Boundary control for PDE flexible manipulators: Accommodation to both actuator faults and sensor faults

Abstract

This paper focuses on the controller design and vibration elimination for a flexible single-link manipulator. The flexible single-link manipulator considered in this paper is described by partial differential equations (PDEs).Considering actuator faults and sensor faults simultaneously, a novel boundary controller is designed for the flexible manipulator system. The actuator faults are special since the control directions are unknown. In the proposed controller, the Nussbaum-type function is used, and an adaptive law is applied. The system performance analysis is given with the aid of Lyapunov approach, and the closed-loop PDE system is guaranteed to have semi-global uniform ultimate boundedness (SGUUB). In simulation, several cases are carried out to validate the effectiveness of the proposed controller, under actuator faults and sensor faults.

Iterative Learning Tracking Control for a Vehicle-Manipulator System With Input Constraint

“…Remark 1: Unlike most of the control research on robotic manipulators [1]- [8], [11]- [13], [20], [22], [26], [28], [30], [31], in this study, a mobile vehicle-manipulator system with constant-tension, saturation constraint and disturbance uncertainty is studied. ILC incorporated with adaptive technology is applied to address the tracking control and saturation nonlinearities issues, where two saturation functions and two hyperbolic tangent functions are adopted to handle with the saturation constraint and an adaptive law is utilized to cope with uncertain disturbances.…”

“…The control problem is discussed for an axially moving accelerated/decelerated system in [29], where an auxiliary system is applied to ensure constraint satisfaction. In [30], the actuator faults and sensor faults issues are solved si-multaneously for a single-link manipulator through the comprehensive application of Nussbaum function and adaptive technology. Although great attention has been paid to input constraints studies, there is little work on mobile vehiclemounted flexible manipulator with saturation nonlinearity, let alone to integrate ILC, hyperbolic tangent function and saturation function aiming at stabilizing such a closed-loop control system and guaranteeing the learning convergence, which motivates this study.…”

Nussbaum function‐based adaptive boundary control for flexible manipulator with unknown control directions and nonlinear time‐varying actuator faults

“…Remark There are several existing results on the control of flexible manipulators modeled using PDEs. In References 18 and 28, researchers investigated angle tracking and vibration control issues. Literature 18 considers unknown control directions and assumes that the actuators are fault‐less.…”

“…The authors in Reference 27 proposed an adaptive fault‐tolerant control scheme for a PDE based riser‐vessel system model to compensate for multiplicative actuator faults. An adaptive control strategy was developed to deal with the reduced effectiveness of single‐link flexible manipulators (modeled by PDEs) caused by a damaged actuator 28 . In Reference 29, a robust adaptive control strategy was developed using cascade ODEs and PDEs to achieve control goals, whether the actuator suffers from multiplicative or additive faults.…”

“…Unlike the Nussbaum function‐based PDE control strategies proposed in References 18‐20 that only consider the unknown control directions given the assumption that the actuators are fault‐free, this study develops a novel controller by applying Nussbaum functions with fast growth rates that can simultaneously compensate for the uncertainty caused by multiple unknown control directions, actuator faults, and external disturbances. In particular, the unknown actuator failures considered in this study vary with time. Unlike the existing results obtained in fault‐tolerant control of flexible systems (designed using PDEs), where the fault parameters are modeled to be time‐invariant, 27‐29 this study investigates tracking and vibration control issues of flexible manipulators with nonlinear time‐varying actuator faults, that is, where the multiplicative and additive fault parameters are time‐varying. Compared with time‐invariant faults, the time‐varying faults addressed in this study are more in line with practical engineering. An innovative Nussbaum function‐based adaptive boundary control scheme is proposed for flexible manipulators based on a PDE model with angle and vibrations.…”