شناسایی جعبه خاکستری غیر خطی با استفاده از مدل محلی اعمال شده برای روبات های صنعتی

In this paper, we study the problem of estimating unknown parameters in nonlinear gray-box models that may be multivariable, nonlinear, unstable, and resonant at the same time. A straightforward use of time-domain predication-error methods for this type of problem easily ends up in a large and numerically stiff optimization problem. We therefore propose an identification procedure that uses intermediate local models that allow for data compression and a less complex optimization problem. The procedure is based on the estimation of the nonparametric frequency response function (FRF) in a number of operating points. The nonlinear gray-box model is linearized in the same operating points, resulting in parametric FRFs. The optimal parameters are finally obtained by minimizing the discrepancy between the nonparametric and parametric FRFs. The procedure is illustrated by estimating elasticity parameters in a six-axis industrial robot. Different parameter estimators are compared and experimental results show the usefulness of the proposed identification procedure. The weighted logarithmic least squares estimator achieves the best result and the identified model gives a good global description of the dynamics in the frequency range of interest for robot control.

When building a mathematical model of a physical object, the user generally has two sources of information; prior knowledge and experimental data. This gives the two modeling extremes, white-box models that are the result of extensive physical modeling from first principles, and black-box models, where the model is just a vehicle to describe the experimental data without any physical interpretations of its parameters. In between comes gray-box models that are parameterizations based on various degrees of physical insights. Compared with identification methods using black-box models, gray-box models have some particular benefits. By including prior information, the model set (number of parameters) can be reduced while still providing a good approximation of the true system. This gives a reduced mean-square error (bias and variance) ( Ljung, 2008). Since the gray-box model in contrast to the black-box model has a physical interpretation, the model is also useful in many ways, such as design optimization and virtual prototyping, which are important areas in industry. Some standard references for identification of gray-box models are Bohlin (2006), Ljung (1999), and Schittkowski (2002). There are also software packages available for identifying such models, e.g., Bohlin (2006), Kristensen, Madsen, and Jørgensen (2004), Ljung (2007), and Schittkowski (2002).

The problem of estimating unknown parameters in a nonlinear gray-box model has been studied. It has been shown in Section 2.2 that a time-domain prediction error method can be approximated by a frequency domain procedure that uses intermediate local models. This allows for data compression and a simplified optimization problem. The procedure is based on the estimation of the nonparametric FRF in a number of operating points. The nonlinear gray-box model is linearized in the same operating points and the optimal parameters are obtained by minimizing the discrepancy between the nonparametric FRFs and the parametric FRFs (the FRFs of the linearized gray-box model). Two different standard parameter estimators (NLS and LLS), as well as the selection of weights in the estimators, have been studied.