Spectral estimation of continuous-time processes: Performance comparison between periodic and Poisson sampling schemes

Abstract

instabilities especially in the residual modes where there is little or no stability margin. In a very simple and mathematically well-known example of a flexible system, we have illustrated the residual mode instability caused by spillover (Section V).Observation spillover can be virtually eliminated with a phase-locked loop prefilter (Section IV) and the closed-loop system poles then become the controlled poles, the estimator poles, and the residual poles (Section III) and no instabilities can occur. Allowances for the effect of control spillover on system response can often be made in the origrnal design [28]. When spillover is taken into account this control scheme has several advantages:1) Many modes can be controlled by only a few actuators and sensors.2) Actuators and sensors need not occur in pairs and they need not be at the same locations.3) The controller design requires only a knowledge of the elastic mode frequencies mode shapes at the locations of the actuators and sensors. ( l h s information can be approximated by existing computer programs for quite complicated dynamic structures.) 4) The system performance can be altered by changing parameters in the on-board control computer and this requires no modification of the physical structure (e.g., adding passive dampers); this may also make it possible to handle several different system configurations (e.g., control while assembling a structure in space).The active controller proposed here using a linear feedback control law, a state estimator, and a sensor prefilter is a straightforward method for controlling N modes of a flexible system and eliminating the disasterous effects of spillover from the residual modes. It uses well-known state variable control techniques which reveal the design tradeoffs available and it could be used as a starting point for a practical feedback controller for flexible systems, especially large spacecraft where it holds many advantages (e.g., 1221, 1301). Further investigation is necessary in two basic areas to bring these concepts to maturity: 1) Effect of dynamics of actuators, sensors, and prefilter (some preliminary work in [3 I]).2) Adaptive control, i.e., an estimator that adjusts its internal model parameters to better match those of the system it is attempting to follow (several adaptive methods available for model referenced systems, e.g., (321, [33D. REFERENCES 1 V. Larson, P. Likins, and E. Marsh "Optimal estimation and attitude control of a AES-13, pp. 3547, 1977.

Strong consistency with rates of spectral estimation of continuous-time processes: from periodic and poisson sampling schemes

“…It puts additional constraints on ψ that are not required in the standard spectral estimation of discrete-parameter processes. In fact, we have the following lemma due to Masry [9]. LEMMA 3.1 Let the covariance function R x (t) of the process X be such that…”

Spectral analysis methods for Poisson sampled measurements

“…In point of fact, in a series of LDA sampling instants the number of sampling instants per distinct time interval is Poisson distributed while the sampling intervals resemble realizations of an exponential white noise process. The propagation equation for the so-called Poisson sampling process is [4] for an exponential white noise process with mean , known as the sampling-interval process; , and are assumed to be mutually independent.…”

Consistent Estimation of Non-bandlimited Spectral Density From Uniformly Spaced Samples

“…A systematic numerical comparison is not available in the literature. A simulated example given by Masry [24] was meant only to highlight the problem of aliasing and to demonstrate how it can be overcome with irregular sampling. Studies by Roughan [18] in the special case of active measurements for network performance produced mixed results, which led the author to conclude that, while spectral estimators based on Poisson sampling have less efficiency (i.e., high variance), such techniques could be used to detect periodicities in the system, and to determine which rate of regular sampling would be inadequate.…”