CN116810774A - Gear inspection global terminal sliding mode limited time delay observation control method - Google Patents
Gear inspection global terminal sliding mode limited time delay observation control method Download PDFInfo
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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
- 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
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J18/00—Arms
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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
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Abstract
A gear inspection global terminal sliding mode limited time delay observation control method comprises the steps of constructing a model-free control frame based on a mathematical model of an N-joint mechanical arm of a gear inspection robot system and defining a tracking error equation of the N-joint mechanical arm of the gear inspection robot system; real-time observation compensation is carried out on uncertainty parameters and unknown external disturbances of the gear inspection robot system by using a delay observer; based on an N-joint mechanical arm tracking error equation of the gear inspection robot system, a mechanical arm tracking error proportional term, a mechanical arm tracking error nonsingular terminal integral term and a mechanical arm tracking error initial term are combined to construct a finite time convergence global nonsingular terminal sliding mode surface; hybrid approach law based on power approach law and constant-speed approach law, and design of a gear inspection robot system N-joint mechanical arm global terminal sliding mode limited time delay observation controllerThe method comprises the steps of carrying out a first treatment on the surface of the And a track tracking test taking the N-joint mechanical arm of the gear inspection robot system as a target is verified.
Description
Technical Field
The invention relates to the technical field of industrial robot control systems, in particular to a gear inspection global terminal sliding mode limited time delay observation control method.
Background
Industrial robots are devices with multiple joints or multiple degrees of freedom, generally composed of a mechanical part, a sensing part, and a control part, and are widely used in the industrial fields of automobile manufacturing, logistics storage and transportation, precision electronics, and the like. Inspection robots are an important branch of industrial robots, where gear inspection robots are often used in gear quality process inspection. The gear inspection robot consists of a multi-joint manipulator and a vision device, and the multi-angle detection of the end vision device is realized by controlling the displacement of the tail end track of the gear inspection robot. The gear inspection robot is used as a multidimensional nonlinear system, and has uncertainty: uncertainty parameters and unknown external disturbances. The traditional control method based on the model has certain congenital defects, and the problems of low control precision, slow response speed and the like caused by the lack of an accurate system model cannot be solved.
Disclosure of Invention
In view of the existing problems, a method for controlling limited time delay observation of a sliding mode of a gear inspection global terminal is provided for solving the problems that a traditional model-based control method for an N-joint mechanical arm of a gear inspection robot system is low in precision, slow in response speed and the like.
In order to solve the technical problems, the invention provides the following technical scheme: based on a mathematical model of the N-joint mechanical arm of the gear inspection robot system, constructing a model-free control frame and defining a tracking error equation of the N-joint mechanical arm of the gear inspection robot system; real-time observation compensation of uncertainty parameters and unknown external disturbances of the gear inspection robot system is achieved by using a delay observer; based on a tracking error equation of an N-joint mechanical arm of the gear inspection robot system, a finite time convergence global nonsingular terminal sliding mode surface is constructed by combining a tracking error proportional term of the N-joint mechanical arm of the gear inspection robot system, a tracking error nonsingular terminal integral term of the N-joint mechanical arm of the gear inspection robot system and a tracking error initial term of the N-joint mechanical arm of the gear inspection robot system; the mixed approach law based on the power approach law and the constant-speed approach law is adopted to design a limited time delay observation controller tau (t) of a sliding mode of a global terminal of an N-joint mechanical arm of the gear inspection robot system.
As a preferable scheme of the gear inspection global terminal sliding mode limited time delay observation control method, the invention comprises the following steps:
the gear inspection robot system comprises: the system comprises an image operation center, a high-power camera and an N-joint mechanical arm.
