Tip position control of flexible single‐link manipulators in the frequency domain without model reduction

Abstract

This article develops the fundamentals of the tip position control of flexible single‐link robotic manipulators in the frequency domain without approximating the model. Analytic transfer functions of the hub angle and tip position are derived without any model order reduction. Conditions for the stability of the transfer functions are presented by considering the payload mass change as an uncertain parameter. Using the D‐decomposition method, a simple procedure is introduced to design an output feedback controller which guarantees the stability and a desired tracking performance. The introduced design method leads to less conservatism comparing with design methods established upon model reduction. The controller structure includes two proportional‐derivative and integral loops and needs only two measurements of joint angle and tip position which are easily implementable. A numerical example is provided to demonstrate the merit of the achieved results.

An intelligent control method for a flexible-link manipulator with uncertain backlash and model uncertainty

“…In [6], a solution was proposed for controlling such a manipulator in the frequency domain using a full-order transfer function model. In [7], a novel approach was developed to control the tip position of a flexible single-link manipulator in the frequency domain. In this study, a single-link flexible manipulator was also selected for control research.…”

“…Consequently, there is an urgent need to develop effective vibration control methods to stabilize flexible manipulators. A single-link flexible manipulator is the most typical model among flexible manipulators [6,7]. In [6], a solution was proposed for controlling such a manipulator in the frequency domain using a full-order transfer function model.…”