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Abstract: A method for the identification of MIMO input-output LPV models in closed-loop is proposed. The model is assumed to display both linear and non-linear behavior in which the latter is dependent on the scheduling parameters, and cubic splines are used to represent the non-linear dependence. For the estimation of both linear and non-linear parameters, the separable least square method is employed. The linear parameters are obtained by a least square identification algorithm, while the non-linear parameters are obtained using a recursive Levenberg-Marquardt algorithm. To identify such a model in closed-loop, we use a non-linear version of a two-step method. A neural network ARX model will be used in the first step for two purposes. Firstly, to generate noise-free input signal to get an unbiased model and secondly to generate noise-free scheduling signal for consistent identification. The proposed method is applied to an arm-driven inverted pendulum. The resulting model is compared with a linear time-invariant model, and with an LPV model that depends polynomially on the scheduling parameters. Experimental results indicate that the cubic spline model outperforms the other ones in terms of accuracy.

Note:

Abstract: A method for the identification of MIMO input-output LPV models in closed-loop is proposed. The model is assumed to display both linear and non-linear behavior in which the latter is dependent on the scheduling parameters, and cubic splines are used to represent the non-linear dependence. For the estimation of both linear and non-linear parameters, the separable least square method is employed. The linear parameters are obtained by a least square identification algorithm, while the non-linear parameters are obtained using a recursive Levenberg-Marquardt algorithm. To identify such a model in closed-loop, we use a non-linear version of a two-step method. A neural network ARX model will be used in the first step for two purposes. Firstly, to generate noise-free input signal to get an unbiased model and secondly to generate noise-free scheduling signal for consistent identification. The proposed method is applied to an arm-driven inverted pendulum. The resulting model is compared with a linear time-invariant model, and with an LPV model that depends polynomially on the scheduling parameters. Experimental results indicate that the cubic spline model outperforms the other ones in terms of accuracy.