As a preferable scheme of the gear inspection global terminal sliding mode limited time delay observation control method, the invention comprises the following steps:
the gear inspection robot system N joint mechanical arm mathematical model:
wherein, the left side of the equation is respectively: n-joint mechanical arm inertia force item of gear inspection robot systemCentrifugal force and coriolis force item of N-joint mechanical arm of gear inspection robot system>Gravity item G (q (t)) n×1 N-joint mechanical arm friction force item of gear inspection robot systemExternal disturbance term τ d (t)∈R n×1 ；m(q(t))∈R n×n For gear inspection robot system N joint arm inertial matrix, +.>The centrifugal force matrix and the coriolis force matrix of the N-joint mechanical arm of the gear inspection robot system are adopted; the right side of the equation is the control force term tau (t) epsilon R of the N-joint mechanical arm of the gear inspection robot system n×1 。
Based on the mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed:
wherein m (q (t))εR n×n Parameter adjustment gain matrix without physical meaning for N-joint mechanical arm model-free frame controller of gear inspection robot system, d (t) epsilon R n×1 For the uncertainty parameter and unknown external disturbance of the gear inspection robot system, the method is defined as follows:
defining the tracking error of the N joint mechanical arm of the gear inspection robot system as follows:
e(t)＝q * (t)-q(t)
wherein ,q* (t) is a target track of the N-joint mechanical arm of the gear inspection robot system, q (t) is an actual track of the N-joint mechanical arm of the gear inspection robot system, and e (t) is a tracking error of the N-joint mechanical arm of the gear inspection robot system;
taking a second-order differential from the tracking error of the N-joint mechanical arm of the gear inspection robot system to obtain:
wherein ,is the second order derivative of e (t); />Is q * Second order differentiation of (t); />Is the second order derivative of q (t);
defining an N-joint mechanical arm tracking error equation of the gear inspection robot system:
as a preferable scheme of the gear inspection global terminal sliding mode limited time delay observation control method, the invention comprises the following steps:
defining a delay observer:
wherein ,representing uncertainty parameters and unknown external disturbance estimated values of a gear inspection robot system, wherein tau (t-delta t) represents a limited time delay observation controller of a global terminal sliding mode of an N-joint mechanical arm of the gear inspection robot system at the moment t-delta t, and q (t-delta t) represents an actual track of the N-joint mechanical arm of the gear inspection robot system at the moment t-delta t>Representing the second order differential of the actual track of the N joint mechanical arm of the gear inspection robot system at the time t-delta t.
As a preferable scheme of the gear inspection global terminal sliding mode limited time delay observation control method, the invention comprises the following steps:
defining a finite time convergence global nonsingular terminal sliding mode surface:
wherein ,kp e (t) represents a tracking error proportion term k of an N-joint mechanical arm of the gear inspection robot system p Is the parameter-adjusting gain of the device,representing nonsingular terminal integral term k of tracking error of N-joint mechanical arm of gear inspection robot system i P, j is the tuning gain of the gain, which satisfies the following conditions: p is p<j<2p and p, j are positive odd numbers, k p e (0) represents an initial item of tracking error of an N-joint mechanical arm of the gear inspection robot system, s 1 (t)，s 2 (t)，…，s n (t) is a finite time converging global nonsingular terminal sliding mode face sub-sliding mode face;
taking first-order differentiation of the global nonsingular terminal sliding mode surface:
wherein ,the first-order differentiation of the sliding mode surface of the global nonsingular terminal is converged in limited time;
taking outThe finite convergence time is:
wherein ,ts Is the convergence time and c is any constant.
As a preferable scheme of the gear inspection global terminal sliding mode limited time delay observation control method, the invention comprises the following steps:
defining the power approach law:
wherein a >0 and 1> beta >0 are tuning gains;
defining the isokinetic approach law:
wherein b >0 is the tuning gain;
based on the power approach law and the constant velocity approach law, defining the mixed approach law:
wherein ,
as a preferable scheme of the gear inspection global terminal sliding mode limited time delay observation control method, the invention comprises the following steps:
based on a delay observer, a finite time convergence global nonsingular terminal sliding mode surface and a mixed approach law based on a power approach law and a constant-speed approach law, a model-free control frame is used for designing a gear inspection robot system N joint mechanical arm global terminal sliding mode finite time delay observation controller tau (t):
the invention has the beneficial effects that: (1) The method is based on a mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed, and a tracking error equation of the N-joint mechanical arm of the gear inspection robot system is defined; (2) On the basis, the delay observer is utilized to realize observation compensation of all disturbance; (3) The method is characterized in that a finite-time convergence global nonsingular terminal sliding mode surface is constructed by combining a tracking error proportion term, a nonsingular terminal integral term and an initial term of an N-joint mechanical arm of the gear inspection robot system, so that the convergence speed in a near steady state is improved, and the problem of singularity is avoided; (4) The mixed approach law based on the power approach law and the constant-speed approach law is adopted, and the controller design is realized under a model-free framework, so that the problems of missing of an accurate model, low control precision, slow response speed and the like are solved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
wherein ：
fig. 1 is a control schematic diagram of a gear inspection global terminal sliding mode limited time delay observation control method according to an embodiment of the invention.
