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Synthesis, Nonlinear design ◮ Introduction ◮ Relative degree & zero-dynamics (rev.) ◮ Exact Linearization (intro) ◮ Control Lyapunov functions ◮ Lyapunov redesign ◮ Nonlinear damping ◮ Backstepping ◮ Control Lyapunov functions (CLFs) ◮ passivity ◮ robust/adaptive Ch 13.1-13.2, 14.1-14.3 Nonlinear Systems, Khalil The Joy of Feedback, P V Kokotovic Why nonlinear design methods? ◮ Linear design degra
Session 1 Reading assignment Liberzon chapters 1 – 2.4. Exercises 1.1. = Liberzon Exercise 1.1 1.2. = Liberzon Exercise 1.5 1.3. = Liberzon Exercise 2.2 1.4. = Liberzon Exercise 2.3 1.5. Read Liberzon Chap.2.3.3 and explain how we can avoid assuming y ∈ C2. Prove Lemma 2.2 (Liberzon Exercise 2.4). 1.6. = Liberzon Exercise 2.5 (State the brachistochrone problem first.) 1.7. = Liberzon Exercise 2.6
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise1.pdf - 2025-02-16
Session 3 Reading assignment Liberzon chapters 4.1, 4.3 – 4.5. Exercises 3.1. = Liberzon Exercise 4.1. (Deriving the Euler-Lagrange equation for brachistochrone is enough. No need to derive that its solutions are cycloids.) 3.2. = Liberzon Exercise 4.8 3.3. = Liberzon Exercise 4.10 3.4. = Liberzon Exercise 4.11 3.5. = Liberzon Exercise 4.12 3.6. = Liberzon Exercise 4.15 3.7. = Liberzon Exercise 4.
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise3.pdf - 2025-02-16
Session 5 Reading assignment Liberzon chapter 5. Exercises 5.1. = Liberzon Exercise 5.2 5.2. = Liberzon Exercise 5.3 5.3. = Liberzon Exercise 5.4 5.4. = Liberzon Exercise 5.5 5.5. = Liberzon Exercise 5.6 5.6. = Linerzon Exercise 5.7 1
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise5.pdf - 2025-02-16
Optimal Control 2018 Kaoru Yamamoto Optimal Control 2018 L1: Functional minimization, Calculus of variations (CV) problem L2: Constrained CV problems, From CV to optimal control L3: Maximum principle, Existence of optimal control L4: Maximum principle (proof) L5: Dynamic programming, Hamilton-Jacobi-Bellman equation L6: Linear quadratic regulator L7: Numerical methods for optimal control problems
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/lecture2eight.pdf - 2025-02-16
Instruments | Division of Physical Chemistry Faculty of Science Search Division of Physical Chemistry Department of Chemistry Department of Chemistry Kemicentrum Safety and security Contact About Education News and events Research People Instruments COMMONS Center Center for Scattering Methods Home > Instruments Denna sida på svenska This page in English Instruments The Division of Physical Chem
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Förmåner | Akademikerförening Scania Hoppa till huvudinnehåll Öppna sökruta Öppna Huvudmeny Sök på saco.se Bli medlem GDPR och hantering personuppgifter Engagera dig Kontaktpersonrollen Skyddsombudsrollen Ledamot i styrelsen Ledamot i valberedningen Revisorsrollen Frågor vi driver Färdriktning Arbetsmiljö Förmåner Kompetens Ledarskap Lön Mångfald, rättvisa och inkludering Företagskultur Lön Öka di
Targets groups | Vattenhallen Science Center Skip to main content This site uses cookies to enhance the user experience. By continuing to use the site you agree that cookies are used according to our Cookie Policy (on the website of LTH) . Essential cookies These cookies are necessary for the website to function and cannot be turned off in our systems. These cookies do not store any personally ide
https://www.vattenhallen.lu.se/vattenhallen-english/the-planetarium/shows-in-english/targets-groups/ - 2025-02-16
LUNDS UNIVERSITY Department of Archaeology and Ancient History Reading list - ARKN07, The Archaeology of Social Identities, 15 hp Established by the Board of Department: 2011-11-08 Alberti, B. 2006. Archaeology, Men, and Masculinities. I: Nelson, M. S. (red.) Handbook of Gender in Archaeology. New York, Toronto, Oxford. p. 401-434. 33 p. Axboe, M. 1999. Towards the Kingdom of Denmark. I: Dickinson
https://www.ark.lu.se/media/utbildning/dokument/kurser/ARKN07/20132/Readning_list_ARKN07_2.pdf - 2025-02-16
