JinHyoung Oh

Semilinear Duhem model for rate-independent and rate-dependent hysteresis

The classical Duhem model provides a finite-dimensional differential model of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. 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 nontrivial input-output closed curve (that is, hysteresis) at arbitrarily low input 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. Finally, the reversal behavior and orientation of the rate-independent model are discussed.

Duhem modeling of friction-induced hysteresis

In this article we recast the Dahl, LuGre, and Maxwell-slip models as extended, generalized, or semilinear Duhem models. We classified each model as either rate independent or rate dependent. Smoothness properties of the three friction models were also considered. We then studied the hysteresis induced by friction in a single-degree-of-freedom system. The resulting system was modeled as a linear system with Duhem feedback. For each friction model, we computed the corresponding hysteresis map. Next, we developed a DC servo motor testbed and performed motion experiments. We then modeled the testbed dynamics and simulated the system using all three friction models. By comparing the simulated and experimental results, it was found that the LuGre model provides the best model of the gearbox friction characteristics. A manual tuning approach was used to determine parameters that model the friction in the DC motor.

Nonlinear feedback models of hysteresis

In the present article we investigate multistability and hysteresis within the context of linear systems with nonlinear feedback. For concreteness and simplicity, we focus primarily on single-input, single-output linear systems with companion-form realizations. For various choices of the realization parameters, we characterize the input-output equilibria set. We analyze this set in detail for the case of a deadzone nonlinearity, and we determine the values of the realization parameters that give rise to traversal-type or bifurcation-type hysteresis. The rich diversity of hysteretic phenomena that can be generated by interconnecting a linear system with a feedback nonlinearity is the motivation for this article.

Counterclockwise Dynamics of a Rate-Independent Semilinear Duhem Model

Counterclockwise hysteresis maps are known to be dissipative in the energy sense as well as in the system-theoretic sense. In a recent paper, Angeli studied feedback interconnections of counterclockwise systems, where counterclockwise refers to the net signed area of the input-output map, which need not be a simple closed curve. In the present paper we apply this notion to the study of hysteretic models. In particular, we give conditions under which the semilinear Duhem model is counterclockwise.

On the LuGre model and friction-induced hysteresis

In this paper, we study hysteresis induced by friction in a simple mass-spring system and then in a dc servo motor experimental setup. The experimental setup is modeled and simulated using the Dahl, LuGre, and Maxwell-slip friction models. Comparison of the experimental and simulation results reveals that the LuGre model provides the best model of the testbeds friction-induced hysteresis

Duhem Models for Hysteresis in Sliding and Presliding Friction

In this paper we analyze the Dahl, LuGre, and Maxwell-slip friction models as Duhem hysteresis models. We classify each model as either a generalized or a semilinear Duhem model, and we analyze the rate-independent or ratedependent behavior of the corresponding input-output map. This unified treatment of Duhem-based friction models is used to investigate friction-induced hysteresis.

Fixed-structure controller design for discrete-time systems with actuator amplitude and rate saturation constraints

We develop fixed-order (i.e., full- and reduced-order) controllers for linear discrete-time systems with actuator amplitude and rate saturation constraints. The problem is formulated as a multiobjective problem involving a convex combination of an l/sub 1/ norm and the H/sub 2/ norm to capture actuator saturation constraints and closed-loop system performance in the face of exogenous white noise disturbances.

Step convergence analysis of nonlinear feedback hysteresis models

In this paper we consider nonlinear feedback hysteresis models. Since hysteresis is defined as a nontrivial input-output map under quasi-DC inputs, the relationship between step convergence and the hysteresis map of the model is investigated. The class of models that exhibit hysteresis is determined and the shape of the hysteresis map is characterized. We focus on the deadzone nonlinearity, which has implications for backlash modeling. Numerical examples are presented to verify the analysis.

Linear Controller Analysis and Design for Systems with Input Hystereses Nonlinearities

Abstract An output feedback control analysis and design framework for linear systems with input hystereses nonlinearities is developed. Specifically, by transforming the hystereses nonlinearities into dissipative input–output dynamical operators, dissipativity theory is used to analyze and design linear controllers for systems with hysteretic actuators. The overall framework guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system state associated with the plant and the controller. Furthermore, the remainder of the state associated with the hysteresis dynamics is shown to be semistable; that is, solutions of the hysteretic system converge to Lyapunov stable equilibrium points determined by the system initial conditions.

Modeling and Identification of Rate-Independent Hysteresis Using a Semilinear Duhem Model 1

Abstract In this paper we consider a semilinenr Duhem model. The input-output map of the model is rate-independent, thus yielding persistent phase shift (that is. hysteresis) at arbitrarily low frequency. For the semilinear Duhem model we reparameterize the response in terms of the control input, and we provide sufficient conditions for convergence to a hysteresis map. A constrained least squares method is developed to identify the hysteresis map using the semilinear Duhem model.