Fig. 2 is a schematic diagram of tracking target tracks (aim 1) of a dual-joint mechanical arm of a gear inspection robot and track tracking of a global terminal sliding mode limited time delay observation control method (GTSMFTTDC) according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of tracking target tracks (aim 2) of a dual-joint mechanical arm of a gear inspection robot and track tracking of a global terminal sliding mode limited time delay observation control method (GTSMFTTDC) according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of tracking target track (aim 1) of a dual-joint mechanical arm of a gear inspection robot and track tracking based on a model conventional PD control method (PDFC) according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of tracking target track (aim 2) of a dual-joint mechanical arm of a gear inspection robot and track tracking based on a model conventional PD control method (PDFC) according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the attached drawings.
So that the manner in which the above recited objects, features and advantages of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments, some of which are illustrated in the appended drawings. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present invention is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
Referring to fig. 1, for an embodiment of the present invention, a method for controlling limited time delay observation of a sliding mode of a global terminal for gear inspection is provided, and the method organically and uniformly performs design of a limited time delay observation controller τ (t) of the sliding mode of the global terminal for gear inspection of the present invention by using a mathematical model of an N-joint mechanical arm of the gear inspection robot system, a time delay observer, a limited time convergence global non-singular terminal sliding mode surface, and a mixed approach law, and referring to fig. 1, the method specifically includes:
s1: based on a mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed, and a tracking error equation of the N-joint mechanical arm of the gear inspection robot system is defined.
The gear inspection robot system comprises: the system comprises an image operation center, a high-power camera and an N-joint mechanical arm.
The gear inspection robot system N joint mechanical arm mathematical model:
wherein, the left side of the equation is respectively: n-joint mechanical arm inertia force item of gear inspection robot systemCentrifugal force and coriolis force item of N-joint mechanical arm of gear inspection robot system>Gravity item G (q (t)) n×1 N-joint mechanical arm friction force item of gear inspection robot systemExternal disturbance term τ d (t)∈R n×1 ；M(q(t))∈R n×n For gear inspection robot system N joint arm inertial matrix, +.>The centrifugal force matrix and the coriolis force matrix of the N-joint mechanical arm of the gear inspection robot system are adopted; the right side of the equation is the control force term tau (t) epsilon R of the N-joint mechanical arm of the gear inspection robot system n×1 。
Based on the mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed:
wherein m (q (t))εR n×n Parameter adjustment gain matrix without physical meaning for N-joint mechanical arm model-free frame controller of gear inspection robot system, d (t) epsilon R n×1 For the uncertainty parameter and unknown external disturbance of the gear inspection robot system, the method is defined as follows:
defining the tracking error of the N joint mechanical arm of the gear inspection robot system as follows:
e(t)＝q * (t)-q(t)
wherein ,q* (t) is the target track of the N-joint mechanical arm of the gear inspection robot system, q (t) is the actual track of the N-joint mechanical arm of the gear inspection robot system, and e (t) is the tracking error of the N-joint mechanical arm of the gear inspection robot system.
Taking a second-order differential from the tracking error of the N-joint mechanical arm of the gear inspection robot system to obtain:
wherein ,is the second order derivative of e (t); />Is q * Second order differentiation of (t); />Is the second order derivative of q (t).
