Algebraic parameters identification of DC motors: methodology and analysis

Abstract

A fast, non-asymptotic, algebraic parameter identification method is applied to an uncertain DC motor to estimate the uncertain parameters: viscous friction coefficient and inertia. In this work, the methodology is developed and analysed, its convergence, a comparative study between the traditional recursive least square method and the algebraic identification method is carried out, and an analysis of the estimator in a noisy system is presented. Computer simulations were carried out to validate the suitability of the identification algorithm.

Keywords:

• parameter estimation
• algebraic identification
• DC motor
• identification for control
• continuous-time systems

Acknowledgements

This research was partly supported by the Spanish Government via Project C.I.C.Y.T., Ref.: DPI2006-13834., Ministerio de Trabajo y Asuntos Sociales project Ref. 12/06 (Spain), by the Junta de Comunidades de Castilla-La Mancha and by the European Social Fund.

Notes

Notes

1. The magnitude without the hat corresponds to the output of the motor gear.

2. The Laplace transform of a function f(t) is represented by ℒ[f(t)] = F(s). Thus, , , , ℒ[tf(t)] = −dF(s)/ds, ℒ[t ² f(t)] = (−1)²d² F(s)/ds ² and ℒ[t ⁿ f(t)] = (−1) ⁿ d ⁿ F(s)/ds ⁿ for n = 1, 2, 3, ….

3. ∫⁽ⁿ⁾φ(t) representing the iterated integral with .

4. Note that then, the Coulomb's friction coefficient is ξ _r = J _r nμ _r .

5. For more information on transforming a continuous system into a discrete system and vice versa see VanLandingham (1985) and Feliu (1986).