CN111443604B - Fuzzy sliding mode controller of worm pipeline robot and design method thereof - Google Patents

Fuzzy sliding mode controller of worm pipeline robot and design method thereof Download PDF

Info

Publication number
CN111443604B
CN111443604B CN202010240534.7A CN202010240534A CN111443604B CN 111443604 B CN111443604 B CN 111443604B CN 202010240534 A CN202010240534 A CN 202010240534A CN 111443604 B CN111443604 B CN 111443604B
Authority
CN
China
Prior art keywords
pipeline robot
sliding mode
worm
worm pipeline
force
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.)
Active
Application number
CN202010240534.7A
Other languages
Chinese (zh)
Other versions
CN111443604A (en
Inventor
黄欣浩
肖玲斐
隆亦周
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.)
Nanjing University of Aeronautics and Astronautics
Original Assignee
Nanjing University of Aeronautics and Astronautics
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 Nanjing University of Aeronautics and Astronautics filed Critical Nanjing University of Aeronautics and Astronautics
Priority to CN202010240534.7A priority Critical patent/CN111443604B/en
Publication of CN111443604A publication Critical patent/CN111443604A/en
Application granted granted Critical
Publication of CN111443604B publication Critical patent/CN111443604B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16L—PIPES; JOINTS OR FITTINGS FOR PIPES; SUPPORTS FOR PIPES, CABLES OR PROTECTIVE TUBING; MEANS FOR THERMAL INSULATION IN GENERAL
    • F16L2101/00—Uses or applications of pigs or moles
    • F16L2101/30—Inspecting, measuring or testing
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16L—PIPES; JOINTS OR FITTINGS FOR PIPES; SUPPORTS FOR PIPES, CABLES OR PROTECTIVE TUBING; MEANS FOR THERMAL INSULATION IN GENERAL
    • F16L55/00—Devices or appurtenances for use in, or in connection with, pipes or pipe systems
    • F16L55/26—Pigs or moles, i.e. devices movable in a pipe or conduit with or without self-contained propulsion means
    • F16L55/28—Constructional aspects

Landscapes

  • Engineering & Computer Science (AREA)
  • Software Systems (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Health & Medical Sciences (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Manipulator (AREA)
  • Gear Transmission (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a fuzzy sliding mode controller of a worm pipeline robot and a design method thereof, aiming at the problem that the worm pipeline robot is difficult to realize accurate reference instruction tracking under the condition of no feedback controller, in particular to the characteristics that the worm pipeline robot is strong in nonlinearity and the friction force is difficult to estimate, the fuzzy sliding mode feedback controller with a friction force estimator is designed, and meanwhile, the general sliding mode surface is optimized and improved to adapt to the motion mode of the worm pipeline robot, so that the tracking of the mass center speed of the worm pipeline robot is finally realized, and the tracking characteristic of the mass center position of the worm pipeline robot is ensured to have good performance. Simulation results show that the designed controller can realize the rapid tracking of the mass center speed of the worm pipeline robot and enable the tracking error of the mass center position of the robot to be small.

