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Untitled 1 The Feedback Ampl ifier Karl Johan Åström Department of Automatic Control LTH Lund University The Feedback Ampl ifier K. J. Åström 1. Introduction 2. Black’s Invention 3. Bode 4. Nyquist 5. More Recent Developments 6. Summary Theme: Pure feedback. Lectures 1940 1960 2000 1 Introduction 2 Governors | | | 3 Process Control | | | 4 Feedback Amplifiers | | | 5 Harry Nyquist | | | 6 Aerospac
L08TheSecondWave.pdf The Second Wave K. J. Åström Department of Automatic Control LTH Lund University History of Control – The Second Wave 1. Introduction 2. Major Advances 3. Computing 4. Control Everywhere 5. Summary History of Control – The Second Wave Introduction ! Use of control in widely different areas unified into a single framework by 1960 ! Education mushrooming, more than 36 text
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/HistoryOfControl/2016/L08TheSecondWave_8.pdf - 2026-04-24
Untitled 1 Automatic Cont rol in Lund Karl Johan Åström Department of Automatic Control, LTH Lund University Automatic Cont rol in Lund 1. Introduction 2. System Identification and Adaptive Control 3. Computer Aided Control Engineering 4. Relay Auto-tuning 5. Two Applications 6. Summary Theme: Building a New Department and Samples of Activities. Lectures 1940 1960 2000 1 Introduction 2 Governors |
A Brief History of Event-Based Control Marcus T. Andrén Department of Automatic Control Lund University Marcus T. Andrén A Brief History of Event-Based Control Concept of Event-Based Example with impulse control [Åström & Bernhardsson, 1999] Periodic Sampling Event-Based Sampling Event-Based: Trigger sampling and actuation based on signal property, e.g |x(t )| >δ (Lebesgue sampling) A.k.a aperiodi
History of Robotics History of Robotics Martin Karlsson Dept. Automatic Control, Lund University, Lund, Sweden November 25, 2016 Martin Karlsson November 30, 2016 1 / 14 Outline Introduction What is a robot? Early ideas The first robots Modern robots Major organizations Ubiquity of robots Future challenges Martin Karlsson November 30, 2016 2 / 14 Introduction The presenter performs research in rob
MLGA.key Let's make the lab great! 2017-05-03 Vision • Small & cheap processes, which students can bring home (and perhaps use remotely over internet) • Pedagogic lab manuals, introducing control concepts and encouraging hacking • A PhD course, where we develop the lab together and learn new (control) engineering skills, as well as gain team work experience Let's focus on getting something simple
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/LabDevelopment/2017/intro.pdf - 2026-04-24
Robotics and Human Machine Interaction Lab Prof. Dr.-Ing. Ulrike Thomas Motion Planning - Trajectory calculation, PRM, RRT 1. Trajectory planning a) Lin and ptp are the two most common methods for trajectory planning, de- scribe them briefly. b) The simplest way to calculate a trajectory (ptp) is a 3rd order polynomial. Why shouldn’t this be applied? c) Calculate the progression of a two-axis mani
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/MotionPlanning2019/exercise_RRT_Monday.pdf - 2026-04-24
Lecture 3. The maximum principle In the last lecture, we learned calculus of variation (CoV). The key idea of CoV for the minimization problem min u∈U J(u) can be summarized as follows. 1) Assume u∗ is a minimizer, and choose a one-parameter variation uϵ s.t. u0 = u∗ and uϵ ∈ U for ϵ small. 2) The function ϵ 7→ J(uϵ) has a minimizer at ϵ = 0. Thus it satisfies the first and second order necessary
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/Lecture3.pdf - 2026-04-24
Exercise for Optimal control – Week 1 Choose two problems to solve. Disclaimer This is not a complete solution manual. For some of the exercises, we provide only partial answers, especially those involving numerical problems. If one is willing to use the solution manual, one should judge whether the solutions are correct or wrong him/herself. Exercise 1 (Fundamental lemma of CoV). Let f be a real
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex1-sol.pdf - 2026-04-24
Exercise for Optimal control – Week 2 Choose one problem to solve. Exercise 1 (Insect control). Let w(t) and r(t) denote, respectively, the worker and reproductive population levels in a colony of insects, e.g. wasps. At any time t, 0 ≤ t ≤ T in the season the colony can devote a fraction u(t) of its effort to enlarging the worker force and the remaining fraction u(t) to producing reproductives. T
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex2.pdf - 2026-04-24
