Suppression of chaotic vibrations in nonlinear systems by the example of a mechanical tachometer

2021 ◽  
Vol 14 (2) ◽  
pp. 73-79
Author(s):  
Vladimir Shashikhin ◽  
Ludmila Potapova ◽  
Svetlana Budnic
Keyword(s):  
Nonlinear Systems ◽  
Closed System ◽  
State Feedback ◽  
Dynamic Chaos ◽  
Characteristic Parameters ◽  
Regular Motion ◽  
Chaotic Vibrations ◽  
Chaotic Mode

A method for controlling dynamic chaos is proposed by introducing state feedback and changing the spectrum of Lyapunov characteristic parameters of a closed system to achieve the desired result - the transition from chaotic mode to regular motion. The solution of this problem is considered on the example of stabilization of a mechanical tachometer. The parameters of the controller in the feed-back circuit are determined by the method of modal con-trol synthesis.

Diagnosing Irregularities of Nonlinear Dynamic Systems With Implementation of Periodicity-Ratio

2008 ◽  
Author(s):  
Liming Dai ◽  
Guoqing Wang
Keyword(s):  
Nonlinear Systems ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
The Other ◽  
Nonlinear Dynamic Systems ◽  
Deterministic System ◽  
Final States ◽  
Regular Motion ◽  
Chaotic Vibrations ◽  
Irregular Behavior

Among the irregular responses of nonlinear dynamic systems, chaotic responses of nonlinear systems are probably the most attractive phenomena along with the new observations in the last decades. A nonlinear deterministic system may behavior chaotically under regular such as periodic excitations. Regular motion of a system subjected to periodic exertions is usually periodic. In contrast with regular motions, final states of chaotic vibrations are extremely nonperiodic. This research is to analyzing the irregular behavior of dynamic systems with implementation of a newly developed criterion named Periodicity-Ratio. The development of a methodology for diagnosing the irregular motions from the regular motions of a dynamic system is presented. The Periodicity-Ratio describes the degree of periodicity of motion and can be conveniently used to distinguish a nonperiodic motion from a regular vibration or oscillation and to diagnose whether or not a motion is chaotic and the other irregular responses of the nonlinear dynamic systems, without plotting any figures. The analyses on the irregular behavior of nonlinear dynamic systems with the implementation of the Periodicity-Ratio will be demonstrated.

fuzzy state-feedback control design for nonlinear systems with -stability constraints: An LMI approach

2008 ◽  
Vol 78 (4) ◽  
pp. 514-531 ◽  
Author(s):  
Wudhichai Assawinchaichote ◽  
Sing Kiong Nguang ◽  
Peng Shi ◽  
El-Kébir Boukas
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
State Feedback ◽  
Control Design ◽  
State Feedback Control ◽  
Lmi Approach ◽  
Fuzzy State
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