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Abstract:We consider the motion of a two-link flexible arm with nonuniform cross section. We obtain the equations of motion by using the extended Hamilton's principle. These equations consist of coupled partial differential equations and (nonlinear) ordinary differential equations with appropriate boundary conditions. Our control problem is to achieve the given desired link angles and suppress the link vibrations. To solve this problem, we propose a novel control scheme which consists of a dominant control law together with a parallel controller. We show that with the proposed controller, the control objectives are satisfied. Our stability analysis is based on the Lyapunov approach and LaSalle's invariance principle extended to infinite-dimensional systems. We also present some simulation results, which indicate that large parameter uncertainties such as tip and hub mass changes are also handled effectively by the proposed controller.

In electrospinning process nanostructured solid fibres are produced from charged polymer jet oriented at external electrostatic field. Materials such as polymer, composites and tissue scaffold fibres have been fabricated with electrospinning techniques. The typical obstacle of electrospun fibre production is the whipping instability, resulting from the chaotic oscillation of polymer jet. In this Letter, feasibility of suppressing the whipping instability is analysed and explained using a mathematical model based on the usage of secondary electrostatic field created by finite length hollow cylinder. It is shown that the three-dimensional path of polymer jet calculated by computer simulations focus the characteristic spot size of the deposited electrospun fibre to a smaller diameter, which is coherent to the experimental observations

We consider a flexible structure modeled as a shear beam which is free to rotate on the horizontal plane. We first model the system by using partial differential equations and we propose boundary feedback laws to achieve set-point regulation of the rotation angle as well as to suppress elastic vibrations. The main advantage of the proposed design, which consists of a decoupling controller together with an observer, is that it is easy to implement. We utilize a coordinate transformation based on an invertible integral transformation by using Volterra form and backstepping techniques. We show that with the proposed controller, the control objectives are satisfied. © The Author(s) 2011 Reprints and permissions: sagepub.co.uk/ journalsPermissions.nav