Stability analysis of normalized frequency adaptive comb filter

作者：Chu, Zhao Bi^*; Ding, Ming; Du, Shao Wu; Feng, Xiao Ying

来源：Acta Automatica Sinica, 2010, 36(11): 1581-1593.

DOI：10.3724/SP.J.1004.2010.01581

• Coupled nonlinear differential equations
• Integral manifold
• Normalized frequencies
• Normalized frequency estimation
• Semistability
• Stability analysis
• Steady state performance
• Unknown periodic disturbance

A normalized frequency adaptive comb filter composed of a number of normalized frequency estimators in parallel is proposed to track unknown frequency and unknown amplitude of each component of an almost periodic signal. The filter consists of two coupled nonlinear differential equations respectively for updating frequencies and estimating state variables. A nonlinear autonomous equation for frequency estimation is deduced after average method is applied to the almost periodic dynamic system resulting from system decoupling by slow integral manifold. Three kinds of local stability of the autonomous system: the exponential stability of isolated equilibrium point, the semistability on center manifold, and the robustness under unknown periodic disturbance are proved. The convergence and the boundedness of amplitude estimation and signal tracking as well as the effect of parameters on the transient and steady-state performance of frequency and amplitude are investigated. Each sinusoidal component and its amplitude are accurately tracked on the condition of given intervals instead of the values of frequencies. The response speed is independent of the component amplitude. Simulation results reveal the validity of the proposed algorithm.

• 出版日期2010
• 单位合肥工业大学