding mode control without a model:
Figure BDA0002371879910000053
the invention provides a finite time convergence sliding mode control method of a parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying for the first time, so as to realize high-precision track tracking control of the parallel robot for conveying. The method has the characteristics and beneficial effects that:
1) because the time delay estimation technology is adopted to obtain the system dynamics information containing uncertain factors such as unknown dynamics, external interference, friction and the like on line, a dynamics model of the parallel robot for conveying does not need to be established.
2) Because the robust accurate differentiator of the parallel robot system for conveying is designed for feedforward compensation, an accurate observation value of the time delay estimation error can be obtained within limited time, so that the influence of the nonlinear and uncertain time delay estimation error of the parallel robot system for conveying on the control performance is inhibited, and the robustness of the system is improved;
3) a finite time convergence smooth second-order sliding mode control law of a parallel robot system for conveying is designed, the robustness of the system is improved, meanwhile, sliding mode control buffeting is weakened, and the second-order sliding mode algorithm enables sliding mode variables and derivatives thereof to converge to an original point in finite time. Therefore, the method can effectively improve the motion tracking control performance of the parallel robot for conveying in practical application.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a schematic view of a parallel robot for transportation.
FIG. 2 is a schematic diagram of a finite time convergence sliding mode control system incorporating a robust precision differentiator feed forward compensation technique.
Fig. 3 is a schematic diagram of the lifting and overturning conveying mechanism.
FIG. 4 is a hardware platform of a parallel robot prototype system and control system for transportation.
Fig. 5 is a trace plot for each active joint. Fig. 5(a) is a first slider trajectory tracking curve, fig. 5(b) is a second slider trajectory tracking curve, and fig. 5(c) is a first capstan trajectory tracking curve.
FIG. 6 is a plot of active joint trajectory tracking error. Fig. 6(a) is a first slider trajectory tracking error curve, fig. 6(b) is a second slider trajectory tracking error curve, and fig. 6(c) is a first capstan trajectory tracking error curve.
Fig. 7 shows the driving torque of the motor corresponding to each active joint. Fig. 7(a) shows the driving torque of the first slide block corresponding to the motor, fig. 7(b) shows the driving torque of the second slide block corresponding to the motor, and fig. 7(c) shows the driving torque of the first driving wheel corresponding to the motor.
Fig. 8 is a delay estimation error observation curve. Fig. 8(a) is an observation curve of a first component of the delay estimation error, fig. 8(b) is an observation curve of a second component of the delay estimation error, and fig. 8(c) is an observation curve of a fifth component of the delay estimation error.
In fig. 1: 1. guide rail 2, base 3, walking driving motor 4, speed reducer 5, moving slide block 6, lifting driving motor 7, connecting rod 8, driven wheel 9, driving wheel 10, connecting rod 11, vehicle body 12, overturning driving motor 13 and electric cylinder
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
As shown in fig. 1-3, wherein the components in fig. 1 are respectively: 1. the device comprises a guide rail 2, a base 3, a walking driving motor 4, a speed reducer 5, a movable sliding block 6, a lifting driving motor 7, a connecting rod 8, a driven wheel 9, a driving wheel 10, a connecting rod 11, a vehicle body 12, a turnover driving motor 13 and an electric cylinder. Firstly, aiming at a parallel robot for conveying, performing inverse kinematics solution analysis on the parallel robot by adopting an analytical method, and further solving a positive kinematics solution and a Jacobian matrix of the parallel robot; secondly, determining an expected motion track of the midpoint of the connecting rods of the parallel robots for conveying according to the requirements of the automobile electrophoretic coating process, and solving the expected motion track of the active joint by combining with inverse kinematics; secondly, unknown dynamics information such as nonlinear terms, uncertain terms and the like in the parallel robot system for conveying is obtained and compensated by adopting a time delay estimation technology; further, a robust accurate differentiator observation time delay estimation error of the parallel robot system for conveying is designed, and a finite time convergence sliding mode control method of the parallel robot system for conveying without a model and combining with a feedforward compensation technology of the robust accurate differentiator is provided; secondly, constructing a finite time convergence sliding mode control system of the parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying by adopting a distributed structure; and finally, sending the calculated driving control quantity of each active joint of the parallel robot for conveying to each motor driver so as to realize the expected movement. The specific method comprises the following steps:
1. and (3) carrying out inverse kinematics analysis on the parallel robot for conveying by adopting an analytical method, and further solving a positive kinematics solution and a Jacobian matrix of the parallel robot for conveying.
