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

Abstract

Abstract 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.