3,273 research outputs found
Pole Assignment With Improved Control Performance by Means of Periodic Feedback
This technical note is concerned with the pole placement of continuous-time linear time-invariant (LTI) systems by means of LQ suboptimal periodic feedback. It is well-known that there exist infinitely many generalized sampled-data hold functions (GSHF) for any controllable LTI system to place the modes of its discrete-time equivalent model at prescribed locations. Among all such GSHFs, this technical note aims to find the one which also minimizes a given LQ performance index. To this end, the GSHF being sought is written as the sum of a particular GSHF and a homogeneous one. The particular GSHF can be readily obtained using the conventional pole-placement techniques. The homogeneous GSHF, on the other hand, is expressed as a linear combination of a finite number of functions such as polynomials, sinusoidals, etc. The problem of finding the optimal coefficients of this linear combination is then formulated as a linear matrix inequality (LMI) optimization. The procedure is illustrated by a numerical example
Multichannel Sampling of Pulse Streams at the Rate of Innovation
We consider minimal-rate sampling schemes for infinite streams of delayed and
weighted versions of a known pulse shape. The minimal sampling rate for these
parametric signals is referred to as the rate of innovation and is equal to the
number of degrees of freedom per unit time. Although sampling of infinite pulse
streams was treated in previous works, either the rate of innovation was not
achieved, or the pulse shape was limited to Diracs. In this paper we propose a
multichannel architecture for sampling pulse streams with arbitrary shape,
operating at the rate of innovation. Our approach is based on modulating the
input signal with a set of properly chosen waveforms, followed by a bank of
integrators. This architecture is motivated by recent work on sub-Nyquist
sampling of multiband signals. We show that the pulse stream can be recovered
from the proposed minimal-rate samples using standard tools taken from spectral
estimation in a stable way even at high rates of innovation. In addition, we
address practical implementation issues, such as reduction of hardware
complexity and immunity to failure in the sampling channels. The resulting
scheme is flexible and exhibits better noise robustness than previous
approaches
Representations of linear dual rate system via single SISO LTI filter, conventional sampler and block sampler
In this brief, it is proved that a linear dual-rate system can be represented via a series cascade of: 1) a conventional expander, a single-input single-output (SISO) linear time-invariant (LTI) filter and a block decimator, or 2) a block expander, an SISO LTI filter and a conventional decimator. Hence, incompatible nonuniform filter banks could achieve perfect reconstruction via LTI filters, conventional samplers and block samplers without expanding the input-output dimension of a subsystem of linear dual-rate systems or converting the nonuniform filter banks to uniform filter banks. The main advantage of the proposed representations is to avoid complicated design of the circuit layout caused by connecting subsystems with large input-output dimension or a lot of subsystems togethe
Signal Reconstruction via H-infinity Sampled-Data Control Theory: Beyond the Shannon Paradigm
This paper presents a new method for signal reconstruction by leveraging
sampled-data control theory. We formulate the signal reconstruction problem in
terms of an analog performance optimization problem using a stable
discrete-time filter. The proposed H-infinity performance criterion naturally
takes intersample behavior into account, reflecting the energy distributions of
the signal. We present methods for computing optimal solutions which are
guaranteed to be stable and causal. Detailed comparisons to alternative methods
are provided. We discuss some applications in sound and image reconstruction
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