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- Sandberg, Henrik
(författare)
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Model Reduction for Linear Time-Varying Systems
- 2004
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The thesis treats model reduction for linear time-varying systems. Time-varying models appear in many fields, including power systems, chemical engineering, aeronautics, and computational science. They can also be used for approximation of time-invariant nonlinear models. Model reduction is a topic that deals with simplification of complex models. This is important since it facilitates analysis and synthesis of controllers. The thesis consists of two parts. The first part provides an introduction to the topics of time-varying systems and model reduction. Here, notation, standard results, examples, and some results from the second part of the thesis are presented. The second part of the thesis consists of four papers. In the first paper, we study the balanced truncation method for linear time-varying state-space models. We derive error bounds for the simplified models. These bounds are generalizations of well-known time-invariant results, derived with other methods. In the second paper, we apply balanced truncation to a high-order model of a diesel exhaust catalyst. Furthermore, we discuss practical issues of balanced truncation and approximative discretization. In the third paper, we look at frequency-domain analysis of linear time-periodic impulse-response models. By decomposing the models into Taylor and Fourier series, we can analyze convergence properties of different truncated representations. In the fourth paper, we use the frequency-domain representation developed in the third paper, the harmonic transfer function, to generalize Bode's sensitivity integral. This result quantifies limitations for feedback control of linear time-periodic systems.
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| 2. |
- Ekvall, Jenny
(författare)
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Dryer Section Control in Paper Machines During Web Breaks
- 2004
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Web breaks in the dryer section of a paper machine cause loss of production and quality problems. After a web break, the steam pressure in the cylinders must be reduced to avoid overheating. The goal of this project is to determine optimal steam pressure trajectories during web breaks, so that the production is restarted with the same drying properties of the cylinder as before the break. A detailed physical dynamic model of the drying cylinder has been developed. The model describes the relations between the steam valve position, the steam pressure, the cylinder temperature, and the paper temperature. The model is based on partial differential equations that describe heat conductivity for the cylinder and the paper web, and mass balances of water and dry material in the paper. The accuracy of the model has been verified through experiments made at the M-real paper mill in Husum, Sweden. Verifications are made both during normal operation and during web breaks. The dynamic model has been reduced in order to derive simple transfer functions between the steam pressure and the cylinder temperature, and between a logic signal that is active during web breaks and the cylinder temperature, respectively. The transfer functions obtained were used to find the optimal steam pressure trajectory during web breaks. A new feed-forward strategy for steam pressure control during web breaks is presented. The strategy has been tested on a paper machine with good results. The strategy is built on feed-forward compensation and has been well received at the mill.
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| 3. |
- Fält, Mattias
(författare)
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Convergence Analysis and Improvements for Projection Algorithms and Splitting Methods
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Non-smooth convex optimization problems occur in all fields of engineering. A common approach to solving this class of problems is proximal algorithms, or splitting methods. These first-order optimization algorithms are often simple, well suited to solve large-scale problems and have a low computational cost per iteration. Essentially, they encode the solution to an optimization problem as a fixed point of some operator, and iterating this operator eventually results in convergence to an optimal point. However, as for other first order methods, the convergence rate is heavily dependent on the conditioning of the problem. Even though the per-iteration cost is usually low, the number of iterations can become prohibitively large for ill-conditioned problems, especially if a high accuracy solution is sought.In this thesis, a few methods for alleviating this slow convergence are studied, which can be divided into two main approaches. The first are heuristic methods that can be applied to a range of fixed-point algorithms. They are based on understanding typical behavior of these algorithms. While these methods are shown to converge, they come with no guarantees on improved convergence rates.The other approach studies the theoretical rates of a class of projection methods that are used to solve convex feasibility problems. These are problems where the goal is to find a point in the intersection of two, or possibly more, convex sets. A study of how the parameters in the algorithm affect the theoretical convergence rate is presented, as well as how they can be chosen to optimize this rate.
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| 4. |
- Gäfvert, Magnus, et al.
(författare)
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Proposal for a distributed computer control system in heavy-duty trucks
- 2000
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In designing safety-critical real-time distributed control-systems a great potential lies in combining methods within the areas of dependable computer systems and control theory. In this report a brake system on a heavy-duty truck is used as a case study to discuss the choice of distribution level of the computer system and the control algorithms. The distrubution levels of these system aspects are othogonal in the sense that they may be chosen independently for a certain system configuration. A system configuration is obtained by mapping a specific control algorithm architecture on a computer/communications architecture. To explore different system architectures the combinations of three different distribution levels for the control algorithms and computer/communication systems are investigated with respect to dependability and required information exchange. The result is a proposal on the choice of final distribution level of the brake system.
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| 8. |
- Johnsson, Charlotta
(författare)
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Whitepaper: S88 for Beginners
- 2004
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Are you interested in or curious about Batch Control, ISA S88, and/or Plant Automation in general, then this whitepaper is for you. In the following three pages you will learn the basics about Batch Control and ISA S88 and you will understand how you can benefit from knowing them. For a deeper understanding I recommend you to read the other whitepapers in this series as well as reading the ISA S88 standard.
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| 9. |
- Johnsson, Charlotta
(författare)
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Whitepaper: S88 for Universities
- 2004
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- If you are working at a university teaching a course in automation, and/or process control or if you are a student in interested in those subjects 14 this paper is for you! You might already have heard about the S88 batch control standard 14 how it tries to define terminology and concepts that makes design and operation of process control plants easier. In this paper, we will try to briefly explain, in understandable words and easy phrases, why it is definitely worthwhile for you to read and understand this standard. So that you, being a teacher, can provide your students with something very interesting that also makes your students extra valuable on the market when graduating, or so that you, being a student, have the knowledge to chose a course that really inspires you and teaches you the stuff that industry looks for.
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| 10. |
- Jouini, Taouba
(författare)
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Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters.
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