Exercise for Optimal control – Week 3 Choose 1.5 problems to solve. Disclaimer This is not a complete solution manual. For some of the exercises, we provide only partial answers, especially those involving numerical problems. If one is willing to use the solution manual, one should judge whether the solutions are correct or wrong by him/herself. Exercise 1. Consider a harmonic oscillator ẍ + x =
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex3-sol.pdf - 2026-04-24
Exercise for Optimal control – Week 5 Choose one problem to solve. Exercise 1. Use tent method to derive the KKT condition (google it if you don’t know) for the nonlinear optimization problem: min f(x) subject to gi(x) ≤ 0, i = 1, · · · ,m hj(x) = 0, j = 1, · · · , l where f , gi, hj are continuously differentiable real-valued functions on Rn. Exercise 2. Find a variation of inputs uϵ near u∗ that
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex4.pdf - 2026-04-24
Exercise for Optimal control – Week 6 Choose 1.5 problems to solve. Exercise 1. Derive the policy iteration scheme for the LQR problem min u(·) ∞∑ k=1 x⊤ k Qxk + u⊤ k Ruk with Q = Q⊤ ≥ 0 and R = R⊤ > 0 subject to: xk+1 = Axk +Buk. Assume the system is stabilizable. Start the iteration with a stabilizing policy. Run the policy iteration and value iteration on a computer for the following matrices:
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex6.pdf - 2026-04-24
5 Lecture 5. Proof of the maximum principle 5.1 The tent method We continue with the static nonlinear optimization problem: min g0(x) subject to gi(x) ≤ 0, i = 1, · · · ,m (LM) in which {gi}mi=0 ∈ C1(Rn;R). Suppose that the problem is feasible, i.e., there exists an admissible x∗ which minimizes g0(x). Recall that we defined the following sets: Ωi = {x ∈ Rn : gi(x) ≤ 0}, i = 1, · · · ,m and for x1
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/lec5.pdf - 2026-04-24
7 Lecture 7. Dynamic programming II 7.1 Policy iteration In previous lecture, we studied dynamic programming for discrete time systems based on Bellman’s principle of optimality. We studied both finite horizon cost J = φ(xN ) + N−1∑ k=1 Lk(xk, uk), uk ∈ Uk and infinite horizon cost J = ∞∑ k=1 L(xk, uk), uk ∈ U(xk). The key ingredients we obtained were the Bellman equations. For finite horizon, J∗
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/lec7.pdf - 2026-04-24
Boiler Modeling Goal: To present a major industrial modeling effort (pre Modelica). Practice balance equations. To illustrate that it takes time to obtain good simple models. Rodney Bell: Nature does not willingly part with its secrets! 1. Introduction 2. Global Balance Equations 3. Steam Distribution 4. The Model 5. Simulation 6. Experiments 7. Conclusions Introduction ◮ Long term research projec
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/PhysicalModeling/Lectures/Boilerseight.pdf - 2026-04-24
L1-Introduction 2022-03-07 1 Modeling Karl Johan Åström Department of Automatic Control LTH Lund University from Physics to Languages and Software 1 Modeling ØEssential for the development of science, example: Brahe, Kepler, Newton Ø Essential element of all engineering Ø Process design and optimization Ø Insight and understanding Ø Control design and optimization Ø Implementation – The internal m
PowerPoint Presentation Equation and Object-oriented Modeling Modeling Course – Automatic Control Hilding Elmqvist Mogram AB and Modelon AB In collaboration with: Martin Otter, Gerhard Hippman, Andrea Neumayr, Oskar Åström Assistants: Karl Johan Åström and Oskar Åström Content • Introduction • Part 1: Equation Oriented Modeling (Modia) • structural and symbolic algorithms • DAE index reduction • e
Automotive Modeling—An Overview of Model Components Contents: 1. Introduction 2. Propulsion and powertrain dynamics 3. Braking system and wheel dynamics 4. Tire–road interaction models 5. Steering and suspension dynamics 6. Chassis dynamics 7. Experiments and model calibration 8. Summary Lecture on May 5: Mathias Strandberg from Modelon will discuss automotive modeling using Modelica and Modelon I
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/PhysicalModeling/Lectures/L9B-Automotive.pdf - 2026-04-24
Physical modeling – Power systems Physical modelling – AC Power systems OLOF SAMUELSSON, INDUSTRIAL ELECTRICAL ENGINEERING AND AUTOMATIO N E S A V MW and Mvar Outline • The electric power system • Electromagnetic transients • Phasor model at steady state – power flow • Electro-mechanical and mechanical oscillations • Dynamic phasor simulation • Linearized DAE and ODE • Modal analysis • Case study:
