On Saturation Control of a Non-Ideal Vibrating Portal Frame Foundation Type Shear-Building

Abstract

In this paper, we examine the nonlinear control method based on the saturation phenomenon and of systems coupled with quadratic nonlinear ties applied to a shear-building portal plane frame foundation that supports an unbalanced direct current with limited power supply (non-ideal system). We analyze the equations of motion by using the method of averaging and numerical simulation. The interaction of the non-ideal structure with the saturation controller may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. Special attention is focused on passage through resonance when the non-ideal excitation frequency is near the portal frame natural frequency and when the non-ideal system frequency is approximately twice the controller frequency (two-to-one internal resonance).

Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

“…Dynamical behavior of an elastic nonideal portal frame with fractional nonlinearities taken into account the full interactions of the vibration systems with an energy source of limited supply is investigated [9]. A nonlinear control method based on the saturation phenomenon of systems coupled with quadratic nonlinearities in a shear building portal frame is studied [10]. A portal frame structure based on energy harvesters with piezo electric coupling exhibiting chaotic behavior is investigated and an optimal control scheme to regulate the energy captured to a designed operating frequency is preferred [11].…”

On nonlinear dynamics and control of a robotic arm with chaos

“…In That paper a mathematical model of the electromechanical shaker was described and its parameters were identified. The effectiveness of the nonlinear saturation control in vibration attenuation for a non-ideal portal frame was investigated by [6]. The Optimal Linear Feedback Control was proposed by [7].…”

On the Response of the Small Buildings to Vibrations

“…The reduction of vibrations for a resonant structure was studied by Felix, Balthazar and Brasil [9], [10] and Souza et al [11] using tuned liquid column. A tuned liquid column connected to the structure works due to the inertial secondary system principle, by which the damper counteracts the forces producing the vibration.…”