Description

Fuzzy sliding mode controller of worm pipeline robot and design method thereof
Technical Field
The invention belongs to the technical field of worm pipeline robots, and particularly relates to a fuzzy sliding mode controller of a worm pipeline robot and a design method of the fuzzy sliding mode controller.
Background
With the development of society, pipelines play more and more obvious roles in the fields of industrial production, energy transportation, urban construction and the like. In the industrial production field, large-scale power plants, hydroelectric power plants and other places are often transported by using pipelines; in the field of energy transportation, pipeline transportation is an excellent transportation mode for transporting a large amount of gaseous or liquid energy; in the aspect of urban construction, the pipeline can realize functions of pollution discharge, power supply, network communication and the like.
But with it create a number of plumbing problems including plugging, rusting, corrosion, leakage, aging, etc. Since most of the materials in the pipeline are materials that are not touched by human body, and are not very beneficial to the detection and maintenance of the pipeline, the demand of the pipeline robot is greatly increased in recent years.
The pipeline robot belongs to a branch of a special robot. The walking mode can be mainly divided into wheel type, crawler type, creeping type and the like. The wheel type pipeline robot realizes the motion of the pipeline robot under the action of the friction force between the roller and the pipe wall, but the driving force is limited. The tracked pipeline robot has larger dragging capacity but weaker over-bending capacity. The crawling type pipeline robot is divided into a crawling type robot and a snake-shaped robot, and is designed by learning the motion modes of reptiles such as inchworms, earthworms and the like by applying the bionics principle. The crawling type pipeline robot has good adaptability to the pipe diameter and the curvature radius, but the intermittent motion mode brings trouble to the robot control.
A worm pipeline robot [1] [2] designed by Russian professor Sattarov learns the movement mode of worms, has a novel structure, can better adapt to the size of the pipe diameter, and has the movement principle that the force moving forwards is generated by utilizing the alternate change of spring force, electromagnetic force and friction force. But the disadvantage is that no feedback controller is designed for the worm pipeline robot, the controller is only an open loop system, the specified speed and the specified position are difficult to be reached according to the instruction requirement, and the controller accuracy is low. The invention carries out theoretical analysis on the worm pipeline robot designed in the document [1] [2] and carries out feedback controller design aiming at the defects of the worm pipeline robot.
The sliding mode variable structure control is a special nonlinear control in nature, and the nonlinearity of the sliding mode variable structure control is mainly represented by discontinuity of control action. Aiming at the characteristic of strong nonlinearity of a worm pipeline robot, the sliding mode control has the advantages that: the method can directly derive the control law capable of stabilizing the system based on the stability condition, and meanwhile, the characteristics of the system are irrelevant to external interference, so that the robustness of the system is strong. Therefore, the sliding mode feedback controller is designed to control the worm pipeline robot. But sliding mode control also has its drawbacks: when the state track of the system reaches the sliding mode surface, the system is difficult to move towards the balance point along the sliding mode surface, and the system does reciprocating motion on two sides of the sliding mode surface, so that the phenomenon of buffeting occurs. In addition, sliding mode control has the problem that the sliding mode parameters are difficult to determine.
In order to overcome the defects of sliding mode control, a fuzzy rule is introduced to adjust sliding mode parameters. The fuzzy rule is designed based on expert experience, and can better solve the problem that the non-linearity of the parameters of the sliding film is difficult to determine.
Reference documents:
1.R.R.Sattarov and M.A.Almaev.:Electromagnetic worm-like locomotion system for in-pipe robots:Design and vibration-driven motion analysis,Dynamics of Systems,Mechanisms and Machines(Dynamics),pp.1-6.Omsk(2017).
2.Sattarov,Robert&Almaev,Marsel.:Electromagnetic worm-like locomotion system for in-pipe robots:novel design of magnetic subsystem.IOP Conference Series:Earth and Environmental Science.(2019)
disclosure of Invention
The invention aims to provide a fuzzy sliding mode controller of a worm pipeline robot and a design method thereof, so as to realize feedback control of the worm pipeline robot, improve the tracking accuracy of the mass center speed and position instruction of the worm pipeline robot and optimize the performance of the worm pipeline robot in the operation process.
In order to achieve the purpose, the invention adopts the technical scheme that:
a design method of a fuzzy sliding mode controller of a worm pipeline robot comprises the following steps:
the motion of the worm pipeline robot is that the displacement of the mass center of the worm pipeline robot is changed due to the mutual change of the periodic spring force and the electromagnetic force;
carrying out stress analysis on the worm pipeline robot, and setting: m is1≠m2Wherein m is1、m2The mass of a contact ring and the mass of a vibration ring of the worm pipeline robot are respectively; newton's second law equation is listed:
Figure BDA0002432389940000021
wherein x is1、
Figure BDA0002432389940000022
x2、
Figure BDA0002432389940000023
Respectively the displacement and acceleration of a contact ring of the worm pipeline robot and the displacement and acceleration of a vibration ring; c is the spring rate, FemIs electromagnetic force, beta is the angle between the pipe and the horizontal plane, FfrIs the friction force, there are:
Figure BDA0002432389940000031
where μ is the dry friction coefficient of the tube wall, FNThe contact ring is subjected to a positive pressure on the wall of the pipe,
Figure BDA0002432389940000032
is contact ring velocity, FaThe contact ring is subjected to resultant force except friction force;
order to
Figure BDA0002432389940000033
Is a state quantity, wherein
Figure BDA0002432389940000034
For ring velocity of oscillation, u-FemFor input, equation (1) is written in the form of a state space equation:
Figure BDA0002432389940000035
wherein:
Figure BDA0002432389940000036
wherein b is a coefficient;
the mass center displacement and the speed of the worm pipeline robot are expressed by the following formulas:
Figure BDA0002432389940000037
order to
Figure BDA0002432389940000038
Equation (4) can be written as:
Figure BDA0002432389940000039
setting the condition 1: the desired centroid axial velocity is
Figure BDA0002432389940000041
The expected centroid displacement is taken as the integral of the centroid axial velocity
Figure BDA00024323899400000412
Setting the condition 2: desired centroid axial velocity
Figure BDA0002432389940000042
With desired centroid axial acceleration
Figure BDA0002432389940000043
Known, the tracking error of the centroid speed and the acceleration of the worm pipeline robot is written as follows:
Figure BDA0002432389940000044
according to equation (5), the above equation is rewritten as:
Figure BDA0002432389940000045
designing a sliding mode function s:
Figure BDA0002432389940000046
wherein sigma1Is a sliding mode design parameter, and needs to design sigma1>0 is used for ensuring the stability of the sliding mode surface, namely, S ═ e is satisfiedcoM|s(ecoM) 0, S is a sliding mode surface, and sliding mode functions S are established as 0 in the sliding mode surface;
substituting formula (6) into formula (7), and making sigma ═ sigma1 1]M, wherein
Figure BDA0002432389940000047
Get formula (8)
Figure BDA0002432389940000048
Differentiating equation (8):
Figure BDA0002432389940000049
substituting formula (3) for formula (9):
Figure BDA00024323899400000410
according to the sliding mode theory, the next step is to design an approach law, and the following approach law is selected:
Figure BDA00024323899400000411
wherein sgn(s) is a sign function, k is greater than 0, epsilon is greater than 0, and k and epsilon are two parameters of a sliding mode approach law respectively; equation (11) and equation (10) are made to be correspondingly equal to each other, resulting in:
Figure BDA0002432389940000051
therefore, the sliding mode control law is:
Figure BDA0002432389940000052
since F (X) includes an unknown frictional force FfrIn the form of(13) Since u cannot be directly calculated, a friction force estimator is designed according to the characteristics of the worm pipeline robot, as shown in equation (14), for estimating the friction force
Figure BDA0002432389940000053
Represents;
Figure BDA0002432389940000054
wherein alpha is the ratio of the axial force to the circumferential force, and the static friction force is set to be equal to the sliding friction force; the corresponding f (X):
Figure BDA0002432389940000055
finally, the designed sliding mode control law expression is as follows:
Figure BDA0002432389940000056
the motion of the worm pipeline robot is simplified into a cycle for analysis, and the cycle is divided into three stages:
the first stage is as follows: the alternating current power supply voltage is equal to zero, the electromagnetic force borne by the worm system is zero, the supporting pad contacting the wall part of the pipe is pressed against the pipe wall by the longitudinal spring force at the moment, the transverse spring is in a relaxed state, and the positive pressure is maximum;
and a second stage: the voltage of the alternating current power supply is gradually increased until the peak is reached, and an excitation coil connected with the alternating current power supply generates excitation current; exciting current to generate electromagnetic force, mutually attracting the contact ring, the vibration ring part and the two ferromagnetic half rings of the contact ring part together, compressing the spring, reducing the positive pressure of the supporting pad of the contact ring part on the tube wall surface, and slowly contracting the whole worm pipeline robot at the moment, but hardly moving the mass center;
and a third stage: alternating current supply voltage reduces, and exciting current reduces, and the electromagnetic force reduces, and positive pressure increase, frictional force increase, and horizontal spring needs the extension, because the frictional force increase that the supporting pad of contact ring part received suppresses contact ring reverse movement, and only receives the spring force of increase and the electromagnetic force that reduces on the vibration ring, forward motion to worm pipeline robot barycenter displacement moves forward.
The optimal values of the parameters k and epsilon in the sliding mode control law are determined by the following method:
for ε, m1Presenting a functional relation with the optimal value of epsilon, and expressing the function by using a piecewise function;
for k, m1The optimal value of k is in a nonlinear relation, so that the optimal value of k is obtained by using a single-input single-output fuzzy rule and carrying out fuzzification, logical reasoning, fuzzy solution and other steps.
