Topic
Describing function
About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.
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TL;DR: In this article, the authors performed linear and nonlinear aeroelastic analysis of a fighter-type wing with a control surface using frequency-domain and time-domain analyses.
Abstract: Linear and nonlinear aeroelastic analyses of a fighter-type wing with a control surface have been performed by using frequency-domain and time-domain analyses. Modes from free vibration analysis and a doublet-hybrid method are used for the computation of subsonic unsteady aerodynamic forces. The fictitious mass modal approach is used to reduce the problem size and the computation time in the linear and nonlinear flutter analyses. For the nonlinear flutter analysis, the control surface hinge is represented by a free-play spring and is linearized by using the describing function method. The linear and nonlinear flutter analyses indicate that the flapping mode of the control surface and the hinge stiffness have significant effects on the flutter characteristics. From the nonlinear flutter analysis, limit-cycle oscillation and chaotic motion are observed in a wide range of air speed below the linear flutter boundary, and a jump of limit-cycle oscillation amplitude is observed.
51 citations
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15 Sep 2000-Jsme International Journal Series C-mechanical Systems Machine Elements and Manufacturing
TL;DR: In this paper, the gas force is represented in terms of equivalent stiffness and equivalent damping by employing the describing function approach so that analysis of steady state response characteristics and jump phenomenon can be done in a way simpler than by the full nonlinear model.
Abstract: In linear electrodynamic oscillating compressors, gas force has nonlinear characteristics depending on the stroke of piston. Static and dynamic components of the force are coupled to each other. Furthermore, mechanical part is coupled with electromagnetic part. Hence, dynamics analysis of the whole system is very complicated. In this paper, the gas force is represented in terms of equivalent stiffness and equivalent damping by employing the describing function approach so that analysis of steady state response characteristics and jump phenomenon can be done in a way simpler than by the full nonlinear model. In order to illustrate accuracy of the equivalent model, the frequency response characteristics of the proposed model are compared with those of the full nonlinear model. Jump phenomena depending on the amplitude of supply voltage is also investigated by using the equivalent model and the necessary conditions for jump to occur are derived.
50 citations
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06 Jul 2016TL;DR: The validity and predictive value of the control design procedure (both in terms of stability and performance) will be demonstrated by means of (measurement) results obtained from an industrial wafer stage system.
Abstract: In dealing with inherent limitations during stage control design, the possibilities of a second-order reset element (SORE) are studied, in particular, a second-order low-pass filter with reset. Inducing significantly less phase lag, which follows from describing function analysis, SOREs allow for a significant increase of bandwidth in comparison to linear second-order elements. Being part of a reset control design procedure, loop-shaping of the linear feedback loop with a reset element will be based on a describing function description of this element. For the reset control system, closed-loop stability will be verified by solving linear matrix inequalities. The validity and predictive value of the control design procedure (both in terms of stability and performance) will be demonstrated by means of (measurement) results obtained from an industrial wafer stage system.
50 citations
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TL;DR: In this paper, the authors proposed a mathematical framework that accurately quantifies oscillation characteristics for a general class of nonlinear car-following laws, which is comprised of three modules: expression of car following models in terms of oscillation components, analyses of local and asymptotic stabilities, and quantification of propagation characteristics.
Abstract: Unlike linear car-following models, nonlinear models generally can generate more realistic traffic oscillation phenomenon, but nonlinearity makes analytical quantification of oscillation characteristics (e.g, periodicity and amplitude) significantly more difficult. This paper proposes a novel mathematical framework that accurately quantifies oscillation characteristics for a general class of nonlinear car-following laws. This framework builds on the describing function technique from nonlinear control theory and is comprised of three modules: expression of car-following models in terms of oscillation components, analyses of local and asymptotic stabilities, and quantification of oscillation propagation characteristics. Numerical experiments with a range of well-known nonlinear car-following laws show that the proposed approach is capable of accurately predicting oscillation characteristics under realistic physical constraints and complex driving behaviors. This framework not only helps further understand the root causes of the traffic oscillation phenomenon but also paves a solid foundation for the design and calibration of realistic nonlinear car-following models that can reproduce empirical oscillation characteristics.
50 citations
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TL;DR: In this article, a constant in gain lead in phase (CgLp) element using nonlinear reset technique is proposed for high-tech precision positioning applications, which can be integrated with PID and tested on one of the DOFs of a planar precision positioning stage.
Abstract: This paper presents a novel “Constant in gain Lead in phase” (CgLp) element using nonlinear reset technique. PID is the industrial workhorse even to this day in high-tech precision positioning applications. However, Bode's gain phase relationship and waterbed effect fundamentally limit performance of PID and other linear controllers. This paper presents CgLp as a controlled nonlinear element which can be introduced within the framework of PID allowing for wide applicability and overcoming linear control limitations. Design of CgLp with generalized first-order reset element and generalized second-order reset element (introduced in this paper) is presented using describing function analysis. A more detailed analysis of reset elements in frequency domain compared to existing literature is first carried out for this purpose. Finally, CgLp is integrated with PID and tested on one of the DOFs of a planar precision positioning stage. Performance improvement is shown in terms of tracking, steady-state precision, and bandwidth.
50 citations