Hi Davood,

your main difficulty comes from the fact that you are trying to obtain linear models. This will generally NOT work for systems with hysteresis because such systems are NOT linearizable about an operating point, which is the underlying assumption of trying linear models for nonlinear systems. Other nonlinearizable (in the sense of truncating a Taylor series) examples include bilinear systems, that is, systems that have a dominant time constant in one direction (i.e. heating) and a very different one in the other direction (i.e. cooling). As a matter of fact thermal systems fall into this category.

You either ignore hysteresis or you go for nonlinear models.

Dear Coleg,

Plese view next links, maybe there are usefull:

https://www.researchgate.net/publication/258344221_Robust_Control_Solutions_for_Some_Classes_of_Hysteretic_Processes

https://www.researchgate.net/publication/257139649_Hysteresis_Control_of_a_%28BaSr%29TiO3_Based_Actuator_a_Comparison_of_Prandtl-Ishlinskii_and_Nonlinear_Compensator_Numerical_Methods

As base ideea process imput, is encreased-decreased; there are obtained statig gain or dynamic model.

Best regards,

Ciprian Lupu

Data Robust Control Solutions for Some Classes of Hysteretic Processes

Data Hysteresis Control of a (BaSr)TiO3 Based Actuator a Comparis...

Your problem can be solved by using correlation method.

Hi Davood,

your main difficulty comes from the fact that you are trying to obtain linear models. This will generally NOT work for systems with hysteresis because such systems are NOT linearizable about an operating point, which is the underlying assumption of trying linear models for nonlinear systems. Other nonlinearizable (in the sense of truncating a Taylor series) examples include bilinear systems, that is, systems that have a dominant time constant in one direction (i.e. heating) and a very different one in the other direction (i.e. cooling). As a matter of fact thermal systems fall into this category.

You either ignore hysteresis or you go for nonlinear models.

I completly agree with comments provided by  prof Lui Antonio Aguirre. I believe that it is the source of your problem

depending on the system,drawing a graph between Magnetization M and applied field H

forms a loop of hysteresis.

In some systems,we get a linear kind of loop,by zooming we can see a loop and also we can observe positive and negative magnetizations with smaller magnitudes

i found this kind of results in my systems

I also agree with Prof Aguirre. One approach to approximate your system could be instead to represent it as two systems (hybrid) and sort data according to direction of response (or other key states) to fit the two system dynamics approximately with linear or NL equations - i.e.  sometimes apparent hysteresis comes from switching dynamic states which could in principle each be linear (though not always) Check your representative euqations

thanks to all.

Dear Davood,

You may estimate a nonlinear system using a multi-level random signal instead of a traditional two-valued PRBS excitation input. The use of PRBS requires model linearization and multiple parts estimation, which is not suitable for your case. It consists of a white noise signal with high and low-frequency components, or with an approximately constant power spectral density so that your hysteresis model can be well characterized. I would not recommend the use of NARMAX and similar models for your problem (hysteresis persistent memory sequences). Instead, Preisach or L2P (Limiting loop proximity hysteresis model) [1] models may describe quite accurately your experimental data. The L2P is a simple algebraic model to describe magnetic hysteresis and has been successfully applied to other types of phenomena [2]. With only four parameters, it has low computational cost and reduced mathematical complexity, thus permitting a fast numerical implementation. You may use metaheuristics such as PSO and GA techniques for parameter estimation, or hybrid techniques including least-square and classical optimization. Despite the good performance in accuracy exhibited by metaheuristics, the PSO has shown a much better performance in terms of computational cost when it comes to hysteresis modeling. You may find the L2P model implemented in free software packages [3].

[1] de Almeida, L.A.L.; Deep, G.S.; Lima, A.M.N.; Neff, H., "Limiting loop proximity hysteresis model," Magnetics, IEEE Transactions on , vol.39, no.1, pp.523,528, Jan 2003

doi: 10.1109/TMAG.2002.806344

[2] Liu, Y., Moura, M. S., Costa, A. J., de Almeida, L. A. L., Paranjape, M., & Fontana, M. (2014). Hysteresis modeling in ballistic carbon nanotube field-effect transistors. Nanotechnology, Science and Applications, 7, 55–61. doi:10.2147/NSA.S58003

[3] HysterSoft is a computer program for the simulation of hysteresis and related phenomena in hysteretic systems. It provides a user-friendly simulation framework, in which various mathematical models of hysteresis can be implemented numerically relatively easy. HysterSoft version 2.0 comes with the following models already implemented by default (these models are called predefined models): the backlash operator, the Bouc-Wen model, the Coleman-Hodgdon model, the stop (elastic-plastic) operator, the energetic model, the Jiles-Atherton model, the Langevin model, the limiting-loop proximity model, the Preisach model (including the cases in which the Preisach distribution is specified analytically or using discrete values defined on a mesh), and the rectangular-loop model. Users can also add additional models to the program by using predefined templates. These models are called user-defined models. http://www.eng.fsu.edu/ms/HysterSoft/#

Department of Electrical and Computer Engineering

Florida State University and Florida A&M University