The fuzzy sliding mode controller of the worm pipeline robot obtained by the method is used for realizing axial speed tracking of the mass center of the worm pipeline robot, and the expression is as follows:
Figure BDA0002432389940000061
has the advantages that: aiming at the problem that a worm pipeline robot is difficult to realize accurate reference instruction tracking without a feedback controller, particularly aiming at the characteristics that the worm pipeline robot is strong in nonlinearity and friction is difficult to estimate, the fuzzy sliding mode feedback controller with the friction estimator is designed, and meanwhile, a common sliding mode surface is optimized and improved to adapt to the motion mode of the worm pipeline robot, so that the tracking of the centroid speed of the worm pipeline robot is finally realized, and the tracking characteristic of the centroid position has good performance. Simulation results show that the designed controller can realize the rapid tracking of the mass center speed of the worm pipeline robot and enable the tracking error of the mass center position of the robot to be small.
Drawings
FIG. 1 is a schematic view of a worm pipeline robot according to an embodiment of the present invention;
FIG. 2 is a schematic view of a worm pipeline robot according to an embodiment of the present invention;
FIG. 3 is a general structure diagram of the robot control of the worm pipe in the present invention;
FIG. 4a is a simulation diagram of the control overall structure Simulink of the worm pipeline robot in the invention;
FIG. 4b is a simulation diagram of a fuzzy sliding mode controller Simulink with a friction force estimator according to the present invention;
FIG. 5a is a two-dimensional graph of a simulation result of a friction estimator;
FIG. 5b is a three-dimensional diagram of a simulation result of the friction estimator;
FIG. 6a is a centroid displacement tracking curve of unadjusted sliding mode parameters in an embodiment of the present invention;
FIG. 6b is a graph of the controller output for an unadjusted sliding mode parameter in an embodiment of the present invention;
FIG. 7a is a centroid displacement tracking curve after sliding mode parameters are adjusted in an embodiment of the present invention;
fig. 7b is the output curve of the controller after adjusting the sliding mode parameters according to the embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings.
As shown in fig. 1, the constituent structure of the worm pipeline robot includes a total of two parts: a vibration ring portion and a contact ring portion. The axial spring connects two parts, each consisting of two ferromagnetic half-rings. The contact ring portion is provided with a circumferential spring connecting the two half rings and a support pad for contacting the pipe wall. An alternating current power supply is arranged on one side of the vibration ring for supplying power, and an excitation coil connected with the power supply is wound on the semi-ring of the vibration ring. At the same time, the side is also provided with two non-magnetic blocks, and air is filled in the non-magnetic blocks, so that mutual vibration between the two half rings of the vibration ring is prevented.
The motion of the worm pipeline robot mainly comprises that the periodic spring force and the electromagnetic force change mutually to cause the change of the displacement of the mass center of the worm pipeline robot. The motion can be analyzed in a simplified cycle, which is divided into three phases:
the first stage is as follows: the alternating current power supply voltage is equal to zero, the electromagnetic force borne by the worm system is zero, the supporting pad contacting the wall part of the pipe is pressed against the pipe wall by the longitudinal spring force at the moment, the transverse spring is in a relaxed state, and the positive pressure is maximum;
and a second stage: the voltage of an alternating current power supply is gradually increased until the peak is reached, an excitation coil connected with the alternating current power supply generates excitation current, the excitation current generates electromagnetic force, the contact ring, the vibration ring part and the two ferromagnetic half rings of the contact ring part are mutually attracted together, a spring is compressed, the positive pressure of a supporting pad of the contact ring part on the wall surface of the tube is reduced, at the moment, the whole worm pipeline robot is slowly contracted, and the mass center is almost not moved;
and a third stage: alternating current supply voltage reduces, and exciting current reduces, and the electromagnetic force reduces, and positive pressure increase, frictional force increase, and horizontal spring needs the extension, because the frictional force increase that the supporting pad of contact ring part received suppresses contact ring reverse movement, and only receives the spring force of increase and the electromagnetic force that reduces on the vibration ring, forward motion to worm pipeline robot barycenter displacement moves forward.
And (3) carrying out stress analysis on the worm pipeline robot, as shown in figure 2, and setting: m is1≠m2Wherein m is1、m2The mass of a contact ring and the mass of a vibration ring of the worm pipeline robot are respectively; newton's second law equation is listed:
Figure BDA0002432389940000071
wherein x is1、
Figure BDA0002432389940000072
x2、
Figure BDA0002432389940000073
Respectively the displacement and acceleration of a contact ring of the worm pipeline robot and the displacement and acceleration of a vibration ring; c is the spring rate, FemIs an electromagnetic forceBeta is the angle between the pipe and the horizontal plane, FfrIs the friction force, there are:
