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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 - 2025-07-11
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 - 2025-07-11
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 - 2025-07-11
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 - 2025-07-11
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
() 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
() 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 - 2025-07-11
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 - 2025-07-11
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 - 2025-07-11
Untitled 1 Process Cont rol Karl Johan Åström Department of Automatic Control LTH Lund University Process Cont rol K. J. Åström 1. Introduction 2. The Industrial Scene 3. Pneumatics 4. Theory? 5. Tuning 6. More Recent Development 7. Summary Theme: Measurement Control Instrumentation and Communication (pneumatic). Lectures 1940 1960 2000 1 Introduction 2 Governors | | | 3 Process Control | | | 4 Ae
History of Real Time Systems History of Real Time Systems Gautham Department of Automatic Control, Lund University 1/14 Gautham: History of Real Time Systems Overview Introduction 1940s 1950s 1960s RTOS A look at RTSS Cloud. The future? 2/14 Gautham: History of Real Time Systems Real Time Systems I Real Time Systems describes hardware and software systems subject to a ”real-time constraint”, for e
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/HistoryOfControl/2016/hoc_Gautham.pdf - 2025-07-11
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 - 2025-07-11
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 - 2025-07-11
Nonlinear Control Theory 2017 L1 Nonlinear phenomena and Lyapunov theory L2 Absolute stability theory, dissipativity and IQCs L3 Density functions and computational methods L4 Piecewise linear systems, jump linear systems L5 Relaxed dynamic programming and Q-learning L6 Controllability and Lie brackets L7 Synthesis: Exact linearization, backstepping, forwarding Exercise sessions: Solve 50% of prob
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/NonlinearControl/2017/fu_lec02_2017eight.pdf - 2025-07-11
Session 2 Reading assignment Liberzon chapters 2.5 – 3. Exercises 2.1. = Liberzon Exercise 2.9. Reading the discussion in Chapter 1.2.2 will be helpful. 2.2. = Liberzon Exercise 2.10 2.3. = Liberzon Exercise 2.14 2.4. = Liberzon Exercise 3.2 2.5. = Liberzon Exercise 3.5 2.6. = Liberzon Exercise 3.6 for k = 1 and n = 2. 2.7. = Liberzon Exercise 3.8 1
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise2.pdf - 2025-07-11
Session 4 Reading assignment Liberzon chapter 4.2. Exercises 4.1. = Liberzon Exercise 4.2 4.2. = Liberzon Exercise 4.3 4.3. = Liberzon Exercise 4.4 4.4. = Liberzon Exercise 4.5 4.5. = Liberzon Exercise 4.6 1
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2018/exercise4.pdf - 2025-07-11
