A Review of Sample and Hold Systems and Design of a New Fractional Algorithm

Abstract

Digital systems require sample and hold (S&H) systems to perform the conversion from analog to digital and vice versa. Besides the standard zero and first order holds, we find in the literature other versions, namely the fractional and exponential order holds, involving parameters that can be tuned to produce a superior performance. This paper reviews the fundamental concepts associated with the S&H and proposes a new fractional version. The systems are modeled both in the time and Laplace domains. The new S&H stemming from fractional calculus generalizes these devices. The different S&H systems are compared in the frequency domain and their relationships visualized by means of hierarchical clustering and multidimensional scaling representations. The novel strategy allows a better understanding of the possibilities and limitations of S&H systems.

On the Equivalence between Integer- and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems

“…• All the ARMA systems, continuous-time or discrete-time, are considered as time-invariant, meaning that the corresponding equations are defined by constant parameters. • We used the bilateral Laplace transform (LT) [13]:…”

“…The second approach finds an equivalent discrete-time system by matching the poles and zeroes of the transfer functions of the two systems [4,25]. In the third approach, the continuous-time excitation of the system is held constant between each pair of sampling instants by assuming a zero-order hold [13]. The continuous-time system is then excited by this input, and the result is a discrete-time output.…”

Special Issue: “Control and Automation”

“…To implement such fractional order controllers, digital realizations are often required which use sample and hold (S&H) circuits to perform the conversion from analog to digital and vice versa. An excellent review of these S&H systems, as well as a new fractional order design of such systems, is presented in [4]. The proposed approach models these systems both in the time and Laplace domains and is a generalization of the classical devices, enabling a better understanding of the possibilities and limitations of S&H systems.…”

On the Stabilization of a Network of a Class of SISO Coupled Hybrid Linear Subsystems via Static Linear Output Feedback

“…Therefore, the stabilization theory is relevant in continuous-time systems, discrete-time systems and the hybrid ones which have mixed continuous-time and discretetime parts. See, for instance, [1][2][3][4][5][6][7][8][9][10][11][12][13] and some related references therein. The discretization of continuous-time systems can be performed to constant sampling rates or to non-uniform ones [3,6] so as to take the sampling rate as an extra design function which can be accommodated to the rate of variation of the signals of interest in the system under study.…”

“…In this case, it is not only needed to stabilize the closed-loop modes (stabilization problem) but also to prescribe the values of both the zeros and poles of the closed-loop transfer function to prescribed values defined by the reference model [8,9]. Different devices and design techniques which should be examined to decide on combining discretization tools with continuous-time analysis in complex dynamic systems are the use of appropriate sampling and hold devices [8][9][10] to update discretized signal information for control purposes, the eventual influence of delays either in the input or output, or in the sates, and also the possible stabilization via state or output feedback involving either centralized control, i.e. involving all the available output information, or decentralized control, i.e.…”