Improved finite word length characteristics in digital control using delta operators
TL;DR: In this article, it is shown that the shift operator and its associated Z -transform can be replaced by delta operators and their associated transform, which is designated a Δ-transform.
Abstract: This paper examines some of the consequences of finite word lengths in digital control. It is shown that, in many cases of practical importance, the usual shift operator formulation is inferior to an alternative formulation which we designate the delta operator approach. This latter approach is shown to give better coefficient representation and less roundoff noise in many cases. We thus argue that the shift operator and its associated Z -transform can be replaced by delta operators and their associated transform which we designate a Δ-transform. An added advantage of this approach is that discrete designs and transforms converge to their continuous-time counterparts as the sampling rate is increased.
Citations
More filters
09 Oct 2006
TL;DR: The proportional-resonant (PR) controllers and filters, and their suitability for current/voltage control of grid-connected converters, are described in this article.
Abstract: The recently introduced proportional-resonant (PR) controllers and filters, and their suitability for current/voltage control of grid-connected converters, are described. Using the PR controllers, the converter reference tracking performance can be enhanced and previously known shortcomings associated with conventional PI controllers can be alleviated. These shortcomings include steady-state errors in single-phase systems and the need for synchronous d-q transformation in three-phase systems. Based on similar control theory, PR filters can also be used for generating the harmonic command reference precisely in an active power filter, especially for single-phase systems, where d-q transformation theory is not directly applicable. Another advantage associated with the PR controllers and filters is the possibility of implementing selective harmonic compensation without requiring excessive computational resources. Given these advantages and the belief that PR control will find wide-ranging applications in grid-interfaced converters, PR control theory is revised in detail with a number of practical cases that have been implemented previously, described clearly to give a comprehensive reference on PR control and filtering.
1,483 citations
TL;DR: In this article, an integrated approach to the design of practical adaptive control algorithms is presented, where many existing ideas are brought together, and the effect of various design parameters available to a user is explored.
Abstract: An integrated approach to the design of practical adaptive control algorithms is presented. Many existing ideas are brought together, and the effect of various design parameters available to a user is explored. The theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators. It is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics. >
590 citations
TL;DR: One of the key conclusions here is a set of rules of thumb, giving limitations on the closed loop bandwidth which are imposed by unstable open loop poles, non-minimum phase zeros and/or time delays.
330 citations
01 Feb 1992
TL;DR: An attempt is made to organize and survey recent work, and to present it in a unified and accessible form, on the need for a new approach suitable for high-speed processing and the use of difference operators in numerical analysis.
Abstract: An attempt is made to organize and survey recent work, and to present it in a unified and accessible form. The need for a new approach suitable for high-speed processing is discussed in the context of several applications in control and communications, and a historical perspective of the use of difference operators in numerical analysis is presented. The general systems calculus, based on divided-different operators is introduced to unify the continuous-time and discrete-time systems theories. This calculus is then used as a framework to treat the three problems of system state estimation; system identification and time-series modeling; and control system design. Realization aspects of algorithms based on the difference operator representation, including such issues as coefficient rounding and implementation with standard hardware, are also discussed. >
276 citations
TL;DR: This alternative model is used to develop a new discrete model reference adaptive control law and a convergence analysis for the algorithm is presented.
269 citations
References
More filters
TL;DR: The zeros of the discrete time system obtained when sampling a continuous time system are explored and theorems for the limiting zeros for large and small sampling periods are given.
866 citations
TL;DR: This alternative model is used to develop a new discrete model reference adaptive control law and a convergence analysis for the algorithm is presented.
269 citations
TL;DR: For poles close to the unit circle and near z = 1, the usual realizations of recursive or IIR digital filters are highly sensitive to the coefficient quantization and have large roundoff noise as mentioned in this paper.
Abstract: For poles close to the unit circle and near z = 1 , the usual realizations of recursive or IIR digital filters are highly sensitive to the coefficient quantization and have large roundoff noise. As the sampling rate is increased the poles approach z = 1 and the problems become more severe. For these situations several new digital filter structures are presented for which the above errors remain constant and generally insignificant as the sampling rate is increased. Results on sensitivity and the roundoff errors for these new structures are presented and compared with conventional realizations. Some numerical results are also presented showing order of magnitude improvements.
161 citations
01 Sep 1980
TL;DR: In this paper, hybrid self-tuning controllers are introduced which combine two sample rates to give both discrete time and continuous time features, and the limiting properties of such algorithms, as the sample rate increases, correspond to a continuous-time control law.
Abstract: Hybrid self-tuning controllers are introduced which combine two sample rates to give both discrete time and continuous-time features. The limiting properties of such algorithms, as the sample rate increases, are shown to correspond to a continuous-time control law. Undesirable intersample behaviour associated with the discrete-time control of continuous systems with high pole-zero excess is thus avoided. The results are illustrated by the control of a triple integrator.
81 citations
IBM1
TL;DR: In this article, a new measure of sensitivity specifically applicable to the realization of a linear discrete system on a digital computer is presented, and a realization is obtained which is "best" for a large class of systems of interest with regard to minimizing storage requirements, arithmetic operations, parameter accuracy, and eigenvalue sensitivity.
Abstract: The first part of this paper presents a new measure of sensitivity specifically applicable to the realization of a linear discrete system on a digital computer. It is also shown that the sensitivity of the eigenvalues to parameter inaccuracies in the realization depends strongly on the choice of state variables. From these considerations, a realization is obtained which is "best" for a large class of systems of interest with regard to minimizing storage requirements, arithmetic operations, parameter accuracy, and eigenvalue sensitivity. The second half of the paper considers the very practical problem of determining the number of bits accuracy required in the computer-stored parameters of the system to achieve satisfactory performance. For the realization found to be a best compromise, equations are obtained for determining these bit requirements. Examples are given showing the application of this realization to the computer implementation of a discrete filter, and a comparison is given to other possible realizations.
78 citations