Systems and Control Theory (B-KUL-H04X3B)
Aims
The student is able to apply the basic time-domain system identification procedure for linear time-invariant systems with one input and one output. This includes: selection of a system model structure, selection of a system excitation, linear-least squares model parameter estimation and validation of the model accuracy.
The student is able to linearize a nonlinear system, that is, to derive an approximate linear model for a given or to be determined equilibrium state.
The student is able to analyze continuous and discrete time system in time domain and in frequency domain, based on different system representations, e.g. a transfer function or a state space model description.
The student is able to analyze (periodic, non-periodic continuous and discrete time) signals in the frequency domain, knows how to sample signals and to select an appropriate sampling rate.
The student is able to transform a continuous time model to discrete time and is familiar with aliasing.
The student is able to analyze the stability of systems, controllability and observability of state space models.
The student knows the difference between the different types of stability.
The student can calculate the energy dissipation in a linear system.
For a given linear time-invariant single-input single-output system and given design specification in time domain or frequency domain, the student is able to
- design a classical compensator using frequency-domain methods (choosing a type of compensator and determining its parameters);
- design a compensator based on state-feedback, including a closed-loop state estimator;
- add feed forward to a classical compensator or a state-feedback compensator to eliminate steady-state errors on various input signals;
- evaluate the designs above critically.
The student is able to design a Kalman filter to estimate the states of a linear or nonlinear system optimally, and to evaluate the design critically.
Previous knowledge
- solving linear differential and difference equations with constant coefficients in time and frequency domain
- solving system linear first-order differential and difference equations with constant coefficients in time and frequency domain
- basic knowledge of Fourier series and Fourier transform
- complex function theory
- applied linear algebra
- solving systems of linear equations
- elementary matrix operations
- eigenvalues and eigenvectors
Order of Enrolment
This course unit is a prerequisite for taking the following course units:
H04P5A : Embedded Control Systems
H04P9A : Integrated Project
H04Q7A : Advanced Model Based Control
H06U9A : Advanced Robot Control Systems (No longer offered this academic year)
H06U9B : Advanced Robot Control Systems
H00R9A : Embedded Control Systems
Identical courses
This course is identical to the following courses:
H00S4A : Systeemanalyse en regeltechniek
Is included in these courses of study
- Courses for Exchange Students Faculty of Engineering Science (Leuven)
- Master of Mechanical Engineering (Leuven) 120 ects.
- Master of Mechanical Engineering (Programme for Engineering Technology Students) (Leuven) 120 ects.
- Master in de ingenieurswetenschappen: werktuigkunde (programma voor studenten gestart in 2024-2025 of later) (Leuven) 120 ects.
Activities
3.5 ects. Control Theory: Lectures (B-KUL-H04X3a)
Content
- Introduction to least-squares time domain system identification
- Linearization of nonlinear systems
- Introduction to control systems
- Basic properties of feedback systems
- Performance of feedback systems
- Root locus analysis and design
- Frequency-response based compensator design
- State feedback based comensator design
- Optimal control (LQR) and optimal estimation (Kalman filter)
Course material
Study cost: 76-100 euros (The information about the study costs as stated here gives an indication and only represents the costs for purchasing new materials. There might be some electronic or second-hand copies available as well. You can use LIMO to check whether the textbook is available in the library. Any potential printing costs and optional course material are not included in this price.)
- G.F. Franklin, J.D. Powell, A. Emami-Naeini, Feedback control of dynamic systems, Prentice Hall, Inc., 2002 or later editions
- Handouts of the theory lectures slides
- Reference material for the part on system modelling (Toledo).This reference material is part of the book: J.L. Shearer, A.T. Murphy, H.H. Richardson, Introduction to system dynamics, Addisson-Wesley Publishing Company, 1971
- Handouts of exercise and lab sessions
Is also included in other courses
1.5 ects. Control Theory: Exercises (B-KUL-H04X4a)
Content
Description of exercise sessions and lab-sessions
- Ex. 1: linearization of nonlinear models + time-domain system identification
- Ex. 2: properties of systems with and without feedback
- Ex. 3: stability of feedback systems (root locus and Bode diagram)
- Ex. 4: design of classical feedback controllers in the frequency domain
- Ex. 5: design of state feedback controllers based on pole placement
- Ex. 6-7: Kalman filtering and linear quadratic optimal regulation (LQR) (quadratic optimal state feedback control and estimation)
Course material
Texts for the exercise sessions and lab session are available on Toledo : overview and summary of subjects of each session, description of the exercises, and selected solutions.
Is also included in other courses
1.5 ects. Systems Theory: Lectures (B-KUL-H09W4a)
Content
- Basic signals
- Continuous-time and discrete-time system analysis in time domain
- Continuous-time and discrete-time system analysis using the Laplace transform / z-transform
- Analysis of signals and systems (continuous-time and discrete-time ) in frequency domain
- Stability of linear systems
- Energy and power in signals and systems
Course material
Study cost: 76-100 euros (The information about the study costs as stated here gives an indication and only represents the costs for purchasing new materials. There might be some electronic or second-hand copies available as well. You can use LIMO to check whether the textbook is available in the library. Any potential printing costs and optional course material are not included in this price.)
- G.F. Franklin, J.D. Powell, A. Emami-Naeini, Feedback control of dynamic systems, Prentice Hall, Inc., 2002 (sold by VTK)
- K. Gopalan, Introduction to signal and system analysis, Cengage Learning, 2009 (sold by VTK)
- Handouts of the theory lectures slides
- Handouts of exercise sessions (Toledo)
0.5 ects. Systems Theory: Exercises (B-KUL-H09W5a)
Content
- Ex. S1: simulation diagrams, state-space models and system analysis
- Ex. S2: Fourier series and transformation, discretization of continuous-time models
- Ex. S3: Bode diagram, stability, controllability, observability, calculation of energy dissipation
Course material
Texts for the exercise sessions are available on Toledo: overview and summary of subjects of each session, description of the exercises and selected solutions.
Evaluation
Evaluation: Systems and Control Theory (B-KUL-H24X3b)
Explanation
The evaluation consists of two parts: exercise exam systems theory and project based evaluation for control theory.
The evaluation of the systems theory part counts for 2/7 of the overall evaluation. The evaluation of the control theory part
counts for 5/7 of the overall evaluation.
If the total obtained result is 10/20 or more, but a result of less than 10/20 is obtained for one of the two parts, the total result is adapted to 9/20.
Both parts of the evaluation must be completed in order to complete the course examination.
Systems theory: Written exam in the examination period
- Closed book, with a formulary
- Exercises
- Assessing insight, no theoretical questions
Control theory:
The basis for the evaluation is a project on an experimental set-up.
The students work in groups of two on this project.
The project consists of four assignments that relate to different parts of the course.
A separate report must be submitted for each assignment.
The evaluation is based on these reports.
Each report counts for 25% of the total score for control theory.