In this article we first review properties of the LuGre model, including zero-slip displacement, invariance, and passivity. An extension to include velocity-dependent microdamping is also discussed. The resulting model is then used to analyze stick-slip motion. The analysis shows that stick-slip motion modeled by the LuGre model is a stiff system with different behavior in the stick and slip modes as well as dramatic transitions between these modes. The dependence of limit cycles on parameters is discussed along with the notion of rate dependence.

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Revisiting the LuGre friction model

Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.

Modeling and Control of Piezo-Actuated Nanopositioning Stages: A Survey

Microgrids are a new concept for future energy distribution systems that enable renewable energy integration and improved energy management capability. Microgrids consist of multiple distributed generators (DGs) that are usually integrated via power electronic inverters. In order to enhance power quality and power distribution reliability, microgrids need to operate in both grid-connected and island modes. Consequently, microgrids can suffer performance degradation as the operating conditions vary due to abrupt mode changes and variations in bus voltages and system frequency. This paper presents controller design and optimization methods to stably coordinate multiple inverter-interfaced DGs and to robustly control individual interface inverters against voltage and frequency disturbances. Droop-control concepts are used as system-level multiple DG coordination controllers, and control theory is applied to device-level inverter controllers. Optimal control parameters are obtained by particle-swarm-optimization algorithms, and the control performance is verified via simulation studies.

Control Methods of Inverter-Interfaced Distributed Generators in a Microgrid System

This note presents a modification of the integrated friction model structure proposed by Swevers et al. (2000), called the Leuven model. The Leuven model structure allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. This note presents two modifications of the Leuven model. A first modification overcomes a recently detected shortcoming of the original Leuven model: a discontinuity in the friction force which occurs during certain transitions in presliding. A second modification, using the general Maxwell slip model to implement the hysteresis force, eliminates the problem of stack overflow, which can occur with the implementation of the hysteresis force.

Technical Note: modification of the Leuven integrated friction model structure

This paper investigates the robustness of positive-position feedback control of flexible structures with colocated force actuators and position sensors. In particular, the theory of negative-imaginary systems is used to reveal the robustness properties of multi-input, multi-output (MIMO) positive-position feedback controllers and related types of controllers for flexible structures. The negative-imaginary property of linear systems can be extended to nonlinear systems through the notion of counterclockwise input-output dynamics.

Feedback Control of Negative-Imaginary Systems

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.

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

Duhem modeling of friction-induced hysteresis

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.

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Counterclockwise Dynamics of a Rate-Independent Semilinear Duhem Model

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 testbed's friction-induced hysteresis.

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On the LuGre model and friction-induced hysteresis

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.

JinHyoung Oh

Papers

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

Duhem modeling of friction-induced hysteresis

Counterclockwise Dynamics of a Rate-Independent Semilinear Duhem Model

On the LuGre model and friction-induced hysteresis

Duhem Models for Hysteresis in Sliding and Presliding Friction