SYSTEM IDENTIFICATION AND MODEL PREDICTIVE CONTROL FOR INTERACTING SERIES PROCESS WITH NONLINEAR DYNAMICS

This thesis discusses the empirical modeling using system identification technique and the implementation of a linear model predictive control with focus on interacting series processes. In general, a structure involving a series of systems occurs often in process plants that include processing sequences such as feed heat exchanger, chemical reactor, product cooling, and product separation. The study is carried out by experimental works using the gaseous pilot plant as the process. The gaseous pilot plant exhibits the typical dynamic of an interacting series process, where the strong interaction between upstream and downstream properties occurs in both ways. The subspace system identification method is used to estimate the linear model parameters. The developed model is designed to be robust against plant nonlinearities. The plant dynamics is first derived from mass and momentum balances of an ideal gas. To provide good estimations, two kinds of input signals are considered, and three methods are taken into account to determine the model order. Two model structures are examined. The model validation is conducted in open-loop and in closed-loop control system. Real-time implementation of a linear model predictive control is also studied. Rapid prototyping of such controller is developed using the available equipments and software tools. The study includes the tuning of the controller in a heuristic way and the strategy to combine two kinds of control algorithm in the control system. A simple set of guidelines for tuning the model predictive controller is proposed. Several important issues in the identification process and real-time implementation of model predictive control algorithm are also discussed. The proposed method has been successfully demonstrated on a pilot plant and a number of key results obtained in the development process are presented

Model Order Reduction for Gas and Energy Networks

To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order reduction algorithms. For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and parametric model reduction for nonlinear systems. This research resulted in the "morgen" (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of "morgen" and associated numerical experiments testing model reduction adapted to gas network models

Overcoming the timescale barrier in molecular dynamics: Transfer operators, variational principles and machine learning

One of the main challenges in molecular dynamics is overcoming the ‘timescale barrier’: in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject

Black Holes, Qubits and Octonions

We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory. The first example is provided by the measure of the tripartite entanglement of three qubits, known as the 3-tangle, and the entropy of the 8-charge STU black hole of N=2 supergravity, both of which are given by the [SL(2)]^3 invariant hyperdeterminant, a quantity first introduced by Cayley in 1845. There are further relationships between the attractor mechanism and local distillation protocols. At the microscopic level, the black holes are described by intersecting D3-branes whose wrapping around the six compact dimensions T^6 provides the string-theoretic interpretation of the charges and we associate the three-qubit basis vectors, |ABC> (A,B,C=0 or 1), with the corresponding 8 wrapping cycles. The black hole/qubit correspondence extends to the 56 charge N=8 black holes and the tripartite entanglement of seven qubits where the measure is provided by Cartan's E_7 supset [SL(2)]^7 invariant. The qubits are naturally described by the seven vertices ABCDEFG of the Fano plane, which provides the multiplication table of the seven imaginary octonions, reflecting the fact that E_7 has a natural structure of an O-graded algebra. This in turn provides a novel imaginary octonionic interpretation of the 56=7 x 8 charges of N=8: the 24=3 x 8 NS-NS charges correspond to the three imaginary quaternions and the 32=4 x 8 R-R to the four complementary imaginary octonions. N=8 black holes (or black strings) in five dimensions are also related to the bipartite entanglement of three qutrits (3-state systems), where the analogous measure is Cartan's E_6 supset [SL(3)]^3 invariant.Comment: Version to appear in Physics Reports, including previously omitted new results on small STU black hole charge orbits and expanded bibliography. 145 pages, 15 figures, 41 table

Reduced realizations and model reduction for switched linear systems:a time-varying approach

In the last decades, switched systems gained much interest as a modeling framework in many applications. Due to a large number of subsystems and their high-dimensional dynamics, such systems result in high complexity and challenges. This motivates to find suitable reduction methods that produce simplified models which can be used in simulation and optimization instead of the original (large) system. In general, the study aims to find a reduced model for a given switched system with a fixed switching signal and known mode sequence. This thesis concerns first the reduced realization of switched systems with known mode sequence which has the same input-output behavior as original switched systems. It is conjectured that the proposed reduced system has the smallest order for almost all switching time duration. Secondly, a model reduction method is proposed for switched systems with known switching signals which provide a good model with suitable thresholds for the given switched system. The quantitative information for each mode is carried out by defining suitable Gramians and, these Gramians are exploited at the midpoint of the given switching time duration. Finally, balanced truncation leads to a modewise reduction. Later, a model reduction method for switched differential-algebraic equations in continuous time is proposed. Thereto, a switched linear system with jumps and impulses is constructed which has the identical input-output behavior as original systems. Finally, a model reduction approach for singular linear switched systems in discrete time is studied. The choice of initial/final values of the reachability and observability Gramians are also investigated