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E. A. Misawa - One of the best experts on this subject based on the ideXlab platform.

  • A describing function approach to the design of robust Limit-Cycle controllers
    Nonlinear Dynamics, 2011
    Co-Authors: Neusa Maria Franco De Oliveira, Karl Heinz Kienitz, E. A. Misawa
    Abstract:

    The design of robust Limit-Cycle controllers is introduced for autonomous systems with separable SISO nonlinearities. The objective is to design a controller to secure specified robust oscillation amplitude and frequency. The method consists of quasi-linearization of the nonlinear element via a Describing Function (DF) approach and then shaping the loop to reach desired Limit-Cycle characteristics. As the DF method is used, loop shaping takes place in the Nyquist plot. An example is given to illustrate the robustness of the controlled system to uncertainties in the linear subsystem model.

  • An algebraic approach to the design of robust Limit Cycle controllers
    Proceedings of the 2003 American Control Conference 2003., 2003
    Co-Authors: Neusa Maria Franco De Oliveira, Karl Heinz Kienitz, E. A. Misawa
    Abstract:

    The design of robust Limit Cycle controllers introduced here can be used for autonomous systems with separable single-input-single-output nonlinearities and unavoidable Limit Cycles. The objective is to design a controller to secure specified oscillation amplitude and frequency. The method consists of quasi-linearization of the nonlinear element via a describing function (DF) approach and then shaping the loop to reach desired Limit Cycle characteristics. As the DF method is used, loop shaping takes place in the Nyquist plot.

M Wisse - One of the best experts on this subject based on the ideXlab platform.

  • controlling the walking speed in Limit Cycle walking
    The International Journal of Robotics Research, 2008
    Co-Authors: D G E Hobbelen, M Wisse
    Abstract:

    “Limit Cycle Walking” is a relatively new paradigm for the design and control of two-legged walking robots. It states that achieving stable periodic gait is possible without locally stabilizing the walking trajectory at every instant in time, as is traditionally done in most walking robots. Well-known examples of Limit Cycle Walkers are the Passive Dynamic Walkers, but recently there are also many actuated Limit Cycle Walkers. Limit Cycle Walkers generally use less energy than other existing bipeds, but thus far they have not been as versatile. This paper focuses on one aspect of versatility: walking speed. We study how walking speed can be varied, which way is energetically beneficial and how walking speed affects a walker's ability to handle disturbances (that is, disturbance rejection). The study is performed using one prototype and one simulation model. The speed of these two walkers is adapted by changing three parameters: the amount of ankle push-off, upper body pitch and step length. The study has resulted in four conclusions. (1) Steady-state speeds between 0.24 and 0.68 m s-1 (for a 0.6 m leg length) were obtained, with loss of stability determining the lower Limit and actuation Limits determining the upper Limit. This result shows the applicability of Limit Cycle Walking for versatile walking machines. (2) For any speed, powering the gait by leaning the body forward costs less energy than using ankle push-off. (3) In contrast to the apparent tradeoff between speed and stability in traditional walking robots, in Limit Cycle Walking we find that increasing the walking speed, independent of how this is done, automatically results in an increasing disturbance rejection. (4) A combination of feedforward actuation adjustment and step-to-step feedback from walking speed shows that it is possible to change walking speed in only a few steps and maintain a desired speed when performing tasks such as carrying loads and walking on slopes. In particular, this fourth conclusion underlines the applicability of the concept of Limit Cycle Walking for versatile two-legged walking machines.

  • ankle actuation for Limit Cycle walkers
    The International Journal of Robotics Research, 2008
    Co-Authors: D G E Hobbelen, M Wisse
    Abstract:

    Limit Cycle Walkers are bipeds that exhibit a stable cyclic gait without requiring local controllability at all times during gait. Well-known example are McGeer's “Passive Dynamic Walkers”, but the concept expands to actuated bipeds as involved in this study. Current state-of-the-art Limit Cycle Walkers excel in being very energy efficient, but their ability to handle disturbances (i.e. disturbance rejection) is still Limited. A way to improve this ability while maintaining low energy consumption is the use of ankle actuation, which has so far seen few applications in this type of walker. In this paper we study the effect of (1) applying (passive) stiffness in the ankle joint, (2) applying control in the stance ankle based only on local sensor information and (3) modulating ankle push-off. For all three strategies the paper shows how they influence energy use and disturbance rejection of a simple point mass walking model, a more realistic model and a physical prototype. We find that applying a passive ank...

