A robust nonlinear position observer for synchronous motors with relaxed excitation conditions

ABSTRACT

A robust, nonlinear and globally convergent rotor position observer for surface-mounted permanent magnet synchronous motors was recently proposed by the authors. The key feature of this observer is that it requires only the knowledge of the motor's resistance and inductance. Using some particular properties of the mathematical model it is shown that the problem of state observation can be translated into one of estimation of two constant parameters, which is carried out with a standard gradient algorithm. In this work, we propose to replace this estimator with a new one called dynamic regressor extension and mixing, which has the following advantages with respect to gradient estimators: (1) the stringent persistence of excitation (PE) condition of the regressor is not necessary to ensure parameter convergence; (2) the latter is guaranteed requiring instead a non-square-integrability condition that has a clear physical meaning in terms of signal energy; (3) if the regressor is PE, the new observer (like the old one) ensures convergence is exponential, entailing some robustness properties to the observer; (4) the new estimator includes an additional filter that constitutes an additional degree of freedom to satisfy the non-square integrability condition. Realistic simulation results show significant performance improvement of the position observer using the new parameter estimator, with a less oscillatory behaviour and a faster convergence speed.

KEYWORDS:

• Robust observer
• nonlinear regressor, permanent magnet motor

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. For brevity, we adopt here the notation ξ_ij := col(ξ_i, ξ_{i + 1}, …, ξ_j), for all $i,j\in \mathbb{N}$, i < j.

2. To simplify the presentation, this terms are neglected in the sequel, referring the reader to Bobtsov et al. (2015) and Aranovskiy, Bobtsov, Ortega, and Pyrkin (2015) for the analysis including these terms.

3. That is, the output of the operator when it is applied with zero initial conditions.

4. It is essential to emphasize that for any matrix $A\in {\mathbb{R}}^{q\times q}$, we have that $\text{adj}\left\{A\right\}A=det\left\{A\right\}{I}_q$, even if A is not full rank (Lancaster & Tismenetsky, 1985).

Additional information

Funding

This article is supported by Government of Russian Federation (grant number 074-U01, GOSZADANIE 2014/190 (project 2118)), the Ministry of Education and Science of Russian Federation (project 14.Z50.31.0031).