Defining an N-joint mechanical arm tracking error equation of the gear inspection robot system:
s2: and the delay observer is utilized to realize real-time observation compensation of the uncertainty parameters and unknown external disturbances of the gear inspection robot system.
Defining a delay observer:
wherein ,representing uncertainty parameters and unknown external disturbance estimated values of a gear inspection robot system, wherein tau (t-delta t) represents a limited time delay observation controller of a global terminal sliding mode of an N-joint mechanical arm of the gear inspection robot system at the moment t-delta t, and q (t-delta t) represents an actual track of the N-joint mechanical arm of the gear inspection robot system at the moment t-delta t>Representing the second order differential of the actual track of the N joint mechanical arm of the gear inspection robot system at the time t-delta t.
S3: based on a tracking error equation of the N-joint mechanical arm of the gear inspection robot system, a finite time convergence global nonsingular terminal sliding mode surface is constructed by combining a tracking error proportional term of the N-joint mechanical arm of the gear inspection robot system, a tracking error nonsingular terminal integral term of the N-joint mechanical arm of the gear inspection robot system and a tracking error initial term of the N-joint mechanical arm of the gear inspection robot system.
Defining a finite time convergence global nonsingular terminal sliding mode surface:
wherein ,kp e (t) represents a tracking error proportion term k of an N-joint mechanical arm of the gear inspection robot system p Is the parameter-adjusting gain of the device,representing nonsingular terminal integral term k of tracking error of N-joint mechanical arm of gear inspection robot system i P, j is the tuning gain of the gain, which satisfies the following conditions: p is p<j<2p and p, j are positive odd numbers, k p e (0) represents an initial item of tracking error of an N-joint mechanical arm of the gear inspection robot system, s 1 (t)，s 2 (t)，…，s n And (t) is a finite time convergence global nonsingular terminal sliding mode face sub-sliding mode face.
Taking first-order differentiation of the global nonsingular terminal sliding mode surface:
wherein ,is the first order differential of the sliding mode surface of the limited-time convergence global nonsingular terminal sliding mode surface.
Taking outThe finite convergence time is:
wherein ,ts Is the convergence time and c is any constant.
S4: the mixed approach law based on the power approach law and the constant-speed approach law is adopted, a limited time delay observation controller tau (t) of a global terminal sliding mode of an N-joint mechanical arm of the gear inspection robot system is designed, and the stability of the controller tau (t) is verified.
Defining the power approach law:
wherein a >0 and 1> beta >0 are tuning gains.
Defining the isokinetic approach law:
wherein b >0 is the tuning gain.
Based on the power approach law and the constant velocity approach law, defining the mixed approach law:
wherein ,
based on a delay observer, a finite time convergence global nonsingular terminal sliding mode surface and a mixed approach law based on a power approach law and a constant-speed approach law, a model-free control frame is used for designing a gear inspection robot system N joint mechanical arm global terminal sliding mode finite time delay observation controller tau (t):
the Lyapunov function is:
wherein, from a>0，b>0, then
Referring to fig. 1, which is a control schematic diagram of a limited time delay observation control method of a global terminal sliding mode of an N-joint mechanical arm of a gear inspection robot system, the method of the invention is further described, and a main control diagram process is as follows: firstly, constructing a model-free control frame based on a mathematical model of an N-joint mechanical arm of a gear inspection robot system and defining a tracking error equation of the N-joint mechanical arm of the gear inspection robot system; secondly, constructing a delay observer and a limited time convergence global nonsingular terminal sliding mode surface based on the tracking error of an N-joint mechanical arm of the gear inspection robot system; finally, designing a gear inspection robot system N joint mechanical arm global terminal sliding mode limited time delay observation controller tau (t) through a hybrid approach law.
Preferably, the embodiment also needs to explain that, compared with the prior art, the invention discloses a gear inspection global terminal sliding mode limited time delay observation control method, aiming at realizing tracking of the target track of the N joint mechanical arm of the inspection robot system by adopting a limited time convergence global nonsingular terminal sliding mode, thereby achieving the purpose of limited time convergence; the method comprises the steps that a delay observer is used for predicting uncertainty parameters and unknown external disturbances of a gear inspection robot system in real time, so that disturbance compensation of the uncertainty system is realized; and then the rapidity of the power approach law and the stability of the general constant-speed approach law are fully utilized by mixing the approach laws.
