Robust finite-time estimation of biased sinusoidal signals: A volterra operators approach

Abstract

A novel finite-time convergent estimation technique is proposed for identifying the amplitude, frequency and phase of a biased sinusoidal signal. Resorting to Volterra integral operators with suitably designed kernels, the measured signal is processed yielding a set of auxiliary signals in which the influence of the unknown initial conditions is removed. A second-order sliding mode-based adaptation law-fed by the aforementioned auxiliary signals-is designed for finite-time estimation of the frequency, amplitude, and phase. The worst case behavior of the proposed algorithm in presence of the bounded additive disturbances is fully characterized by Input-to-State Stability arguments. The effectiveness of the estimation technique is evaluated and compared with other existing tools via extensive numerical simulations.

Switching-based Rejection of an Unknown Harmonic Disturbance in Uncertain Stable Linear Systems under Measurement Noise

“…for all t ∈ [t a , t b ), where y ss (t) = a|W (jω )| sin(ω t + φ 0 + ∠W (jω )) is the steady state response and ι(•) is an exponentially decay term, represents the transient response. The objective is to estimate the unknown frequency ω in finite time using the robust parametric finite-time estimation methodology proposed in [12]. According to [12], the deadbeat estimator is designed for pure sinusoidal signal and the frequency estimation errorω :=ω − ω * is ISS with respect to any additive norm-bounded noise, which, in our case, is given by the sum of the transient response ι(t) and the measurement noise ν(t).…”

“…The objective is to estimate the unknown frequency ω in finite time using the robust parametric finite-time estimation methodology proposed in [12]. According to [12], the deadbeat estimator is designed for pure sinusoidal signal and the frequency estimation errorω :=ω − ω * is ISS with respect to any additive norm-bounded noise, which, in our case, is given by the sum of the transient response ι(t) and the measurement noise ν(t). Therefore, to obtain an accurate frequency estimate, the deadbeat estimator should be activated and fed by y…”

“…Without loss of generality, set ε 0 ≤ν. Then as shown in Section 5 of [12], there exist class-K ∞ functions γ(•),γ (•) such that, at the end of the identification phase,ω in the presence of the measurement noise ν satisfies…”

“…Building on prior work in [8] and [12], a sequential estimation / control strategy is adopted to solve Problem 1. Specifically, over a certain time interval, only one of two distinct actions is performed: in the first one, the controller operates in identification mode.…”

“…Specifically, over a certain time interval, only one of two distinct actions is performed: in the first one, the controller operates in identification mode. During this phase, the controller is disconnected from the plant (i.e., u(t) = 0) and the frequency of the disturbance is estimated in finite time via the deadbeat method of [12]. A norm-estimator of the state trajectory is employed to obtain a suitable time where the response of the system has reached steady-state in order for the estimation algorithm to provide a reliable estimate of the frequency.…”