Ubaid M. Al-Saggaf

Quantitative Reliability Evaluation of Repairable Phased-Mission Systems Using Markov Approach

A quantitative reliability model for a phased mission system is developed using a Markov process. Two cases for the mission-phase change times are assumed: 1) to be known in advance and 2) to be random variables. A method of solution is presented and illustrated by examples. The solution of phased-mission systems is equivalent to solving a sequence of uni-phase systems with appropriate initial conditions.

Model reduction via balanced realizations: an extension and frequency weighting techniques

Two model-reduction methods for discrete systems related to balanced realizations are described. The first is a technique which utilizes the least controllable and observable subsystem in deriving a balanced discrete reduced-order model. For this technique as L/sup infinity / norm bound on the reduction error is given. The second method is a frequency-weighting technique for discrete- and continuous-time systems where the input-normal or output-normal realizations are modified to include a simple frequency weighting. For this technique, L/sup infinity / norm bounds on the weighted reduction errors are obtained. >

An error bound for a discrete reduced order model of a linear multivariable system

The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an Linftybound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.

New model reduction scheme for bilinear systems

A new method for the approximation of bilinear systems is proposed. The reduction scheme applies to both stable and unstable bilinear systems. The technique uses generalized input normal representations to retain the dominant part of the original system. The algorithm is evaluated on a synchronous induction generator and is shown to lead to acceptable reduced approximations of the original system. A frequency weighting is also introduced in the reduction scheme to further improve the approximation.

On model reduction

Three model reduction methods are described. These are the discrete balanced realizations of Mullis and Roberts [1],[2] where a characterization of the reduction error is given and a previously unknown L¿ norm bound on the reduction error, is obtained. Another method is a new model reduction technique for discrete time systems which has the advantage that the reduced order model is balanced and has an L¿ norm bound on the reduction error. The last method derived is a frequency weighting technique for continuous and discrete systems where it is possible to specify the approximation accuracy with frequency and also, for this method, an L¿ norm on the weighted reduction error is obtained.

Model reduction for discrete unstable systems based on generalized normal representations

The input and output normal representations of stable systems are generalized for unstable systems. These are then used to reduce the order of unstable discrete-time linear multivariable systems resulting in reduced order models with the same number of unstable poles as the full order model and with an a priori upper bound on the reduction error. The generalized normal representations are then modified to include a frequency weighting resulting in frequency weighted generalized normal representations. These are used to derive frequency weighted reduced order models for unstable discrete systems with the same number of unstable poles as the full order model and with an a priori upper bound on the frequency weighted reduction error.

Subsystem interconnection and near optimum control of discrete balanced systems

The relationship between subsystem interconnection of discrete balanced systems and the Hankel singular values is explored. Upper bounds on the spectral norm of the submatrices of the discrete balanced representation are derived by approximating the matrix Riccati equation by its power series expansion with respect to two scalar parameters related to the Hankel singular values. For diagonalizable symmetric discrete-time systems, the relation between the eigenvalues of the subsystems and the eigenvalues of the overall system is explored. It is shown that an upper bound on the distance between corresponding eigenvalues in these two sets is related to the ratio of the Hankel singular values. >

Approximate balanced-truncation model reduction for large scale systems†

The complexity of a large scale system makes the computations of reduced order models based on balancing impractical. However, typically there is a weak coupling between the subsystems of a large scale system. This is used here to derive approximate balanced-truncation reduced order models for large scale systems with reliable and tractable computations.

Practical model reduction techniques for power systems

Abstract Four relatively recent techniques for model reduction (balanced, weighted balanced, optimal Hankel and weighted optimal Hankel) are reviewed. The usefulness of these techniques for obtaining reduced-order models of power systems for dynamic control purposes, their effectiveness, and the merits of the simplified models are illustrated on a single-machine infinite-bus system. The methods are evaluated on the basis of Lα errors, transient responses, and steady-state errors. The superiority of the frequency-weighting methods is clearly demonstrated.

Reduced order controller design for discrete time systems

Robust discrete control system design techniques and model reduction are discussed. A new linear quadratic guussian/loop transfer recovery procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has the desired loop shape, and then recovered by a realizable linear quadratic gaussian controller. To do this, results that show the effects of the weighting matrices (noise intensities) on linear quadratic regulator (Kalman-Bucy filter) return difference and inverse-return difference arc derived and a procedure to recover the linear quadratic regulator loop transfer function is described. The complexity of the resulting controller is then reduced without causing closed-loop instability. Two methods for model reduction are considered. The first is the discrete balanced realization and the second is P frequency weighting technique where it is possible to vary the approximation accuracy with frequency. The controller design and re...