Referring to fig. 2 to 5, there is provided test verification of a gear inspection global terminal sliding mode limited time delay observation control method, including:
in order to verify and explain the technical effects adopted in the method, in the embodiment, a model-based traditional PD control method (PDFC) and the method of the invention are selected for comparison test, and the test results are compared by a scientific demonstration means to verify the true effects of the method.
In order to verify that the method has limited time convergence, delay observer compensation, mixed approach law rapidity and stability compared with the traditional method, the method adopts a global terminal sliding mode limited time delay observation control method (GTSMFTTDC), and carries out real-time measurement comparison on the output track and tracking error of the N-joint mechanical arm of the gear inspection robot system respectively in the tracking target tracks (aim 1 and aim) of the double-joint mechanical arm of the gear inspection robot system and the model-based traditional PD control method (PDFC).
Test environment: referring to fig. 1, the N-joint mechanical arm of the gear inspection robot system is operated on a simulation platform to simulate and track target tracks (aim 1 and aim) of the two-joint mechanical arm of the gear inspection robot system, and the target tracks are tested by using a global terminal sliding mode limited time delay observation control method (GTSMFTTDC) and a model-based traditional PD control method (PDFC) respectively, so as to obtain test result data. All tests are performed by starting automatic test equipment and realizing simulation test of a comparison method by using MATLAB software programming, and simulation data are obtained according to experimental results; each method tests 3 groups of data, each group of data is sampled for 10s, each group of data input track and tracking error are obtained through calculation, and the calculation error is compared with the expected target track input through simulation.
Referring to fig. 2 to 5, in order to track the target track (aim and aim) of the dual-joint mechanical arm of the gear inspection robot system, the track tracking diagram of the comparison between the global terminal sliding mode limited time delay observation control method (GTSMFTTDC) and the model-based traditional PD control method (PDFC) is provided.
Double-joint mechanical arm parameters: connecting rod 1 mass m 1 Length l of connecting rod 1 =1 kg 1 Distance l of centroid to joint 1 =1m c1 1/2m, connecting rod 1 moment of inertia I 1 =1/12 kg·m, connecting rod 2 mass m e Distance l of link 2 to joint 2 =3 kg ce =1m, connecting rod 2 moment of inertia I e =2/5 kg·m, centroid and joint 2 angle δ e Coefficient of friction e =0 1 = -7/12, gravitational acceleration e 2 ＝9.81。
Referring to fig. 2 to 5, m (q (t))= [ 1.5.0.6]，Δt＝0.003，k 1p ＝10000000，k 2p ＝300000000000，k 1i ＝20000，k 2i ＝2，p＝[3 5]，j＝[5 7]，a＝[60 3.5]，b＝[0.3 0.5]，β＝0.5，K p ＝[3 5]，K d ＝[5000 70]The global terminal sliding mode limited time delay observation control method (GTSMFTTDC) and the model-based traditional PD control method (PDFC) can be used for tracking the target track (aiml and aim) of the double-joint mechanical arm of the gear inspection robot system as a whole. The global terminal sliding mode limited time delay observation control method (GTSMFTTDC) has small tracking error, and can adaptively adjust dynamic tracking performance for different target tracks, but the model-based traditional PD control method (PDFC) has the problem of poor robustness, and is expressed as follows: as shown in fig. 4, the time is 6-10 s, a certain steady-state error exists, as shown in fig. 5, and the whole time has larger tracking deviation.
In summary, the gear inspection global terminal sliding mode limited time delay observation control method provided by the invention is superior to other methods in rapidity and self-adaptability, and is characterized in that: under a model-free control framework. The delay observer is utilized for compensation, and a global nonsingular terminal sliding mode surface with mixed approach law is constructed to be converged for a limited time, so that the rapidity and the stability are ensured.
