Introduction

He, Wei; Ge, Shuzhi Sam; How, Bernard Voon Ee; Choo, Yoo Sang

doi:10.1007/978-1-4471-5337-5_1

Cited by 3 publications

(2 citation statements)

References 154 publications

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“…He et al. offer methods for designing observers and controllers of mechanical systems in offshore engineering (He et al., 2014). An observer-based control scheme for controlling the link, to follow the desired trajectory, was proposed by Nguyen and Egeland (2005).…”

Section: Introductionmentioning

confidence: 99%

A robust observer design for a flexible manipulator based on a PDE model

Jiang

Liu

2016

Journal of Vibration and Control

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This paper proposes a robust observer for a flexible single-link manipulator based on the partial differential equation (PDE) dynamic model. Unlike observers for the PDE model introduced by previous researchers, this observer is designed to estimate the distributed spatiotemporally varying states with unknown boundary disturbance and spatially distributed disturbance. The asymptotic stability of the proposed observer is proved by theoretical analysis and demonstrated by simulation results.

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Section: Introductionmentioning

confidence: 99%

A robust observer design for a flexible manipulator based on a PDE model

Jiang

Liu

2016

Journal of Vibration and Control

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“…We can use the position sensor, angle sensor and a laser displacement sensor to get the measurements x , θ(t) and y(x,t), respectively (Ge et al., 1998). In addition, zxxx(x,t) can be obtained by a shear force sensor, then zxxxx(x,t) can be calculated with backward difference algorithm (He et al., 2011a, 2014).…”

Section: Observer Design and Analysismentioning

confidence: 99%

Boundary control for a flexible manipulator with a robust state observer

Jiang

Liu

2016

Journal of Vibration and Control

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In this paper, a boundary controller for a flexible manipulator is proposed based on a partial differential equation (PDE) robust observer. In the previous work we have proposed a PDE robust observer to estimate the infinite dimensional states of the flexible manipulator with unknown boundary disturbance and spatially distributed disturbance. On the basis of the proposed robust state observer, a boundary controller is designed to achieve the stability control, regulate the joint position and suppress elastic vibration in this paper. The stabilities of the proposed observer and the boundary controller are validated by theoretical analysis. Numerical simulations are provided to demonstrate the effectiveness of the closed-loop system.

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Spatiotemporal adaptive state feedback control of a linear parabolic partial differential equation

Wang

2023

Intl J Robust & Nonlinear

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This article deals with the issue of asymptotic stabilization for a linear parabolic partial differential equation (PDE) with an unknown space-varying reaction coefficient and multiple local piecewise uniform control. Clearly, the unknown reaction coefficient belongs to a function space. Hence, the fundamental difficulty for such issue lies in the lack of a conceptually simple but effective parameter identification technique in a function space. By the Lyapunov technique combined with a variant of Poincaré-Wirtinger inequality, an update law is derived for estimate of the unknown reaction coefficient in a function space.Then a spatiotemporal adaptive state feedback control law is constructed such that the estimate of the unknown coefficient is bounded and the closed-loop PDE is asymptotically stable in the sense of spatial  1 norm if a sufficient condition given in terms of space-time varying linear matrix inequalities (LMIs) is fulfilled for the estimated coefficient and the control gains. Both analytical and numerical approaches are proposed to construct a feasible solution to the space-time varying LMI problem. With the aid of the semigroup theory, the well-posedness and regularity of the closed-loop PDE is also analyzed. Moreover, two extensions of the proposed adaptive control scheme are discussed: the PDE in N-D space and the PDE with unknown diffusion and reaction coefficients. Finally, numerical simulation results are presented to support the proposed spatiotemporal adaptive control design.

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Introduction

Cited by 3 publications

References 154 publications

A robust observer design for a flexible manipulator based on a PDE model

A robust observer design for a flexible manipulator based on a PDE model

Boundary control for a flexible manipulator with a robust state observer

Spatiotemporal adaptive state feedback control of a linear parabolic partial differential equation

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