Differential and Integral Equations

Boundary stabilization of a flexible manipulator with rotational inertia

Bao-Zhu Guo, Jun-Min Wang, and Siu-Pang Yung

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We design a stabilizing linear boundary feedback control for a one-link flexible manipulator with rotational inertia. The system is modelled as a Rayleigh beam rotating around one endpoint, with the torque at this endpoint as the control input. The closed-loop system is nondissipative, so that its well posedness is not easy to establish. We study the asymptotic properties of the eigenvalues and eigenvectors of the corresponding operator $\mathcal A$ and establish that the generalized eigenvectors form a Riesz basis for the energy state space. It follows that $\mathcal A$ generates a $C_0$-semigroup that satisfies the spectrum-determined growth assumption. This semigroup is exponentially stable under certain conditions on the feedback gains. If the higher-order feedback gain is set to zero, then we obtain a polynomial decay rate for the semigroup.

Article information

Differential Integral Equations, Volume 18, Number 9 (2005), 1013-1038.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93D15: Stabilization of systems by feedback
Secondary: 35P10: Completeness of eigenfunctions, eigenfunction expansions 35Q72 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 70E60: Robot dynamics and control [See also 68T40, 70Q05, 93C85] 74M05: Control, switches and devices ("smart materials") [See also 93Cxx] 93C85: Automated systems (robots, etc.) [See also 68T40, 70B15, 70Q05]


Guo, Bao-Zhu; Wang, Jun-Min; Yung, Siu-Pang. Boundary stabilization of a flexible manipulator with rotational inertia. Differential Integral Equations 18 (2005), no. 9, 1013--1038. https://projecteuclid.org/euclid.die/1356060120

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