Figure BDA0002432389940000081
where μ is the dry friction coefficient of the tube wall, FNThe contact ring is subjected to a positive pressure on the wall of the pipe,
Figure BDA0002432389940000082
is contact ring velocity, FaThe contact ring is subjected to resultant force except friction force;
order to
Figure BDA0002432389940000083
Is a state quantity, wherein
Figure BDA0002432389940000084
For ring velocity of oscillation, u-FemFor input, equation (1) is written in the form of a state space equation:
Figure BDA0002432389940000085
wherein:
Figure BDA0002432389940000086
wherein b is a coefficient;
the mass center displacement and the speed of the worm pipeline robot are expressed by the following formulas:
Figure BDA0002432389940000087
order to
Figure BDA0002432389940000088
Equation (4) can be written as:
Figure BDA0002432389940000089
setting the condition 1: the desired centroid axial velocity is
Figure BDA00024323899400000810
The expected centroid displacement is taken as the integral of the centroid axial velocity
Figure BDA00024323899400000912
Setting the condition 2: desired centroid axial velocity
Figure BDA0002432389940000091
With desired centroid axial acceleration
Figure BDA0002432389940000092
Known, the tracking error of the centroid speed and the acceleration of the worm pipeline robot is written as follows:
Figure BDA0002432389940000093
according to equation (5), the above equation is rewritten as:
Figure BDA0002432389940000094
designing a sliding mode function s:
Figure BDA0002432389940000095
wherein sigma1Is a sliding mode design parameter, and needs to design sigma1>0 is used for ensuring the stability of the sliding mode surface, namely, S ═ e is satisfiedcoM|s(ecoM) 0, S is a sliding mode surface, and sliding mode functions S are established as 0 in the sliding mode surface;
substituting formula (6) into formula (7), and making sigma ═ sigma1 1]M, wherein
Figure BDA0002432389940000096
Get formula (8)
Figure BDA0002432389940000097
Differentiating equation (8):
Figure BDA0002432389940000098
substituting formula (3) for formula (9):
Figure BDA0002432389940000099
according to the sliding mode theory, the next step is to design an approach law, and the following approach law is selected:
Figure BDA00024323899400000910
wherein sgn(s) is a sign function, k is greater than 0, epsilon is greater than 0, and k and epsilon are two parameters of a sliding mode approach law respectively;
equation (11) and equation (10) are made to be correspondingly equal to each other, resulting in:
Figure BDA00024323899400000911
therefore, the sliding mode control law is:
Figure BDA0002432389940000101
since F (X) includes an unknown frictional force FfrSince u cannot be directly obtained by equation (13), it is possible to obtain u from a worm pipe machineThe characteristics of the robot, a friction force estimator is designed, as shown in formula (14), for estimating the friction force
Figure BDA0002432389940000102
Represents;
Figure BDA0002432389940000103
wherein alpha is the ratio of the axial force to the circumferential force, and the static friction force is set to be equal to the sliding friction force; the corresponding f (X):
Figure BDA0002432389940000104
finally, the designed sliding mode control law expression is as follows:
Figure BDA0002432389940000105
the sliding mode parameters have great influence on the control effect of the worm pipeline robot, so that the optimal values of k and epsilon need to be determined. Simulation shows that the mass m of the contact ring1The optimum values of k and epsilon will be affected.
For ε, m1And presents a certain functional relationship with the optimal value of epsilon and can be represented by a piecewise function.
For k, m1The optimal value of k is in a nonlinear relation, so that the optimal value of k is obtained by using a single-input single-output fuzzy rule and carrying out fuzzification, logical reasoning, fuzzy solution and other steps.
Sliding mode parameter simulation without setting
Consider a worm pipeline robot with Simulink simulation parameters as shown in table 1.
TABLE 1 simulation parameters of worm pipeline robot
Figure BDA0002432389940000111
The above parameters were entered using the m-file and after run, fig. 5a and 5b were obtained.
Sliding mode parameter simulation through fuzzy rule and piecewise function setting
The segment function equation (16) is substituted with ∈ 2.
Figure BDA0002432389940000112
The gain k is substituted for the fuzzy controller output.
Defining an input-output fuzzy set:
for input m1Four fuzzy sets are defined, denoted by "small" (S) "smaller" (SM), "large" (BM), and "large" (B), respectively.
The parameters k are also denoted by "small" (S) "small" (SM), "large" (BM) and "large" (B), respectively.
Then m is1＝{S,MS,MB,B} k＝{S,MS,MB,B}
Determining the corresponding ambiguity domain as
m1＝{0.24,0.35,0.5,0.7}
k＝{26,18,15,10}
The fuzzy control rules are shown in table 2:
TABLE 2 fuzzy rule Table
Figure BDA0002432389940000121
And (6) performing simulation to obtain simulation image curve graphs 6a and 6b after parameter setting.
The synovial controller algorithm is implemented as follows:
step 1: establishing a Simulink simulation diagram of the overall control structure of the worm pipeline robot, as shown in FIG. 4 a;
step 2: establishing a Simulink simulation diagram of a worm pipeline robot object according to a kinetic equation obtained by theoretical analysis;
and step 3: according to the sliding mode controller obtained by theoretical analysis design, establishing a Simulink simulation diagram of the fuzzy sliding mode controller with the friction force estimator, as shown in FIG. 4 b;
and 4, step 4: performing simulation on MATLAB/Simulink;
the friction force estimator simulation results verify as shown in fig. 5a and 5 b.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (4)

