CN111168682B - Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method - Google Patents

Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method Download PDF

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CN111168682B
CN111168682B CN202010056924.9A CN202010056924A CN111168682B CN 111168682 B CN111168682 B CN 111168682B CN 202010056924 A CN202010056924 A CN 202010056924A CN 111168682 B CN111168682 B CN 111168682B
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conveying
parallel robot
sliding mode
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differentiator
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高国琴
叶梦阳
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Jiangsu University
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    • 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

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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

Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method
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.
The literature, "dynamics modeling and control research of compliant joint parallel robot" (Tianhao et al, journal of agricultural machinery 45, 5 2014, page 278-. 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 a 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 the 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 GDA0003475610710000021
in the formula, J is a Jacobian matrix of the parallel robot system for conveying;
Figure GDA0003475610710000022
is an active joint pose vector of the parallel robot for conveying, wherein x1，x2，x3，x4Respectively representing the displacement of four sliding blocks of a parallel robot for conveying，
Figure GDA0003475610710000023
Respectively showing the rotation angles of two driving wheels of the parallel robot for conveying,
Figure GDA0003475610710000024
is the active joint velocity vector;
Figure GDA0003475610710000025
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 GDA0003475610710000031
Wherein xd1，xd2，xd3，xd4Respectively show the expected displacement of four sliding blocks of the parallel robot for conveying,
Figure GDA0003475610710000032
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 GDA0003475610710000033
wherein M (q) is a symmetric positive definite inertial matrix;
Figure GDA0003475610710000034
are terms of Copenforces and centrifugal forces; g (q) is the gravity term (in n.m);
Figure GDA0003475610710000035
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 GDA0003475610710000036
The kinetic model (1) is abbreviated as:
Figure GDA0003475610710000037
in the formula,
Figure GDA0003475610710000038
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 GDA0003475610710000039
in the formula,
Figure GDA00034756107100000310
is that
Figure GDA00034756107100000311
The delay estimate of (a); the above variable with the subscript t- η represents the value of the variable at that time, 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 GDA0003475610710000041
wherein,
Figure GDA0003475610710000042
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 GDA0003475610710000043
is the delay estimate of N;
is provided with
Figure GDA0003475610710000044
And
Figure GDA0003475610710000045
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 GDA0003475610710000046
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 GDA0003475610710000047
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. ofj∈R6，j＝0，1，2；；λi＝diag(λi1，λi2，…，λi6)，(i＝0，1，2)；L＝diag(l1，l2，…，l6) Is that
Figure GDA0003475610710000048
Lipshitz constant and li＞0，
Figure GDA0003475610710000049
Let x be (x)1，…，xn)TThe symbol sign (x) is defined as1)，…，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 GDA00034756107100000410
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 GDA0003475610710000051
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 GDA0003475610710000052
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 GDA0003475610710000053
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.
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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. Where (a) in fig. 5 is a first slider trajectory tracking curve, (b) in fig. 5 is a second slider trajectory tracking curve, and (c) in fig. 5 is a first capstan trajectory tracking curve.
FIG. 6 is a plot of active joint trajectory tracking error. Where (a) in fig. 6 is a first slider trajectory tracking error curve, (b) in fig. 6 is a second slider trajectory tracking error curve, and (c) in fig. 6 is a first capstan trajectory tracking error curve.
Fig. 7 shows the driving torque of the motor corresponding to each active joint. Wherein, (a) in fig. 7 is the first slider corresponding to the motor driving torque, (b) in fig. 7 is the second slider corresponding to the motor driving torque, and (c) in fig. 7 is the first driving pulley corresponding to the motor driving torque.
Fig. 8 is a delay estimation error observation curve. Where (a) in fig. 8 is an observation curve of the first component of the delay estimation error, (b) in fig. 8 is an observation curve of the second component of the delay estimation error, and (c) in fig. 8 is an observation curve of the 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 conveyingTAs a system generalized coordinate, where Z (unit m) is the displacement of the connecting rod midpoint in the Z direction, and β (unit rad) is the angle of counterclockwise rotation of the end effector about the Y axis. And (3) carrying out inverse kinematics analysis on the parallel robots for conveying by adopting an analytical method, solving an inverse position solution equation, and carrying out inversion on the inverse position solution equation to obtain a positive kinematics solution. Further, two ends of the inverse solution equation of the kinematics are subjected to derivation, and the motion vector is obtained
Figure GDA0003475610710000071
In the formula, J is a Jacobian matrix of the parallel robot system for conveying;
Figure GDA0003475610710000072
is a posture vector of an active joint of a parallel robot for conveying,
Figure GDA0003475610710000073
is the active joint velocity vector;
Figure GDA0003475610710000074
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 GDA0003475610710000075
(xdiThe unit m is a function of the number m,
Figure GDA0003475610710000076
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 GDA0003475610710000077
wherein M (q) is a symmetric positive definite inertial matrix;
Figure GDA0003475610710000078
are terms of Copenforces and centrifugal forces; g (q) is the gravity term (in n.m);
Figure GDA0003475610710000079
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 GDA0003475610710000081
The kinetic model (1) is abbreviated as:
Figure GDA0003475610710000082
in the formula,
Figure GDA0003475610710000083
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 GDA0003475610710000084
in the formula,
Figure GDA0003475610710000085
(unit N.m) is
Figure GDA0003475610710000086
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 GDA0003475610710000087
Replacing system dynamics information items
Figure GDA0003475610710000088
The resulting delay estimation error is:
Figure GDA0003475610710000089
multiplying both sides of the dynamic model (2) by
Figure GDA00034756107100000810
And substituting the formula (4) to obtain
Figure GDA00034756107100000815
The expression of (a) is:
Figure GDA00034756107100000811
in the formula,
Figure GDA00034756107100000812
(unit n.m) represents the virtual control law, then the actual control law is:
Figure GDA00034756107100000813
defining the trajectory tracking error of the active joint as:
e＝q-qd
selecting sliding mode variables as follows:
Figure GDA00034756107100000814
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 GDA0003475610710000091
and (3) designing a robust accurate differentiator to observe the delay estimation error epsilon according to the formula (9):
Figure GDA0003475610710000092
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. ofj∈R6，j＝0，1，2；；λi＝diag(λi1，λi2，…，λi6)，(i＝0，1，2)；L＝diag(l1，l2，…，l6) Is that
Figure GDA0003475610710000093
Lipshitz norm of (unit N.m/s)1 is counted andi＞0，
Figure GDA0003475610710000094
let x be (x)1，…，xn)TThe symbol sign (x) is defined as1)，…，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 GDA0003475610710000095
Then the observation error dynamics is obtained by the two formulas (9) and (10):
Figure GDA0003475610710000096
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 GDA0003475610710000097
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 (5)