Adaptive Control Bo Bernhardsson and K. J. Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson and K. J. Åström Adaptive Control Adaptive Control 1 Introduction 2 Model Reference Adaptive Control 3 Recursive Least Squares Estimation 4 The Self-Tuning Regulator 5 Real Adaptive Controllers 6 Summary Bo Bernhardsson and K. J. Åström Adaptive Control Introduction Adapt to adjus
IQC toolbox IQC toolbox Gustav Nilsson May 25, 2016 IQC - Integral Quadratic Constraints • A unifying framework for systems analysis • Generalizes stability theorems such as small gain theorem and passivity theorem • Generalizes many concepts from robust control analysis • (Fairly) easy to build computer tools (convex optimization) Outline • Some theory on IQC • IQCβ toolbox • Live demo ICQ - Theo
() Pole Placement Design Bo Bernharsson and Karl Johan Åström Department of Automatic Control LTH, Lund University Bo Bernharsson and Karl Johan Åström Pole Placement Design Pole Placement Design 1 Introduction 2 Simple Examples 3 Polynomial Design 4 State Space Design 5 Robustness and Design Rules 6 Model Reduction 7 Oscillatory Systems 8 Summary Theme: Be aware where you place them! Bo Bernharss
() Robust Control, H∞, ν and Glover-McFarlane Bo Bernharsson and Karl Johan Åström Department of Automatic Control LTH, Lund University Bo Bernharsson and Karl Johan Åström Robust Control, H∞, ν and Glover-McFarlane Robust Control 1 MIMO performance 2 Robustness and the H∞-norm 3 H∞-control 4 ν-gap metric 5 Glover-MacFarlane Theme: You get what you ask for! Bo Bernharsson and Karl Johan Åström Rob
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/Robust.pdf - 2025-02-16
ACC 1990 Benchmark Example References ACC 1990, pp. 961-962, The problem ACC 1990, pp. 963-973, Several Solutions ACC 1991, pp. 1931-1932, Mats Liljas design and comments The problem is to design a controller for a scalar linear system consisting of two-mass spring system. There are 4 states.
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/acc90.html - 2025-02-16
Aircraft dynamics with wind gust turbulence References Anderson and Moore p 222 The problem is to damp out the turbulence giving forward and aft acceleration on an aircraft. The model is of order 6. There is one input: rudder position. Matlab-code Model and code in fig822.m .
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/anderson222.html - 2025-02-16
ex02.dvi Exercise Session 2 1. Describe your results on Handin 1. 2. Sketch the Nichols curves for the following systems 1 s(s + 1)(s + 10) , 1 1 − s , exp (−s) 1 + s , 1 − s s(1 + s) , 1 s2 + 2ζs + 1 , (ζ small) For what feedback gains is the closed loop system stable? 3. Plot the root-loci for the following systems s s2 − 1 , (s + 1)2 s3 , 1 s(s2 + 2ζs + 1) , (ζ small) 4. Transform the systems i
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/ex02.pdf - 2025-02-16
ex4.dvi Exercise 4 Poleplacement and PID 1. Use Euclid’s algorithm to find all solutions to the equation 7x+ 5y = 6 where x and y are integers. 2. Use Euclid’s algorithm to find all solutions to the equation s2 x(s) + (0.5s+ 1)y(s) = 1 where x(s) and y(s) are polynomials. Use the results to find a solution to the equation s2 f (s) + (0.5s+ 1)(s) = (s2 + 2ζcω cs+ω2 c)(s 2 + 2ζoωos+ω2 o) such that t
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/ex4.pdf - 2025-02-16
ex6.dvi Exercise 6 LQG and H∞ 1. Use the appropriate Riccati equation to prove the Kalman filter identity R2 + C2(sI − A)−1 R1(−sI − AT)−1CT 2 = [Ip + C2(sI − A)−1 L]R2[Ip + C2(−sI − AT)−1 L]T Use duality to deduce the return difference formula Q2 + BT(−sI − AT)−1Q1(sI − A)−1B = [Im + K(−sI − AT)−1B]T Q2[Im + K(sI − A)−1B] 2. Consider the Doyle-Stein LTR example from the LQG lecture G(s) = s+ 2 (s
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/ex6.pdf - 2025-02-16
Extremum-seeking Control Extremum-seeking Control Tommi Nylander and Victor Millnert May 25, 2016 1 / 14 Short introduction I Non-model based real-time optimization I When limited knowledge of the system is available I E.g. a nonlinear equilibrium map with a local minimum I Popular around the middle of the 1950s I Revival with proof of stability 1 I Very attractive with the increasing complexity o