selecting pose parameters x ═ (z, beta) of the middle points of the connecting rods of the parallel robots for conveyingTand as a generalized coordinate of the system, wherein Z (unit m) is the displacement of the middle point of the connecting rod in the Z direction, β (unit rad) is the angle of anticlockwise rotation of the end effector around the Y axis
Figure BDA0002371879910000071
In the formula, J is a Jacobian matrix of the parallel robot system for conveying;
Figure BDA0002371879910000072
is a posture vector of an active joint of a parallel robot for conveying,
Figure BDA0002371879910000073
is the active joint velocity vector;
Figure BDA0002371879910000074
is the connecting rod midpoint velocity vector.
2. According to the requirements of the automobile electrophoretic coating process, an expected motion track of the midpoint of the connecting rod of the parallel robot for conveying is designed, and the expected motion track of the active joint is obtained by combining with a kinematic inverse solution.
Determining an expected motion track x of the middle point of the connecting rod of the parallel robot for conveying according to the electrophoretic coating process requirements of the automobile body-in-white in-slot, overturning and out-slotd＝(zd，βd)TWherein z isd(unit m) is the desired displacement of the midpoint of the connecting rod in the Z direction, βd(in rad) is the desired angle of counterclockwise rotation of the end effector about the Y axis. Further obtaining the expected motion trail of the active joint by combining the inverse solution equation of kinematics
Figure BDA0002371879910000075
(xdiThe unit m is a function of the number m,
Figure BDA0002371879910000076
unit rad).
3. And a time delay estimation technology is adopted to obtain a dynamics model of the parallel robot for conveying, which contains uncertain factors such as unknown dynamics, external interference, friction and the like, on line in real time.
The general form of the kinetic model of the parallel robot for transportation is:
Figure BDA0002371879910000077
in the formula, M (q) is a symmetric positive definite inertia matrix;
Figure BDA0002371879910000078
are terms of Copenforces and centrifugal forces; g (q) is the gravity term (in N.m);
Figure BDA0002371879910000079
is the friction term (in n.m); tau isdIs an external interference term (unit n.m); τ is the control moment vector (in n.m).
Introducing positive definite constant diagonal matrix for applying time delay estimation technique
Figure BDA0002371879910000081
The kinetic model (1) is abbreviated as:
Figure BDA0002371879910000082
in the formula (I), the compound is shown in the specification,
Figure BDA0002371879910000083
the unit n.m represents a kinetic information item including uncertain factors such as nonlinear unknown dynamics of the parallel robot for transportation, external disturbance, friction, and the like.
The real-time online acquisition of the kinetic information of the parallel robot system for conveying by adopting the time delay estimation technology comprises the following steps:
Figure BDA0002371879910000084
in the formula (I), the compound is shown in the specification,
Figure BDA0002371879910000085
(unit N.m) is
Figure BDA0002371879910000086
is the delay time, η (in units of s) is the delay time, and minimum of η can be set as the sampling period.
4. Aiming at a time delay estimation error generated by a time delay estimation technology, a robust accurate differentiator of a parallel robot system for conveying is designed to observe the time delay estimation error within a limited time.
The time delay estimation technique adopts time delay value
Figure BDA0002371879910000087
Replacing system dynamics information items
Figure BDA0002371879910000088
The resulting delay estimation error is:
Figure BDA0002371879910000089
multiplying both sides of the dynamic model (2) by
Figure BDA00023718799100000810
And substituting the formula (4) to obtain
Figure BDA00023718799100000811
The expression of (a) is:
Figure BDA00023718799100000812
in the formula (I), the compound is shown in the specification,
Figure BDA00023718799100000813
(unit n.m) represents the virtual control law, then the actual control law is:
Figure BDA00023718799100000814
defining the trajectory tracking error of the active joint as:
e＝q-qd
selecting sliding mode variables as follows:
Figure BDA00023718799100000815
where A is a positive definite diagonal matrix.
Derivation of s in equation (8) with respect to time and substitution of equation (5) can give:
Figure BDA0002371879910000091
and (3) designing a robust accurate differentiator to observe the delay estimation error epsilon according to the formula (9):
Figure BDA0002371879910000092
in the formula, z0，z1，z2∈R6，z1(unit N.m) is an observed value of ε, z1Will converge to epsilon (in n.m) within a finite time; v. ofi∈R6(i＝1，2)；λi＝diag(λi1，λi2，…，λi6)，(i＝0，1，2)；L＝diag(l1，l2，…，l6) Is that
Figure BDA0002371879910000097
Lipshitz constant (in N.m/s) and li＞0，
Figure BDA0002371879910000093
Let x be (x)1，…，xn)TThe symbol sign (x) is defined as (sign (x)1)，…，sign(xn))T，|x|qsign(x)＝(|x1|qsign(x1)，…，|xn|qsign(xn))T。
Let us consider the observation error sigma0＝z0-s，σ1＝z1-ε，
Figure BDA0002371879910000094
Then the observation error dynamics is obtained by the two formulas (9) and (10):
Figure BDA0002371879910000095
then sigma0，σ1，σ2Will converge to 0 within a finite time. Thus, z1The value of the delay estimation error epsilon is converged to within a finite time.
