course-details-portlet

TTK4115

Linear System Theory

Choose study year
Credits 7.5
Level Third-year courses, level III
Course start Autumn 2024
Duration 1 semester
Language of instruction English
Location Trondheim
Examination arrangement School exam

About

About the course

Course content

Theory for linear multivariable systems, state space models, discretization, canonical forms and realizations, stability, controllability and observability, state feedback, LQR optimal control, state estimation, the Kalman filter and Extended Kalman Filter, descriptions of stochastic processes and random signals.

Learning outcome

Knowledge: Detailed knowledge about state space representation of linear time invariant systems in continuous and discrete time. Knowledge about representation and characterization of random signals in linear systems. Detailed knowledge about fundamental concepts like controllability, observability and stability for linear multivariable systems. Substantial knowledge about methods for construction of multivariable controllers for linear systems, and algorithms and methods for state estimation. Use of state estimation for feedback in linear control systems. Knowledge of linearization of nonlinear systems.

Skills: Being able to formulate specifications and dynamic models as a basis for design of linear control systems and state estimators under influence of noise and disturbances. Being able to transform models between continuous and discrete time, and between state space and transfer function matrix representations. Being able to design and tune parameters of controllers with LQR and pole placement. Being able to design and tune parameters of observers and Kalman filters. Being able to apply linear algebra and Matlab for analysis and design of linear control systems. Being able to apply Simulink for rapid prototyping and experimental testing of control systems.

General competence: Understand strengths and limitations of theoretical analysis versus experimental testing. Good system understanding, i.e. how sub-systems consisting of hardware, software, physical systems and humans interact. Have a solid basis for advanced studies in control engineering.

Learning methods and activities

Lectures, a compulsory laboratory project, compulsory assignments.

Compulsory assignments

  • Assignments

Further on evaluation

A written exam is the basis for the final grade in the course. To qualify for the exam, the laboratory project and 4 out of 6 written assignments must have been approved. The requirements for approval of the laboratory project will be described at the start-up of the course. If there is a re-sit examination, the examination form may change from written to oral. In the case that the student receives an F/Fail as a final grade after both ordinary and re-sit exam, then the student must retake the course in its entirety.

Course materials

Information will be given when the course starts.

Primary material is from:

  • Chi-Tsong Chen. Linear system theory and design. Oxford University Press, New York, 4th international edition, 2014.
  • Robert Brown. Introduction to random signals and applied Kalman filtering : with MATLAB exercises. John Wiley & Sons, Inc., Hoboken, NJ, 4th edition, 2012.

Credit reductions

Course code Reduction From
SIE3015 7.5 sp
This course has academic overlap with the course in the table above. If you take overlapping courses, you will receive a credit reduction in the course where you have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently.

Subject areas

  • Technological subjects

Contact information

Course coordinator

Department with academic responsibility

Department of Engineering Cybernetics

Examination

Examination

Examination arrangement: School exam
Grade: Letter grades

Ordinary examination - Autumn 2024

School exam
Weighting 100/100 Examination aids Code D Date 2024-12-03 Time 09:00 Duration 4 hours Exam system Inspera Assessment
Place and room for school exam

The specified room can be changed and the final location will be ready no later than 3 days before the exam. You can find your room location on Studentweb.

Sluppenvegen 14
Room SL420
2 candidates
Room SL274
5 candidates
Room SL311 grønn sone
46 candidates
Room SL123
1 candidate
Room SL311 lyseblå sone
82 candidates
Room SL311 brun sone
82 candidates
Room SL120
15 candidates

Re-sit examination - Summer 2025

School exam
Weighting 100/100 Examination aids Code D Duration 4 hours Exam system Inspera Assessment
Place and room
The specified room can be changed and the final location will be ready no later than 3 days before the exam. You can find your room location on Studentweb.