Modeling, identification, and control of rate-independent and rate-dependent hysteresis

Hysteresis is a ubiquitous phenomenon arising in diverse areas of engineering. In this dissertation we discuss the finite-dimensional differential models of hysteresis and its application on identification and control. First we consider rate-independent and rate-dependent semilinear Duhem models. The vector field is given by the product of a function of the input rate and linear dynamics. If the input rate function is positively homogeneous, then the resulting input-output map of the model is rate independent, yielding persistent input-output closed curve (that is, hysteresis) at arbitrarily low frequency. If the input rate function is not positively homogeneous, the input-output map is rate dependent and can be approximated by a rate-independent model for low frequency inputs. Sufficient conditions for convergence to a limiting input-output map are developed for rate-independent and rate-dependent models. The reversal behavior and orientation of the rate-independent model are also discussed. Furthermore, an effect of dither on the semilinear Duhem model is investigated.; We also develop identification methods for rate-independent and rate-dependent hysteresis based on the semilinear Duhem model. For the rate-independent hysteresis, we parameterize the system in terms of the input signal, and the system has the form of a linear system with ramp forcing. For the rate-dependent hysteresis, the system can be viewed as a switching linear time-invariant system for triangle wave inputs. Least squares-based methods are developed to identify the rate-independent and rate-dependent semilinear Duhem model. Numerical examples are considered to verify the proposed identification methods.; Finally, we develop a nonlinear feedback hysteresis model. Since hysteresis is defined as the response in the limit of DC operation, we investigate the relationship between hysteretic maps and step convergence of the system using the limiting equilibria map. For the first-order nonlinear feedback hysteresis model, a graphical analysis for the step convergence is discussed. As a specialization of the nonlinear feedback hysteresis model, we consider a deadzone-based backlash hysteresis model. The class of models that exhibits hysteresis is determined and the shape of the hysteretic map is characterized.