5. Finite time observation z based on delay estimation error epsilon (unit N.m)1(unit N.m), and the design is carried out by combining the formula (6), and the finite time convergence sliding mode controller of the parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying is as follows:
Figure BDA0002371879910000096
wherein m is not less than 1, alpha1＝diag(α11，α12，…，α16)，α2＝diag(α21，α22，…，α26)。
6. A finite time convergence sliding mode control system of a parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying is constructed by adopting a distributed structure.
As shown in fig. 4, a finite time convergence sliding mode distributed control system combined with a robust precise differentiator feedforward compensation technology is constructed for a parallel robot for transportation, and the system is composed of an upper computer PC and a lower computer UMAC multi-axis motion controller, wherein the upper computer is responsible for system management, the lower computer realizes motion control, and the two parts realize information interaction through network communication to complete motion control of the parallel robot. Then, the hardware module of the parallel robot control system is selected, and the hardware module mainly comprises a Personal Computer (PC), a multi-axis motion controller (UMAC), a servo control system, a proximity switch and the like. The PC of the upper computer is provided with an Intel core i 7-47903.60 GHz processor, and mainly realizes the functions of system initialization, data processing, code compiling, real-time monitoring of the running state of the mechanism and the like; the lower computer UMAC mainly comprises a TURBO PMAC2 OPT-5C0 type CPU main board card, two ACC-24E2A type shaft board cards, an ACC-65E type I/O board card, an ACC-E1 type power supply board card and the like; the servo drive system comprises four HG-KR73BJ type alternating current servo motors with MR-J4-70A type servo drivers and four HG-SR102BJ type alternating current servo motors with MR-J4-100A type servo drivers, and the position detection equipment adopts a 22-bit (4194304pulses/rev) high-resolution absolute position encoder. And finally, constructing a control system software platform and finishing the development of an upper computer application program and a lower computer motion program.
7. And sending the calculated control quantity of each active joint of the parallel robot for conveying to each motor driver so as to realize the expected movement.
By Matlab simulation and parallel connection robot prototype system experiments for conveying, the control effects of the model-free finite time convergence sliding mode control (FTSMC) combined with the robust precise differentiator and the model-free first-order Sliding Mode Control (SMC) are compared, and the track tracking curve of each active joint shown in the figure 5, the tracking error curve of each active joint shown in the figure 6, the driving torque curve of the motor corresponding to each active joint shown in the figure 7 and the time delay estimation error observation curve shown in the figure 8 are respectively obtained.
Fig. 5 and fig. 6 show that under the condition that uncertain factors such as external interference, friction, delay estimation error and the like exist, the model-free finite time convergence sliding mode control method combined with the robust precise differentiator provided by the invention enables each joint of the parallel robot for conveying to have higher track tracking precision. This is because the system robustness is relatively strong, and the system uncertainty is strongly inhibited. Fig. 7 shows that the proposed control method has a significant buffeting suppression effect, which is an advantage of the obtained smooth sliding mode control law. Fig. 8 shows that the control method can realize accurate observation of the delay estimation error, and the effectiveness of the robust accurate differentiator is shown.
In conclusion, the parallel robot for conveying combines the robust accurate differentiator finite time convergence sliding mode control method. Firstly, performing kinematic analysis on the parallel robot for conveying and giving an expected motion track; secondly, a time delay estimation technology is adopted to obtain a dynamics model containing uncertain factors such as unknown dynamics, external interference and friction of the parallel robot for conveying on line in real time; aiming at a time delay estimation error generated by a time delay estimation technology, a finite time convergence robust accurate differentiator of a parallel robot system for conveying is designed for observation; further, a finite time convergence sliding mode controller is designed based on a feedforward compensation effect of a time delay estimation error observation value. Finally, the limited time convergence sliding mode control of the parallel robot for conveying combined with the robust accurate differentiator feedforward compensation technology is realized through software programming. On the premise of not needing a dynamic model of the parallel robot for conveying and uncertain information of the system, the method can improve the robustness of the system and has a remarkable restraining effect on the buffeting of the sliding mode control, and the variable and the derivative of the sliding mode are both limited in time and converged to the original point, so that the motion tracking precision of the parallel robot for conveying is improved.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (8)