1. A design method of a fuzzy sliding mode controller of a worm pipeline robot is characterized by comprising the following steps: the method comprises the following steps:
the motion of the worm pipeline robot is that the displacement of the mass center of the worm pipeline robot is changed due to the mutual change of the periodic spring force and the electromagnetic force;
carrying out stress analysis on the worm pipeline robot, and setting: m is1≠m2Wherein m is1、m2The mass of a contact ring and the mass of a vibration ring of the worm pipeline robot are respectively; newton's second law equation is listed:
Figure FDA0002902075800000011
wherein x is1、
Figure FDA0002902075800000012
x2、
Figure FDA0002902075800000013
Respectively the displacement and acceleration of a contact ring of the worm pipeline robot and the displacement and acceleration of a vibration ring; c is the spring rate, FemIs electromagnetic force, beta is the angle between the pipe and the horizontal plane, FfrIs the friction force, there are:
Figure FDA0002902075800000014
where μ is the dry friction coefficient of the tube wall, FNThe contact ring is subjected to a positive pressure on the wall of the pipe,
Figure FDA0002902075800000015
is contact ring velocity, FaThe contact ring is subjected to resultant force except friction force;
order to
Figure FDA0002902075800000016
Is a state quantity, wherein
Figure FDA0002902075800000017
For ring velocity of oscillation, u-FemFor input, equation (1) is written in the form of a state space equation:
Figure FDA0002902075800000018
wherein:
Figure FDA0002902075800000021
wherein b is a coefficient;
the mass center displacement and the speed of the worm pipeline robot are expressed by the following formulas:
Figure FDA0002902075800000022
order to
Figure FDA0002902075800000023
Equation (4) can be written as:
Figure FDA0002902075800000024
setting the condition 1: the desired centroid axial velocity is
Figure FDA0002902075800000025
The expected centroid displacement is taken as the integral of the centroid axial velocity
Figure FDA0002902075800000026
Setting the condition 2: desired centroid axial velocity
Figure FDA0002902075800000027
With desired centroid axial acceleration
Figure FDA0002902075800000028
Known, the tracking error of the centroid speed and the acceleration of the worm pipeline robot is written as follows:
Figure FDA0002902075800000029
Figure FDA00029020758000000210
according to equation (5), the above equation is rewritten as:
Figure FDA00029020758000000211
designing a sliding mode function s:
Figure FDA0002902075800000031
wherein sigma1Is a sliding mode design parameter, and needs to design sigma1More than 0 is used for ensuring the stability of the sliding mode surface, namely S ═ e is satisfiedcoM|s(ecoM) 0, S is a sliding mode surface, and sliding mode functions S are established as 0 in the sliding mode surface;
substituting formula (6) into formula (7), and making sigma ═ sigma1 1]M, wherein
Figure FDA0002902075800000032
Get formula (8)
Figure FDA0002902075800000033
Differentiating equation (8):
Figure FDA0002902075800000034
substituting formula (3) for formula (9):
Figure FDA0002902075800000035
according to the sliding mode theory, the next step is to design an approach law, and the following approach law is selected:
Figure FDA0002902075800000036
wherein sgn(s) is a sign function, k is more than 0, epsilon is more than 0, and k and epsilon are two parameters of a sliding mode approach law respectively;
equation (11) and equation (10) are made to be correspondingly equal to each other, resulting in:
Figure FDA0002902075800000037
therefore, the sliding mode control law is:
Figure FDA0002902075800000038
since F (X) includes an unknown frictional force FfrSince u cannot be directly obtained by equation (13), a friction estimator is designed according to the characteristics of the worm pipeline robot, and friction is estimated by equation (14)
Figure FDA0002902075800000039
Represents;
Figure FDA00029020758000000310
wherein alpha is the ratio of the axial force to the circumferential force, and the static friction force is set to be equal to the sliding friction force; the corresponding f (X):
Figure FDA0002902075800000041
finally, the designed sliding mode control law expression is as follows:
Figure FDA0002902075800000042
2. the design method of the fuzzy sliding-mode controller of the worm pipeline robot according to claim 1, characterized in that: the motion of the worm pipeline robot is simplified into a cycle for analysis, and the cycle is divided into three stages:
the first stage is as follows: the alternating current power supply voltage is equal to zero, the electromagnetic force borne by the worm system is zero, the supporting pad contacting the wall part of the pipe is pressed against the pipe wall by the longitudinal spring force at the moment, the transverse spring is in a relaxed state, and the positive pressure is maximum;
and a second stage: the voltage of the alternating current power supply is gradually increased until the peak is reached, and an excitation coil connected with the alternating current power supply generates excitation current; exciting current to generate electromagnetic force, mutually attracting the contact ring, the vibration ring part and the two ferromagnetic half rings of the contact ring part together, compressing the spring, reducing the positive pressure of the supporting pad of the contact ring part on the tube wall surface, and slowly contracting the whole worm pipeline robot at the moment, but hardly moving the mass center;
and a third stage: alternating current supply voltage reduces, and exciting current reduces, and the electromagnetic force reduces, and positive pressure increase, frictional force increase, and horizontal spring needs the extension, because the frictional force increase that the supporting pad of contact ring part received suppresses contact ring reverse movement, and only receives the spring force of increase and the electromagnetic force that reduces on the vibration ring, forward motion to worm pipeline robot barycenter displacement moves forward.
3. The design method of the fuzzy sliding-mode controller of the worm pipeline robot according to claim 1, characterized in that: the optimal values of the parameters k and epsilon in the sliding mode control law are determined by the following method:
for ε, m1Presenting a functional relation with the optimal value of epsilon, and expressing the function by using a piecewise function;
for k, m1The optimal value of k is in a nonlinear relation, so that the optimal value of k is obtained by fuzzification, logical reasoning and fuzzy solution by using a single-input single-output fuzzy rule.
4. A fuzzy sliding-mode controller for a worm pipeline robot obtained by the method of claim 1, characterized in that: the sliding mode controller is used for realizing axial speed tracking of the mass center of the worm pipeline robot, and the expression of the sliding mode controller is as follows:
Figure FDA0002902075800000051
CN202010240534.7A 2020-03-31 2020-03-31 Fuzzy sliding mode controller of worm pipeline robot and design method thereof Active CN111443604B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010240534.7A CN111443604B (en) 2020-03-31 2020-03-31 Fuzzy sliding mode controller of worm pipeline robot and design method thereof