It should be appreciated that embodiments of the invention may be implemented or realized by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer readable memory. The methods may be implemented in a computer program using standard programming techniques, including a non-transitory computer readable storage medium configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner, in accordance with the methods and drawings described in the specific embodiments. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language. Furthermore, the program can be run on a programmed application specific integrated circuit for this purpose.
Furthermore, the operations of the processes described in the present invention may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes (or variations and/or combinations thereof) described herein may be performed under control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications), by hardware, or combinations thereof, collectively executing on one or more processors. The computer program includes a plurality of instructions executable by one or more processors.
Further, the method may be implemented in any type of computing platform operatively connected to a suitable computing platform, including, but not limited to, a personal computer, mini-computer, mainframe, workstation, network or distributed computing environment, separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, and so forth. Aspects of the invention may be implemented in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and/or write storage medium, RAM, ROM, etc., such that it is readable by a programmable computer, which when read by a computer, is operable to configure and operate the computer to perform the processes described herein. Further, the machine readable code, or portions thereof, may be transmitted over a wired or wireless network. When such media includes instructions or programs that, in conjunction with a microprocessor or other data processor, implement the steps described above, the invention includes these and other different types of non-transitory computer-readable storage media. The invention also includes the computer itself when programmed according to the methods and techniques of the present invention. A computer program can be applied to the input data to perform the functions described herein to convert the input data to generate output data that is stored to the non-volatile memory. The output information may also be applied to one or more output devices such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on a display.
The above description is merely of preferred embodiments of the present invention, and the scope of the present invention is not limited to the above embodiments, but all equivalent modifications or variations according to the present disclosure will be within the scope of the claims.
Claims (7)
1. A gear inspection global terminal sliding mode limited time delay observation control method is characterized in that: the method comprises the following steps:
s1, constructing a model-free control frame based on a mathematical model of an N-joint mechanical arm of a gear inspection robot system and defining a tracking error equation of the N-joint mechanical arm of the gear inspection robot system;
s2, utilizing a delay observer to realize real-time observation compensation of uncertainty parameters and unknown external disturbances of the gear inspection robot system;
s3, based on a tracking error equation of an N-joint mechanical arm of the gear inspection robot system, constructing a finite time convergence global nonsingular terminal sliding mode surface by combining a tracking error proportional term of the N-joint mechanical arm of the gear inspection robot system, a tracking error nonsingular terminal integral term of the N-joint mechanical arm of the gear inspection robot system and a tracking error initial term of the N-joint mechanical arm of the gear inspection robot system;
s4, designing a limited time delay observation controller tau (t) of a global terminal sliding mode of an N-joint mechanical arm of the gear inspection robot system by adopting a mixed approach law based on a power approach law and a constant-speed approach law.
2. The method for controlling limited time delay observation of a sliding mode of a gear inspection global terminal according to claim 1, which is characterized by comprising the following steps: in step S1, the gear inspection robot system includes: the system comprises an image operation center, a high-power camera and an N-joint mechanical arm.
