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

Abstract

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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