Stability analysis of a voltage-based controller for robot manipulators

Jorge Orrante-Sakanassi, Victor Santibañez, Javier Moreno-Valenzuela

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

A voltage-based control scheme for robot manipulators has been presented in recent literature, where feedback linearization is applied in the electrical equations of the DC motors in order to cancel the electrical current terms. However, in this paper we show that this control technique generates a system of the form Ex = Ax + Bu, where E is a singular matrix, that is to say, a generalized state-space system or singular system. This paper introduces a formal stability analysis of the respective system by considering the state-space equation as a singular system. Furthermore, in order to avoid the singularity of the closed-loop system, modified voltage-based control schemes are proposed, whose Lyapunov stability analyses conclude semiglobal asymptotic stability for the set-point control case and uniform boundedness of the solutions and semiglobal convergence of the position, as well as velocity errors for the tracking control case. The proposed control systems are simulated for the tracking and set-point cases using the CICESE Pelican robot driven by DC motors. © 2013 Orrante-Sakanassi et al.; licensee InTech.
Original languageAmerican English
JournalInternational Journal of Advanced Robotic Systems
DOIs
StatePublished - 9 Jan 2013

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Manipulators
Robots
Controllers
Electric potential
DC motors
Feedback linearization
Asymptotic stability
Closed loop systems
Control systems

Cite this

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title = "Stability analysis of a voltage-based controller for robot manipulators",
abstract = "A voltage-based control scheme for robot manipulators has been presented in recent literature, where feedback linearization is applied in the electrical equations of the DC motors in order to cancel the electrical current terms. However, in this paper we show that this control technique generates a system of the form Ex = Ax + Bu, where E is a singular matrix, that is to say, a generalized state-space system or singular system. This paper introduces a formal stability analysis of the respective system by considering the state-space equation as a singular system. Furthermore, in order to avoid the singularity of the closed-loop system, modified voltage-based control schemes are proposed, whose Lyapunov stability analyses conclude semiglobal asymptotic stability for the set-point control case and uniform boundedness of the solutions and semiglobal convergence of the position, as well as velocity errors for the tracking control case. The proposed control systems are simulated for the tracking and set-point cases using the CICESE Pelican robot driven by DC motors. {\circledC} 2013 Orrante-Sakanassi et al.; licensee InTech.",
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Stability analysis of a voltage-based controller for robot manipulators. / Orrante-Sakanassi, Jorge; Santibañez, Victor; Moreno-Valenzuela, Javier.

In: International Journal of Advanced Robotic Systems, 09.01.2013.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Santibañez, Victor

AU - Moreno-Valenzuela, Javier

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AB - A voltage-based control scheme for robot manipulators has been presented in recent literature, where feedback linearization is applied in the electrical equations of the DC motors in order to cancel the electrical current terms. However, in this paper we show that this control technique generates a system of the form Ex = Ax + Bu, where E is a singular matrix, that is to say, a generalized state-space system or singular system. This paper introduces a formal stability analysis of the respective system by considering the state-space equation as a singular system. Furthermore, in order to avoid the singularity of the closed-loop system, modified voltage-based control schemes are proposed, whose Lyapunov stability analyses conclude semiglobal asymptotic stability for the set-point control case and uniform boundedness of the solutions and semiglobal convergence of the position, as well as velocity errors for the tracking control case. The proposed control systems are simulated for the tracking and set-point cases using the CICESE Pelican robot driven by DC motors. © 2013 Orrante-Sakanassi et al.; licensee InTech.

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