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CN-122008214-A - Tracking control method for flexible mechanical arm under preset time

CN122008214ACN 122008214 ACN122008214 ACN 122008214ACN-122008214-A

Abstract

The invention provides a tracking control method for a flexible mechanical arm under preset time, which comprises the steps of considering coupling effects comprising link dynamics and motor actuator dynamics, establishing a high-order nonlinear dynamics model of the single-link flexible joint mechanical arm based on an Euler-Lagrange equation, defining a tracking error of the flexible mechanical arm and an adaptive filter to achieve error convergence in a limited time, establishing a preset time function and an obstacle Lignomf function, establishing an error conversion function, converting the tracking error constraint into unconstrained, and constructing and updating an actual controller of the flexible mechanical arm according to the adaptive filter, the error conversion function, the preset time function and the obstacle Lignomf function. The method and the device can ensure that the flexible mechanical arm can track the target track with high precision within the preset time arbitrarily appointed by the user, and all signals in the closed loop system are kept bounded.

Inventors

  • PENG JIGUANG
  • LIU ZHI

Assignees

  • 广东工业大学
  • 人工智能与数字经济广东省实验室(广州)

Dates

Publication Date
20260512
Application Date
20260213

Claims (10)

  1. 1. A tracking control method for a flexible mechanical arm at a preset time, comprising: considering a coupling effect comprising link dynamics and motor actuator dynamics, and establishing a high-order nonlinear dynamics model of the single-link flexible joint mechanical arm based on an Euler-Lagrange equation so as to describe a state conversion relation among the link position, the link speed, the motor rotor position and the motor rotor speed of the flexible mechanical arm; defining a tracking error and an adaptive filter of the flexible mechanical arm to realize error convergence in a limited time; Constructing a preset time function and a barrier Libypriv function, establishing an error conversion function, and converting tracking error constraint into unconstrained; And constructing and updating an actual controller of the flexible mechanical arm according to the self-adaptive filter, the error conversion function, the preset time function and the combined barrier Liziplov function.
  2. 2. The tracking control method for a flexible mechanical arm at a preset time according to claim 1, wherein the consideration includes a coupling effect of link dynamics and motor actuator dynamics, and the establishing a high-order nonlinear dynamics model of the single-link flexible joint mechanical arm based on the euler-lagrangian equation includes: the high-order nonlinear dynamics model of the single-link flexible joint mechanical arm is expressed as follows: ; ; Wherein, the Respectively representing the position, the speed and the acceleration vectors of the connecting rod; respectively representing the angular position, angular velocity and angular acceleration vector of the rotor; representing an inertia matrix; Representing the coriolis force and centrifugal force terms; Representing a gravity vector; representing friction terms, positive definite diagonal matrix Respectively corresponding to joint flexibility, actuator inertia and inherent damping items; Representing the torque input to each actuator.
  3. 3. The tracking control method for a flexible mechanical arm at a preset time according to claim 1, wherein the defining the tracking error of the flexible mechanical arm includes: The dynamic model taking into account the reference trajectory signal is expressed as: ; ; Wherein, the Representing a reference output signal; representing the derivative of the reference output signal, function Representing a function that is known to be smooth and bounded; The error variable configuration is expressed as: ; ; ; Wherein, the Representing the filter output signal; The virtual controller is represented by a virtual controller, Representing the filter error.
  4. 4. The tracking control method for a flexible mechanical arm at a preset time according to claim 1, wherein the adaptive filter includes: the adaptive filter is expressed as: ; ; ; Wherein, the Representing the filter output signal; representing a virtual control signal to be filtered; representing a time-varying adaptive filter gain; 、 、 are all preset positive design parameters; representing flexible mechanical arm No The filter initial value of the order, s=1, 2,3.
  5. 5. The tracking control method for a flexible mechanical arm at a preset time according to claim 1, wherein the constructing a preset time function includes: The preset time function is expressed as: ; Wherein, the , Representing an initial value of the function; representing a stable error range after the preset time is reached; The preset time is set; Representing a convergence rate adjustment parameter; representing the singular order; is positive parameter, s represents the first The filter initial value of the order.
  6. 6. The tracking control method for a flexible mechanical arm at a preset time according to claim 1, wherein the barrier li-epstein function comprises: establishing a barrier li epruff function that is not constrained by the initial error conditions is expressed as: ; Wherein, the Is that In shorthand form, define a tight set The starting position moment, So that ; If and only if Or alternatively Then Representing tracking error Finally is constrained to Within the range; Wherein, the Representing a preset time function of the design; is an error variable not constrained by an initial value; Is that Is set to an initial value of (1); Is that Is set to be a constant value.
  7. 7. The tracking control method for a flexible mechanical arm at a preset time according to claim 1, wherein the constructing an error transfer function includes: error transfer function Expressed as: ; Wherein, the Representing a preset switching adjustment time, and Representing a waveform shaping constant; Representing a convergence rate adjustment positive parameter; t is the system run time.
  8. 8. The tracking control method for a flexible mechanical arm at a preset time according to claim 1, wherein the constructing and updating the actual controller of the flexible mechanical arm according to the adaptive filter, the error transfer function, the preset time function, and the combined barrier li-epruff function includes: the 1 st order virtual controller of the flexible mechanical arm is expressed as: ; Wherein, the Representing leader signals Is the first derivative of (a); Representing a preset positive parameter; 2 nd-order virtual controller and self-adaptive law of flexible mechanical arm Expressed as: ; The corresponding adaptive law is expressed as: ; Wherein, the ; Representation of Is a function of the estimated value of (2); ; all expressed as designable positive parameters; Representation of ; Representing a 2 nd order error variable; representing a basis function vector; The 3 rd order virtual controller of the flexible mechanical arm is expressed as: ; Wherein, the Representing a preset positive parameter; representing a3 rd order error variable; Representing the first derivative of the 3 rd order filter signal; actual controller of flexible mechanical arm And adaptive rate The method comprises the following steps: ; ; Wherein, the 、 And Is a preset positive parameter; ; Representing the first derivative of the 3 rd order filter signal; Representing the 4 th order error variable, and S4 represents the basis function vector.
  9. 9. An electronic device for tracking control of a flexible mechanical arm at a preset time, comprising: A storage medium for storing a computer program, A processing unit, which is used for exchanging data with the storage medium, and executing the computer program by the processing unit when the tracking control is performed for the preset time of the flexible mechanical arm, so as to perform the steps of the tracking control method for the preset time of the flexible mechanical arm according to any one of claims 1-8.
  10. 10. A computer-readable storage medium, characterized by: the computer readable storage medium has a computer program stored therein; The computer program, when run, performs the steps of the tracking control method for a flexible mechanical arm at a preset time according to any one of claims 1-8.

