http://control.disp.uniroma2.it/galeani/CO/materiale/automatica2000.pdf

Survey Constrained model predictive control: Stability and optimality

Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.- Semigroups Everywhere.- A Brief History of the Exponential Function.

https://www.springer.com/productFlyer_978-0-387-98463-6.pdf?SGWID=0-0-1297-1590487-0

One-Parameter Semigroups for Linear Evolution Equations

The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders.

https://hal-polytechnique.archives-ouvertes.fr/hal-01020654/document

Dynamic mode decomposition of numerical and experimental data

1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

/pdf/essentials-of-robust-control-3kaks6yk3h.pdf

Essentials of Robust Control

Time-delay systems: an overview of some recent advances and open problems

A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002). The empirical Galerkin model is based on an eight-dimensional Karhunen–Loeve decomposition of a numerical simulation and incorporates a new ‘shift-mode’ representing the mean-field correction. The inclusion of the shift-mode significantly improves the resolution of the transient dynamics from the onset of vortex shedding to the periodic von Karman vortex street. In addition, the Reynolds-number dependence of the flow can be described with good accuracy. The inclusion of stability eigenmodes further enhances the accuracy of fluctuation dynamics. Mathematical and physical system reduction approaches lead to invariant-manifold and to mean-field models, respectively. The corresponding two-dimensional dynamical systems are further reduced to the Landau amplitude equation.

/pdf/a-hierarchy-of-low-dimensional-models-for-the-transient-and-mndofad8te.pdf

A hierarchy of low-dimensional models for the transient and post-transient cylinder wake

The book focuses on the physical and mathematical foundations of model-based turbulence control: reduced-order modelling and control design in simulations and experiments. Leading experts provide elementary self-consistent descriptions of the main methods and outline the state of the art. Covered areas include optimization techniques, stability analysis, nonlinear reduced-order modelling, model-based control design as well as model-free and neural network approaches. The wake stabilization serves as unifying benchmark control problem.

Reduced-Order Modelling for Flow Control

Drag reduction strategies for the turbulent flow around a D-shaped body are examined experimentally and theoretically. A reduced-order vortex model describes the interaction between the shear layer and wake dynamics and guides a path to an efficient feedback control design. The derived feedback controller desynchronizes shear-layer and wake dynamics, thus postponing vortex formation. This actuation is tested in a wind tunnel. The Reynolds number based on the height of the body ranges from 23000 to 70000. We achieve a 40% increase in base pressure associated with a 15% drag reduction employing zero-net-mass-flux actuation. Our controller outperforms other approaches based on open-loop forcing and extremum-seeking feedback strategies in terms of drag reduction, adaptivity, and the required actuation energy.

Feedback shear layer control for bluff body drag reduction

This paper addresses the problem of torque ripple minimization in permanent magnet synchronous motors (PMSMs) and proposes an adaptive feedback structure as a solution. A model of PMSM that includes a torque ripple phenomenon is first developed and tested. While slightly different from the conventional one, our model is still compact and suitable for control. All parameters of the model have physical interpretation, and can either be measured directly or estimated in a numerically reliable procedure. An adaptive control algorithm is then described, enabling speed tracking while minimizing the torque ripple. Finally, the proposed algorithm is verified in simulations and implemented in a hardware setup. Experimental results show significant reduction of torque ripple (by 27 dB). Extensive analysis and simulations of hardware imposed limitations were performed as well, revealing and quantifying the issues that might affect practical ripple minimization performance.

Design and implementation of an adaptive controller for torque ripple minimization in PM synchronous motors

This paper presents a time-domain, optimal-control approach to worst-case design, an alternative to frequency-domainH∞ techniques. The generic linear-quadratic set-up of the “standardH∞ problem” is discussed. The resultsinclude a characterization of suboptimal values, as well as a parametrization of all suboptimal compensators, interms of two coupled indefinite Riccati equations. Both the usual infinite-horizon, time-invariant case and the finite-horizon, time-varying case, are treated. The latter is beyond the scope of frequency-domain analysis.

Gilead Tadmor

Papers

A hierarchy of low-dimensional models for the transient and post-transient cylinder wake

Reduced-Order Modelling for Flow Control

Feedback shear layer control for bluff body drag reduction

Design and implementation of an adaptive controller for torque ripple minimization in PM synchronous motors

Worst-case design in the time domain: The maximum principle and the standardH∞ problem