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Control System Synthesis - Robust control - PhD Class - Fall 2020 Control System Synthesis - Robust control PHD CLASS - FALL 2020 Uncertainty and robustness Where does uncertainty come from? Modelling uncertainty Robustness Small gain theorem Robust stability Robust performance Robust synthesis H∞ -synthesis H∞ -Loopshaping synthesis µ-analysis and synthesis 1 Introduction 2 Fundamentals 3 Design
Control System Synthesis - Data-driven control - PhD Class - Fall 2020 Control System Synthesis - Data-driven control PHD CLASS - FALL 2020 Introduction to data-driven control The importance of data-driven approaches Model-based and data-driven control Overview of data-driven control technique Predictive and learning DDC Use of local models Use of repetitive experiments Robust DDC Using convex opt
PID Control Karl Johan Åström Tore Hägglund Department of Automatic Control, Lund University September 23, 2020 PID Control 1. Introduction 2. The Controller 3. Stability 4. Performance and Robustness 5. Empirical Tuning Rules 6. Tuning based on Optimization 7. Relay Auto-tuning 8. Limitations of PID Control 9. Summary Theme: The most common controller. Introduction ◮ PID control is widely used in
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2020/PIDeight.pdf - 2025-07-11
Control System Synthesis - PhD Class Exercise session 2 October 8, 2020 1 Inverted pendulum on a cart Figure 1: Inverted pendulum. The equations of motion are : (M +m)ẍ+ bẋ+mlθ̈ cos θ −mlθ̇2 sin θ = F (J +ml2)θ̈ +mgl sin θ = −mlẍ cos θ (1) where: • M = 0.5kg is the mass of the cart • m = 0.2kg is the mass of the pendulum • b = 0.1N/m/sec is the coefficient of friction for the cart • l = 0.3m is
Control System Synthesis - PhD Class Handin 1: Temperature control in a heat exchanger 24/09/2020 A chemical reactor called “stirring tank” is depicted below. The top inlet delivers liquid to be mixed in the tank. The tank liquid must be maintained at a constant temperature by varying the amount of steam supplied to the heat exchanger (bottom pipe) via its control valve. Variations in the temperat
flexservo.dvi Handin - Flexible Servo The process consists of three horizontal pulleys connected by two elastic belts. SensorDC motor The transfer function from motor to sensor can take 3 forms (Ts = 50ms): Unloaded: B = 0.28261z−3 + 0.50666z−4 A = 1− 1.41833z−1 + 1.58939z−2 − 1.31608z−3 + 0.88642z−4 Half Load: B = 0.10276z−3 + 0.18123z−4 A = 1− 1.99185z−1 + 2.20265z−2 − 1.84083z−3 + 0.89413z−4 Fu
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2020/handin2.pdf - 2025-07-11
Untitled 1 History of Cont rol - Int roduc tion Karl Johan Åström Department of Automatic Control LTH Lund University Int roduc tion 1. Introduction 2. Practical Information 3. A Thumbnail History 4. The Power of Feedback 5. Summary Theme: Those who ignore history are doomed to repeat it. Those who cannot remember the past are condemned to repeat it. (George Santayana) Why bot her? ◮ Fun ◮ Useful
L05ASMENyquistLecture.pdf A S M E N y q u is t L e c tu re 2 0 0 5 N yq u is t an d H is S em in al P ap er s K ar l J o h an Å st rö m D ep ar tm en t o f M ec h an ic al E n g in ee ri n g U n iv er si ty o f C al if o rn ia S an ta B ar b ar a A S M E N y q u is t L e c tu re 2 0 0 5 H ar ry N yq u is t 18 89 -1 97 6 A G if te d S ci en ti st a n d E n g in ee r Jo h n so n -N yq u is t n o is
() Automatic Control Emerges Karl Johan Åström Department of Automatic Control LTH Lund University Karl Johan Åström Automatic Control Emerges Automatic Control Emerges K. J. Åström 1 Introduction 2 The Computing Bottleneck 3 State of the Art around 1940 4 WWII 5 Servomechanisms 6 Summary Theme: Unification, theory, and analog computing. Karl Johan Åström Automatic Control Emerges Lectures 1940 19
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/HistoryOfControl/2016/L07ControlEmerges.pdf - 2025-07-11
