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1

Analysis of a nonlinear tuned mass damper by using the multi-scale method

Liu Junfeng, Yao Ji, Huang Kun, Zhang Qing, Ze Li

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 3

463--477

EN

A tuned mass damper is a kind of vibration damping device which has been widely used in tall buildings, machinery, bridges, aerospace engineering and other fields. In practical engineering applications, due to large deformation caused by large displacement, errors in engineering constructions and the existence of limit devices, the structure and tuned mass dampers inevitably produce some nonlinear characteristics, but these nonlinearities are often ignored. The results of this study confirm that the nonlinearity of the structure and the mass damper should be considered in the process of optimal frequency design, otherwise there will be a large deviation between the design optimal frequency of the mass damper and the actual optimal frequency. In this paper, nonlinear characteristics of the tuned mass damper and the main structure are considered. The first-order differential equations are obtained by using the complex average method, and the nonlinear equations of the tuned mass damper system are derived by using the multi-scale method. On this basis, the parameters are determined. The numerical results show that the error of the approximate solution method is small in the given example. The nonlinear tuned mass damper with nonlinear design exhibits a better control performance.

2

Gain scheduled controller design for thermo-optical plant

Veselý V, Osuský J, Sekaj I.

Archives of Control Sciences

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2014

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Vol. 24, no. 3

333--349

EN

This paper presents a gain scheduled controller design for MIMO and SISO systems in the frequency domain using the genetic algorithms approach. The proposed method is derived from the M-delta structure of closed loop MIMO (SISO) systems and the small gain theory is exploited to obtain the stability condition. An example of real system illustrates the effectiveness of the proposed output feedback gain scheduled controller design method and also the possibility to improve its performance using the genetic algorithm.

3

Model-free reconfiguration mechanism for fault tolerance

Jain T., Yamé J. J., Sauter D.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 1

125-137

EN

The problem of fault tolerant control is studied from the behavioral point of view. In this mathematical framework, the concept of interconnection among the variables describing the system is a key point. The problem is that the behavior we intend to control is not known. Therefore, we are interested in designing a fault accommodation scheme for an unknown behavior through an appropriate behavioral interconnection. Here we deal simply with the trajectories that are generated by the system in real time. These trajectories determine the behavior of a system in various (faulty/healthy) modes. Based on the desired interconnected behavior, only the trajectories that obey certain laws are selected. These laws, representing the desired behavior, can indeed be achieved by a regular interconnection. Thus, when the trajectories do not belong to a certain desired behavior, it is considered to be due to the occurrence of a fault in the system. The vantage point is that the fault tolerant control problem now becomes completely a model-free scheme. Moreover, no explicit fault diagnosis module is required in our approach. The proposed fault tolerance mechanism is illustrated on an aircraft during the landing phase.

4

Robust force/position control based on mechatronic solution

Osypiuk R., Tarasiejski L., Domek S.

Advances in Manufacturing Science and Technology

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2007

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Vol. 31, nr 3

27-43

EN

Application of a mechatronic system to improve the effectiveness of the position/force control for industrial manipulators is discussed in the paper. Owing to high stiffness of the kinematic chain and variable environment stiffness, there is a need to employ advanced control systems in order to provide stable force control. The concept proposed and presented in the paper is meant for use with a 6DOF platform, however preliminary tests have been performed on a 1DOF system.

PL

Dokonano analizy zastosowania mechatronicznego systemu w celu poprawy efektywności sterowania położeniem i siłą dla manipulatorów przemysłowych. Duża sztywność łańcucha kinematycznego oraz zmienna sztywność otoczenia powodują konieczność stosowania zaawansowanych systemów dla zapewnienia stabilnego przebiegu procesu regulacji siły. Proponowano i omówiono hipotezę z użyciem platformy 6DOF. Wstępny eksperyment praktyczny wykonano dla systemu z jednym stopniem swobody.

5

Comparison of Linear Control Methods for an AMB System

Grega W., Piłat A.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 2

245-255

EN

The contactless nature of active magnetic bearings brings about many advantages over the conventional bearing while industrial real-time applications are often limited by the significant complexity of control algorithms. This paper presents the application of an LQ controller to an active magnetic bearing system (AMB). Two control strategies are presented and compared: local and global. In the first case the rotor is modelled as two separated masses located at the bearing. In the second case rotor stabilization is considered globally as a problem of the rotating rigid body suspended in a magnetic field. The second approach is especially important for high-speed rotating machines. The control performance of both algorithms was analysed using an experimental AMB laboratory system.