Line Spectra Chaotification With Nonlinear Time-delay Feedback Control

According to the continuous broadband spectra feature of chaos, chaotification ofthe nonlinear isolation system can be employed to change or reconfigure the frequencyspectrum of the power machinery vibration transmitted to the base of submarine. It isused to weaken or eliminate the line spectra feature of waterborne radiation noise inorder to enhance the stealth capability. At present, this innovative technique is facingseveral obstacles, including obtaining high-quality chaos with small energy control inlarge parametric range and preserving chaotic state under the variable conditions. Forthis purpose, a chaotification method based on nonlinear time-delay feedback controlis introduced in this dissertation. The effects on chaotification performance arediscussed in association with the configuration of the control parameters of thetime-delay controller. Based on the application background, this dissertation studiesthe line spectra chaotification issue with nonlinear time-delay feedback control undermulti-source excitation. The theoretical research reveals that the critical control gainfor chaotification depends on the stiffness of vibration isolation system. Thus, anisolation raft system based on quasi-zero-stiffness design is proposed in combinationwith time-delay control for line spectrum reconstruction. The main results of thisdissertation can be described as follow:Approach chaos through period-doubling bifurcation is one of the typical paths ofthe onset of chaos. It is very essential that the variation trend of the line spectraconfiguration and intensity can be revealed during the period-doubling bifurcation.The analytical relationship between T-periodic solution and2T-periodic solution nearany period-doubling bifurcation point of Duffing system has been obtained bymathematical derivation. The frequency spectrum relationship between them is furtherrevealed. It has been proved that the whole information of the T-periodic solutionwould be passed to the2T-periodic solution, and the original frequency spectrumcomponents will not decrease during the period-doubling bifurcation of Duffingsystem. The system frequency spectrum will add new frequency spectrum componentson the basis of inheriting the original frequency spectrum components. The more theperiod-doubling bifurcation, the more new frequency spectra appear until the onset ofchaos. And the original discrete line spectra would become continuous when thesystem is chaotic. The line spectrum maximum of system does not decrease during the period-doubling bifurcation, only likely to remain unchanged or rise.Based on the differential geometry theory and the Devaney’s definition of chaos,the analytical function of nonlinear time-delay feedback control is derived to atwo-dimensional vibration isolation floating raft system. This significance of this workis to provide a standard program for controller design and develop a chaotificationapproach with rigid mathematical proofs. The effects on chaotification performanceare investigated in association with the configuration of the control parameters,including the feedback control gain, time-delay and feedback frequency. Compared tothe linear time-delay feedback control, the nonlinear time-delay feedback control holdsthe favorable aspects including the capability of chaotification across a large range ofparametric domain, the advantage of using small control and the flexibility ofdesigning control feedback forms.Based on the particular application background, this dissertation studies thechaotification issue with nonlinear time-delay feedback control for a double-layervibration isolation floating raft system under multi-source excitation. It is one of thekey issues related to the implementation of application technology on chaotification.Under multi-source excitation, the effects of the control gain, time-delay and feedbackfrequency parameters on chaotification has been investigated, and discussion has alsobeen extended to the case of the single-source excitation.We find that the system can be much easily disturbed into chaotic state when thesystem’s stiffness is small. So, a kind of quasi-zero-stiffness electromagnet isolationsystem is proposed. When the system load varies, the coil control current and thestepping motor can be adjusted to maintain the static equilibrium position in thehorizontal direction. The isolation device with low natural frequency vibrates in thevicinity of the equilibrium position and the dynamic stiffness keeps small. A largefrequency range of vibration isolation can be achieved with good low-frequencyisolation effect.The nonlinear time-delay feedback control function has been derived for thechaotification on a double-layer QZS system. Numerical simulations have illustratedthe superior performance of the QZS system in terms of the required critical controlgain and the suppression of line spectra in comparison with a nonlinear model. In thereconstruction of line spectrum patterns, chaotification can effectively change a narrowband line spectrum induced by a harmonic excitation into a spectrum pattern withbroad bandwidth. We have examined the performance of the new system in low,intermediate and high frequency bands divided according to the natural frequencies of the system. It showed that the feature of line spectra could be completely eliminatedfor the intermediate and high frequency bandwidth. It is relatively difficult to removethe line spikes in the low frequency band, but the signal feature can be greatlyweakened through a chaotification process. The simulation results also show thatchaotification can effectively improve the quality of chaos by adjusting the controlparameters.