Dual-input Describing Function Method Research Articles

Novel Single-Stage Self-Oscillating Dimmable Electronic Ballast With High Power Factor Correction

A novel self-oscillating electronic ballast with dimming capability and high power factor correction (PFC) is proposed in this paper. The single-stage electronic ballast integrates a buck-boost PFC stage with a half-bridge LCC series-parallel resonant inverter. The buck-boost semistage operating in discontinuous conduction mode inherently has high PFC. The inverter is dimmable in self-oscillation mode, which is achieved using pulsewidth modulation and variable-frequency controls. The dimming circuit is simple and low cost. The self-sustained oscillation of the dimmable electronic ballast for fluorescent lamps was verified using the dual-input describing function method. A prototype of a 10-W dimmable electronic ballast was implemented to verify the theoretical analysis.

Kepler’s equation and limit cycles in a class of PWM feedback control systems

The aim of this paper is to point out some new results concerning the ripple instability in the closed-loop control system using pulse width modulators (PWM), with natural sampling, as power amplifier. The presented analysis, based on the dual-input describing function method and the theoretical framework of Kepler’s problem, shows an equivalence between the computation of switching instants of the PWM and the eccentric anomaly of the planet orbit around the sun, giving a simple stability criterion and a sufficient condition for the absence of solutions of the harmonic balance equation and, therefore, the probable absence of limit cycles of a period of a multiple of that characteristic of the modulator. The derived stability criterion, by using the describing function method, is successively compared with the local stability of the closed-loop PWM system for first- and second-order plants. In the first case it has been formally proved that the proposed criterion ensures the local stability of an equilibrium point, while in the second one a Monte Carlo simulation has confirmed that the selection of the modulator parameters, according to the proposed criterion, gives an effective method to avoid limit cycles and to ensure the local stability.

Nonlinear Aeroelastic Analysis of a Deployable Missile Control Fin

The nonlinear aeroelastic characteristics of a deployable missile control fin have been investigated. Modes from free vibration analysis and a doublet-point method are used for the computation of supersonic unsteady aerodynamic forces. The minimum-state approximation is used to approximate the aerodynamic forces. The fictitious mass modal approach is applied to reduce the problem size and the computation time in the linear and nonlinear flutter analyses. For the nonlinear flutter analysis, the deployable hinge is represented by an asymmetric bilinear spring and is linearized using the dual-input describing function method. From the nonlinear flutter analysis, three different types of limit-cycle oscillations are observed in the wide range of airspeed over the linear flutter boundary. The aeroelastic characteristics of the missile control fin can become more stable due to the existence of the deployable hinge nonlinearity.

Applications of describing functions to estimate the continuous and discontinuous conduction mode for a DC-to-DC buck converter

For a DC-to-DC buck converter, the performance of the conductor is significantly different for the converter operating on the continuous conduction mode (CCM) or discontinuous conduction mode (DCM). The operating condition on the CCM and DCM is addressed for a saturated inductor. It is shown that the inductor plays an essential role for the converter operating on the CCM and DCM. It is known that when the load is large, the inductance for the inductor always changes. This is due to the fact that when the current load is large, the inductance always suffers from saturation or hystersis. Because the inductance is nonlinear, it very difficult to estimate the actual value for the nonlinear inductance during large current situations. With the dual-input describing function method, the nonlinear inductor can be linearised and the inductance can be estimated during the large current situations. It can be shown that when the inductance of the inductor is saturated, the operating region of the discontinuous conduction mode (DCM) of the buck converter will extend drastically, which means the converter will easily operate in the discontinuous conduction mode. An experimental example verifies these results.

Study of Oscillations in a Particular Case of Yates-Pardee-Goodwin Metabolic Pathway with Coupling

The aim of this work is to study the effect of coupling on a metabolic pathway. Specifically we assume that metabolites can exchange matter with outside pools via passive diffusion. The existence of periodic solutions in such a system is considered and resolved using the dual input describing function method. In one particular case of coupling for all permissible parameter sets the minimum dimension is given so that it is possible to detect a periodic solution. The results obtained are compared with previously derived results for systems without coupling. It is concluded that coupling with exterior pools of metabolites can give rise to steady state instead of periodic solution.

Reaction wheel low-speed compensation using a dither signal

A method for improving low-speed reaction wheel performance on a three-axis controlled spacecraft is presented. The method combines a constant amplitude offset with an unbiased, oscillating dither to harmonically linearize rolling solid friction dynamics. The complete, nonlinear rolling solid friction dynamics using an analytic modification to the experimentally verified Dahl solid friction model were analyzed using the dual-input describing function method to assess the benefits of dither compensation. The modified analytic solid friction model was experimentally verified with a small dc servomotor actuated reaction wheel assembly. Using dither compensation abrupt static friction disturbances are eliminated and near linear behavior through zero rate can be achieved. Simulated vehicle response to a wheel rate reversal shows that when the dither and offset compensation is used, elastic modes are not significantly excited, and the uncompensated attitude error reduces by 34:1.

Self-excited vibration of a magnetic bearing system with flexible structures.

It is well known that self-excited vibrations in the passive axis of magnetic bearings may be caused by internal damping when the rotor is driven over critical speed. On the other hand, in the active axis of magnetic bearings, self-excited vibrations of high resonance frequency may occur at zero rotational speed. A self-excited vibration with two frequencies was observed on a 4-axis-active-type magnetic bearing which was developed for high speed rotating machinery. In this paper, we discuss the cause and mechanism of the self-excited vibration. The experimental results and computer simulation proved that the self-excited vibration is caused by interaction between nonlinearity of the power amplifiers and structural flexibility. The self-excited vibration mechanism is clarified by applying the root-locus method and approximate dual-input describing function method.

Quasi-linear analysis of oscillating servo-systems with random inputs

This paper presents an approximate analysis of oscillating servo systems with random inputs. The power spectrum relations for these systems are established by extending the dual-input describing function method. The analysis shows that the system exhibits a quasi-linear mode of operation similar to that previously shown to exist for a sinusoidal input. Distortion components resulting from the closed loop system are examined, and conditions for quasi-linear operation (small distortion) are given in terms of signal level and bandwidth. Some analog computer results are presented to demonstrate the applicability of the quasi-linear theory to the random input case.

Frequency response of feedback relay amplifiers

The frequency response of feedback relay amplifiers is analysed by the dual-input describing-function method. At low signal frequencies, the amplifier behaves like a saturating linear amplifier. This picture is modified at higher frequencies, owing to synchronous effects, and it is difficult to achieve satisfactory operation when the ratio of the input-signal frequency to the periodic excitation frequency is appreciable. To eliminate synchronous effects within the signal band, restrictions must be imposed on the forward linear-transfer function. The theory is compared with an experimental example.