Course syllabus

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SSY285 Linear Control System Design sp2 2021

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)

Available through course homepage:

  • Linear control system design - Exercises with solutions
  • Lab PM
  • 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
  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, 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, 5.9, 5.12   5.1-5.5, 5.7, 5.8, 5.11, 5.13, 5.14
4 (w47) 6.5, 6.6, 6.8, 9.1, 9.3 6.2, 6.3, 6.7, 9.2
5 (w48) 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, 7.7

 

 

 

 

 

 

 

 

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 persons and solve those together. Deadline for grouping is Wednesday 3, 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 homepage.

  • 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  17:00 - 17:15 
Rita Laezza (M)
 SB-H6 Group 3 Group 4 Group 6 Group 8 Group 9 Group 10 Group 11
Yixiao Wang (M)    
SB-H6 Group 12 Group 13 Group 15 Group 18 Group 19 Group 20 Group 21
Anand Ganesand (M) 
SB-H6 Group 22 Group 41 Group 24 Group 25 Group 26 Group 27 Group 28
Huang Zhang (M/E)
 SB-H5 Group 30 Group 31 Group 36 Group 37 Group 39 Group 40 Group 46
Albert Skegro (E) 
SB-H5 Group 2 Group 5 Group 14 Group 32 Group 34 Group 42 Group 45
Godwin Peprah (K/M)
SB-H5 Group 16 Group 17 Group 29 Group 43 Group 44 Group 47 Group 7

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 19
4 (w47) A2
5 (w48) A2 A2,  December 3
6 (w49) A3
7 (w50) A3 A3,  December 17

Consultation Hours (start week 2):

  • Rita Laezza (Mechanical): 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 5310 Nyquist+, EDIT Bldg. 
  • Huang Zhang (Mechanical/Electrical): Wednesdays, 17:15-18:15, room SB-H5
  • Godwin Peprah (Chemical/Mechanical): Thursdays, 17:00-18:00, room 5343+, EDIT, Hörsalsvägen 11 
  • Yixiao Wang (Mechanical): Thursdays, 14:00-15:00 via Zoom for Dec 16 (ID 68563657183 ) 

*Consultation session on 30th Nov'21 (Tuesday) has been preponed to 29th Nov'21 (Monday). This week is an exception as there would be two consultation sessions (one each for Electrical and Mechanical) running in parallel on 29th Nov'21.

+use the stairs/lift near Hörsalsvägen 11 entrance to access the 5th Floor door bell.

 

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:
    • Tanklab, 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 (3 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 homepage. Registration opens Monday, 22nd of November.

   

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, except that it will be physical and not remote this time. Lectures and assignments will be slightly changed, but cover the same topics.

Course representatives

MPSYS        napbergman@gmail.com             Algot Bergman

MPSYS        sree.ds10@gmail.com                  Sreekanth Dinamagattanahalli Sreenivas

MPSYS        aishwarya2998@gmail.com         Aishwarya Kanchan

MPEPO       shaurya@student.chalmers.se     Shaurya Sharma

MPMOB      suyashywagh752@gmail.com     Suyash Wagh

Learning objectives and syllabus

Learning objectives:

  • Design control algorithms for linear time-invariant (LTI) dynamical systems with some state-space methods presented.
  • Become familiar with the concept of the state-space terminology.
  • Linearize nonlinear continuous time multivariable models (MIMO). Have some 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.

 

Course summary:

Date Details Due