Design of noise and period-time robust high-order repetitive control, with application to optical storage

Repetitive control is useful if periodic disturbances or setpoints act on a control system. Perfect (asymptotic) disturbance rejection is achieved if the period time is exactly known. The improved disturbance rejection at the periodic frequency and its harmonics is achieved at the expense of a degraded system sensitivity at intermediate frequencies. A convex optimization problem is defined for the design of high-order repetitive controllers, where a trade-off can be made between robustness for changes in the period time and for reduction of the error spectrum in-between the harmonic frequencies. The high-order repetitive control algorithms are successfully applied in experiments with the tracking control of a CD-player system.     

Identification of low-order parameter-varying models for large-scale systems

In this paper we propose a novel procedure for obtaining low-dimensional models of large-scale multi-phase, non-linear, reactive fluid flow systems. Our approach is based on the combination of methods of proper orthogonal decompositions, black-box system identification techniques and non-linear spline based blending of local linear black-box models to create a reduced order linear parameter-varying model. The proposed method, which is of empirical nature, gives computationally very efficient low-order process models for large-scale processes. The proposed method does not need Galerkin type of projections on equation residuals to obtain the reduced order models and the proposed method is of generic nature. The efficiency of the proposed approach is illustrated on a benchmark problem of an industrial glass manufacturing process where the process non-linearity and non-linearity arising due to the corrosion of refractory materials is approximated using a linear parameter varying model. The results show good performance of the proposed framework.     

Rational representations of behaviors: Interconnectability and stabilizability

This paper presents an analysis of representation and stability properties of dynamical systems whose signals are assumed to be square summable sequences. Systems are defined as families of trajectories with no more structure than linearity and shift invariance. We depart from the usual input-output and operator theoretic setting and view relationships among system variables as a more general starting point for the study of dynamical systems. Parametrizations of two model classes are derived in terms of analytic functions which define kernel and image representations of dynamical systems. It is shown how state space models are derived from these representations. Uniqueness and minimality of these representations are completely characterized. Elementary properties like stabilizability, regularity, and interconnectability of dynamical systems are introduced and characterized in this set theoretic framework.Part of this research has been made possible by a grant from the European Community for the Systems Identification and Modeling Network (SIMONET).This research has been made possible by a fellowship of the Royal Netherlands Academy of Sciences and Arts.     

A locally convergent Jacobi iteration for the tensor singular value problem

Multi-linear functionals or tensors are useful in study and analysis multi-dimensional signal and system. Tensor approximation, which has various applications in signal processing and system theory, can be achieved by generalizing the notion of singular values and singular vectors of matrices to tensor. In this paper, we showed local convergence of a parallelizable numerical method (based on the Jacobi iteration) for obtaining the singular values and singular vectors of a tensor.     

Average H 2 control by randomized algorithms

In this paper the problem of average H 2 control design will be studied. It is well known that this problem in its general form cannot be solved analytically or even numerically in an efficient way. We will employ so called randomized algorithms in order to solve the controller synthesis problem. The method of controller design wil be llustrated in an example of an active suspension system.     

On continuity and consistency of ℓ∞ optimal models

This paper is concerned with the question of continuity of the mapping from observed time series to models. The behavioral framework is adopted to formalize a model identification problem in which the observed time series is decomposed into a part explained by a model and a remaining part which is ascribed to noise. The misfit between data and model is defined symmetrically in the system variables and measured in the ℓ_∞ or amplitude norm. With the introduction of proper notions of convergence, it is shown that the misfit function continuously depends on both the data and the model. Two notions of consistency are formalized and it is shown that the continuity of the misfit function implies a consistent identification of optimal and suboptimal models.