https://users.encs.concordia.ca/~ymzhang/publications/ARC32-2-98Zhang_pp.229-252.pdf

Bibliographical review on reconfigurable fault-tolerant control systems

Linear Robust Control

Robust Control Design with MATLAB (second edition) helps the student to learn how to use well-developed advanced robust control design methods in practical cases. To this end, several realistic control design examples from teaching-laboratory experiments, such as a two-wheeled, self-balancing robot, to complex systems like a flexible-link manipulator are given detailed presentation. All of these exercises are conducted using MATLAB Robust Control Toolbox 3, Control System Toolbox and Simulink. By sharing their experiences in industrial cases with minimum recourse to complicated theories and formulae, the authors convey essential ideas and useful insights into robust industrial control systems design using major H-infinity optimization and related methods allowing readers quickly to move on with their own challenges. The hands-on tutorial style of this text rests on an abundance of examples and features for the second edition: rewritten and simplified presentation of theoretical and methodological material including original coverage of linear matrix inequalities; new Part II forming a tutorial on Robust Control Toolbox 3; fresh design problems including the control of a two-rotor dynamic system; and end-of-chapter exercises. Electronic supplements to the written text that can be downloaded from extras.springer.com/isbn include: M-files developed with MATLAB help in understanding the essence of robust control system design portrayed in text-based examples; MDL-files for simulation of open- and closed-loop systems in Simulink; and a solutions manual available free of charge to those adopting Robust Control Design with MATLAB as a textbook for courses. Robust Control Design with MATLAB is for graduate students and practising engineers who want to learn how to deal with robust control design problems without spending a lot of time in researching complex theoretical developments.

Robust control design with MATLAB

This paper presents the Cholesky factor--alternating direction implicit (CF--ADI) algorithm, which generates a low rank approximation to the solution X of the Lyapunov equation AX+XAT=-BBT. The coefficient matrix A is assumed to be large, and the rank of the right-hand side -BBT is assumed to be much smaller than the size of A. The CF--ADI algorithm requires only matrix-vector products and matrix-vector solves by shifts of A. Hence, it enables one to take advantage of any sparsity or structure in A.
This paper also discusses the approximation of the dominant invariant subspace of the solution X. We characterize a group of spanning sets for the range of X. A connection is made between the approximation of the dominant invariant subspace of X and the generation of various low order Krylov and rational Krylov subspaces. It is shown by numerical examples that the rational Krylov subspace generated by the CF--ADI algorithm, where the shifts are obtained as the solution of a rational minimax problem, often gives the best approximation to the dominant invariant subspace of X.

/pdf/low-rank-solution-of-lyapunov-equations-egxo173yka.pdf

Low Rank Solution of Lyapunov Equations

In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and wide applicability for simulating large-scale mathematical models in engineering and the sciences. Recently, MOR has been intensively further developed for increasingly complex dynamical systems. Wide applications of MOR have been found not only in simulation, but also in optimization and control. In this survey paper, we review some popular MOR methods for linear and nonlinear large-scale dynamical systems, mainly used in electrical and control engineering, in computational electromagnetics, as well as in micro- and nano-electro-mechanical systems design. This complements recent surveys on generating reduced-order models for parameter-dependent problems (Benner et al. in 2013; Boyaval et al. in Arch Comput Methods Eng 17(4):435–454, 2010; Rozza et al. Arch Comput Methods Eng 15(3):229–275, 2008) which we do not consider here. Besides reviewing existing methods and the computational techniques needed to implement them, open issues are discussed, and some new results are proposed.

Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective

In this paper we present a numerically reliable algorithm to compute the balanced realization of a stable state-space system that may be arbitrarily close to being unobservable and/or uncontrollable. The resulting realization, which is known to be a good approximation of the original system, must be minimal and therefore may contain a reduced number of states. Depending on the choice of partitioning of the Hankel singular values, this algorithm can be used either as a form of minimal realization or of model reduction. This illustrates that in finite precision arithmetic these two procedures are closely related. In addition to real matrix multiplication, the algorithm only requires the solution of two Lyapunov equations and one singular value decomposition of an upper-triangular matrix.

Truncated balanced realization of a stable non-minimal state-space system

A flowmeter is disclosed. The flowmeter includes a vibratable flowtube, and a driver connected to the flowtube that is operable to impart motion to the flowtube. A sensor is connected to the flowtube and is operable to sense the motion of the flowtube and generate a sensor signal. A controller is connected to receive the sensor signal. The controller is operable to determine an individual flow rate of each phase within a multi-phase flow through the flowtube.

Multi-phase coriolis flowmeter

A multi-phase process fluid is passed through a vibratable flowtube. Motion is induced in the vibratable flowtube. A first apparent property of the multi-phase process fluid based on the motion of the vibratable flowtube is determined, and an apparent intermediate value associated with the multi-phase process fluid based on the first apparent property is determined. A corrected intermediate value is determined based on a mapping between the intermediate value and the corrected intermediate value. A phase-specific property of a phase of the multi-phase process fluid is determined based on the corrected intermediate value.

Wet gas measurement

Two-phase flow metering of heavy oil using a Coriolis mass flow meter: A case study

A flowmeter is disclosed. The flowmeter includes a vibratable flowtube, and a driver connected to the flowtube that is operable to impart motion to the flowtube. A sensor is connected to the flowtube and is operable to sense the motion of the flowtube and generate a sensor signal. A controller is connected to receive the sensor signal. The controller is operable to determine a first flow rate of a first phase within a two-phase flow through the flowtube and determine a second flow rate of a second phase within the two-phase flow.

Michael Tombs

Papers

Truncated balanced realization of a stable non-minimal state-space system

Multi-phase coriolis flowmeter

Wet gas measurement

Two-phase flow metering of heavy oil using a Coriolis mass flow meter: A case study

Multiphase coriolis flowmeter