Dept. of Appl.Math @ ucc.ie
Systems with Hysteresis
Welcome

Contents

What is `Hysteresis'

Preisach Model

Closed loop systems
   Pendulum in magnetic field
   ODE with Relay
   ODE with Weiss model
   ODE with Preisach model

Complex behavior

Other Hysterons

Advanced modelling

Bibliography

ODE with Relay

If the pendulum is a magnetic monocrystal, that is, it may have only two values of magnetization, then the nonlinearity $P$ is described by the nonideal relay $R_{\alpha ,\beta }$. Consider the following modification of model (3)

\begin{displaymath} x''+x=A\sin(\sqrt{2} t)+b R_{-1,1}x(t). \end{displaymath}

An applet, allowing experimentation with parameters $A$ and $b$, is given below. The Preisach nonlinearity $P$ used in the model above is the one used before. The two pictures of the pendula on the top show the behavior of the monocrystal pendulum in the magnetic field (black) and the pendulum without it (red). Graphs of pendula positions versus time can be found at the bottom part of the applet.