Experimental control of a ‎f‎lexible ‎l‎ink ‎by ‎the ‎method ‎of‎ ‎Controlled Lagrangian

The Controlled Lagrangian method is a branch of energy shaping methods that is designed to control underactuated mechanical systems. The method employs the mechanical energy (kinetic energy plus potential energy) of an artificial Lagrangian system, that generates similar equations of motion to the original underactuated system, as the Lyapunov function. This paper presents an application of the Controlled Lagrangian method to control an underactuated flexible link, and the results of a theoretical study through simulations confirmed by the results from an experimental setup. It is shown that the method’s performance is acceptable from a practical point of view as well as theoretical perspective. The simulations and the experimental results are presented in the sequel tovalidate the theoretical studies. The effect of changing controller gains on the designed controller performance is studied in more detail under the terms of the system’s mechanical energy. Moreover, gain tuning is also performed to attain high quality performance in the experimental study by the aid of their influence in the system’s nergy.Comparison of the proposed method with the partial feedback linearization method shows the degree of robustness of the proposed method. The simplicity of the gain tuning shows that the method can be implemented conveniently to control mechanical systems</span

Dynamic behavior of a functionally graded plate resting on Winkler elastic foundation and in contact with fluid

A semi-analytical method is developed to consider free vibrations of a functionally graded elastic plate resting on Winkler elastic foundation and in contact with a quiescent fluid. Material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The fluid is considered to be incompressible and inviscid. In the analysis, the effect of an in-plane force in the plate due to the weight of the fluid is taken into account. By satisfying the compatibility conditions along the interface of fluid and plate, the fluid-structure interaction is taken into account and natural frequencies and mode shapes of the coupled system are acquired by employing energy methods. The results obtained from the present approach are verified by those from a finite element analysis. Besides, the effects of volume fractions of functionally graded materials, Winkler foundation stiffness and in-plane forces on the dynamic of plate are elucidated.19 page(s