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Approximation of Frequency Response for SampledData Control Systems
"... This paper proves that the frequency response gains of fastsample/fasthold approximations of a sampleddata system converge to that of the original system as the sampling rate gets faster. While this may appear to hold trivially, there is a serious technical di#culty, and the proof is indeed nontri ..."
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This paper proves that the frequency response gains of fastsample/fasthold approximations of a sampleddata system converge to that of the original system as the sampling rate gets faster. While this may appear to hold trivially, there is a serious technical di#culty, and the proof is indeed nontrivial. It is also guaranteed that this convergence is uniform on the total frequency range. The latter property is necessary to guarantee that a single approximant can be used for frequency response computation for the overall frequency range. A numerical example is given to illustrate the result
Computer Control: An Overview
, 2003
"... Computers are today essential for implementing controllers in many different situations. The computers are often used in embedded systems. An embedded system is a builtin computer/microprocessor that is a part of a larger system. Many of these computers implement control functions of different phys ..."
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Computers are today essential for implementing controllers in many different situations. The computers are often used in embedded systems. An embedded system is a builtin computer/microprocessor that is a part of a larger system. Many of these computers implement control functions of different physical processes,
Linear Periodically TimeVarying DiscreteTime Systems: Aliasing and LTI Approximations
, 1996
"... Linear periodically timevarying (LPTV) systems are abundant in control and signal processing; examples include multirate sampleddata control systems and multirate filterbank systems. In this paper, several ways are proposed to quantify aliasing effect in discretetime LPTV systems; these are asso ..."
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Linear periodically timevarying (LPTV) systems are abundant in control and signal processing; examples include multirate sampleddata control systems and multirate filterbank systems. In this paper, several ways are proposed to quantify aliasing effect in discretetime LPTV systems; these are associated with optimal timeinvariant approximations of LPTV systems using operator norms. Keywords: periodic systems, multirate systems, optimization, aliasing, discretetime systems. 1 Introduction Examples of linear periodically timevarying (LPTV) systems are abundant: In control, multirate sampleddata systems are designed to exploit their cost advantage in digital implementation [6, 5]; in signal processing, multirate filter banks, which are typically LPTV, are designed for efficient coding and transmission of digital signals [11]. Different from linear timeinvariant (LTI) systems, aliasing exists in LPTV systems; this may cause adverse effect for robustness against high frequency uncer...
On a Key Sampling Formula Relating the Laplace and Transforms
 Systems & Control Letters
, 1997
"... This note provides a new, rigorous derivation of a key sampling formula for discretizing an analogue system. The required conditions are formulated in timedomain, and give a clear characterization of the classes of signals and systems to which the formula applies. Keywords: Z transform, sampleddat ..."
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This note provides a new, rigorous derivation of a key sampling formula for discretizing an analogue system. The required conditions are formulated in timedomain, and give a clear characterization of the classes of signals and systems to which the formula applies. Keywords: Z transform, sampleddata systems, frequency response. 1 Introduction A formula that is crucial to the understanding of the frequencydomain properties of a sampleddata system is the following, G d (e sT ) = 1 T 1 X k=1 G(s + jk! s ); (1) where G is the Laplace transform of a continuoustime signal g, G d is the Z transform of the sequence of its samples, fg(kT)g 1 k=0 , and T and ! s = 2=T denote the sampling period and sampling frequency, respectively. This formula displays the fundamental fact that the frequency response of a sampled signal is built upon the superposition of infinitely many copies of its continuoustime frequency response. The formula has been known for some time in the literature o...
Sampling from a systemtheoretic viewpoint: Part I—concepts and tools
 IEEE Trans. Signal Processing
, 2010
"... This paper studies a systemtheoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid modelmatching problem in which performance is measured by system norms. The ..."
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This paper studies a systemtheoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid modelmatching problem in which performance is measured by system norms. The paper is split into three parts. In Part I we present the paradigm and revise the lifting technique, which is our main technical tool. In Part II optimal samplers and holds are designed for various analog signal reconstruction problems. In some cases one component is fixed while the remaining are designed, in other cases all three components are designed simultaneously. No causality requirements are imposed in Part II, which allows to use frequency domain arguments, in particular the lifted frequency response as introduced in Part I. In Part III the main emphasis is placed on a systematic incorporation of causality constraints into the optimal design of reconstructors. We consider reconstruction problems, in which the sampling (acquisition) device is given and the performance is measured by the L2norm of the reconstruction error. The problem is solved under the constraint that the optimal reconstructor is lcausal for a given l ≥ 0, i.e., that its impulse response is zero in the time interval (−∞,−lh), where h is the sampling period. We derive a closedform
Singular Perturbation Control for Vibration Rejection in HDDs Using the PZT Active Suspension as Fast Subsystem Observer
"... Abstract—Currently, position sensors other than the read/write head are not embedded into current hard disk drives (HDDs) due to signaltonoise ratio and nanometer resolution issues. Moreover, a noncollocated sensor fusion creates nonminimum phase zero dynamics which degrades the tracking performan ..."
