Effects Of Higher Order Harmonics Research Articles

Minimum altitude variation orbits. Analysis of characteristics and stability

The article discusses the regularities of satellite motion in almost circular orbits under the influence of the second zonal harmonic of the geopotential. The aim of the research is to determine the parameters of orbits with a minimum change in radius and to study the properties of these orbits. It is shown that the problem of determining the parameters of orbits with a minimum change in radius is of theoretical and practical interest. These orbits are the closest to Keplerian circular orbits. The practical interest in such orbits is determined by the possibility of using them for scientific research and Earth observation systems. Based on the analysis of the literature, it was concluded that the solution of the problem under consideration is not complete by now: the algorithm for determining the parameters of the orbits are not well founded and unnecessarily complicated; there is no analytical analysis of the stability of the orbits of the minimum change in radius. The efficiency of application of the previously developed theory of describing the motion of satellites in almost circular orbits for determining the parameters of orbits with a minimum change in radius is shown. For this purpose, the solutions of the first approximation of the motion of satellites in almost circular orbits under the influence of the second zonal harmonic of the geopotential have been improved. These solutions make it easy to determine the parameters of the orbits of the minimum change in radius. The averaged equations of the second approximation of the influence of the second zonal harmonic on the satellite motion are constructed and, on their basis, the stability of the orbits with a minimum change in radius is proved. It is shown that the second approximation in small parameters completely describes the main regularities of the long-period satellite motion under the influence of the second zonal harmonic of the geopotential. With the help of numerical studies, the instability of orbits with a minimum change in radius is shown with allowance for the effect of higher order harmonics of the geopotential. Analysis of the area of possible application of orbits with a minimum change in radius showed that such orbits can be of practical importance for very low and ultra low orbits, where the control action on the satellite movement is carried out at least once every two days.

Tuning procedure for event-based PI controllers under regular quantization with hysteresis

In this paper a tuning procedure is proposed for event based PI controllers with Regular Quantization with Hysteresis (RQH) sampling law. The RQH is a generalization of Symmetric Send on Delta (SSOD) strategy which decreases the robustness requirements to avoid limit cycle oscillations and reduce the number of events needed for control, improving the overall performance of PI controllers in networked control systems. The tuning procedure takes into account not only classical robustness margins but also takes advantage of some specific robustness measures to avoid limit cycle oscillations induced by the sampler. As the robustness analysis depends on the Describing Function (DF) method, a study evaluating the effect of high order harmonics is provided, showing the validity of the tuning procedure. Some examples are included in which the usefulness of the tuning procedure is shown.

Fast SPICE-Compatible Simulation of Low-Power On-Chip PWM DC–DC Converters With Improved Ripple Accuracy

The circuit averaging technique has long been used as the basis for modeling the behavioral effects of switched-mode pulsewidth-modulated (PWM) dc–dc power converter circuits due to its simplicity and efficiency in simulation. However, circuit-averaged models struggle to capture the effects of higher order harmonics on the output waveforms. Alternatively, multiharmonic models that capture high-frequency characteristics of output waveforms are typically very complex and computationally expensive. A general, efficient, and accurate multiharmonic modeling and simulation technique for low-power on-chip PWM dc–dc converters is presented in this article. The technique is based on the large-signal averaged model of the PWM switch cell and on the Fourier series expansion of the typical converter waveforms. Its applicability range includes current-mode-controlled dc–dc converters. The method is exemplified on a buck and on a boost converter and achieves a speedup of one order of magnitude with an accuracy loss below 3% over the transistor-level simulation. The method accounts for nonideal circuitry and supports any number of harmonics.