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010240534.7A CN111443604B (en) 2020-03-31 2020-03-31 Fuzzy sliding mode controller of worm pipeline robot and design method thereof

Publications (2)

Publication Number Publication Date
CN111443604A CN111443604A (en) 2020-07-24
CN111443604B true CN111443604B (en) 2021-04-06

Family

ID=71650882

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010240534.7A Active CN111443604B (en) 2020-03-31 2020-03-31 Fuzzy sliding mode controller of worm pipeline robot and design method thereof

Country Status (1)

Country Link
CN (1) CN111443604B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112540536B (en) * 2020-11-27 2022-04-22 南京航空航天大学 Design method of sliding mode optimization controller of worm pipeline robot

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104410107A (en) * 2014-11-27 2015-03-11 江苏科技大学 Passive integral sliding mode control method for double-fed wind power system
CN106444799A (en) * 2016-07-15 2017-02-22 浙江工业大学 Quadrotor unmanned plane control method based on fuzzy expansion state observer and adaptive sliding formwork
KR101801302B1 (en) * 2016-10-06 2017-12-21 동명대학교산학협력단 Robot hand and surface robot system using of the same for working
CN207129036U (en) * 2017-06-20 2018-03-23 常州机电职业技术学院 Worm robot
CN108008720A (en) * 2017-10-31 2018-05-08 哈尔滨理工大学 The fuzzy sliding mode Trajectory Tracking Control and method of a kind of wheeled mobile robot
CN108502053A (en) * 2018-06-13 2018-09-07 安徽新华学院 A kind of wheeled robot platform accuracy control method
CN110286585A (en) * 2019-03-15 2019-09-27 南京航空航天大学 A kind of mechanical system double integral Sliding Mode Control Design Method based on extension interference estimator
JP2019181680A (en) * 2018-04-10 2019-10-24 王磊 Automation manipulation robot

