Filtyp
2022.02.14 - New publication in Nature Communications | Division of Chemical Physics Search Division of Chemical Physics Department of Chemistry | Faculty of Science Department of Chemistry Kemicentrum Safety and security About Research Education People Publications Open Positions Home > News > News Archive > 2022.02.14 - New publication in Nature Communications Denna sida på svenska This pa
Session 1 Linear Control Systems. Examples. Linearization. Transition Matrix. Reading Assignment Rugh (1996 edition) chapters 1-4 and scan Chapter 20 until Example 20.7. The main new thing is to do linearization along a trajectory rather than at an equilibrium, and the definition and properties of the transition matrix Φ(t, τ). Exercise 1.1 = Rugh 1.9 Exercise 1.2 = Rugh 1.20 (spectral norm) Exerc
Session 3 Reachability and Controllability. Observability and Reconstructability. Controller and Observer Forms. Reading Assignment Rugh, Ch 9, 13, 14 (only Theorem 14.9) (for continuous-time systems) and Ch 25 (for discrete-time systems). Exercise 3.1 = Rugh 9.1. Exercise 3.2 = Rugh 9.2 Exercise 3.3 = Rugh 9.4 Exercise 3.4 = Rugh 9.5 Exercise 3.5 = Rugh 9.7 Exercise 3.6 a. Show that {A,B} is cont
Session 5 LTV stability. Quadratic Lyapunov functions. Reading Assignment Rugh Ch 6,7,12 (skip proofs of 7.8, 12.6 and 12.7),14 (pp240-247), and (22,23,24,28) Exercise 5.1 = Rugh 6.3 iii+iv Exercise 5.2 = Rugh 6.11 Exercise 5.3 = Rugh 7.3 Exercise 5.4 = Rugh 8.3 Exercise 5.5 = Rugh 7.6 Exercise 5.6 = Rugh 7.11 Exercise 5.7 = Rugh 7.20 Exercise 5.8 = Rugh 23.2 Hand in problems Exercise 5.9 = Rugh 8
Session 7 Polynomial Matrix Descriptions, Poles and Zeros of MIMO systems Reading Assignment Rugh, Ch. 16-17. Exercises Exercise 7.1 Make sure you can handle the Maple routines Matrix, Hermite- Form, SmithForm. Hint: ?MatrixPolynomialAlgebra[HermiteForm] gives some help text. Exercise 7.2 = Rugh 16.1 Exercise 7.3 = Rugh 16.2 Exercise 7.4 Determine the Smith form, i.e. the invariant polynomials, fo
LionSealWhite Linear Systems, 2019 - Lecture 1 Introduction Multivariable Time-varying Systems Transition Matrices Controllability and Observability Realization Theory Stability Theory Linear Feedback Multivariable input/output descriptions Some Bonus Material 1 / 21 LionSealWhite Lecture 1 State equations Linearization Examples Transition matrices Rugh, chapters 1-4 Main news: Linearization aroun
LionSealWhite Lecture 5 LTV stability concepts Quadratic Lyapunov functions Feedback, Well-posedness, Internal Stability Rugh Ch 6,7,12 (skip proofs of 12.6 and 12.7),14 (pp240-247) + (22,23,24,28) Zhou, Doyle, Glover pp 117-124 1 / 31 LionSealWhite Stability For LTI systems ẋ = Ax the stability concept was easy, we had the two concepts i) Stability: x(t) remains bounded ii) Asymptotic stability:
LionSealWhite Lecture 7 Theory for polynomial matrices Hermite and Smith normal forms Smith McMillan form Poles and Zeros Rugh Ch 16-17 (can skip proofs of 16.7,17.4,17.5,17.6) 1 / 36 LionSealWhite Polynomial matrix fraction descriptions There are two natural generalisation to the SISO description G(s) = n(s) d(s) Right polyomial matrix fraction description: G(s) = NR(s)DR(s)−1 { DR(s)X(s) = U(s)
1 A History of A4. A History of Automatic Control C.C. Bissell Automatic control, particularly the application of feedback, has been fundamental to the devel- opment of automation. Its origins lie in the level control, water clocks, and pneumatics/hydraulics of the ancient world. From the 17th century on- wards, systems were designed for temperature control, the mechanical control of mills, and th
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 - 2025-08-10
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
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 - 2025-08-10
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 - 2025-08-10
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 - 2025-08-10
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 - 2025-08-10
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 - 2025-08-10
