Fixed-Time Tracking Control for Flexible Joint Manipulator With Prescribed Performance Constraint

Abstract

This paper studies the transient and steady performance constraints on flexible joint manipulator system with exogenous disturbance, and proposes a fixed-time prescribe performance tracking control method based on the singular perturbation model. For the fast subsystem, a subcontroller with superior transient performance is proposed that guarantees the suppression of flexible vibration in fixedtime. The remaining slow subsystem can be linked with rigid methods to achieve output constraints, a type of time-varying error constraint boundary is first constructed, which broadens the initial error constraint boundary of the time-varying tangent barrier Lyapunov function. Then, a slow subcontroller based on a nonsingular fast-integration terminal sliding mode is constructed to make any initial tracking error converge in fixed-time. Finally, a nonlinear disturbance observer is used to counteract the exogenous disturbance. The simulation results show that the controller achieves the prescribe performance.

Identification and Control of Flexible Joint Robots Based on a Composite-Learning Optimal Bounded Ellipsoid Algorithm and Prescribe Performance Control Technique

“…This paper aims to ensure the angular position of joints, q, accurately tracking a designated reference, q d , while meeting pre-specified transient and steady-state performance criteria. Leveraging the singular perturbation technique (SPT), the high-order singular perturbation model ( 7) is successfully decomposed into two lower-order subsystems: (9) and (12). According to Tikhonov's theory [36], controlling these reduced-order subsystems suffices to solve the trajectory tracking problem for the original system, thereby simplifying the controller design process.…”

“…Another study by Sun et al [11] introduced a nonlinear hybrid control scheme for a redundant parallel robot system, leveraging SPT and Tikhonov's theorem to achieve both trajectory tracking and vibration suppression. Chen et al proposed a prescribed performance controller for FJRs with exogenous disturbances, incorporating SPT and a time-varying tangent barrier Lyapunov function to expand the initial error constraint boundary [12]. However, these methods fail to identify and compensate for unknown dynamics in FJRs, resulting in relatively large control errors.…”

Fast luffing control of flexible boom of mobile elevated work platform with uncertain control input gain

“…Among various feedback control methods, because the structure of the single-link flexible manipulator is relatively simple, model-based control methods have been widely studied, such as singular perturbation method, 15–17 sliding mode control, 18–20 robust control, 21,22 LQR, 23,24 etc. In these literatures, the mathematical model of flexible manipulator is established by homogeneous beam or concentrated mass.…”