Course syllabus

SSY285 Linear Control System Design sp2 2022

Course is offered by the Department of Electrical Engineering.

 

Contact details

Address: Maskingränd, Building EDIT, Floor 5Ö

 

Course material

Text book:

  • Control Theory - Multivariable and Nonlinear Methods by Torkel Glad and Lennart Ljung (ISBN: 978-0-748-40878-8, Taylor and Francis). Available at STORE (Chalmers)

Examples of complementary literature

  • Feedback systems, an introduction for scientists and engineers by K. J. Åström and R. M. Murray (ISBN-13: 978-0-691-13576-2), Princeton University Press. Covers also basic control, but lacks focus on multivariable systems and thereby some results used in this course.
  • Linear optimal control systems by H. Kwakernaak and R. Sivan (ISBN-0-471-51110-2), John Wiley and Sons. Old textbook, pedagogical and theoretical. Lacks robustness theory.
  • Multivariable feedback design by J.M. Maciejowski (ISBN 0-201-18243-2), Chapters 1-5. Cover only continuous time.
  • Computer controlled systems by K.J. {\AA}str\"{o}m and B. Wittenmark (ISBN 0-13-314899-8). Pedagogical and covers more or less the same topics, but only discrete time.

Available through course homepage:

  • Linear control system design - Exercises with solutions
  • Lab Manual
  • Assignments (3)
  • Lecture slides
  • Complementary material uploaded during course

 

Course purpose

The purpose of this course is to introduce and investigate techniques to analyze and design model based control systems. Linear state space modeling framework is applied to create a basis for different type of controller and state estimation methods. Starting from a pure state-feedback concept down to the optimal control methods, a large variety of feedback control techniques are presented with special attention on applications. Kalman filtering as an optimal way of state reconstruction is discussed in details. In this course, systems with multiple input and outputs are also analyzed from input-output point of view, through transfer function matrices. Disturbances, modeling uncertainties and robustness are also highlighted in the course. Exercises are playing an important role along the entire course.

 

Schedule: TimeEdit

 

Course design

The course builds on four modules:

  1. Lectures: Weekly on Mondays 10:00 - 11:45 and Wednesdays 10:00 - 11:45 in HB3
  2. Exercise demonstrations: Weekly on Wednesdays 13:15 - 15:00
  3. Assignment and exercise tutoring: Weekly on Wednesdays 15:15 - 17:15
  4. Lab: Week 5, 6 and 7, according to schedule

 

Preliminary lecture plan (weeks)

  1. MIMO modelling for control (Chapter 1 & 2)
  2. Properties of linear systems (Chapter 3 & 4)
  3. Disturbances and state estimation (Chapter 5)
  4. Closed system and Linear quadratic (LQ) control (Chapter 5, 6 & 9)
  5. LQG control (Chapter 9)
  6. Controller structure and design (Chapter 8 & 9)
  7. Basic limitations in control design (Chapter 7)

   

Exercise demonstrations

Exercise demonstration and problem solving will take place on Wednesdays in SB-H5 and SB-H6 from 13:15 to 15:00, tentatively according to the table below.

 Week

 At demonstration (if time)
Additional recommended
1 (w44) 2.1, 2.4, 2.7, 3.3          2.3, 2.6, 2.8, 2.11, 2.13, 2.14
2 (w45) 3.4, 3.7, 3.9, 3.11 3.1, 3.5, 3.6, 3.8, 3.12, 3.13, 3.14, 3.15
3 (w46) 4.2, 4.3, 5.6, 5.12   5.2, 5.5, 5.7, 5.8, 5.11, 5.13, 5.14
4 (w47) 5.9, 6.5, 6.6, 6.8, 9.1 5.3, 5.4, 6.2, 6.3, 6.7, 9.2
5 (w48) 9.3, 9.4, 9.7, 9.13  9.6, 9.9, 9.10, 9.11, 9.12, 9.14
6 (w49) 8.3, 9.5, 9.8 8.1, 8.2, 8.4
7 (w50) 7.1, 7.4, 7.6 7.2, 7.5

 

 

 

 

 

 

 

 

Assignments

Depending on background and preferences one can choose freely, but compulsory, between a chemical, mechanical or electrical engineering application. For each chosen application there are three take-home assignments.

Students are to create groups of 3 people and solve those together. Deadline for grouping is Wednesday, week 1! Deadline for choosing Assignment Topic is Friday, week 1!

Each group will be assigned a tutoring slot each week to get assistance with the hand-ins. The schedule will be available on Canvas.