1. A finite time convergence sliding mode control method for a parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying is characterized by comprising the following steps of:
1) the parallel robot for conveying is used as a controlled object, the inverse kinematics solution analysis is carried out on the parallel robot for conveying by adopting an analytical method, and the positive kinematics solution and the Jacobian matrix are further obtained;
2) according to the requirements of the automobile electrophoretic coating process, an expected motion track of the midpoint of the connecting rods of the parallel robots for conveying is designed, and the expected motion track of the active joint is obtained by combining with inverse kinematics;
3) a time delay estimation technology is adopted to obtain a dynamics model of the parallel robot for conveying, which contains uncertain factors such as unknown dynamics, external interference and friction on line in real time;
4) aiming at the time delay estimation error generated by the time delay estimation technology in the step 3), a robust accurate differentiator of the parallel robot system for conveying is designed to observe the time delay estimation error within a limited time;
5) based on the step 3) and the step 4), performing feedforward compensation by using an observed value obtained by the robust accurate differentiator, and designing a finite time convergence sliding mode controller for the parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying;
6) constructing a finite time convergence sliding mode control system of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying by adopting a distributed structure;
7) and sending the control quantity of each active joint of the parallel robot for conveying obtained by calculation to each motor driver so as to enable the parallel robot to move according to the expected track.
2. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying according to claim 1, characterized in that: in the step 1), two ends of the inverse kinematics solution equation are subjected to derivation, so that:
Figure FDA0002371879900000011
in the formula, J is a Jacobian matrix of the parallel robot system for conveying;
Figure FDA0002371879900000012
is an active joint pose vector of the parallel robot for conveying, wherein x1,x2,x3,x4Respectively showing the displacement of four slide blocks of the parallel robot for conveying,
Figure FDA0002371879900000013
respectively showing the rotation angles of two driving wheels of the parallel robot for conveying,
Figure FDA0002371879900000014
is the active joint velocity vector;
Figure FDA0002371879900000015
is the connecting rod midpoint velocity vector.
3. The method as claimed in claim 1, wherein the parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying comprisesThe time-limited convergence sliding mode control method is characterized by comprising the following steps: in the step 2), according to the electrophoretic coating process requirements of the automobile body-in-white groove, the overturning and the groove discharging, the expected motion track of the middle point of the connecting rod of the parallel robot for conveying is determined to be xd＝(zd,βd)TWherein z isdfor the desired displacement of the midpoint of the connecting rod in the Z direction, betadThe expected motion trail of the active joint is further obtained for the expected angle of the end effector rotating around the Y axis in the anticlockwise direction by combining with the inverse solution equation of kinematics
Figure FDA0002371879900000021
Wherein xd1,xd2,xd3,xd4Respectively show the expected displacement of four sliding blocks of the parallel robot for conveying,
Figure FDA0002371879900000022
respectively showing the expected rotation angles of the two driving wheels of the parallel robot for conveying.
4. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying according to claim 1, characterized in that: the specific process of the step 3) is as follows:
the general form of the kinetic model of the parallel robot for transportation is:
Figure FDA0002371879900000023
in the formula, M (q) is a symmetric positive definite inertia matrix;
Figure FDA0002371879900000024
are terms of Copenforces and centrifugal forces; g (q) is the gravity term (in N.m);
Figure FDA0002371879900000025
is the friction term (in n.m); tau isdIs the external interference term (in N.m); τ is the control moment vector (in n.m);
introducing positive definite constant diagonal matrix for applying time delay estimation technique
Figure FDA0002371879900000026
The kinetic model (1) is abbreviated as:
Figure FDA0002371879900000027
in the formula (I), the compound is shown in the specification,
Figure FDA0002371879900000028
representing dynamics information items containing uncertain factors such as nonlinear unknown dynamics, external interference, friction and the like of the parallel robot for conveying;
the real-time online acquisition of the kinetic information of the parallel robot system for conveying by adopting the time delay estimation technology comprises the following steps:
Figure FDA0002371879900000029
in the formula (I), the compound is shown in the specification,
