Relationship between parameter estimation method based on Bode diagram and co-quad diagram

Abstract

In order to improve the simulation system and to develop the control system with high performance, the dynamical model of the controlled object must precisely be derived. Ordinarily, the parameters are estimated by using the characteristic point data on the Bode diagram. As is well-known, this method is widely used in the production field. Meanwhile, the co-quad diagram based parameter estimation method was also known. It is said that this method can derive more precise modal parameters than the conventional method can. However, an explanation for the theoretical background is insufficient. In this paper, this reason is clarified by introducing the sensitivity function. Firstly the frequency response curve of both the Bode diagram and the co-quad diagram are shown for the compliance, the mobility, and the inertance. Next the parameter estimation formulas are derived by using the co-quad diagram. Secondly, by introducing the sensitivity function, it is shown that the co-quad based method has better performance from the parameter estimation point of view than the conventional one has. Finally, the parameter estimation method based on the co-quad diagram is applied to the measured inertance response and it is confirmed that the realistic parameters can derive in comparison with these from the Bode diagram.