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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
() Bottom-Up Architectures Bo Bernhardsson and K. J. ÃĚstrÃűm Department of Automatic Control LTH, Lund University Bo Bernhardsson and K. J. ÃĚstrÃűm Bottom-Up Architectures Bottom-Up Architectures 1 Introduction 2 Basic Architectures 3 Large Parameter Variations 4 Otto J. M. Smith’s Specials 5 Miscellaneous 6 Soft Computing 7 Summary Theme: Brick by brick. Bo Bernhardsson and K. J. ÃĚstrÃűm Botto
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/BottomUp.pdf - 2025-07-08
() Iterative Learning Control (ILC) Bo Bernhardsson and Karl Johan Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson and Karl Johan Åström Iterative Learning Control (ILC) ILC ILC - the main idea Time Domain ILC approaches Stability Analysis Example: The Milk Race Frequency Domain ILC Example: Marine Vibrator Material: Bo Bernhardsson and Karl Johan Åström Iterative Learn
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/ILC.pdf - 2025-07-08
() Loop Shaping Bo Bernhardsson and Karl Johan Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson and Karl Johan Åström Loop Shaping Loop Shaping 1 Introduction 2 Loop shaping design 3 Bode’s ideal loop transfer funtion 4 Minimum phase systems 5 Non-minimum phase systems 6 Fundamental Limitations 7 Performance Assessment 8 Summary Theme: Shaping Nyquist and Bode Plots Bo B
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/Loopshaping.pdf - 2025-07-08
() Model Predictive Control (MPC) Bo Bernhardsson and Karl Johan Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson and Karl Johan Åström Model Predictive Control (MPC) Model Predictive Control (MPC) MPC Problem Setup and Parameters Optimization Problem MPC Tools How to get Integral Action Example - Quad Tank Explicit MPC and CVXGEN Material: Rawlings (2000), Tutorial over
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/MPC.pdf - 2025-07-08
Control System Design - PID Control Bo Bernhardsson and Karl Johan Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson and Karl Johan Åström Control System Design - PID Control Control System Design - PID Control 1 Introduction 2 The Basic Controller 3 Performance and Robustness 4 Tuning Rules 5 Relay Auto-tuning 6 Limitations of PID Control 7 Summary Theme: The most common
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/PIDControl.pdf - 2025-07-08
() Requirements Bo Bernhardsson and Karl Johan Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson and Karl Johan Åström Requirements Requirements and Limitations 1 Introduction 2 The basic feedback system 3 A broad view of control system design 4 Command signal following - System inversion 5 Disturbances 6 Process uncertainty 7 Robustness 8 Summary Theme: Requirements
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/Requirements.pdf - 2025-07-08
ex01.dvi Exercise Session 1 1. To evaluate a controlled system the maximum values of the sensitivity function and the complementary sensitivity functions have been computed giving max ω |S(iω)| = 2.45, max ω |T (iω)| = 1.70 Use these numbers to estimate the largest amplification of disturbances that may occur. Also provide an estimate of the precision in the transfer function required for the clos
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/ex01.pdf - 2025-07-08
ex3.dvi Exercise Session 3 1. Describe your results on Handin 2. 2. a) Show that state feedback control u = −Lx̂ + lryr, where x̂ is given by a Kalman filter, can be written as U(s) = −Cfb(s)Y (s) + Cff (s)Yr(s) with Cfb(s) = L(sI − A + BL − KC)−1K Cff (s) = (I − L(sI − A + BL − KC)−1B)lr = (I + L(sI − A + KC)−1B)−1lr b) Show that the controller above can be written as R(s)U = −S(s)Y + T (s)Yr wit
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/ex3.pdf - 2025-07-08
ex5.dvi Exercise 5 BottomUp and Interaction 1. Explain why the standard Smith predictor does not work for processes with integration or unstable dynamics. 2. Smith’s controller for a process P(s) = P0(s)e −sL with time delay is given by C(s) = C0(s)Cpred(s), Cpred(s) = 1 1+ P0(s)C0(s)(1− e−sL) where C0 is the nominal controller for the process P0 without delay and L is the time delay. The transfer
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/ex5.pdf - 2025-07-08