Figure FDA00023718799000000212
is that
Figure FDA00023718799000000211
the above variable with subscript t- η represents the value of the variable at that moment, i.e. the time lag value of the variable, where η is the delay time and the minimum value of η can be set as the sampling period.
5. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying according to claim 4, characterized in that: in the step 4), a robust accurate differentiator of the parallel robot system for conveying is designed to delay estimation errors when the robust accurate differentiator is observed in a limited time:
when a time delay estimation technology is adopted to obtain a dynamic model of the parallel robot for conveying on line, because a sampling value at the previous moment is used to approximate the current values of a nonlinear term and an uncertain term of a parallel robot system for conveying, a time delay estimation error is generated, and the expression is as follows:
Figure FDA0002371879900000031
wherein the content of the first and second substances,
Figure FDA0002371879900000032
for a positive constant diagonal matrix, N ∈ R6Represents a dynamics information item containing uncertain factors such as nonlinear unknown dynamics, external interference, friction and the like of the parallel robot for conveying,
Figure FDA0002371879900000033
is the delay estimate of N;
is provided with
Figure FDA0002371879900000034
And
Figure FDA0002371879900000035
defining the track tracking error of the active joint of the parallel robot for conveying as follows:
e(t)＝q(t)-qd(t)
selecting sliding mode variables of the parallel robot model-free combined robust accurate differentiator finite time convergence sliding mode control for conveying as follows:
Figure FDA0002371879900000036
wherein A is a positive definite diagonal matrix;
in order to obtain a finite time observation value of a time delay estimation error epsilon of a nonlinear term and an uncertain term of the parallel robot for conveying, a robust accurate differentiator of the parallel robot system for conveying is designed as follows:
Figure FDA0002371879900000037
wherein u is a virtual control law, z0,z1,z2∈R6，z1Is an observed value of epsilon, z1Will converge to epsilon within a finite time; v. ofi∈R6(i＝1,2)；λi＝diag(λi1,λi2,…,λi6),(i＝0,1,2)；L＝diag(l1,l2,…,l6) Is that
Figure FDA0002371879900000038
Lipshitz constant and li＞0，
Figure FDA0002371879900000039
Let x be (x)1,…,xn)TThe symbol sign (x) is defined as (sign (x)1),…,sign(xn))T，|x|qsign(x)＝(|x1|qsign(x1),…,|xn|qsign(xn))T。
6. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying according to claim 5, characterized in that: in the step 5), a finite time observation value z is obtained by using a robust accurate differentiator of the parallel robot system for conveying1Carrying out feedforward compensation, and designing a virtual control law u of model-free finite time convergence sliding mode control as follows:
Figure FDA0002371879900000041
wherein m is not less than 1, alpha1＝diag(α11,α12,…,α16)，α2＝diag(α21,α22,…,α26) And w is an intermediate variable introduced when designing the virtual control law u.
7. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying according to claim 6, characterized in that: further comprising:
virtual control law u under finite time convergence sliding mode control without model and observed value z obtained by robust accurate differentiator of parallel robot system for conveying1Under the feedforward compensation action on the delay estimation error epsilon, the dynamic of the sliding mode variable s is as follows:
Figure FDA0002371879900000042
because the sliding mode variable dynamic system controlled by the finite time convergence sliding mode of the model-free combined robust precise differentiator has stable finite time, the sliding mode variable and the derivative thereof both have finite time convergence to the origin, and because the sliding mode variable and the derivative thereof have finite time convergence to the origin
Figure FDA0002371879900000043
Is continuous, so the virtual control law u is not only continuous but also smooth.
8. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying according to claim 7, characterized in that: the step 5) further comprises that under the condition that a parallel robot dynamics model for conveying and system uncertainty information are not needed, a dynamics model is estimated based on the time delay of the parallel robot for conveying, and according to a virtual control law u of model-free finite time convergence sliding mode control, a finite time convergence sliding mode control law tau of a model-free combined robust precise differentiator feedforward compensation technology is designed as follows:
Figure FDA0002371879900000044
CN202010056924.9A 2020-01-17 2020-01-17 Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method Active CN111168682B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010056924.9A CN111168682B (en) 2020-01-17 2020-01-17 Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010056924.9A CN111168682B (en) 2020-01-17 2020-01-17 Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method

