System Identification by Multi Decimation

Abstract

The least-squares (LS) method is one of the most familiar and useful system identification method. However, there are many problems to be solved when one applies the LS method to the actual system. For example, it is difficult to identify lower frequency region accurately, because the cost function in the conventional LS method weights higher frequency region. This paper proposes a new identification method which uses multiple decimation operation, so we call it MD (MultiDecimation) method. The decimation, consists of the low-pass filtering and the resampling whose sampling rate is decreased, is widely used in the area of the signal processing. The advantages of the MD method are (a) By deviding the frequency region of the system, the characteristics in lower frequency region can be identified accurately as well as that in higher frequency region, (b) Data scaling can be carried out individually in each devided frequency region, and (c) By focusing on the narrow band, vibrational characteristics which are difficult to identify by the LS method can be identified accurately.In industrial robots, there are many vibrational modes which are caused by speed-reduction mechanisms, in the wide frequency range. It is necessary to identify these vibrational modes accurately so as to design stable servo controllers.So, we apply the MD method to the identification of robot arm, and we show the efficiency of the MD method through the identification experiments.

Time Series Motion Generation Considering Long Short-Term Motion

“…Pre-processing consists of a low-pass filter (LPF), which can remove sensing noise, and down-sampling, which avoids overfitting in high frequency regions. The least-squares method is one of the most widely used system identification methods; however, the cost function weighs high frequency regions more than low frequency regions [18] [19]. Although it is possible to prevent overfitting in the high frequency range by decimation, it varies depending on the frequency range to be identified.…”

“…Robotic physical dynamic characteristics spread from the low frequency region to the high frequency region and so on. Because the cost function in the usual least-squares method emphasizes high frequency regions results in poor identification accuracy in low frequency regions, Adachi et al proposed the MD identification method [18]. This method makes it possible to identify low frequency region characteristics as accurately as those in the high frequency region.…”