Global asymptotic stability of the PD control with computed feedforward in closed loop with robot manipulators

1999 ◽  
Vol 32 (2) ◽  
pp. 683-688 ◽  
Author(s):  
Victor Santibañez ◽  
Rafael Kelly
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Robot Manipulators ◽  
Pd Control

PD control with feedforward compensation for robot manipulators: analysis and experimentation

Robotica ◽  
2001 ◽  
Vol 19 (1) ◽  
pp. 11-19 ◽  
Author(s):  
Victor Santibañez ◽  
Rafael Kelly
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Classical Model ◽  
Experimental Tests ◽  
Torque Control ◽  
Direct Drive ◽  
Pd Control ◽  
Control Scheme

One of the simplest and natural appealing motion control strategies for robot manipulators is the PD control with feedforward compensation. Although successful experimental tests of this control scheme have been published since the beginning of the eighties, the proof of global asymptotic stability has remained unattended until now. The contribution of this paper is to prove that global asymptotic stability can be guaranteed provided that the proportional and derivative gains are adequately selected. The performance of the PD control with feedforward compensation evaluated on a two degrees-of-freedom direct-drive arm appears as fine as the classical model-based computed torque control scheme.

Stabilization of Nonlinear Strict-Feedback Systems With Time-Varying Delayed Integrators

2011 ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Loop System ◽  
Time Varying ◽  
Feedback Systems ◽  
Closed Loop System ◽  
Feedback Form ◽  
Globally Asymptotically Stable ◽  
Strict Feedback

We consider nonlinear systems in the strict-feedback form with simultaneous time-varying input and state delays, for which we design a predictor-based feedback controller. Our design is based on time-varying, infinite-dimensional backstepping transformations that we introduce, to convert the system to a globally asymptotically stable system. The solutions of the closed-loop system in the transformed variables can be found explicitly, which allows us to establish its global asymptotic stability. Based on the invertibility of the backstepping transformation, we prove global asymptotic stability of the closed-loop system in the original variables. Our design is illustrated by a numerical example.

Global Asymptotic Stability of PD Control for PM Stepper Motor Servo-Systems

2011 ◽  
Vol 14 (5) ◽  
pp. 1449-1457 ◽  
Author(s):  
R. V. Carrillo-Serrano ◽  
V. M. Hernández-Guzmán ◽  
V. Santibáñez
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Stepper Motor ◽  
Pd Control ◽  
Servo Systems

Asymptotic Stabilization of Delayed Systems with Input and Output Saturations

2017 ◽  
Vol 6 (2) ◽  
pp. 63
Author(s):  
Adel Mahjoub ◽  
Nabil Derbel
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Delayed Systems ◽  
Asymptotic Stabilization ◽  
Input And Output ◽  
Delayed System ◽  
The Stability

We consider in this paper the problem of controlling an arbitrary linear delayed system with saturating input and output. We study the stability of such a system in closed-loop with a given saturating regulator. Using inputoutput stability tools, we formulated sufficient conditions ensuring global asymptotic stability.

scholarly journals An asinh-type regulator for robot manipulators with global asymptotic stability

Automatika ◽  
2020 ◽  
Vol 61 (4) ◽  
pp. 574-586
Author(s):  
Fernando Reyes-Cortes ◽  
Basil M. Al-Hadithi
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Robot Manipulators

A relaxed structural mechanics and fuzzy control for fluid–structure dynamic analysis

2019 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tim Chen ◽  
Safiullahand Khurram ◽  
CYJ Cheng
Keyword(s):  
Asymptotic Stability ◽  
Control Systems ◽  
Chaotic System ◽  
Global Asymptotic Stability ◽  
Design Methodology ◽  
Closed Loop ◽  
Fuzzy Controller ◽  
Closed Loop System ◽  
Content Type ◽  
System A

Purpose This paper aims to deal with the problem of the global stabilization for a class of tension leg platform (TLP) nonlinear control systems. Design/methodology/approach It is well-known that, in general, the global asymptotic stability of the TLP subsystems does not imply the global asymptotic stability of the composite closed-loop system. Findings An effective approach is proposed to control chaos via the combination of fuzzy controllers, fuzzy observers and dithers. Research limitations/implications If a fuzzy controller and a fuzzy observer cannot stabilize the chaotic system, a dither, as an auxiliary of the controller and the observer, is simultaneously introduced to asymptotically stabilize the chaotic system. Originality/value Thus, the behavior of the closed-loop dithered chaotic system can be rigorously predicted by establishing that of the closed-loop fuzzy relaxed system.

Anti-windup for Euler-Lagrange Plants

2011 ◽  
Author(s):  
Luca Zaccarian ◽  
Andrew R. Teel
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Industrial Robots ◽  
Robot Arm ◽  
Compensation Scheme ◽  
Nonlinear Plants ◽  
Puma Robot ◽  
Selection Of

This chapter considers a specific case study where the model recovery anti-windup (MRAW) framework is applied to a class of nonlinear plants consisting of all fully actuated Euler-Lagrange systems. For such plants, an anti-windup construction is proposed that is capable of recovering global asymptotic stability of the closed loop with saturation as long as the unconstrained controller guarantees global asymptotic stability and local exponential stability of the unconstrained closed loop. The chapter first explains how MRAW for the saturated closed loop can be performed by generalizing the compensation scheme for linear plants, highlighting the selection of the stabilizer as a key aspect of successful anti-windup augmentation. It then presents some simulation examples to demonstrate the proposed anti-windup construction, including its application to a simple nonlinear robot arm and to models of two industrial robots, the PUMA robot and the SCARA robot.

Asymptotic Stabilization of Delayed Systems with Input and Output Saturations

2017 ◽  
Vol 6 (2) ◽  
pp. 64
Author(s):  
Adel Mahjoub ◽  
Nabil Derbel
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Input Output ◽  
Delayed Systems ◽  
Output Stability ◽  
Input And Output ◽  
Delayed System ◽  
The Stability

We consider in this paper the problem of controlling an arbitrary linear delayed system with saturating input and output. We study the stability of such a system in closed-loop with a given saturating regulator. Using input-output stability tools, we formulated sufficient conditions ensuring global asymptotic stability.

scholarly journals An adaptive output feedback motion tracking controller for robot manipulators: Uniform global asymptotic stability and experimentation

2013 ◽  
Vol 23 (3) ◽  
pp. 599-611 ◽  
Author(s):  
Antonio Yarza ◽  
Victor Santibanez ◽  
Javier Moreno-Valenzuela
Keyword(s):  
Asymptotic Stability ◽  
Output Feedback ◽  
Global Asymptotic Stability ◽  
Motion Tracking ◽  
Robot Manipulators ◽  
Reference Trajectory ◽  
Feedback Controllers ◽  
Tracking Controller ◽  
Noisy Signals ◽  
First Time

Abstract This paper deals with two important practical problems in motion control of robot manipulators: the measurement of joint velocities, which often results in noisy signals, and the uncertainty of parameters of the dynamic model. Adaptive output feedback controllers have been proposed in the literature in order to deal with these problems. In this paper, we prove for the first time that Uniform Global Asymptotic Stability (UGAS) can be obtained from an adaptive output feedback tracking controller, if the reference trajectory is selected in such a way that the regression matrix is persistently exciting. The new scheme has been experimentally implemented with the aim of confirming the theoretical results.

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