Hybrid vibration and rest-to-rest control of a two-link flexible robotic arm using H∞ loop-shaping control design

Abstract

Purpose This study presents a method for simultaneous motion and vibration control of light-weight slender robotic arms, known as flexible manipulators. In this paper, a new control algorithm is proposed for a two-link manipulator with elastic links. Design/methodology/approach The controller includes a MIMO H∞ Loop-Shaping Design (H∞LSD) as the feedback controller, and a command pre-shaping filter as the feed-forward controller. The conventional inputs and outputs of a typical two-link manipulator , that consists of the torques applied by the actuators at the joints, and the joint angles are chosen for the feedback control. Findings It is shown that by selecting a proper desired loop shape, the H∞LSD is able to control the joint angles of the manipulator, and simultaneously, suppress vibrations of the system so that the high frequency chatter due to the structural vibration modes does not appear at the outputs. Then it is shown that when the H∞LSD is equipped with a command pre-shaping filter, more efficient suppression of the chatter at the tip of the manipulator is achieved. The capability and effectiveness of the proposed control strategy in driving and stabilizing the manipulator to desired positions and simultaneously suppressing structural vibrations is shown by the simulation of the flexible manipulator in rest-to-rest maneuvers. Practical implications Flexible Manipulator, Space Manipulators Originality/value A robust MIMO controller is proposed for simultaneous motion and vibration control of flexible manipulator.

Review of modelling and control of flexible-link manipulators

“…Commonly, in the FE models which were used for FLM modelbased control design, each link is modelled with one FE beam element. Sayahkarajy et al 55 proposed modelling of TLFMs using high-resolution FE meshes followed by a modal-order reduction. They proposed a robust control algorithm for rest-to-rest manoeuvring and vibration control of the TLFM.…”

Robust H-Inf Phase Control for Flexible System With Weak Damping

“…Adaptive control can also solve the control problem of systems with uncertainties [6], [7]. H-inf control is widely used in the control problem of this kind of flexible system with uncertainty [8], [9], [10]. For the widely existing flexible system with weak damping, because it is more convenient to use coprime factor perturbations to describe this system so the H-inf loop forming method based on coprime factor perturbations is often used for weakly damped flexible system.…”

H∞Optimization-based robust decoupling control algorithm in linear parameter varying systems using Hadamard weighting

“…Particularly to ensure stability and peformance objectives regardless of bounded difference between nominal plant and actual plant. In the past, Hilel et al (1992), and more recently, Sayahkarajy et al (2016), have demonstrated that H ∞ loop shaping-based design is an attractive approach to achieve robust tracking performance in presence of external disturbances. It is also an excellent control technique to design decoupled control system as it relies on a two-step precedure; that is, firstly, the plant is shaped to the desired frequency spectrum and then the controller is designed to minimize the worst closed-loop gain for disturbance rejection after selecting appropriate performance weights.…”