Open-Closed-Loop PD Iterative Learning Control Corrected With the Angular Relationship of Output Vectors for a Flexible Manipulator

Jian Dong,Bin He,Chenghong Zhang,Ming Ma,Gang Li

doi:10.1109/access.2019.2930559

Abstract

A new iterative learning control (ILC) approach combined with an open-closed-loop PD scheme is presented for a flexible manipulator with a repeatable motion task in the case that only the endpoint pose of the flexible link is measurable. This approach takes advantage of the fact that the ILC performance is independent of the model used, thereby overcoming the drawback of the heavy reliance of PD controllers on the modeling accuracy. The open-closed-loop PD controller is mainly used to simultaneously reduce the effects of the modeling error and disturbances to enhance the controller's robustness. Meanwhile, an angular correction term is introduced by using the angular relationship of the system outputs to reward or penalize the ILC law. Specifically, when the current output tends toward the expected trajectory, the ILC law is enhanced accordingly; otherwise, it is penalized. The convergence conditions for the proposed approach are obtained through theoretical analysis, and experiments using a real flexible manipulator are presented. The results show that the proposed ILC scheme can overcome the impact of the endpoint error caused by link flexibility and has a good control effect.

Highlights

A flexible manipulator [1]–[3] consisting of light, flexible rods offers several advantages over traditional rigid manipulators [4]–[7], including a higher ratio of load to mass, lower inertia, and a faster system response
A flexible manipulator is a non-minimum-phase system with high nonlinearity and a high coupling uncertainty; trajectory tracking is very difficult
These plots clearly demonstrate that the proposed algorithm can ensure lower tracking errors and faster convergence rates in comparison with the traditional open-closed-loop PD-iterative learning control (ILC)

Summary

INTRODUCTION

A flexible manipulator [1]–[3] consisting of light, flexible rods offers several advantages over traditional rigid manipulators [4]–[7], including a higher ratio of load to mass, lower inertia, and a faster system response. Iterative learning methods reduce the requirements for the system accuracy and can compensate for the inadequacy of a flexible manipulator model. K =1 where S is the cross-sectional area of the rod, ρ is the volume density, qk (t) represents the elastic mode coordinates, ωk (x) are the modal functions, γk are the position vectors of the arm, τ is the driving torque acting on the flexible mechanical arm, Ir is the moment of inertia of the motor rotor with respect to the rotor centerline, θ (t) is the angular acceleration of the rigid body motion, t is the time variable, and k is the order of the equation.

CONVERGENCE ANALYSIS

EXPERIMENT

CONCLUSION