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Abstract—Currently, position sensors other than the read/write head are not embedded into current hard disk drives (HDDs) due to signaltonoise ratio and nanometer resolution issues. Moreover, a noncollocated sensor fusion creates nonminimum phase zero dynamics which degrades the tracking performance. In this paper, the singular perturbation theory is applied to decompose the voice coil motor’s (VCM’s) and induced PZT active suspension’s dynamics into fast and slow subsystems, respectively. The control system is decomposed into fast and slow time scales for controller designs, and control effectiveness is increased to tackle more degreesoffreedom via an inner loop vibration suppression with measured highfrequency VCM’s and PZT active suspension’s dynamics from the piezoelectric elements in the suspension. Experimental results on a commercial HDD with a laser doppler vibrometer show the effective suppression of the VCM and PZT active suspension’s flexible resonant modes, as well as an improvement of 39.9 % in 3σ position error signal during track following when compared to conventional notchbased servos. Index Terms—Hard disk drives (HDDs), PZT, singular perturbation. I.
L2induced Norms and Frequencygains of Sampleddata Sensitivity Operators.
"... This paper develops exact, computable formulas for the frequencygain and L2induced norm of the sensitivity operator in a sampleddata control system. With sampleddata, we refer to a system that combines both continuoustime and discretetime signals, and which is studied in continuoustime. Th ..."
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This paper develops exact, computable formulas for the frequencygain and L2induced norm of the sensitivity operator in a sampleddata control system. With sampleddata, we refer to a system that combines both continuoustime and discretetime signals, and which is studied in continuoustime. The expressions are obtained using lifting techniques in the frequencydomain, and have application in performance and stability robustness analysis taking in account full intersample information. Keywords: Sampleddata systems, L2induced norms, Frequency response, Sensitivity analysis, Generalized sampleddata holds. 1 Introduction. This paper studies the computation of the L 2 induced norm of the sensitivity operator in a sampleddata (SD) control system. The term SD indicates that we approach the system in continuoustime, i.e., considering full intersample information. The L 2 induced norm is the operator norm when inputs and outputs belong to the space of squareintegrable signal...
Digital Control
"... this article, however, we confine ourselves to the 0order hold above ..."
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this article, however, we confine ourselves to the 0order hold above
FrequencyDomain Analysis of Linear Periodic Operators with Application to SampledData Control Design
"... The development of controller usually involves two major steps: A design step in which a generalised plant is constructed, followed by a synthesis step in which an optimisation problem is solved for the generalised plant. FrequencyDomain analysis methods are commonly used in the design step; for ex ..."
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The development of controller usually involves two major steps: A design step in which a generalised plant is constructed, followed by a synthesis step in which an optimisation problem is solved for the generalised plant. FrequencyDomain analysis methods are commonly used in the design step; for example loopshaping. In this paper we develop a new frequencydomain analysis method for periodic operators. Specifically, we define the averagepower gain matrix, which for a periodic operator characterises the average power of the asymptotic ("steadystate") response to a sinusoidal input of a single frequency. To illustrate an application of the new analysis method we show how to use the averagepower gain matrix in the H1 loopshaping design of sampleddata, closedloop systems.
Bisection Algorithm for Computing the Frequency Response Gain of SampledData Systems  InfiniteDimensional Congruent Transformation Approach
, 2001
"... This paper derives a bisection algorithm for computing the frequency response gain of sampleddata systems with their intersample behavior taken into account. The properties of the infinitedimensional congruent transformation (i.e., the Schur complement arguments and the Sylvester law of inertia) p ..."
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This paper derives a bisection algorithm for computing the frequency response gain of sampleddata systems with their intersample behavior taken into account. The properties of the infinitedimensional congruent transformation (i.e., the Schur complement arguments and the Sylvester law of inertia) play a key role in the derivation. Specifically, it is highlighted that counting up the numbers of the negative eigenvalues of selfadjoint operators is quite important for the computation of the frequency response gain. This contrasts with the wellknown arguments on the related issue of the sampleddata problem, where the key role is played by the positivity of operators and the loopshifting technique. The effectiveness of the derived algorithm is demonstrated through a numerical example. Index TermsBisection algorithm, frequency response gain, numerical computation, sampleddata systems, Schur complement arguments. I.