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 kinetic model of the parallel robot for conveying, which comprises unknown dynamics, external interference and friction, on line in real time;
the specific process of the step 3) is as follows:
the dynamic model of the parallel robot for conveying is as follows:
Figure FDA0003475610700000011
wherein M (q) is a symmetric positive definite inertial matrix;
Figure FDA0003475610700000012
are terms of Copenforces and centrifugal forces; g (q) is a gravity term;
Figure FDA0003475610700000013
is a friction force term; tau isdAn external interference item; tau is a control moment vector;
introducing positive definite constant diagonal matrix for applying time delay estimation technique
Figure FDA0003475610700000014
The kinetic model (1) is abbreviated as:
Figure FDA0003475610700000015
in the formula,
Figure FDA0003475610700000016
representing dynamic information items including nonlinear unknown dynamics, external interference and friction 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 FDA0003475610700000017
in the formula,
Figure FDA0003475610700000018
is that
Figure FDA0003475610700000019
The delay estimate of (a); the variable with the subscript t-eta represents the value of the variable at this time, i.e., the time lag value of the variable, where eta is the delay time and the minimum value of eta can be set as the sampling period;
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;
in the step 4), designing a robust accurate differentiator of the parallel robot system for conveying to delay the estimation error in the observation within a limited time is specifically as follows:
when a time delay estimation technology is adopted to obtain a dynamic model of the parallel robot for conveying on line, a time delay estimation error is generated by using a sampling value at the previous moment to approximate the current values of a nonlinear item and an uncertain item of a parallel robot system for conveying, and the expression of the time delay estimation error is as follows:
Figure FDA0003475610700000021
wherein,
Figure FDA0003475610700000022
for a positive constant diagonal matrix, N ∈ R6Represents the dynamic information items including the nonlinear unknown dynamics, the external interference and the friction of the parallel robot for conveying,
Figure FDA0003475610700000023
is the delay estimate of N;
is provided with
Figure FDA0003475610700000024
And
Figure FDA0003475610700000025
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 FDA0003475610700000026
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 for conveying is designed as follows:
Figure FDA0003475610700000027
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. ofj∈R6，j＝0,1,2；λi＝diag(λi1，λi2，…，λi6)，i＝0,1,2；L＝diag(l1,l2,…,l6) Is that
Figure FDA0003475610700000028
Lipshitz constant and li＞0，
Figure FDA0003475610700000029
Let x be (x)1,…,xn)TThe symbol sign (x) is defined as1),…,sign(xn))T，|x|qsign(x)＝(|x1|qsign(x1),…,|xn|qsign(xn))T；
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;
in the step 5), an observed value z obtained by using a robust accurate differentiator of the parallel robot for conveying1Carrying out feedforward compensation, and designing a virtual control law u of model-free finite time convergence sliding mode control as follows:
Figure FDA0003475610700000031
wherein m is not less than 1, alpha1＝diag(α11,α12,…,α16)，α2＝diag(α21,α22,…,α26) W is an intermediate variable introduced when the virtual control law u is designed;
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 FDA0003475610700000032
in the formula, J is a Jacobian matrix of the parallel robot for conveying;
Figure FDA0003475610700000033
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 FDA0003475610700000034
respectively showing the rotation angles of two driving wheels of the parallel robot for conveying,
Figure FDA0003475610700000035
is the active joint velocity vector;
Figure FDA0003475610700000036
is the connecting rod midpoint velocity vector.
3. 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 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 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 FDA0003475610700000037
Wherein xd1,xd2,xd3,xd4Respectively show the expected displacement of four sliding blocks of the parallel robot for conveying,
Figure FDA0003475610700000038
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: step 5) also comprises the following steps:
at virtual control law u and observation z1Under the feedforward compensation action on the delay estimation error epsilon, the dynamic of the sliding mode variable s is as follows:
Figure FDA0003475610700000041
the variable of the sliding mode and the derivative thereof are converged to the origin within a limited time
Figure FDA0003475610700000042
Is continuous, so the virtual control law u is not only continuous but also smooth.
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: the step 5) further comprises the step of designing a finite time convergence sliding mode control law tau without a model and combined with a robust precise differentiator feedforward compensation technology according to a virtual control law u, wherein the finite time convergence sliding mode control law tau is as follows:
Figure FDA0003475610700000043
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