Identifikation dynamischer Systeme 2

Non-Invasive Parameter Identification by Using the Least Squares Method

“…The least squares method is a standard method of regression analysis in several fields of engineering [1]. It is based on measured data and a timediscrete model transfer function where the number of measurements is far greater than the model order.…”

“…The solution of a LS problem is the smallest sum of the squares of the errors. In this case, the parameters of the model function are called best fit [1,3]. The solution of a least squares problem can be carried out non-recursively and recursively [1].…”

“…In this case, the parameters of the model function are called best fit [1,3]. The solution of a least squares problem can be carried out non-recursively and recursively [1]. For the intended application on motion controllers, the recursive solution needs to be chosen.…”

“…This expression for the system behaviour (or parts of the system behaviour) can be used directly as model function of the LS problem, as shown in Figure 2 [1,7]. Hence, the estimated parameters of the model correspond with the physical values in the cascade structure.…”

“…The SeqMA as well as the SimMA approach were implemented on an industrial motion controller using the recursive least squares method [1]. The highest order of necessary matrix operations is 3.…”