End‐Point Regulation and Vibration Suppression of a Flexible Robotic Manipulator

Abstract

In this paper, end‐point regulation and vibration suppression are investigated for a flexible robotic manipulator subject to the external disturbances. The dynamics of the flexible robotic manipulator is represented by one partial differential equation (PDE) and five ordinary differential equations (ODEs). Based on the Lyapunov's direct method, boundary control is developed to drive the manipulator to the desired set‐point and simultaneously suppress the vibrations of the flexible manipulator. Considering the unknown spatiotemporally varying disturbance, uniform boundedness of the closed‐loop system is achieved. The control performance of the closed‐loop system is guaranteed by suitably choosing the design parameters. Simulations are provided to illustrate the effectiveness of the proposed control.

Sliding Mode Control for an Inhomogeneous Heat Equation with Global Constraint

“…Theorem 1. For the system dynamics described by (4) and boundary conditions (5) and (6), under Assumptions 1, 2, and the designed control (20), if the initial conditions are bounded, then ‖s(x, t)‖ 2 is uniformly bounded.…”

“…Motivated by applications in many industrial or chemical processes, control for PDE processes has been well documented [1][2][3][4][5]. The infinite-dimensional systems [6][7][8][9] that modeled by the coupled PDEs-ODEs commonly exist in practical applications, such as crane cables [10], flexible manipulators [11][12][13][14], moving materials [15,16], flexible wings for aircraft [17] and aerial refueling systems [18].…”

Implementation of second order sliding mode disturbance observer for a one-link flexible manipulator using Dspace Ds1104

“…Several studies [5,6] have discussed the modeling issues and active control strategies of flexible manipulators, and both, rigid body and flexible motion are always considered either for their modeling or for their control/ observation schemes setting up [7]. In order to model a flexible manipulator, it is more convenient to use the energy approach via the assumptions of a Newton-Euler beam.…”

Analysis, Verification and Comparison on Feedback‐Aided MA Equivalence and Zhang Equivalency of Minimum‐Kinetic‐Energy Type for Kinematic Control of Redundant Robot Manipulators

“…They are similar to the human arm, elephant trunk and snake in the real world [17,18,24]. A fundamental issue in controlling redundant robot manipulators is the redundancy-resolution problem, which is related to the kinematic control of redundant robot manipulators and has attracted extensive attention in scientific researches and engineering applications [1,2,6,[14][15][16][17][18][19][20][21][25][26][27]. The general description of such a redundancy-resolution problem is that, given the desired end-effector Cartesian path r d (t) ∈ R m , the corresponding joint trajectory (t) ∈ R n needs to be generated in real time t. The conventional solution to the redundancy-resolution problem is the pseudoinverse-based method, which is formulated as one minimum-norm particular solution plus a homogeneous solution [21][22][23].…”