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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

TM-AFM nonlinear motion control with robustness analysis to parametric errors in the control signal determination

Balthazar J. M., Tusset A. M., Bueno Á. M.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 1

93--106

EN

Nonlinear motion of the microcantilever probe in the Atomic Force Microscope (AFM) has been extensively studied considering mainly the van der Waals forces. Since the behavior of the microcantilever is vital to quality of generated images, the study of control strategies that force the probe to avoid undesired behavior such as chaotic motion, is also of significant importance. A number of published works has shown that the microcantilever is subject to chaotic motion for a certain combination of parameters. For such a parameter combination, the control system must suppress the chaotic motion. Here, an study of the AFM mathematical model is presented, aiming to find a region of operation of the AFM where the motion is chaotic. In order to suppress the chaotic motion, a periodic orbit of the system is obtained, and the controller forces the system to that periodic orbit. Two control strategies are used, namely: The State Dependent Riccati Equation (SDRE) and the Optimal Linear Feedback Control (OLFC). Both control strategies consider the complete nonlinearities of the system, and the OLFC guarantees the global stability. The numerical simulations carried out showed the efficiency of the control methods as well as the sensitivity of each control strategy to parametric errors. Without the parametric errors, both control strategies were effective in maintaining the system into the desired orbit. On the other hand, in the presence of parametric errors, the SDRE technique was more robust than the OLFC.

4

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.