Publications (2)

Publication Number Publication Date
CN111168682A true CN111168682A (en) 2020-05-19
CN111168682B CN111168682B (en) 2022-04-26

Family

ID=70619928

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010056924.9A Active CN111168682B (en) 2020-01-17 2020-01-17 Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method

Country Status (1)

Country Link
CN (1) CN111168682B (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113176797A (en) * 2021-04-13 2021-07-27 龙泉东土青瓷有限公司 Kiln temperature automatic control method for celadon biscuit firing process
CN114002950A (en) * 2021-07-09 2022-02-01 江苏大学 Model-free self-adaptive nonsingular terminal sliding mode control method for sand blasting and rust removing parallel robot
CN114347031A (en) * 2022-01-18 2022-04-15 广东省智能机器人研究院 Mobile mechanical arm collision avoidance control method and device considering time-varying time lag
CN114516054A (en) * 2022-03-24 2022-05-20 南京航空航天大学 Time delay estimation control method for mechanical arm

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH10329076A (en) * 1997-05-27 1998-12-15 Nok Corp Synchronous moving device
CN102385342A (en) * 2011-09-19 2012-03-21 江苏大学 Self-adaptation dynamic sliding mode controlling method controlled by virtual axis lathe parallel connection mechanism motion
CN107932487A (en) * 2017-12-26 2018-04-20 燕山大学 A kind of multistage coupling parallel institution of slide block type
CN108319145A (en) * 2018-02-27 2018-07-24 江苏大学 A kind of time delay estimation PD sliding-mode controls of New-type mixed-coupled formula automobile electrophoretic coating conveyor structure
CN110007594A (en) * 2019-03-19 2019-07-12 江苏大学 A kind of automobile electrophoretic painting conveying ADAPTIVE ROBUST sliding-mode control of series-parallel robot