  • Distribution through homepage (Modules). Guide is available (Matlab).
  • Questions should be addressed during either tutorial sessions or consultation hours (each TA is responsible for just one/two assignments).
  • Pre-approval of solution by TA during tutorial session is mandatory, before submission.
  • Upload one solution per group using the filename: Group#-Assignment#.pdf
  • Results, at the latest, 1 week after the submission, with feedback.
  • If solution is not approved, there is one occasion for correction, 1 week is given for re-submission (one extra chance)
  • The tutorial session schedule is shown below:
TA Room
 15:15 - 15:30  15:30 - 15:45  15:45 - 16:00  16:00 - 16:15  16:15 - 16:30  16:30 - 16:45  16:45 - 17:00 
Rita Laezza
SB-H6 Group 1  Group 2  Group 3  Group 5  Group 6  Group 7  Group 8 
Anand Ganesan
 SB-H6 Group 9  Group 11  Group 13  Group 19  Group 20  Group 22  Group 23 
Yixiao Wang SB-H6 Group 33  Group 34  Group 37  Group 39  Group 41  Group 43  Group 44 
Albert Skegro SB-H5 Group 10  Group 12  Group 15  Group 16  Group 17  Group 21  Group 25 
Huang Zhang
 SB-H5 Group 27  Group 35  Group 36  Group 38  Group 40  Group 42  Group 50 
Godwin Peprah 
SB-H5 Group 4  Group 14  Group 24  Group 26  Group 30  Group 31  Group 32 

While waiting for your tutorial slot, the room SB L-300 has been booked for you to work in.

Week Schedule for Assignments:

 Week

Tutorial:

Wednesday at 15:15 - 17:15

Submission Deadline:

Friday at 18:00
1 (w44) --
2 (w45) A1
3 (w46) A1 A1,  November 18
4 (w47) A2
5 (w48) A2 A2,  December 2
6 (w49) A3
7 (w50) A3 A3,  December 16

Consultation Hours (start week 2):

  • Rita Laezza (Mechanical) 1: Fridays, 13:00-14:00, room 5422 Hamilton
  • Albert Skegro (Electrical): Mondays, 17:00-18:00, room 5422 Hamilton
  • Anand Ganesan (Mechanical): Tuesdays, 17:00-18:00, room 5422 Hamilton
  • Huang Zhang (Mechanical/Electrical): Wednesdays, 17:15-18:15, room 5422 Hamilton
  • Godwin Peprah (Chemical/Mechanical) 2: Thursdays, 17:00-18:00, room 5422 Hamilton

1 Unavailable for consultation on 25th of November --> Make up consultation at same time on 24th of November, in the same room.

2 Unavailable for in-person consultation on 1st of December. Contact me via email on this day.

 

Lab

Responsible: Rita Laezza

The laboratory exercises will be conducted in lab room 5225, floor 5 EDIT-building (South wing)

  • Three sets of lab devices are available:
    • Double-Tank, Albert Skegro
    • 3DoF Helicopter, Rita Laezza
    • 2DoF Inverted pendulum, Godwin Peprah
  • Conducted in the same groups as the assignments, but each group can choose whichever lab you want.
  • Only one lab session (4 hours) is compulsory (first comes first served) in week 5, 6 (and possibly 7).
  • Consists of two parts:
    • Preparation (solve assignments) is needed and will be checked by lab assistants before starting the lab (student not prepared risks lab rejection)
    • Experiment. Carried out at times booked on Canvas.

Registration through Canvas will open on November 14th, at 12:00.

 

Examination

  • Approved assignments (3 by each group)
  • Approved lab preparation and experiments
  • Passed written exam: Grade 3 (40-60%), 4 (60-80%), 5 (80-100%)

 

Changes made since the last occasion

There are no major changes to the course. Lectures and assignments will be slightly changed, but cover the same topics.

Course representatives

MPSYS        lyupl99@163.com                     Peilin Lyu

MPSYS        sdzuge@gmail.com                    Philip Pettersson

MPMOB     ganasat97@gmail.com              Balaji Sathiya Venkata Narayanan

MPISC        emma.skotte1@gmail.com         Emma Skotte

MPEPO      chenyez@student.chalmers.se  Chenye Zou

 

Learning objectives

  • Master the main concepts of the state-space terminology.
  • Design control algorithms for linear time-invariant (LTI) dynamical systems.
  • Linearize nonlinear continuous time multivariable models (MIMO). Have knowledge on deriving discrete time forms from continuous time LTI descriptions by a suitable sampling.
  • Understand model descriptions for linear time-invariant multivariable systems. Analyze these type of systems from the point of view controllability, observability and stability.
  • Explain and design discrete time multivariable state feedback controllers, based on linear quadratic optimization.
  • Explain, design, and analyze Kalman filters, and apply them for state estimation combined with controller design, i.e. LQG-control. Understand the principle of separation, analyze closed-loop optimal behavior.
  • Become familiar with the the basics of MIMO transfer functions and with their most important analytical properties. Understand concept for frequency domain analysis and synthesis of MIMO systems.
  • Define stability of dynamic systems under the presence of additive and multiplicative uncertainties. Provide with robustness uncertainty tests. Understand and design robust control techniques. Understand basic concept of decentralized and distributed control algorithms.

The course content is defined by the textbook sections specified in the lecture slides, the lecture material, the demonstrated and recommended exercises, the lab and the assignments.