Reset Control for Vibration Disturbance Rejection

The high tech industry which requires fast stable motion with nanometer precision continues to mainly use PID which is limited by fundamental linear control limitations. Floor vibrations as disturbance significantly affect performance and their rejection is particularly affected by these limitations. Reset control has provided a promising alternative to surpass these, while simultaneously allowing the use of industry standard loop-shaping during design. However, the reset action introduced higher order harmonics can induce unwanted dynamics and negatively influence performance. This paper investigates two reset control strategies namely (1) band-pass phase lag reduction and (2) phase compensation to reduce the negative effects of higher order harmonics. The strategies are tested on a precision positioning stage for vibration rejection and the results show that phase compensation provides better performance compared to other tested strategies.

Parametric modeling and experimental characterization of a nonlinear resonant piezoelectric actuator designed for turbulence manipulation

In this work we fabricate and optimize a resonant piezoelectric actuator designed for the manipulation of turbulent flow at airfoils and propose analytical expressions for its nonlinear vibration characteristics. High frequency large displacement manipulation of the turbulent boundary layer offers a promising route to influence the frictional drag and hence minimize fuel consumption in modern aviation. Nonlinear design and resonant operation offer a wide-band and energy efficient operation window respectively. The hard duffing-type piezoelectric actuator is designed for extremely fast system dynamics realizing peak-to-peak amplitudes of up to 700μm in the frequency range of 1100Hz with a 3dB operational bandwidth of approximately 100Hz. A systematic parametric study, based on the derived analytical model, helped to optimize the actuator design. In addition, numerical simulations were performed to analyze the effect of higher order harmonics to a mono-frequency excitation signal. A single degree of freedom duffing-type analytical model was shown to sufficiently predict the nonlinear system dynamics. Furthermore, complete systematic design validation is demonstrated by integration of the resonant actuator in a wind tunnel for a turbulence manipulation study.

The effect of higher order harmonics on second order nonlinear phenomena

A new method which is a combination of the harmonic balance and finite difference techniques (HBFD) is proposed for complete time-harmonic solution of the nonlinear wave equation. All interactions between different harmonics up to an arbitrary order can be incorporated. The effect of higher order harmonics on two important nonlinear optical phenomena, namely, the second harmonic generation (SHG) and frequency mixing is investigated by this method and the results are compared with well-known analytical solutions. The method is quite general and can be used to study wave propagation in all nonlinear media.

Stability study of icosahedral phases in diblock copolymer melt

The stability of three possible icosahedral phases (called here vertex, edge, and face models, respectively) in a diblock copolymer melt is examined, with higher harmonics included in the density-wave mean field theory developed by Leibler. Two cases are examined: (1) diblock copolymer melt with constant coupling vertices, and (2) diblock copolymer melt with general coupling vertices in which, unlike all the previous studies on the effect of higher order harmonics in diblock copolymer melt, the calculation is performed exactly. We find that icosahedral phases are always metastable and the mean-field phase diagram of the diblock copolymer is unchanged.

KBM METHOD OF ANALYZING LIMIT CYCLE FLUTTER OF A WING WITH AN EXTERNAL STORE AND COMPARISON WITH A WIND-TUNNEL TEST

The limit cycles flutters of two models of a wing/store with free play in the junction, one of two-dimensional wing, and the other a delta wing, are investigated. The equivalent linearization method based on the first order asymptotic solution of the KBM method and the method based on the second order asymptotic solution of the KBM method are used to analyze the limit cycle flutter of the wing with store system. The results are compared with those of numerical integration and a wind-tunnel test. It is shown that, in some cases, the features of the limit cycle flutter obtained by numerical integration can be predicted by the equivalent linearization method based on the second order asymptotic solution of the KBM method, whereas the conventional describing function method fails to do so. The results of the wind-tunnel test show that, for free play, the effect of high order harmonics on the limit cycle response to the aeroelasticity system is strong when the limit cycle amplitude is small.

Optimization of RFQ vane parameters using a non-linear beam dynamics code

For optimization of the vane parameters of a heavy-ion RFQ, we used a beam dynamics code including effects of higher-order harmonics in the intervane potential. By using a three-module cavity structure, we obtained not only precise and easy assembling but also stable RF characters during operation.