This dissertation focuses on efficiently forming reduced-order models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reduced-order models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first
algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczos-based methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a combination of theory and examples. Independent of the precise algorithm, a host of supporting tools are also develop ed to form a complete model-reduction package. Techniques for choosing the matching frequencies, estimating the modeling error, insuring the model's stability, treating multiple-input multiple-output systems, implementing parallelism, and avoiding a need for exact factors of large matrix
pencils are all examined to various degrees

https://tel.archives-ouvertes.fr/tel-01711328/document

Krylov Projection Methods for Model Reduction

http://www.mate.tue.nl/mate/pdfs/2041.pdf

Brief Repetitive control for systems with uncertain period-time

The nonsymmetric Lanczos method has recently received significant attention as a model reduction technique for large-scale systems. Unfortunately, the Lanczos method may produce an unstable partial realization for a given, stable system. To remedy this situation, unexpensive implicit restarts are developed which can be employed to stabilize the Lanczos generated model.

Model reduction of state space systems via an implicitly restarted Lanczos method

http://code.eng.buffalo.edu/jrnl/Rep_control_automatica.pdf

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

https://pure.tue.nl/ws/files/4326149/614808.pdf

Advanced Motion Control: An Industrial Perspective*

The design of robust controllers for a compact disc mechanism is considered. Using mu synthesis, a controller has been designed for good track-following. The design problem involves time-domain constraints on signals and robustness requirements for norm-bounded structured plant uncertainty. It is shown that by using weighting functions in the mu framework this problem can be solved, but at the cost of many design iterations. The mu controller has been implemented in an experimental setup with a digitally controlled compact disc player. >

Robust control of a compact disc player

SUMMARY This paper considers the design and implementation of robust multivariable controllers for a compact disc mechanism.The design objective is to achieve good track-following and focusing performance in the presence of track disturbances, external mechanical shocks and structured norm-bounded plant uncertainty. This robust performance problem has been solved in the k-framework using the DK-iteration scheme. Limits of implementation necessitate the use of sophisticated model reduction techniques and the use of two parallel digital signal processors. ( 1998 John Wiley & Sons, Ltd.

http://www.mate.tue.nl/mate/pdfs/1105.pdf

μ-synthesis for a compact disc player

This paper considers robust multivariable control of a compact disc mechanism using digital signal processors. The design problem is to achieve good track-following and focusing performance in the presence of disturbances and norm-bounded structured plant uncertainty. This robust performance problem has been solved in the /spl mu/-framework using the D-K-iteration scheme. After controller order reduction, the /spl mu/-based controller has been implemented using two parallel digital signal processors.

Multivariable control of a compact disc player using DSPs

In fixed-point implementation of digital controllers, the effects of quantization can be reduced by proper scaling of the controller parameters. Commonly, controllers are scaled using l/sub 1/ norm based calculations, i.e., determining the worst case impulse response of the controller. This is only possible, however, if the controller is asymptotically stable. If this is not the case, a solution is to calculate the scaling transformation on the basis of the closed-loop impulse responses. From the experience with actual implementation on a compact disc system, frequency weighting reflecting the disturbance spectrum has to be applied as well to obtain good experimental results. >

Closed-loop scaling in fixed-point digital control

This paper considers a control design nethodology for non-rigid mechanical servo mechanisms with parametric uncertainty. A high bandwidth control design problem for a flexible servo system with varying resonance frequency has been solved using parametric uncertainty modeling and H∞ design techniques. To obtain guaranteed robustness for the varying resonance frequency and other parameter variations as well, μ-synthesis is applied using the D-K iteration scheme. The μ-based controller has been implemented in a Digital Signal Processor. A fast servo behavior has been obtained which shows robust performance for the varying resonance frequency.

G. Schootstra

Papers

Robust control of a compact disc player

μ-synthesis for a compact disc player

Multivariable control of a compact disc player using DSPs

Closed-loop scaling in fixed-point digital control

μ-synthesis of a flexible mechanical servo system