On‐line Parameter Estimation via Algebraic Method: An Experimental Illustration

Delpoux, Romain; Floquet, Thierry

doi:10.1002/asjc.870

Cited by 13 publications

(10 citation statements)

References 31 publications

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“…is symmetric and positive definite it is invertible, and linear system of equations (39) can be solved for t ≥ ε > 0 using efficient numerical method like LU or Cholesky decomposition [18]. Fig.…”

Section: Algebraic Parameter Identificationmentioning

confidence: 99%

“…Next, several further reported applications are mentioned. In [18], the algebraic estimation algorithm is applied for the identification of the parameters of a permanent magnet stepper motor and a magnetic bearing. In [19], an online algebraic identification methodology for parameter and signal estimation in vibrating mechanical system is experimentally verified.…”

Section: Introductionmentioning

confidence: 99%

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

Kasač

Žilić

Milić

et al. 2018

Journal of the Franklin Institute

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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.

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Section: Algebraic Parameter Identificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Kasač

Žilić

Milić

et al. 2018

Journal of the Franklin Institute

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“…En segundo nivel, han sido incorporados en diferentes esquemas de control permitiendo la estimación algebraica de estados y derivadas para aplicaciones de control de movimiento (Menhour et al, 2014), la tolerancia a fallos en sistemas de levitación magnética (Kiltz et al, 2014) y procesos industriales (Martínez-Guerra et al, 2017) y el control de sistemas mecatrónicos basado en el rechazo activo de perturbaciones estimadas algebraicamente (Cortés-Romero et al, 2017). En tercer nivel, los métodos algebraicos han sido utilizados en la estimación de parámetros de sistemas dinámicos lineales y no lineales, demostrando ser útiles en la caracterización de servo-mecanismos (Garrido y Concha, 2013; Miranda-Colorado y Moreno-Valenzuela, 2017), el control de robots (Becedas et al, 2009;Pereira et al, 2013), el control de sistemas mecánicos (García-Rodríguez et al, 2009; Beltrán-Carbajal y Silva-Navarro, 2013), el control de convertidores electrónicos de potencia (Linares et al, 2014;Bougrine et al, 2017) y el control de máquinas eléctricas (Delpoux y Floquet, 2015).…”

Section: Introductionunclassified

Identificación Algebraica de Parámetros Asistida por Observadores GPI para un Helicóptero de Dos Grados de Libertad

2018

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Este artículo propone una alternativa para la estimación de parámetros de un helicóptero de dos grados de libertad que opera bajo control de lazo cerrado. Como principal contribución se plantea una variante de la metodología algebraica de identificación, la cual involucra el uso de observadores proporcional integral generalizados (GPI). Estos observadores están encargados de proveer la estimación de las derivadas de las salidas del sistema para su computo directo en los casos donde existen operaciones no lineales de difícil manipulación analítica. Inicialmente, se establece un identificador algebraico para cada ecuación no-lineal del sistema a fin de estimar los parámetros de interés. Posteriormente, para la selección de los parámetros estimados se adopta el criterio de la integral del cuadrado del error y el correspondiente índice de error. Finalmente, se presentan resultados experimentales que permiten validar la estrategia de identificación utilizada y los parámetros estimados con respecto al modelo asumido.

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“…The overall stability and observability cannot be guaranteed by linear controller and observer. Due to the nonlinearity of magnetic force, the observability and/or parameter estimation of magnetic bearing system is in general difficult (Delpoux and Floquet, 2015, Mizuno et al, 2016). The 3-pole configuration makes the problem even more difficult.…”

Section: Introductionmentioning

confidence: 99%

Smooth voltage controller and observer for a three-pole active magnetic bearing system

Chen

Hsiao²

2017

Mechanical Engineering Journal

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In this study, a simple and smooth voltage controller for a three-pole active magnetic bearing (AMB) system is proposed. It is designed with the backstepping procedure. The first step assumes the currents as the control inputs and designs the smooth current controller that has been proposed in the literature. The second step considers that the currents are not actual inputs, but part of the states. Then, the actual control inputs (voltages) are designed using simple proportional and integral (PI) control to make the error states from the first step to be zero asymptotically. Based on the voltage-controlled AMB system, an observer is designed for the rotor displacement estimation. The observer is based on the input voltages and coil currents that drive the magnetic poles. Such an observer can be utilized in the sensorless control of the AMB system. Due to the strong nonlinearity in the dynamics of 3-pole AMB system, the theory of nonlinear high-gain observer is adopted to design the observer. First, it is shown that the strong nonlinear 3-pole AMB system is observable under the zero input condition, which guarantees the existence of a high-gain observer. Then, the system is transformed into a regular form for the design of observer. Finally, a nonlinear observer is designed following the theory of high-gain observer. The proposed smooth voltage controller and nonlinear observer are verified numerically and experimentally. The results show the effectiveness of the smooth voltage controller and the feasibility of the nonlinear high-gain observer. and Hsiao, Mechanical Engineering Journal, Vol.4, No.5 (2017) [DOI: 10.1299/mej.16-00718] therein). Several methods have been proposed, including linear observer based, linear observer with parameter identification, switching ripple (from switching amplifier) based, and interrogation signal based.The objectives of this study are to propose a smooth voltage controller and to design an observer for the 3-pole AMB system. Due to the strong nonlinearity of the 3-pole AMB system, the stable levitation controller is in general complicated. Although a simple and smooth current controller for the 3-pole AMB system was proposed in (Chen, 2011, Meeker andMaslen, 2006), voltage controller is in general more cost-effective. Based on the voltage-controlled system, the estimation of the rotor position will be achieved by designing an observer. A Luenberger type observer with Kalman filter has been proposed in (Darbandi et al., 2014) based on the linearized 3-pole AMB system. However, the results are valid only when coil currents and rotor displacements are relatively small. The overall stability and observability cannot be guaranteed by linear controller and observer. Due to the nonlinearity of magnetic force, the observability and/or parameter estimation of magnetic bearing system is in general difficult (Delpoux and Floquet, 2015, Mizuno et al., 2016). The 3-pole configuration makes the problem even more difficult. In view of the strong nonlinearity of the 3-pole system...

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On‐line Parameter Estimation via Algebraic Method: An Experimental Illustration

Cited by 13 publications

References 31 publications

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

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

Identificación Algebraica de Parámetros Asistida por Observadores GPI para un Helicóptero de Dos Grados de Libertad

Smooth voltage controller and observer for a three-pole active magnetic bearing system

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