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR100392816B1 (en) * 2002-08-07 2003-07-28 최혁렬 Robot steering apparatus for inspection pipelines

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104410107A (en) * 2014-11-27 2015-03-11 江苏科技大学 Passive integral sliding mode control method for double-fed wind power system
CN106444799A (en) * 2016-07-15 2017-02-22 浙江工业大学 Quadrotor unmanned plane control method based on fuzzy expansion state observer and adaptive sliding formwork
KR101801302B1 (en) * 2016-10-06 2017-12-21 동명대학교산학협력단 Robot hand and surface robot system using of the same for working
CN207129036U (en) * 2017-06-20 2018-03-23 常州机电职业技术学院 Worm robot
CN108008720A (en) * 2017-10-31 2018-05-08 哈尔滨理工大学 The fuzzy sliding mode Trajectory Tracking Control and method of a kind of wheeled mobile robot
JP2019181680A (en) * 2018-04-10 2019-10-24 王磊 Automation manipulation robot
CN108502053A (en) * 2018-06-13 2018-09-07 安徽新华学院 A kind of wheeled robot platform accuracy control method
CN110286585A (en) * 2019-03-15 2019-09-27 南京航空航天大学 A kind of mechanical system double integral Sliding Mode Control Design Method based on extension interference estimator

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
Electromagnetic worm-like locomotion system for in-pipe robots: Design and vibration-driven motion analysis;Robert R. Sattarov;《2017 Dynamics of Systems, Mechanisms and Machines (Dynamics)》;20171116;全文 *

Also Published As

Publication number Publication date
CN111443604A (en) 2020-07-24

Similar Documents

Publication Publication Date Title
CN104065322B (en) Method for controlling output feedback of motor position servo system
Suzumori et al. Fiberless flexible microactuator designed by finite-element method
CN101847009B (en) Biped robot gait energy efficiency optimization method
Plaut Mathematical model of inchworm locomotion
CN111443604B (en) Fuzzy sliding mode controller of worm pipeline robot and design method thereof
Alfayad et al. High performance Integrated Electro-Hydraulic Actuator for robotics. Part II: Theoretical modelling, simulation, control & comparison with real measurements
CN105945925B (en) A kind of bionical snake-shaped robot control method
Liu et al. A self-propelled robotic system with a visco-elastic joint: dynamics and motion analysis
Zhu et al. An improved method combined SMC and MLESO for impedance control of legged robots’ electro-hydraulic servo system
Qian et al. A hybrid Gaussian mutation PSO with search space reduction and its application to intelligent selection of piston seal grooves for homemade pneumatic cylinders
CN104965413A (en) Friction compensation adaptive control method for controlled emission platform
Shen et al. Robust force tracking control via backstepping sliding mode control and virtual damping control for hydraulic quadruped robots
Li et al. Adaptive fractional order non-singular terminal sliding mode controller for underwater soft crawling robots with parameter uncertainties and unknown disturbances
CN106066603B (en) The implementation method of electrohydraulic servo system ADAPTIVE ROBUST positioner with accurate tracking performance
Zhong-Sheng et al. A new feedback-feedforward configuration for the iterative learning control of a class of discrete-time systems
CN112540536B (en) Design method of sliding mode optimization controller of worm pipeline robot
Zhang et al. Sliding mode control: An incremental perspective
Gao et al. Using fuzzy switching to achieve the smooth switching of force and position
He et al. Globally stabilizing a class of underactuated mechanical systems on the basis of finite-time stabilizing observer
Remy et al. Energetics of passivity-based running with high-compliance series elastic actuation
Chakon et al. Analysis of underactuated dynamic locomotion systems using perturbation expansion: the twistcar toy example
Yang et al. Angle error-tracking iterative learning control for pneumatic artificial muscle system
Sankaranarayanan et al. Configuration constrained stabilization of a wheeled mobile robot—theory and experiment
Sun et al. Comparison of two nonlinear model predictive control strategies with observer-based disturbance compensation for a hydrostatic transmission
Sattarov et al. Worm-like locomotion systems for in-pipe robots and its fuzzy sliding mode controller design

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