Ashwani K. Padthe

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.

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.

Computational Study of Microflaps with Application to Vibration Reduction in Helicopter Rotors

of oscillating Gurney flaps, or microflaps, has been conducted. Two-dimensional unsteady airloads, lift, moment and drag, due to an oscillating microflap were computed using a compressible Reynolds-Averaged Navier-Stokes (RANS) flow solver. The CFD results were generated with an overset mesh approach that captures oscillatory microflap motion. Three microflap configurations were examined so as to determine the type most suitable in terms of actuation eciency and practical implementation. Furthermore, a reduced order model (ROM) for the unsteady microflaps was developed based on CFD simulations, using the Rational Function Approximation (RFA) approach. The resulting RFA model is a state-space, time-domain aerodynamic model that accounts for unsteadiness, compressibility and time-varying freestream eect, suitable for use with comprehensive rotorcraft simulations. The agreement between the ROM and direct CFD calculations was found to be excellent even in presence of strong nonlinear flow eects. The approximate model is suitable for incorporation in a comprehensive code, from which the potential of microflaps for active control of vibrations in rotor can be determined. Preliminary studies with open loop control showed that the microflap produces substantial vibration reduction (52% reduction in vertical shear) on a hingeless rotor configuration resembling the MBB BO-105, confirming the control authority of this novel technique.

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.

CFD-based adaptive flow control using ARMARKOV disturbance rejection

In this paper we demonstrate adaptive flow control for an incompressible viscous fluid through a two-dimensional channel without the use of an analytical model. An adaptive disturbance rejection algorithm is implemented within a CFD simulation to reduce the effects of an unknown velocity disturbance on the performance variable z, which is the transverse velocity component of the flow at a downstream location. The algorithm requires minimal knowledge of the system, specifically, the numerator coefficients of the transfer function from the control input to the performance variable. System identification, based on CFD simulations prior to the disturbance rejection simulations, is used to identify the required parameters

Numerical Evaluation of Microflaps for On Blade Control of Noise and Vibration

in reducing noise and vibration in rotorcraft, as well as improving rotor performance. The effectiveness of the microflap is examined using a comprehensive rotorcraft simulation code. The aerodynamic properties of the microflap is modeled using a nonlinear CFD based reduced order aerodynamic model that takes into account unsteadiness, compressibility and time varying freestream eects. Active control studies employing microflaps are conducted on a hingeless rotor configuration resembling the MBB BO-105, and various spanwise configurations of the microflaps, including a single, a dual, and a segmented five-microflap configuration are evaluated. Results indicate that the microflap is capable of substantial reductions in blade vortex interaction (BVI) noise ranging from 3-6 dB. Vibration reduction ranging from 70-90% is also demonstrated. The interaction of vibration and noise reduction is also examined, and it was found reduction in one objective is accompanied by an increase in the other, a trend also observed when using other active approaches. Finally, the microflap is considered for combined vibration reduction and performance enhancement at a high speed cruise flight condition. The results clearly indicate that the microflaps are very eective for both noise and vibration reduction in helicopters, and they may also have potential for rotor performance enhancement.

A Delay-Duhem model for jump-resonance hysteresis

In this paper we present a Duhem hysteretic model that models jump resonance hysteresis in Dufflngs oscillator. In order to obtain the Duhem model, we use a nonlinear oscillator that can output a harmonic signal of specified frequency and amplitude. We also use a sliding time averaging system that captures the mean square value of a variable-period signal. The presented Duhem model represents the excitation frequency versus response amplitude hysteresis of Dufflngs oscillator in the sense of a persistent input-output loop under asymptotically slow periodic excitation. We also show that the jump resonance hysteresis is rate dependent.

Hysteresis Analysis and Feedback Stabilization of Snap-through Buckling

We study a preloaded two-bar linkage that exhibits hysteresis due to the presence of multiple attracting equilibria. The dynamics at the unstable equilibrium, through which a snap-through buckle occurs, are not linearizable due to a singularity that is solution-dependent. We stabilize the unstable equilibrium using two distinct nonlinear controllers. The feedback linearization controller requires knowledge of the linkage parameters, whereas the potential shaping PD-type controller requires only an upper bound on the stiffness.

Duhem Feedback and Friction-Induced Staircase Hysteresis

In this paper we provide a system-theoretic picture of the hysteresis induced by friction. We study the hysteretic response of a linear system connected with a Duhem hysteretic model in the feedback. We then use the popular Dahl and LuGre Duhem friction models to model the mass-spring system with friction, as a linear system with Duhem feedback. We use the feedback model to study the hysteretic response between the external force applied on the mass and the displacement of the mass.