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH10329076A (en) * 1997-05-27 1998-12-15 Nok Corp Synchronous moving device
CN102385342A (en) * 2011-09-19 2012-03-21 江苏大学 Self-adaptation dynamic sliding mode controlling method controlled by virtual axis lathe parallel connection mechanism motion
CN107932487A (en) * 2017-12-26 2018-04-20 燕山大学 A kind of multistage coupling parallel institution of slide block type
CN108319145A (en) * 2018-02-27 2018-07-24 江苏大学 A kind of time delay estimation PD sliding-mode controls of New-type mixed-coupled formula automobile electrophoretic coating conveyor structure
CN110007594A (en) * 2019-03-19 2019-07-12 江苏大学 A kind of automobile electrophoretic painting conveying ADAPTIVE ROBUST sliding-mode control of series-parallel robot

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113176797A (en) * 2021-04-13 2021-07-27 龙泉东土青瓷有限公司 Kiln temperature automatic control method for celadon biscuit firing process
CN113176797B (en) * 2021-04-13 2021-12-21 龙泉东土青瓷有限公司 Kiln temperature automatic control method for celadon biscuit firing process
CN114002950A (en) * 2021-07-09 2022-02-01 江苏大学 Model-free self-adaptive nonsingular terminal sliding mode control method for sand blasting and rust removing parallel robot
CN114347031A (en) * 2022-01-18 2022-04-15 广东省智能机器人研究院 Mobile mechanical arm collision avoidance control method and device considering time-varying time lag
CN114347031B (en) * 2022-01-18 2024-01-16 广东省智能机器人研究院 Mobile mechanical arm collision prevention control method and device considering time-varying time delay
CN114516054A (en) * 2022-03-24 2022-05-20 南京航空航天大学 Time delay estimation control method for mechanical arm

Also Published As

Publication number Publication date
CN111168682B (en) 2022-04-26

Similar Documents

Publication Publication Date Title
CN111168682B (en) Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method
CN109465825B (en) RBF neural network self-adaptive dynamic surface control method for flexible joint of mechanical arm
CN107490965B (en) Multi-constraint trajectory planning method for space free floating mechanical arm
Corradini et al. Discrete time sliding mode control of robotic manipulators: Development and experimental validation
CN112904728B (en) Mechanical arm sliding mode control track tracking method based on improved approach law
CN110007594B (en) Self-adaptive robust sliding mode control method of series-parallel robot for automobile electrophoretic coating and conveying
CN111428317B (en) Joint friction torque compensation method based on 5G and cyclic neural network
CN112894821B (en) Current method based collaborative robot dragging teaching control method, device and equipment
Tan et al. A prediction and compensation method of robot tracking error considering pose-dependent load decomposition
CN111208735B (en) Low-switching gain robust super-spiral sliding mode control method for coating conveying mechanism
Jun-Pei et al. Neural network control of space manipulator based on dynamic model and disturbance observer
CN107505844A (en) Synchronous coordination sliding-mode control of the series parallel type automobile electrophoretic coating conveyor structure based on composition error
CN115122325A (en) Robust visual servo control method for anthropomorphic manipulator with view field constraint
CN111805536A (en) Self-adaptive sliding mode control method for fruit sorting parallel robot mechanism considering coupling effect
Sun et al. A GNN for repetitive motion generation of four-wheel omnidirectional mobile manipulator with nonconvex bound constraints
Zhang et al. Variable gain based composite trajectory tracking control for 4-wheel skid-steering mobile robots with unknown disturbances
CN108319145A (en) A kind of time delay estimation PD sliding-mode controls of New-type mixed-coupled formula automobile electrophoretic coating conveyor structure
Xu et al. Reinforcement learning compensated coordination control of multiple mobile manipulators for tight cooperation
CN116300445A (en) Novel comprehensive error rapid continuous sliding mode control method for task space of automobile electrophoretic coating conveying parallel-serial mechanism
Zhou et al. Coordination control of dual‐arm modular robot based on position feedback using Optotrak3020
CN113752300A (en) Industrial robot energy consumption prediction method
Fehr et al. Identification of friction models for mpc-based control of a powercube serial robot
Wang et al. Learning from demonstration using improved dynamic movement primitives
Zhu et al. TVIE-based fault-tolerant model predictive control for trajectory tracking of mobile robot
Yan et al. Adaptive and intelligent control of a dual-arm space robot for target manipulation during the post-capture phase

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant