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1

SDRE applied to position and vibration control of a robot manipulator with a flexible link

Lima J. J., Tusset A. M., Janzen F. C., Piccirillo V., Nascimento C. B., Balthazar J. M., Brasil R. M. L. R. F.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 4

1067--1078

EN

This paper presents position and vibration control of a flexible robot composed of two rigid and one flexible links. Position is controlled by the current applied to the DC motor armature. To control vibrations of the flexible structure, Shape Memory Alloys (SMA) are used. Due to phase transformations, the SMA can change its stiffness through temperature variation, considering and taking advantage of this characteristic the vibration control is done. Control is achieved via the State Dependent Ricatti Equations (SDRE) technique, which uses suboptimal control and system local stability search. The simulation results show the feasibility of the proposed control for the considered system.

2

On suppression of chaotic motions of a portal frame structure under non-ideal loading using a magneto-rheological damper

Tusset A. M., Piccirillo V., Balthazar J. M., Brasil R. M. L. R. F.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 3

653--664

EN

We consider chaotic motions of a portal frame structure under non-ideal loading. To suppress this chaotic behavior, a controlling scheme is implemented. The control strategy involves application of two control signals and nonlinear feedforward control to maintain a desired periodic orbit, and state feedback control to bring the system trajectory into the desired periodic orbit. Additionally, the control strategy includes an active magneto-rheological damper to actuate the system. The control force of the damper is a function of the voltage applied in the coil of the damper that is based on the force given by the controller.

3

Dynamical jump attenuation in a non-ideal system through a magnetorheological damper

Piccirillo V., Tusset A. M., Balthazar J. M.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 3

595--604

EN

This paper is concerned with the Sommerfeld effect (Jump phenomena) attenuation in an non-ideal mechanical oscillator connected with an unbalanced motor excitation with a limited power supply (non-ideal system) using a magnetorheological damper (MRD). The dynamical response of systems with MRD presents different behavior due to their nonlinear characteristic. MRD nonlinear response is associated with adaptive dissipation related to their hysteretic behavior. The Bouc-Wen mathematical model is used to represent the MRD behavior. Numerical simulations show different aspects about the Sommerfeld effect, illustrating the influence of the different electric current applied in the MRD to control the force developed by this damper.

4

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Piccirillo V., Balthazar J. M., Pontes B. R. Jr., Felix J. L. P.

Journal of Theoretical and Applied Mechanics

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2008

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Vol. 46 nr 3

597-620

EN

In this paper, we present nonlinear dynamic behaviour of a system which consists of a mass connected to a rigid support by a shape memory alloy (SMA) element and a damper. In order to disturb the system, a DC motor with limited power supply is connected to the mass, causing an interaction between the vibrating structure and the energy source. The SMA element is characterised using a one-dimensional phenomenological constitutive model, based on the classical Devonshire theory. We analyse the non-ideal system in form of two coupled nonlinear differential equations. Some interesting nonlinear phenomena as the Sommerfeld effect and nonlinear resonance including periodic, chaotic and hyperchaotic regime are presented.

PL

W pracy przedstawiono opis dynamiki nieliniowego układu złożonego z masy połączonej ze sztywnym podłożem za pośrednictwem elementu z pamięcią kształtu i tłu- mikiem. W celu realizacji wymuszenia w układzie zastosowano silnik prądu stałego z ograniczonym poborem mocy, który pobudza do ruchu masę, tworząc w ten sposób sprzężenie mechaniczne pomiędzy układem drgającym a źródłem energii. Element z pamięcią kształtu opisano za pomocą jednowymiarowego modelu fenomenologicznego opartego na teorii Devenshire’a. Przeanalizowano rozważany nieidealny układ opisany dwoma sprzężonymi nieliniowymi równaniami ruchu. Zaobserwowano i opisano interesujące zjawiska nieliniowe w postaci efektu Sommerfelda i nieliniowego rezonansu w zakresie drgań okresowych, chaotycznych i hiperchaotycznych.