Narrow-band Disturbances Research Articles

Active structural acoustic control of radiation due to broadband disturbances

Active structural acoustic control (ASAC) using the adaptive feedforward LMS algorithm has been demonstrated for narrow-band (harmonic) disturbances. This paper presents an extension of this work to the attenuation of acoustic radiation from structures subject to broadband (random) disturbances. The control compensators are adaptive finite impulse response (FIR) filters. The LMS control algorithm is implemented on a floating point digital signal processor. The control inputs are implemented with piezoelectric ceramic actuators (PZT), and both polyvinylidene flouride (PVDF) structural sensors designed to observe the efficient acoustic radiating modes and far-field microphones are used as error sensors. In the control of harmonically excited systems, satisfactory attenuation is achieved with a single-input, single-output (SISO) controller. In contrast, for systems excited with broadband disturbances, a multi-input, multi-output (MIMO) controller is necessary for significant acoustic attenuation. A MIMO broadband acoustic control system is developed and results for the control of a simply supported plate is presented. [Work supported by Office of Naval Research.]

Dual LQG-Based Methods for Rejection of Narrow Band Disturbances

Abstract In this paper the problem of rejecting sinusoidal disturbances is dealt with in an optimal control setting. First, the existing approaches are concisely surveyed and their deficiencies pointed out. Two main approaches are investigated: Frequency Shaping relies on a frequency weighted LQ cost functional, while Disturbance Modelling augments the system by including a state-space description of the disturbance. The main result of the paper is that a cross term in the LQ cost functional is needed in order to achieve disturbance rejection via Disturbance Modelling. Dually, when resorting to Frequency Shaping, the LQG problem must take into account correlated stale and observation noises.

Comparison and extensions of control methods for narrow-band disturbance rejection

Techniques for designing and implementing algorithms for the control of periodic narrowband disturbances are discussed, and the strong similarities between the different methodologies are shown. The analysis of linear time invariant feedback systems results in a suggestion of how to extend two of the LQ-based multiple-input, multiple-output methodologies to achieve improved performance and stability robustness properties. In the analysis of the adaptive feedforward methods, it is concluded that the popular filtered-x LMS algorithm is useful for implementation, but is best analyzed from a classical linear time invariant feedback perspective. This perspective results in a suggestion of how to extend the multiple error LMS algorithm to achieve improved performance and stability robustness. Stability bounds of the adaptive feedforward approaches are derived in terms of allowable model error.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An adaptive modal-based active control system

Active control for silencing sound and vibration has recently become the subject of much investigation, and is now being enhanced by the advent of adaptive filtering techniques. On another front, modal decomposition for active control problems has been shown to offer a number of practical advantages, as independent modal control can: minimize the number of actuators, sensors, and corresponding dimensionality of the controller, as well as minimize the control energy; provide robustness to system parameter uncertainty; and, minimize the adaptive convergence time by uncoupling the modal responses. In this paper, details are sketched for a narrow-band adaptive modal-based active control system that incorporates all of these features. The major topics addressed deal with modal filters, actuator prefilters, spatial sampling effects, and design methodology. Although this work pertains only to the narrow-band disturbance problem, these techniques can be readily generalized to the wideband case by using temporal filters to separate out different spectral bands for narrow-band modal-based processing. The analytical results are illustrated by numerical example for a vibrating cantilever beam, using a graphics display that was developed for real-time interactive design.

Reduction of radiation-pressure-induced fluctuations in interferometric gravity-wave detectors.

The performance of an interferometric gravity-wave detector is analyzed, treating both the motion of the mirrors and the optical fields quantum mechanically, in continuous time. Kerr cells in each arm of the interferometer are used to counter the effects of radiation-pressure fluctuations, a feedback loop is used to keep the interferometer operating at the proper null, and a large mean-field assumption is used to linearize the analysis. When narrow-band disturbances are being measured, the performance of this interferometer can greatly surpass the standard quantum limit. When the Kerr cells are removed, the interferometer operates at the standard quantum limit, and this analysis agrees with earlier studies.

Synchronization Failures in a Chain of PLL Synchronizers

In digital transmission systems employing PLL repeaters, timing jitter is produced mostly by intersymbol interference (ISI). Despite the fact that IS1 represents a narrow-band disturbance to the PLL for a long chain of N repeaters, it is responsible for cycle slips of the PLL repeater. It is demonstrated that the cycle slip rate is the key parameter determining the error performance of the system. It is shown that the accumulated jitter for a large chain becomes a narrow-band process, which can be replaced by an equivalent low-pass jitter-noise process, which lends itself to analytical treatment. Numerical results of the cycle slip rate are given, based on the solution of a time-dependent Fokker-Planck equation. The results are useful for a wide range of loop transfer functions and phase-detector characteristics. The theoretical findings are confirmed by experimental results.

A phase-front method -- II. Broad frequency band SH-waves

Summary. Two variants of a new approach to modelling the propagation of short-period seismic waves through heterogeneous media are evaluated by considering broad frequency band SH-waves. Like the original narrow frequency band approach, they are based on parabolic approximations in the time domain which are derived by, first, choosing a curvilinear coordinate system which is related to the phase fronts of the displacement field, and then making assumptions about the sizes of terms in the equation of motion. The resulting equations, which allow for diffraction where the diffracted energy propagates near the original direction of propagation, are only valid for disturbances whose wavelengths are small compared with the scale-length of variations in material properties. In the first approximation, a fixed, representative frequency used for narrow frequency band disturbances is replaced by the apparent frequency of the waves at each point in time and space, whereas the second approximation involves decomposing the time variation of the source into narrow frequency band signals. The second approach can be applied to a far wider class of problems. In addition, tests show that it gives much more consistent results.

Spurious Signals Caused by Noise in Triggered Circuits

The expected number of peaks/sec. (nσ+N), caused by noise or by a signal and noise, in excess of a given amplitude, or triggering level, is determined for broad-band noise (a) and for the envelope of a narrow-band disturbance (b). The signals considered here are pulses of various shapes (rectangular, triangular, trapezoidal), or a carrier modulated by these pulses. The expected number of peaks per second is directly proportional to the band width of the noise, and depends in some degree (20–30 percent) on filter shape, the gaussian response yielding a larger value of nσ+N than the rectangular, for the same total input power. Further, nσ+N is greatest when the triggering level is the most probable amplitude. Pulse shape is not significant when the pulses are on only a small fraction of the total period of observation, but becomes so if (1) the time of observation is comparable to the pulse length, and (2) the pulses have sharp leading edges. The latter gives rise to a transient effect which is not ignorable. This transient contribution does not appear in the envelope of narrow-band waves, as long as the maximum time-rate of change of the wave form of the envelope is much less than the central or resonant frequency of the IF, i.e., as long as the concept of ``envelope'' is meaningful. Rectification does not change nσ+N, provided that there is no appreciable distortion of the envelope by video- or audio-filters and that the triggering level of the input is passed by the detector. Improvement, defined in ways appropriate to the systems in question, of one circuit which can tolerate A1 spurious signals/sec. in excess of a given triggering level over another circuit, which can tolerate only A2 such signals (A1&amp;gt;A2), is calculated for broad-band signal and noise, and for narrow-band waves following half-wave linear or quadratic rectification. In general, the improvement is slight (a few db) if the trigger levels of the two circuits are not close to the most probable value of the amplitude and if the ratio of the number of spurious signals allowed/sec. to the band width of the disturbance is small. Significant improvement follows only when the maximum tolerable number of triggering peaks/sec. is the same order of magnitude as the band width of the noise. Tables and figures illustrating the above are included in Part I; the mathematical derivations are contained in Part II.