Finite Word Length Consideration Research Articles

Non-fragile <I>H</I> θ Filtering for Discrete-time Systems with Finite Word Length Consideration

Non-fragile <I>H</I> θ Filtering for Discrete-time Systems with Finite Word Length Consideration

Non-fragile H∞ Filtering for Discrete-time Systems with Finite Word Length Consideration

The nonfragile H ∞ filtering problem affected by finite word length (FWL) for linear discrete-time systems is investigated in this paper. The filter to be designed is assumed to be with additive gain variations, which reflect the FWL effects on filter implementation. A notion of structured vertex separator is proposed to deal with the problem and exploited to develop sufficient conditions for the nonfragile H ∞ filter design in terms of a set of linear matrix inequalities (LMIs). The design renders the augmented system asymptotically stable and guarantees the H ∞ attenuation level less than a prescribed level. A numerical example is given to illustrate the effect of the proposed method.

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.

Optimization of block floating point realizations for digital controllers with finite word length considerations

The closed-loop stability issue of finite-precision realizations was investigated for digital controllers implemented in block-floating-point format. The controller coefficient perturbation was analyzed resulting from using finite word length (FWL) block-floating-point representation scheme. A block-floating-point FWL closed-loop stability measure was derived which considers both the dynamic range and precision. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable block-floating-point FWL closed-loop stability measure was then introduced and the method of computing the value of this measure for a given controller realization was developed. The optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach was adopted to solve the resulting optimal realization problem. A numerical example was used to illustrate the design procedure and to compare the optimal controller realization with the initial realization.

Controller realizations of a teleoperated dual-wrist assembly system with finite word length considerations

This paper presents some implementation issues of finite-precision optimal and quasi-optimal sparse H/sub /spl infin// controller structures applied to a teleoperated dual-wrist assembly system. The relevant stability robustness measures and the optimization search procedures for both the optimal and the quasi-optimal sparse finite word length (FWL) controller realizations are described. Comparative analytical and numerical results show that the sparse FWL controller realizations provide minimum bit lengths, with maximum trivial elements in the controller coefficients and higher stability bounds compared to non-optimal realization. The results illustrate that the FWL methodology presented provides better implementation structures, increased computational speed and FWL stability for teleoperated motion-scaling control systems.

Shift and delta operator realisations for digital controllers with finite word length considerations

The implementation issues of digital controllers with finite word length (FWL) considerations are addressed. Both the shift and delta operator parametrisations of a general controller structure are considered. A unified formulation is adopted to derive a computationally tractable stability related measure that describes FWL closed-loop stability characteristics of different controller realisations. Within a given operator parametrisation, the optimal FWL controller realisation, which maximises the proposed stability related measure, is the solution of a nonlinear optimisation problem. The relationship between the z-operator and /spl delta/-operator controller parametrisations is analysed, and it is shown that the /spl delta/ parametrisation has a better FWL closed-loop stability margin than the z-domain approach under a mild condition. A design example is included to verify the theoretical analysis and to illustrate the proposed optimisation procedure.

Comments on "On the structure of digital controllers with finite word length consideration"

In the above-mentioned paper by Li (ibid. vol.43 (1998)), a condition is presented as necessary and sufficient to give the optimal realization of state space controllers for minimal sensitivity of all closed-loop eigenvalues subject to finite word-length effects. The condition is shown here not to be sufficient. In addition, the condition for minimal sensitivity of a single closed-loop eigenvalue presented in the above-mentioned paper is not complete. The complete conditions are presented in this paper.

Optimizing stability bounds of finite-precision PID controller structures

This paper investigates a recently derived lower bound stability measure for sampled-data controller structures subject to finite-wordlength (FWL) constraints. The optimal realization of the digital PID controller with FWL considerations is formulated as a nonlinear optimization problem, and an efficient strategy based on adaptive simulated annealing (ASA) is adopted to solve this complex optimization problem. A numerical example of optimizing the finite-precision PID controller structure for a simulated steel rolling mill system is presented to illustrate the effectiveness of the proposed strategy.

On the structure of digital controllers with finite word length consideration

It is well known that a stable discrete-time control system may become unstable when the digital controller is actually implemented with a digital control processor due to the finite word length effects and that the stability behavior of the system depends on the structure of the digital controller. Due to the difficulties in adopting the existing stability robustness measures, a new measure is derived, which is tractable and hence enables us to handle the digital controller structure problem easily. The optimal controller structure problem is formulated by maximizing this measure. An analytical solution is presented. An algorithm is developed for finding sparser structures.

Book Review: Digital Control and Implementation—finite wordlength considerations

Book Review: Digital Control and Implementation—finite wordlength considerations

Book Review: Digital Control and Implementation—finite wordlength considerations

Book Review: Digital Control and Implementation—finite wordlength considerations