Hi everyone,
I want to identify linear model for a pneumatic proportional valve that has hysteresis behavior. I split region of system to 9 sub-regions and apply a PRBS as input of system for every sub-region. Input-output data shows that because of hysteresis, upper bound of sub-region does not match on lower bound of next sub-region. for example, for the first sub-region, input PRBS with bounds of [3350 , 4200] is applied that leads to output flow of [7 , 13] as fig. 1.
for second sub-region, to reaching of output flow in range of [13 , 20], input PRBS with bounds of [3850 , 4280] is applied as fig. 2.
As can be seen, these sub-regions have overlap and cause problem for identification. how can i solve this problem ?
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...
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
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