Drive Signal Frequency-Lock Method Based on 90° Phase Shift for Quartz Angular-Rate Sensor

A drive signal frequency-lock method for quartz angular-rate sensor is presented. The calculation result obtained by the equivalent volume force analytic method indicated that when taking the inherent frequency of the drive tines as the drive signal frequency the phase of the reference vibration is 90° behind that of the drive signal, and the square of amplitude is less than that of the maximal amplitude by 1/(4Q~2_d) merely. The curves derived from the finite element analytic method proved that near the inherent frequency the phase shift of the feedback voltage is identical to that of the reference vibration, and the amplitude is proportional to that of the reference vibration, and the phase shift is linear approximatively with the frequency shift. The frequency shift could be calculated according to the phase shift obtained by quadrature correlation detection, so the drive signal frequency could be locked at the inherent frequency of the drive tines by means of iteration.

Tracking error analysis and simulation of FLL-assisted PLL

In order to solve problems in high dynamic environment, a frequency-locked loop （FLL） assisted phase-locked loop （PLL） is put forward for carrier tracking. On the basis of the analysis of discriminators, the total phase error of the tracking loop is analyzed and a general error expression is derived. By using linearization and Jaffe-Rechtin coefficients, the performance of a special first order FLL-assisted second order PLL is analyzed to get a closed expression. Analysis results and simula- tions show that there exist an optimal FLL loop bandwidth and a optimal PLL loop bandwidth which can make the phase jitter much less than that when the PLL is used alone.

High dynamic synchronization algorithm based on cyclic spectral density

A new high dynamic synchronization algorithm using cyclic spectral density was presented according to the theories of cyclic spectral density and its anti-interface and anti-noise properties.The closed forms of frequency error and phase error were obtained,and their performances were analyzed.The in-phase signal throw costas loop was normalized to obtain a cosine signal.Cyclic spectral density of the cosine signal of was computed to obtain the frequency error and the phase error and then results were put into NCO to synchronize.Finally,the performance of the presented algorithms was compared with the conventional algorithms by virtue of simulations,and the simulation results proved the correctness and the superiority of the new algorithms.

Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

We numerically study the dynamics of spiral waves in the excitable system with the excitability modulated by a rectangle wave. The tip trajectories and their variations with the modulation period T are explained by the corre- sponding spectrum analysis. For a large T, the external modulation leads to the occurrence of more frequency peaks and these frequencies change with the modulation period according to their specific rules, respectively. Some of the frequencies and a primary frequency fl determine the corresponding curvature periods, which are locked into rational multiplies of the modulation period. These frequency-locking behaviours and the limited life-span of the frequencies in their variations with the modulation period constitute many resonant entrainment bands in the T axis. In the main bands, which follow the relation T/T12 = m/n, the size variable Rx of the tip trajectory is a monotonic increasing function of T. The rest of the frequencies are linear combinations of the two ones. Due to the complex dynamics, many unique tip trajectories appear at some certain T. We find also that spiral waves are eliminated when T is chosen from the end of the main resonant bands. This offers a useful method of controling the spiral wave.

STRONGLY RESONANT BIFURCATIONS OF NONLINEARLY COUPLED VAN DER POL-DUFFING OSCILLATOR

In this paper, the strongly resonant bifurcations of a nonlinearly coupled Van der Pol-Duffing Oscillator by the classical multi-scale method are studied. It is shown that there exist periodic motions of a single oscillator, frequency-looking and quasi-periodic motions of two oscillators when the parameters vary. Meanwhile, some numerical results are given to test the theoretical ones.

Dynamics of Meandering Spiral Waves Driven by Two-Point Feedback

We numerically study the dynamics of meandering spiral waves in the excitable system subjected to a feedback signal coming from two measuring points located on a straight line together with the initial spiral core. The core location and size radius of the final attractors are computed, and they change with the position of the moving measuring point in a unique way. By the Fourier Spectral analysis, we find the frequency-locked behaviors different from the driving scheme of the external periodic force. It when the moving measuring point approaches closely is also found that the meandering spiral wave can be eliminated the boundary and its feedback gain is large enough. This offers an effective and convenient method for eliminating meandering spiral waves.

Frequency—Locking in Coupled Chaotic Systems

A novel approach is presented for measuring the phase synchronization (frequency-locking) of coupled nonidentical oscillators, which can characterize frequency-locking for chaotic systems without well-defined phase by measuring the mean frequency. Numerical simulations confirm the existence of frequency-locking. The relations between the mean frequency and the coupling strength and the frequency mismatch are given. For the coupled hyperchaotic systems, the frequency-locking can be better characterized by more than one mean frequency curves.