governors.dvi ON GOVERNORS J.C. MAXWELL From the Proceedings of the Royal Society, No.100, 1868. A GOVERNOR is a part of a machine by means of which the velocity of the machine is kept nearly uniform, notwithstanding variations in the driving-power or the resistance. Most governors depend on the centrifugal force of a piece connected with a shaft of the machine. When the velocity increases, this f
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/HistoryOfControl/2016/MaxwellOnGovernors.pdf - 2025-07-11
1 Lecture 1: Introduction (Karl Johan) 2 Lecture 2: Calculus of variation (CoV) and the Maximum principle In this lecture, we are going to learn the maximum principle. The MP is a type of CoV, so we will first study the classical theory of CoV. Then we will try to move from the classical CoV theory to the optimal control setting, there we will immediately encounter some essential difficulties that
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/Lec2.pdf - 2025-07-11
4 Lecture 4. Misc topics on MP and the proof of the MP In the previous lecture, we studied the maximum principle. The main result is the following theorem. Theorem 1. Consider the system ẋ = f(x, u) with cost function J(u) = φ(x(tf )) + ∫ tf 0 L(x, u)dt and boundary constraint x(tf ) ∈ M ⊆ Rn Assume f , φ and L are C1 in x. Let (x∗(·), u∗(·)) correspond to the optimal solution to the minimiza- ti
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/Lecture4.pdf - 2025-07-11
Exercise for Optimal control – Week 1 Choose two problems to solve. Exercise 1 (Fundamental lemma of CoV). Let f be a real valued function defined on open interval (a, b) and f satisfies ∫ b a f(x)h(x)dx = 0 for all h ∈ Cc(a, b), i.e., h is continuous on (a, b) and its support, i.e., the closure of {x : h(x) ̸= 0} is contained in (a, b). 1) Show that f is identically zero if f is continuous. If f
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex1.pdf - 2025-07-11
Exercise for Optimal control – Week 4 Choose one problem 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. Use tent method to derive the KKT conditi
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex4-sol.pdf - 2025-07-11
Exercise for Optimal control – Week 5 Choose 2 problems to solve. Exercise 1. A public company has in year k profits amounting to xk SEK. The management then distributes uk to the shareholders and invests xk − uk in the company itself. Each SEK invested in such way will increase the company profit by θ > 0 the following year so that xk+1 = xk + θ(xk − uk). Suppose x0 ≥ 0 and 0 ≤ uk ≤ xk so that xk
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex5.pdf - 2025-07-11
Exercise for Optimal control – Week 6 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. Derive the policy iteration scheme for t
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex6_sol.pdf - 2025-07-11
Untitled JitterTime 1.2—Reference Manual Anton Cervin Department of Automatic Control Technical Report TFRT-7658, version 3 ISSN 0280–5316 Department of Automatic Control Lund University Box 118 SE-221 00 LUND Sweden © 2020 by Anton Cervin. All rights reserved. Printed in Sweden. Lund 2020 Abstract This technical report describes JITTERTIME, a Matlab toolbox for calculating the time-varying state
https://www.control.lth.se/fileadmin/control/Research/JitterTime/report1_2.pdf - 2025-07-11
The \(h\) function QPgen Home Examples Installation Documentation Licence Authors Citing The \(h\) function The function \(h : \mathbf{R}^p\to\mathbf{R}\cup\{\infty\}\) is separable down to the component and is piecewise linear in each component. The figure shows a 1-dimensional example. The function can model, e.g. ,: Hard constraints (if slopes are infinite) Soft constraints (if finite slope) Th
https://www.control.lth.se/fileadmin/control/Research/Tools/qpgen/hfcn.html - 2025-07-11