() Handin 4 A) Conditional integration are methods where windup is avoided by suspending integration under certain circumstances, for example when the error is large or when the control signal saturates. Construct a counterexample which shows that such methods may result in systems that have equilibria with nonzero error. (Thanks to F. Bagge-Carlsson for raising this question) B) Suggest a scheme
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/handin4.pdf - 2025-07-08
Landaus Flexible Transmission References Hand-out, 4 pages Landau et al, The Combined Pole Placement/ Sensitivity Shaping Method , Internal Report Grenoble, 1994 The problem is to design a SISO controller for a flexible transmission. The same controller should work for three drift cases (0, 50 and 100%). There are several specifications. It is hard to meet all of them simultaneously. Matlab-code T
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/landau.html - 2025-07-08
() Control System Design - LQG Bo Bernhardsson, K. J. Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson, K. J. Åström Control System Design - LQG Lecture - LQG Design Introduction The H2-norm Formula for the optimal LQG controller Software, Examples Properties of the LQ and LQG controller Design tricks, how to tune the knobs What do the “technical conditions” mean? How to
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/lqg.pdf - 2025-07-08
() Control System Design - LQG Part 2 Bo Bernhardsson, K. J. Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson, K. J. Åström Control System Design - LQG Part 2 Lecture - LQG Design What do the “technical conditions” mean? Introducing integral action, etc Loop Transfer Recovery (LTR) Examples For theory and more information, see PhD course on LQG Reading tip: Ch 5 in Macie
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/lqg2.pdf - 2025-07-08
Fundamental Limitations in MIMO Systems Fundamental Limitations in MIMO Systems M.T Andrén J. Berner Control System Synthesis, 2016 M.T Andrén, J. Berner Fundamental Limitations in MIMO Systems Control System Synthesis, 2016 1 / 21 Outline 1 Some concepts Singular values Pole and zero directions Sensitivity functions 2 Bode’s Integral Theorem 3 RHP Poles & Zeros Interpolation Constraints Specifi
() Mini Lectures and Projects Bo Bernhardsson and Karl Johan Åström Department of Automatic Control LTH, Lund University Bo Bernhardsson and Karl Johan Åström Mini Lectures and Projects Mini Lectures Last part of the examination 1-2 persons 15 minutes presentations Decide topic before April 25 Middle of May, date on home page Bo Bernhardsson and Karl Johan Åström Mini Lectures and Projects Suggest
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/minilectures.pdf - 2025-07-08
Mixed H/H2-synthesis and Youla-parametrization Mixed H∞/H2-synthesis and Youla-parametrization Olof Troeng 2016-05-25 Motivation (1/2) Control of electric field in accelerator cavity. Very simple process P(s) = 1 1 + sT e−sτ , Optimal controller? : P(I)(D), LQG, Smith Predictor, (MPC) Inspiration from (Garpinger 2009). Motivation (1/2) Control of electric field in accelerator cavity. Very simple p
Discrete time mixed H2 / H control Discrete time mixed H2/H∞ control Yang Xu Department of Automatic Control Lund University May 25, 2016 Introduction Continuous time mixed H2/H∞ control problem: ◮ Zhou, Kemin, et al. ”Mixed H2 and H∞ performance objectives. I. Robust performance analysis.” Automatic Control, IEEE Transactions on 39.8 (1994): 1564-1574. ◮ Doyle, John, et al. ”Mixed H2 and H∞ perfo
Rootlocus Rootlocus Gautham Department of Automatic Control 1/8 Gautham: Rootlocus Rootlocus Method (Rotortmetoden) Plotting of the root locus 2/8 Gautham: Rootlocus The Rootlocus Method(Rotortmetoden) Introduction I Graphical method of solving algebraic equations introduced by Walter R.Evans. in 1948. I Instead of solving equations for fixed values of parameters, the equation is solved for all va
Lateral Dynamics of Aeroplane References Anderson, Moore, Optimal Control, Linear quadratic methods, 2nd ed , Prentice Hall 1990, Sec 6.2 Harvey and Stein, Quadratic Weights for Regulator Properties , IEEE AC 1978, pp 378-387 Friedland, Control System Design , pp. 40-47. Nice description of Aerodynamics for control The problem is to design a state feedback controller u = -Lx. There are two input s
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2016/steinflyg.html - 2025-07-08
