Nonlinear feedback anti-control of limit cycle and chaos in a mechanical oscillator: theory and experiment

Patel, Bhavik; Kundu, Prasanjit Kumar; Chatterjee, Satyajit

doi:10.1007/s11071-021-06493-1

Cited by 7 publications

(5 citation statements)

References 62 publications

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“…First, a single degree-of-freedom model of the system is considered and then the results are extended to higher DOF systems. The detailed, analytical, numerical and experimental results for a single DOF model are previously reported [55]. However, to maintain continuity, some salient results of the single DOF model are repeated here (along with some new results).…”

Section: Numerical Resultsmentioning

confidence: 92%

“…However, the numerical analysis they presented is not extensive one, particularly the probability of occurrence of different coexisting solutions are not studied in depth. The present paper extends the concept introduced in [55] to multi degrees-of-freedom systems and shows the possibility of generating and controlling the dynamic characteristics of periodic, quasiperiodic, chaotic and hyper-chaotic responses. On top of that, a region of multistability is indentified in the plane of control parameters and the probability of obtaining a particular response is calculated.…”

Section: Introductionmentioning

confidence: 82%

“…For negative control gain, the static equilibrium is locally stable, but not necessarily globally stable [55]. It is also observed that by reversing the sign of control gain from positive to negative, one may obtain chaotic oscillations for a range of filter parameters [55].…”

Section: Generation Of Chaotic Oscillationsmentioning

confidence: 93%

“…Previously, Patel et al [55] have shown that the resonant controller with acceleration feedback and signum function type control law can produce modal limit cycle of desired amplitude in a single DOF mechanical system. They experimentally observed that chaotic oscillation can be produced by switching the sign of the control gain.…”

Section: Comparison With Previous Researchmentioning

confidence: 99%

“…From previous research works, it is evident that the problem of anticontrol of self-excited oscillation and chaos in the mechanical and micromechanical system is an important research problem as it has many practical applications. Patel et al [55] discussed the generation of self-excited oscillations and chaos in a single degree-of-freedom mechanical system by nonlinear acceleration feedback. They have shown and verified experimentally that the proposed control can generate limit cycles at natural frequency and chaos just by flipping the sign of the control gain.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Nonlinear Feedback Synthesis and Control of Periodic, Quasiperiodic, Chaotic and Hyper-Chaotic Oscillations in Mechanical Systems

Kundu

Chatterjee

2022

Preprint

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Self-excited periodic, quasiperiodic and chaotic oscillations have many significant applications in engineering devices and processes. In the present paper a centralized nonlinear controller is proposed to artificially generate and control self-excited periodic, quasiperiodic, chaotic and hyper-chaotic oscillations of required characteristics in a fully-actuated n-DOF spring-mass-damper mechanical system. The analytical relations among the amplitude, frequency and controller parameters for minimum control energy have been obtained using the method of two-time scale. It is shown that the proposed control can generate modal and nonmodal self-excited periodic and quasiperiodic oscillations of desired amplitude and frequency for minimum control energy. The analytical results have been verified numerically with MATLAB SIMULINK. Bifurcation analysis and extensive numerical simulations reveal a region of multistability in the plane of control parameters, where system responses may be periodic, quasiperiodic, chaotic and hyper-chaotic depending on initial conditions. However, it has been shown that the probability of obtaining chaotic and hyper-chaotic oscillations are very high for a wide range of controller parameters. The procedures of controlling the amplitude, frequency and characteristics of chaotic oscillations are also discussed. The results of the present paper is expected to find applications in various macro and micro mechanical systems and applications.

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Section: Numerical Resultsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 82%