Description

Tracking control method for flexible mechanical arm under preset time Technical Field The disclosure relates to the technical field of tracking control of flexible mechanical arms, and in particular relates to a tracking control method for a flexible mechanical arm under preset time. Background In recent years, with the continuous improvement of the requirements of the fields such as aerospace, high-end manufacturing, medical operation and the like on the performance of robots, the flexible mechanical arm gradually replaces the traditional rigid mechanical arm by virtue of the remarkable advantages of light weight, high strength, low energy consumption, sensitive operation, high load self weight ratio and the like, and becomes an important development direction of the new generation of robot technology. For example, flexible robotic arms exhibit great potential for use in the context of in-orbit assembly of large space stations, rapid mounting of precision electronic components, and the like. However, the flexible mechanical arm is a typical distributed parameter system, has the characteristics of strong coupling, nonlinearity, underactuation and the like, and the connecting rod and the joint of the flexible mechanical arm are easy to generate residual vibration in high-speed motion. Therefore, how to realize high-precision track tracking and vibration active suppression of the flexible mechanical arm is a key problem to be solved urgently in the field of control engineering. Although the existing control theory has achieved a certain result, the flexible mechanical arm control in practical engineering application still faces various technical bottlenecks. In the existing flexible mechanical arm control method, requirements for meeting tracking error precision and vibration suppression in a preset time range are generally lacked to be considered. Most of the existing control strategies (such as PID, traditional sliding mode control and the like) can only ensure that the system state is gradually converged in infinite time, or the convergence time is often severely dependent on the initial pose of the mechanical arm and the controller parameters although finite time convergence is realized, so that the upper bound of the convergence time is difficult to accurately preset and adjust. When tasks extremely sensitive to time efficiency such as quick sorting of a production line and grabbing of a spacecraft are executed, if the mechanical arm cannot be guaranteed to converge joint angle errors and elastic vibration of a connecting rod to a preset precision range within preset time designated by a user, the production takt is directly influenced, and even the tasks fail. Moreover, in the existing output constraint control research for the flexible mechanical arm, the assumption premise of comparatively idealization is generally based, namely that the initial tracking error of the system is required to be strictly within a preset performance constraint range. However, in practical engineering applications, the initial state of the flexible mechanical arm is often random and uncertain due to complex operation environment interference (such as abrupt load change) and task diversity. For example, when restarting or switching control modes after emergency braking of the system, a situation that the tracking error at the initial moment exceeds the preset performance function boundary is very easy to occur. The existing control strategy mostly depends on the precondition that the initial state meets constraint, once the precondition fails, the preset performance of the system cannot be guaranteed, even the system instability caused by the singular problem of a controller can be possibly caused, and the complex scene that the initial condition is completely unknown or not constrained in the whole course is difficult to adapt to. In addition, under the back-push control framework, for high-order systems such as flexible joints or flexible connecting rods, the problem of 'calculation complexity explosion' is brought by repeated analysis and derivation of a virtual control law along with the increase of system orders, and the realization of a real-time controller is severely restricted. Although dynamic surface control techniques have been introduced to alleviate this problem by using first order low pass filters instead of differential operations, existing dynamic surface technology architectures generally employ fixed parameter linear filters. To meet the high accuracy requirements of flexible systems for filtering errors, it is often necessary to set the time constant of the filter to a minimum value. However, such extremely small time constants can cause significant "peaking" at the moment of arm start-up, creating a large transient overshoot. This can lead to amplitude saturation or rate saturation of the servo motor, which in severe cases can even damage the actuator or excite more severe structural resonances. Due to