  • swing leg retraction for Limit Cycle walkers improves disturbance rejection
    IEEE Transactions on Robotics, 2008
    Co-Authors: D G E Hobbelen, M Wisse
    Abstract:

    Limit Cycle walkers are bipeds that exhibit a stable cyclic gait without requiring local controllability at all times during gait. A well-known example of Limit Cycle walking is McGeer's ldquopassive dynamic walking,rdquo but the concept expands to actuated bipeds as involved in this study. One of the stabilizing effects in Limit Cycle walkers is the dissipation of energy that occurs when the swing foot hits the ground. We hypothesize that this effect can be enhanced with a negative relation between the step length and step time. This relation is implemented through an open-loop strategy called swing-leg retraction; a predefined time trajectory for the swing leg makes the swing leg move backwards just prior to foot impact. In this paper, we study the effect of swing-leg retraction through three bipeds; a simple point mass simulation model, a realistic simulation model, and a physical prototype. Their stability is analyzed using Floquet multipliers, followed by an evaluation of how well disturbances are handled using the Gait Sensitivity Norm. We find that mild swing-leg retraction is optimal for the disturbance rejection of a Limit Cycle walker, as it results in a system response that is close to critically damped, rejecting the disturbance in the fewest steps. Slower retraction results in an overdamped response, characterized by a positive dominant Floquet multiplier. Likewise, faster retraction results in an underdamped response, characterized by a negative Floquet multiplier.

Hiroya Nakao - One of the best experts on this subject based on the ideXlab platform.

  • phase reduction method for strongly perturbed Limit Cycle oscillators
    Physical Review Letters, 2013
    Co-Authors: Wataru Kurebayashi, Sho Shirasaka, Hiroya Nakao
    Abstract:

    The phase reduction method for Limit Cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also applicable to strongly perturbed Limit Cycle oscillators. The fundamental assumption of our method is that the perturbations can be decomposed into a slowly varying component as compared to the amplitude relaxation time and remaining weak fluctuations. Under this assumption, we introduce a generalized phase parameterized by the slowly varying component and derive a closed equation for the generalized phase describing the oscillator dynamics. The proposed method enables us to explore a broader class of rhythmic phenomena, in which the shape and frequency of the oscillation may vary largely because of the perturbations. We illustrate our method by analyzing the synchronization dynamics of Limit Cycle oscillators driven by strong periodic signals. It is shown that the proposed method accurately predicts the synchronization properties of the oscillators, while the conventional method does not.

  • dynamics of Limit Cycle oscillators subject to general noise
    Physical Review Letters, 2010
    Co-Authors: Denis S Goldobin, Hiroya Nakao, Junnosuke Teramae, Bard G Ermentrout
    Abstract:

    The phase description is a powerful tool for analyzing noisy Limit-Cycle oscillators. The method, however, has found only Limited applications so far, because the present theory is applicable only to Gaussian noise while noise in the real world often has non-Gaussian statistics. Here, we provide the phase reduction method for Limit-Cycle oscillators subject to general, colored and non-Gaussian, noise including a heavy-tailed one. We derive quantifiers like mean frequency, diffusion constant, and the Lyapunov exponent to confirm consistency of the results. Applying our results, we additionally study a resonance between the phase and noise.

  • stochastic phase reduction for a general class of noisy Limit Cycle oscillators
    Physical Review Letters, 2009
    Co-Authors: Junnosuke Teramae, Hiroya Nakao, Bard G Ermentrout
    Abstract:

    We formulate a phase-reduction method for a general class of noisy Limit Cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the Limit Cycle. The equation naturally includes previously proposed and mutually exclusive phase equations as special cases. The validity of the theory is numerically confirmed. Using the method, we reveal how noise and its correlation time affect Limit Cycle oscillations.

Earl H Dowell - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear Limit Cycle oscillation and flutter analysis of clamped curved plates
    Journal of Aircraft, 2020
    Co-Authors: Sadegh Amirzadegan, Earl H Dowell
    Abstract:

    This Paper studies the instability (flutter) and poststability Limit Cycle oscillations of elastic shallow shells in a supersonic gas flow. In a previous paper by the authors, a nonlinear dynamic a...

