Extension of the tuning constant in the Huber's function for robust modeling of piezoelectric systems

Corbier, Christophe; Carmona, J.C.

doi:10.1002/acs.2517

Cited by 5 publications

(3 citation statements)

References 28 publications

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“…Sometimes, complex phenomena are occurred in the system because of atypical changes of the process behavior, output noise, or some hard nonlinearities. This was confirmed by studying data for real phenomena [12][13][14][15]. Such cases are described by non-Gaussian distributions.…”

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confidence: 56%

“…The block structure of pneumatic servo system is given in Figure 2. Moreover, many recent practical and theoretical studies have shown that in real systems, there are some observations that are inconsistent with the largest part of the population (outliers) [13][14][15]. Hence, the assumption that an exact distribution of stochastic disturbance e(k) is unknown will be used, but there is a priori information on the distribution class to which the disturbance belongs.…”

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confidence: 99%

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Identification of time‐varying OE models in presence of non‐Gaussian noise: Application to pneumatic servo drives

Stojanović

Nedić

2016

Intl J Robust & Nonlinear

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Intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which many important details cannot be included in the model. Owing the influence of the combination of heat coefficient, unknown discharge coefficient, and change of temperature, it was supposed that parameters of the pneumatic cylinder are random (stochastic parameters). On the other side, it has been well known that the nonlinear model can be approximated by a linear model with time-varying parameters. Due to the aforementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. In practical conditions, in measurements, there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. In this paper, the robust recursive algorithm for output error models with time-varying parameters is proposed. The convergence property of the proposed robust algorithm is analyzed using the methodology of an associated ordinary differential equation system. Because ad hoc selection of model orders leads to overparameterization or parsimony problem, the robust Akaike's criterion is proposed to overcome these problems. By determining the least favorable probability density for a given class of probability distribution represents a base for design of the robust version of Akaike's criterion. The behavior of the proposed robust identification algorithm is considered through intensive simulations that demonstrate the superiority of the robust algorithm in relation to the linear algorithms (derived under an assumption that the stochastic disturbance has a Gaussian distribution). The good practical values of the proposed robust algorithm to identification of the pneumatic cylinder are illustrated by experimental results.Recent research has shown that the nonlinear model of the system can be approximated, with great accuracy, by a time-varying linear system [10]. On the other hand, due to difficult quantification of phenomena described in (ii), one way to present them is the introduction of stochastic processes. Taking into account the previous considerations, it is assumed that the pneumatic cylinder is described by a linear stochastic output error (OE) model with variable parameters. It should be noted that the OE methods are maximum likelihood estimators as well as the equation error methods. The equation error method is used when the output contains both measurement noise and the disturbance (process noise), while the OE method is used when the output contains only the measurement noise [11].Description of stochastic disturbances by Gaussian process is not justified. Namely, in the population of observations, there are rare, large observations that are inconsistent with the majority of the population. Sometimes, complex phenomena are occurred in the system because of atypical changes of the process behavior, output noise, or s...

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confidence: 56%

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confidence: 99%

Identification of time‐varying OE models in presence of non‐Gaussian noise: Application to pneumatic servo drives

Stojanović

Nedić

2016

Intl J Robust & Nonlinear

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“…Based on this theory, it is possible to get, in the statistical sense, robust recursive algorithms (reduced sensitivity to change of the disturbance distribution) for estimation of the parameters of dynamic phenomena. The application of the above mentioned ideas in the problems of identification and predictions was demonstrated in references [7][8][9][10][11][12][13]. Simulations have shown superiority of robust algorithms in relation to classical (linear) algorithms.…”

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confidence: 99%

A global convergent outlier robust adaptive predictor for MIMO Hammerstein models

Filipović

2016

Intl J Robust & Nonlinear

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Summary The paper considers the outlier‐robust recursive stochastic approximation algorithm for adaptive prediction of multiple‐input multiple‐output (MIMO) Hammerstein model with a static nonlinear block in polynomial form and a linear block is output error (OE) model. It is assumed that there is a priori information about a distribution class to which a real disturbance belongs. Within the framework of these assumptions, the main contributions of this paper are: (i) for MIMO Hammerstein OE model, the stochastic approximation algorithm, based on robust statistics (in the sense of Huber), is derived; (ii) scalar gain of algorithm is exactly determined using the Laplace function; and (iii) a global convergence of robust adaptive predictor is proved. The proof is based on martingale theory and generalized strictly positive real conditions. Practical behavior of algorithm was illustrated by simulations. Copyright © 2016 John Wiley & Sons, Ltd.

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Low-order control-oriented modeling of piezoelectric actuator using Huberian function with low threshold: pseudolinear and neural network models

Corbier

Ugalde

2016

Nonlinear Dyn

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International audienceThis paper presents a new methodology of nonlinear system identification using Huberian function. Pseudolinear and Neural network black box model families are applied to identify a piezoelectric actuator for suspensions and vibration assisted drilling. Huberian function, which is a mixture of L2L2L\₂ and L1L1L\₁ norms with a threshold, is used to estimate a parameters vector in these model families. Pseudolinear black box model with reduced model order and balanced simplicity-accuracy neural network model families are proposed. Moreover, we show the interest to decrease the threshold in the Huberian function by providing efficient models for vibration drilling control. Experimental results are presented and discusse

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Extension of the tuning constant in the Huber's function for robust modeling of piezoelectric systems

Cited by 5 publications

References 28 publications

Identification of time‐varying OE models in presence of non‐Gaussian noise: Application to pneumatic servo drives

Identification of time‐varying OE models in presence of non‐Gaussian noise: Application to pneumatic servo drives

A global convergent outlier robust adaptive predictor for MIMO Hammerstein models

Low-order control-oriented modeling of piezoelectric actuator using Huberian function with low threshold: pseudolinear and neural network models

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