Search results for "describing function"

showing 3 items of 3 documents

Hidden oscillations in aircraft flight control system with input saturation

2013

Abstract The presence of actuator saturation can dramatically degrade the system performance. Since the feedback loop is broken when the actuator saturates the unstable modes of the regulator may then drift to undesirable values. The consequences are that undesired nonlinear oscillations appear and that the settling time may unacceptably increase. Rigorous analysis of nonlinear aircraft models is a very difficult task, that is why a numerical simulation is often used as an analysis and design tool. In this paper difficulties of numerical analysis related to the existence of hidden oscillations in the aircraft control system are demonstrated.

EngineeringSettling timebusiness.industryDescribing functionControl engineeringGeneral MedicineFeedback loopAircraft flight control systemNonlinear systemControl theoryControl systemNonlinear OscillationsbusinessActuatorIFAC Proceedings Volumes
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The Egan problem on the pull-in range of type 2 PLLs

2021

In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for …

PLLtype IIelektroniset piiritEgan problem on the pull-in rangehold-in rangeEgan conjectureglobal stabilityharmonic balance methodsäätöteoriavärähtelyttype 2describing functionphase-locked loopnonlinear analysisGardner problem on the lock-in rangedifferentiaaliyhtälötLyapunov functions
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Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs

2020

The most important design parameters of each phase-locked loop (PLL) are the local and global stability properties, and the pull-in range. To extend the pull-in range, engineers often use type 2 PLLs. However, the engineering design relies on approximations which prevent a full exploitation of the benefits of type 2 PLLs. Using an exact mathematical model and relying on a rigorous mathematical thinking this problem is revisited here and the stability and pull-in properties of the third-order type 2 analog PLLs are determined. Both the local and global stability conditions are derived. As a new idea, the harmonic balance method is used to derive the global stability conditions. That approach…

birth of oscillationselektroniset piirithold-in rangeglobal stabilityEgan conjecturethird-order PLLharmonic balance methodsäätöteoriavärähtelytdescribing functionsäätötekniikkalock-in rangephase-locked loopnonlinear analysispull-in rangetype 2 PLLmatemaattiset mallit
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