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ex4.dvi

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 - 2025-07-08

ex6.dvi

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 - 2025-07-08

Extremum-seeking Control

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

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/extremum-seeking-tommi-victor.pdf - 2025-07-08

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() Gain Scheduling Bo Bernhardsson and Karl Johan Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson and Karl Johan Åström Gain Scheduling Gain Scheduling What is gain scheduling ? How to find schedules ? Applications What can go wrong ? Some theoretical results LPV design via LMIs Conclusions To read: Leith & Leithead, Survey of Gain-Scheduling Analysis & Design To try ou

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/gainscheduling.pdf - 2025-07-08

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() Handin 1 Bo Bernhardsson, K. J. Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson, K. J. Åström Handin 1 Handin 1 - goals Get some practice using the Matlab control system toolbox (or similar) Get started with some control design Bo Bernhardsson, K. J. Åström Handin 1 Example - Double Integrator Consider the double integrator y = 1 s2 u controlled with state-feedback +

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/handin1.pdf - 2025-07-08

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() Handin 3 Consider the (broomstick) system p2 s2 − p2 with p = 6 rad/s ((1 feet). Hint: You might find it useful to read or watch Gunter Stein’s Bode Lecture. a) Find a stabilizing controller achieving pT(iω)p < (Ωa/ω) 2, when ω > Ωa = 10 rad/s Ms := max ω pS(iω)p < 10 b) Try to get as low Ms you can, while maintaining the requirement on T. Bonus: Try to find a theoretical lower bound on Ms (the

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/handin3.pdf - 2025-07-08

handin5.dvi

handin5.dvi Handin 5 - Connected Inverted Pendulums (LQG) x1 x2 φ1 = x5 φ2 = x7 u1 u2 The process consists of two inverted pendulums mounted on movable carts. The carts are connected with a spring. The inputs are the forces on the two carts. The outputs are the cart positions and pendulum angles. The system hence have 2 inputs and 4 outputs. The system parameters correspond to 1m pendulums mounted

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/handin5.pdf - 2025-07-08

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LQG-examples exkj2.m Slow process pole example fig822.m Aircraft turbulence attenuation lqg1.m An example where some eigenvalues are moved by LQG but some others are fixed. lqg2.m An example technical conditions are violated lqg3.m LTR example Doyle and Stein AC 79 exreducedobserver.m Reduced order design mac58.m LTR design example from Maciejowski at the end of lecture 10

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/lqg.html - 2025-07-08

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Thickness Control of a Rolling Mill References Lars Malcom Pedersen's Lic-thesis The problem is to design a controller for the rolling mill at the "danska stalverket". There are two inputs, the signals to the hydraulic valves at the north and south side. The output is a vector describing the (predicted) thickness profile of the plate. There are 6 states. Matlab-code Description mill.ps The model m

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/mill.html - 2025-07-08

Deep-Learning Study Circle: Reinforcement Learning

Deep-Learning Study Circle: Reinforcement Learning Deep-Learning Study Circle: Reinforcement Learning Gabriel Ingesson 0/46 Reinforcement Learning The problem where an agent has to learn a policy (behavior) by taking actions in an environment, with the goal that the policy should maximize a cumulative reward. Different from supervised and unsupervised learning: No labeled training data. Reward sig

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/DeepLearning/2016/RL.pdf - 2025-07-08

Autoencoders

Autoencoders Autoencoders Fredrik Bagge Carlson Fredrik Bagge Carlson, Lund University: Autoencoders Introduction General idea Auto: Greek auto- "self, one’s own" Encode: from en- "make, put in" + code: a system of words, letters, figures, or symbols used to represent others Find a useful encoding, h = f(x), of data x in an unsupervised manner. Trained using an encoder h = f(x) and a decoder x̂ =

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/DeepLearning/2016/autoencoders.pdf - 2025-07-08

Improving Imputation Using Stacked denoising Autoencoder

Improving Imputation Using Stacked denoising Autoencoder Improving Imputation Using Stacked denoising Autoencoder Najmeh Abiri November 22, 2016 Computational Biology and Biological Physics Missing Data Pre-processing data Astronomy Outlier? Biology Missing Data? 1 Missing data in Biology Molecular Patterns of Life 2 Missing data in Biology Generate detailed DNA/protein molecular fingerprints and

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/DeepLearning/2016/improving-imputation-stacked.pdf - 2025-07-08

Untitled

Untitled 1 Automatic Cont rol in Sweden Karl Johan Åström Department of Automatic Control, LTH Lund University Lectures 1940 1960 2000 1 Introduction 2 Governors | | | 3 Process Control | | | 4 Feedback Amplifiers | | | 5 Harry Nyquist | | | 6 Aerospace | | | 7 Automatic Control Emerges ← | | 8 The Second Phase ← ← | 9 Automatic Control in Sweden | | | 10 Automatic Control in Lund | | 11 The Futur

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/HistoryOfControl/2016/L09Swedeneight.pdf - 2025-07-08

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Session 2 Dissipativity and Integral Quadratic Constraints Reading assignment You don’t need to read everything from these papers, but check the main results and some examples. Jan C. Willems was the leading figure of systems and control in the Netherlands for several decades. The other two papers are from our department. • Jan C. Willems, Arch. Rational Mech. and Analysis, 45:5 (1972). • A. Megre

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/2017_E2.pdf - 2025-07-08

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Session 4 Hybrid systems Reading assignment Check the main results and examples of these papers. • Johansson/Rantzer, IEEE TAC, 43:4 (1998). • Chizeck/Willsky/Castanon, Int. J. on Control, 43:1 (1986) Exercise 4.1Consider two pendula[ ẋ1 ẋ2 ] = [ x2 1− x1 ] [ ẋ1 ẋ2 ] = [ x2 −1− x1 ] which are swinging around x1 = 1 and x1 = −1 respectively. a. Find a control law that brings the state to (0, 0)

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/2017_E4.pdf - 2025-07-08

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Session 6 Nonlinear Controllability Reading assignment • Glad, Nonlinear Control Theory, Ch. 8 + Hörmander handout Exercises marked with a “*” are more difficult Exercise 6.1 Consider a car with N trailers. The front-wheels of the car can be controlled, and the car can drive forwards and backwards. Describe a manifold that can be used as state-space. Show that its dimension is N + 4. Exercise 6.2

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/2017_E6.pdf - 2025-07-08