  • power extraction from aeroelastic Limit Cycle oscillations
    Journal of Fluids and Structures, 2011
    Co-Authors: Jared Dunnmon, Samuel C Stanton, Brian P Mann, Earl H Dowell
    Abstract:

    Abstract Nonlinear Limit Cycle oscillations of an aeroelastic energy harvester are exploited for enhanced piezoelectric power generation from aerodynamic flows. Specifically, a flexible beam with piezoelectric laminates is excited by a uniform axial flow field in a manner analogous to a flapping flag such that the system delivers power to an electrical impedance load. Fluid–structure interaction is modeled by augmenting a system of nonlinear equations for an electroelastic beam with a discretized vortex-lattice potential flow model. Experimental results from a prototype aeroelastic energy harvester are also presented. Root mean square electrical power on the order of 2.5 mW was delivered below the flutter boundary of the test apparatus at a comparatively low wind speed of 27 m/s and a chord normalized Limit Cycle amplitude of 0.33. Moreover, subcritical Limit Cycles with chord normalized amplitudes of up to 0.46 were observed. Calculations indicate that the system tested here was able to access over 17% of the flow energy to which it was exposed. Methods for designing aeroelastic energy harvesters by exploiting nonlinear aeroelastic phenomena and potential improvements to existing relevant aerodynamic models are also discussed.

  • modeling viscous transonic Limit Cycle oscillation behavior using a harmonic balance approach
    Journal of Aircraft, 2004
    Co-Authors: Jeffrey P Thomas, Earl H Dowell, Kenneth C Hall
    Abstract:

    Presented is a harmonic-balance computational fluid dynamic approach for modeling Limit-Cycle oscillation behavior of aeroelastic airfoil configurations in a viscous transonic flow. For the NLR 7301 airfoil configuration studied, accounting for viscous effects is shown to significantly influence computed Limit-Cycle oscillation trends when compared to an inviscid analysis. A methodology for accounting for changes in mean angle of attack during Limit-Cycle oscillation is also developed.

  • transonic Limit Cycle oscillation analysis using reduced order aerodynamic models
    Journal of Fluids and Structures, 2004
    Co-Authors: Earl H Dowell, Jeffrey P Thomas, Kenneth C Hall
    Abstract:

    Limit Cycle oscillations have been observed in flight operations of modern aircraft, wind tunnel experiments and mathematical models. Both fluid and structural nonlinearities are thought to contribute to these phenomena. With recent advances in reduced order aerodynamic modeling, it is now feasible to analyze Limit Cycle oscillations that may occur in transonic flow including the effects of structural and fluid nonlinearities. In this paper an airfoil with control surface freeplay (a common structural nonlinearity) is used to investigate transonic flutter and Limit Cycle oscillations. The reduced order aerodynamic model used in this paper assumes the shock motion is small and in proportion to the structural motions.

  • Limit Cycle behavior of an airfoil with a control surface
    Journal of Fluids and Structures, 1998
    Co-Authors: Deman Tang, Earl H Dowell, L N Virgin
    Abstract:

    A three-degree-of-freedom aeroelastic model with freeplay is modeled theoretically using a small number of aerodynamic eigenmodes (i.e. a reduced order model) based upon Peters' finite-state model for two-dimensional aerodynamic flow. The Limit Cycle behavior and the sensitivity to initial conditions for the onset of Limit Cycle oscillations are discussed. A simple and interesting physical explanation for this behavior is presented based on harmonic balance or describing function calculations that have been confirmed by numerical time simulations. The theoretical results are also in good agreement with experiment and a universal scaling law for the dependence of Limit Cycle oscillations and bifurcation parameters on freeplay is elucidated.

Martin Rasmussen - One of the best experts on this subject based on the ideXlab platform.

  • bifurcation analysis of a stochastically driven Limit Cycle
    Communications in Mathematical Physics, 2019
    Co-Authors: Maximilian Engel, Jeroen S W Lamb, Martin Rasmussen
    Abstract:

    We establish the existence of a bifurcation from an attractive random equilibrium to shear-induced chaos for a stochastically driven Limit Cycle, indicated by a change of sign of the first Lyapunov exponent. This relates to an open problem posed by Lin and Young (Nonlinearity 21:899–922, 2008) and Young (Nonlinearity 21:245–252, 2008), extending results by Wang and Young (Commun Math Phys 240(3):509–529, 2003) on periodically kicked Limit Cycles to the stochastic context.

  • bifurcation analysis of a stochastically driven Limit Cycle
    arXiv: Dynamical Systems, 2016
    Co-Authors: Maximilian Engel, Jeroen S W Lamb, Martin Rasmussen
    Abstract:

    We establish the existence of a bifurcation from an attractive random equilibrium to shear-induced chaos for a stochastically driven Limit Cycle, indicated by a change of sign of the first Lyapunov exponent. This addresses an open problem posed by Kevin Lin and Lai-Sang Young, extending results by Qiudong Wang and Lai-Sang Young on periodically kicked Limit Cycles to the stochastic context.