Study On The Similarity Modeling Of Hysteresis

Hysteresis nonlinearity is a kind of very common nonlinear characteristics which widely exists in many fields, such as automatic control, civil engineering, electrical engineering, optical instrument engineering and so on. A lot of hysteresis nonlinear materials are widely used in precision machining and positioning systems due to its high positioning accuracy and the fast response characteristics. Yet the hysteresis nonlinearity which exists in these systems will not only reduce the control precision of the system, but also cause system instability. Therefore, the study of hysteresis nonlinearity has important practical significance. However, traditional modeling method is more complex and takes up larger storage space. To this end, this thesis will study a modeling method based on the similarity, which is without complicated operations and doesn’t need a lot of storage space.First of all, for Bouc-Wen model has the advantage of versatility, high precision and its parameters are easy to identify, we introduce the math description and hysteretic characteristics of the classical Bouc-Wen model and then study its geometric similarity and time-scale similarity. The Euclidean distance function is used for similarity measure and the least squares method and the particle swarm optimization algorithm are respectively applied for parameter estimation.Secondly, in view of the linear model, including the first order and the second order linear model, the geometric similarity and time-scale similarity are studied. Similarly, the Euclidean distance function is used to measure the similarity and the least squares and PSO method are applied to the parameter estimation.Finally, based on the study of Bouc-Wen model and linear model before, the combination, which is called the class Hammerstein model is studied. By the same token,the least squares method is used in the research of the geometric similarity and the PSO algorithm is used in study of the time-scale similarity.