3. The method for observing and controlling the limited time delay of the sliding mode of the gear inspection global terminal according to any one of claims 1 to 2 is characterized by comprising the following steps: in step S1, the mathematical model of the N-joint mechanical arm of the gear inspection robot system is as follows:
wherein, the left side of the equation is respectively: n-joint mechanical arm inertia force item of gear inspection robot systemCentrifugal force and coriolis force item of N-joint mechanical arm of gear inspection robot system>Gravity item G (q (t)) n×1 N-joint mechanical arm friction force item of gear inspection robot systemExternal disturbance term τ d (t)∈R n×1 ；M(q(t))∈R n×n For gear inspection robot system N joint arm inertial matrix, +.>The centrifugal force matrix and the coriolis force matrix of the N-joint mechanical arm of the gear inspection robot system are adopted; the right side of the equation is the control force term tau (t) epsilon R of the N-joint mechanical arm of the gear inspection robot system n×1 ；
Based on the mathematical model of the N-joint mechanical arm of the gear inspection robot system, a model-free control frame is constructed:
wherein m (q (t))εR n×n Model-free frame controller-free object for N-joint mechanical arm of gear inspection robot systemParameter-regulating gain matrix with rational meaning, d (t) E R n×1 For the uncertainty parameter and unknown external disturbance of the gear inspection robot system, the method is defined as follows:
defining the tracking error of the N joint mechanical arm of the gear inspection robot system as follows:
e(t)＝q * (t)-q(t)
wherein ,q* (t) is a target track of the N-joint mechanical arm of the gear inspection robot system, q (t) is an actual track of the N-joint mechanical arm of the gear inspection robot system, and e (t) is a tracking error of the N-joint mechanical arm of the gear inspection robot system;
taking a second-order differential from the tracking error of the N-joint mechanical arm of the gear inspection robot system to obtain:
wherein ,is the second order derivative of e (t); />Is q * Second order differentiation of (t); />Is the second order derivative of q (t);
defining an N-joint mechanical arm tracking error equation of the gear inspection robot system:
4. a method for controlling sliding mode limited time delay observation of a gear inspection global terminal according to any one of claims 1 to 3, which is characterized in that: in step S2, a delay observer is defined:
wherein ,representing uncertainty parameters and unknown external disturbance estimated values of a gear inspection robot system, wherein tau (t-delta t) represents a limited time delay observation controller of a global terminal sliding mode of an N-joint mechanical arm of the gear inspection robot system at the moment t-delta t, and q (t-delta t) represents an actual track of the N-joint mechanical arm of the gear inspection robot system at the moment t-delta t>Representing the second order differential of the actual track of the N joint mechanical arm of the gear inspection robot system at the time t-delta t.
5. A method for controlling sliding mode limited time delay observation of a gear inspection global terminal according to any one of claims 1 to 3, which is characterized in that: in step S3, defining a finite time convergence global nonsingular terminal sliding mode surface:
s(t)＝[s 1 (t) s 2 (t)…s n (t)] T
k p ＝diag[k 1p k 2p …k np ] T
k i ＝diag[k 1i k 2i …k ni ] T
e(t)＝[e 1 (t) e 2 (t)…e n (t)] T
e p/j (t)＝[e 1 p/j (t) e 2 p/j (t)…e n p/j (t)] T
e(0)＝[e 1 (0) e 2 (0)…e n (0)] T
wherein ,kp e (t) represents a tracking error proportion term k of an N-joint mechanical arm of the gear inspection robot system p Is the parameter-adjusting gain of the device,representing nonsingular terminal integral term k of tracking error of N-joint mechanical arm of gear inspection robot system i P, j is the tuning gain of the gain, which satisfies the following conditions: p is p<j<2p and p, j are positive odd numbers, k p e (0) represents an initial item of tracking error of an N-joint mechanical arm of the gear inspection robot system, s 1 (t)，s 2 (t)，…，s n (t) is a finite time converging global nonsingular terminal sliding mode face sub-sliding mode face;
taking first-order differentiation of the global nonsingular terminal sliding mode surface:
wherein ,the first-order differentiation of the sliding mode surface of the global nonsingular terminal is converged in limited time;
taking outThe finite convergence time is:
wherein ,ts Is the convergence time and c is any constant.
6. The method for observing and controlling the limited time delay of the sliding mode of the gear inspection global terminal according to any one of claims 1 to 5 is characterized by comprising the following steps: in step S4, the power approach law is defined:
wherein a >0 and 1> beta >0 are tuning gains;
defining the isokinetic approach law:
wherein b >0 is the tuning gain;
based on the power approach law and the constant velocity approach law, defining the mixed approach law:
wherein ,
7. the method for observing and controlling the limited time delay of the sliding mode of the gear inspection global terminal according to any one of claims 1 to 6 is characterized by comprising the following steps: in step S4, a gear inspection robot system N-joint mechanical arm global terminal sliding mode limited time delay observation controller τ (t) is designed by a model-free control frame based on a delay observer, a limited time convergence global nonsingular terminal sliding mode surface, and a hybrid approach law based on a power approach law and a constant velocity approach law:
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