Partial differential equation modeling and vibration control for a nonlinear 3D rigid‐flexible manipulator system with actuator faults

Abstract

In this paper, modeling and controlling problem for a two-link rigid-flexible manipulator in three-dimensional (3D) space is studied under actuator faults. For modeling, the dynamics of the 3D mechanical system is represented by nonlinear partial differential equations, which is first derived in infinite dimension form. Based on the nonlinear model, the controller is proposed, which can achieve joint angle control and vibration suppression control in the presence of actuator faults. The stability analysis of the closed-loop system is given based on LaSalle invariance principle. Numerical simulations illustrate the effectiveness of the proposed controller. This study will promote the development of nonlinear flexible manipulator systems in 3D space. KEYWORDS actuator faults, nonlinear PDE model, two-link rigid-flexible manipulator, 3D space Int J Robust Nonlinear Control. 2019;29:3793-3807.wileyonlinelibrary.com/journal/rnc

Tangent barrier Lyapunov function‐based constrained control of flexible manipulator system with actuator failure

“…A great deal of researches have been carried out to avoid this problem. [30][31][32][33][34] For a class of dynamic systems with unknown actuator faults, a fault-tolerant controller is designed in Reference 35 to solve the problem. Aiming at the uncertain faults of the rigid-flexible coupling system in Reference 36, a novel fault-tolerant control strategy is put forward on the basis of the sliding mode control method of backstepping.…”

Boundary Control of A Flexible Rotatable Manipulator in Three-Dimensional Space With Input Constraints and Actuator Faults

“…Considering flexible spacecraft, Ji, Liu [29] design an adaptive distributed control scheme to suppress the deformation and ensure the system stable in the presence of actuator fault. Vibration control with actuator faults is addressed to eliminate the deformation of the two-link rigid-flexible manipulator [30]. However, the works mentioned above are about the researches on input constraint and actuator fault tolerance respectively.…”

Disturbance observer‐based adaptive boundary iterative learning control for a rigid‐flexible manipulator with input backlash and endpoint constraint

“…The flexible structure is usually modeled into distributed parameter systems described by partial differential equation (PDE). However, the flexible part modeled by PDE with infinite dimensions is more difficult for control design comparing with the rigid part 6‐9 …”

“…To tackle the aforementioned problem, researchers investigated the PDE control of the flexible manipulator, because their models contain the infinite‐dimensional modes and overcome spillover instability 6 . Recently, boundary control strategy has been widely proposed for addressing flexible structure systems in order to avoid the spillover effects of the truncated model‐based control 6‐8 . In Reference 8, based on the Lyapunov's direct method, boundary control is designed for ensuring the stability of the Timoshenko beam system and copying with the input dead‐zone.…”

“…Another boundary output feedback law is proposed to reject general external disturbance for Euler‐Bernoulli beam systems in Reference 9. Although the boundary control has been studied widely for flexible systems, few studies have addressed for a two‐link rigid‐flexible manipulator 4‐6 . To make up the partial loss of actuators effectiveness, an adaptive boundary compensation control for the rigid‐flexible manipulator is studied in Reference 4.…”