A search algorithm for a class of optimal finite-precision controller realization problems with saddle points

With game theory, we review the optimal digital controller realization problems that maximize a finite word length (FWL) closed-loop stability measure. For a large class of these optimal FWL controller realization problems which have saddle points, a minimax-based search algorithm is derived for finding a global optimal solution. The algorithm consists of two stages. In the first stage, the closed form of a transformation set is constructed which contains global optimal solutions. In the second stage, a subgradient approach searches this transformation set to obtain a global optimal solution. This algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these FWL realization problems. Furthermore, for a small class of optimal FWL controller realization problems which have no saddle point, the proposed algorithm also provides useful information to help solve them

Optimal realizations of floating-point implemented digital controllers with finite word length considerations.

The closed-loop stability issue of finite word length (FWL) realizations is investigated for digital controllers implemented in floating-point arithmetic. Unlike the existing methods which only address the effect of the mantissa bits in floating-point implementation to the sensitivity of closed-loop stability, the sensitivity of closed-loop stability is analysed with respect to both the mantissa and exponent bits of floating-point implementation. A computationally tractable FWL closed-loop stability measure is then defined, and the method of computing the value of this measure is given. The optimal controller realization problem is posed as searching for a floating-point realization that maximizes the proposed FWL closed-loop stability measure, and a numerical optimization technique is adopted to solve for the resulting optimization problem. Simulation results show that the proposed design procedure yields computationally efficient controller realizations with enhanced FWL closed-loop stability performance

A Unifying Framework for Finite Wordlength Realizations.

A general framework for the analysis of the finite wordlength (FWL) effects of linear time-invariant digital filter implementations is proposed. By means of a special implicit system description, all realization forms can be described. An algebraic characterization of the equivalent classes is provided, which enables a search for realizations that minimize the FWL effects to be made. Two suitable FWL coefficient sensitivity measures are proposed for use within the framework, these being a transfer function sensitivity measure and a pole sensitivity measure. An illustrative example is presented

Finite worldlength effects in fixed-point implementations of linear systems

Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 173-194).by Vinay Mohta.M.Eng

Finite Wordlength Controller Realizations using the Specialized Implicit Form

Une forme d'état implicite spécialisée est présentée pour étudier les effets de l'implantation en précision finie des régulateurs. Cette forme permet une description macroscopique des algorithmes à implanter. Elle constitue un canevas unificateur permettant de décrire les différentes structures utilisées pour l'implantation, telles que les réalisations avec l'opérateur delta, la forme directe II en rho, la forme d'état-observateur et bien d'autres formes qui sont d'habitude traitées séparément dans la littérature. Différentes mesures quantifiant les effets de l'implantation sur le comportement en boucle fermée sont définis dans ce contexte. Elles concernent aussi bien la stabilité que la performance. L'écart entre la réalisation à précision infinie et la réalisation à précision finie est évaluée selon la mesure de sensibilité des coefficients et la mesure du bruit de quantification. Le problème consistant à trouver une réalisation dont l'implantation amène un minimum de dégradation peut alors est résolut numériquement. Cette approche est illustrée avec deux exemples

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Optimum Realizations of Sampled-data Controllers for Fwl Sensitivity Minimization

The problem of an optimal finite-word-length state-space realization of a digital controller is investigated. The closed loop to be considered consists of a continuous-time plant,a discrete-time controller, a sampler, a zero-order hold and an antialiasing filter. An effective algorithm is proposed to find the optimal sampled-data controller realization minimizing the sensitivity of the closed-loop performance with respect to coefficient errors in the state variable matrices of the controller realization. In order to get a tractable problem, a two-step procedure is to be used: very fast sampling at a multiple of the sampling frequency followed by 'blocking' or 'lifting' to obtain a single-rate system. The procedure allows consideration of the system's intersample behaviour

Third International Symposium on Space Mission Operations and Ground Data Systems, part 1

Under the theme of 'Opportunities in Ground Data Systems for High Efficiency Operations of Space Missions,' the SpaceOps '94 symposium included presentations of more than 150 technical papers spanning five topic areas: Mission Management, Operations, Data Management, System Development, and Systems Engineering. The papers focus on improvements in the efficiency, effectiveness, productivity, and quality of data acquisition, ground systems, and mission operations. New technology, techniques, methods, and human systems are discussed. Accomplishments are also reported in the application of information systems to improve data retrieval, reporting, and archiving; the management of human factors; the use of telescience and teleoperations; and the design and implementation of logistics support for mission operations