Frequency-shifting-based stable on-line algebraic parameter identification of linear systems

Abstract

In this paper a new approach to algebraic parameter identification of the linear SISO systems is proposed. The standard approach to the algebraic parameter identification is based on the algebraic derivatives in Laplace domain as the main tool for algebraic manipulations like elimination of the initial conditions and generation of linearly independent equations. This approach leads to the unstable time-varying state-space realization of the filters for the on-line parameter estimation. In this paper, the finite difference and shift operators in combination with the frequency-shifting property of Laplace transform is applied instead of algebraic derivatives. Resulting state-space realization of the estimator filters is asymptotically stable and doesn't require switch-of mechanism to prevent overflow of the estimator variables. The proposed method is especially suitable for applications in closed-loop on-line identification where the stable behavior of the estimators is a necessary requirement. The efficiency of the proposed algorithm is illustrated on three simulation examples.

An algebraic approach to on-line signal denoising and derivatives estimation

“…provides a connection between signal derivatives in time instant t and signal value in a previous time t−τ , where τ > 0. To determine the signal derivatives u (i) (t), i = 0, 1, ..., n−1, on the right-hand side of (1), it is necessary to generate n linearly independent equations, which is similar to the algebraic approach to parameter identification [21]. By multiplying the expression (1) with the linearly independent, bounded, square integrable functions g i (τ ), i = 1, ..., n, and integrating along τ from zero to t, the following set of equations is obtained…”

“…Expression (9) can be evaluated for some t ≥ ε > 0, because the matrix M(t) is singular in t = 0 (M ij (0) = 0 for i, j = 1, 2, ..., n). This singularity in the origin is typical for the algebraic estimators, [22,21], and can be avoided by using the following approximation…”

“…A consequence of placing poles far in the left-half plane to provide high estimation accuracy is an impulsive-like transient behavior known as the peaking phenomenon [27,28]. This transient behavior can be avoided with a similar approach as in the case of the algebraic parameter estimation [22,21], by the evaluation of the estimates starting at a later time t ≥ t 0 > 0. Given that the algebraic estimator provides the best accuracy and the best noise attenuation properties in the case of the estimation of the signalû (0) (t), the denoising aspect appears as a specially interesting feature of the proposed estimator.…”

Frequency‐shifting‐based algebraic approach to stable on‐line parameter identification and state estimation of multirotor UAV

“…The problem of inherent instability of algebraic derivative‐based estimators is resolved in , where a frequency‐shifting‐based (FSB) algebraic approach is proposed, providing stable on‐line parameter identification without the need for periodic re‐initialization, like in the case of the conventional algebraic estimators. The proposed FSB algebraic approach is especially suitable for applications in closed‐loop on‐line identification where the stable behavior of the estimators is a necessary requirement.…”

“…In comparison with the previous results, the main contribution of this article is the stable algebraic observer design which provides denoising of the measured position signal and estimation of multirotor velocity. The second contribution is a modified version of the FSB algebraic parameter identification method, which provides a reduction of the number of estimator tuning parameters, in comparison with the original approach . The key feature of the proposed estimators, compared with the algebraic derivative‐based estimators , is the stable state‐space realization of the estimator filters without needs for periodic re‐initialization.…”