Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


After completing the course the student can: explain the main analysis and synthesis methods to be systematically used in the control of multivariable processes, formulate a well-defined control problem for multivariable processes, choose and implement a suitable solution (method and algorithms) to the control problem, evaluate the performance of the solution, understand the fundamental restrictions in control.

Credits: 5

Schedule: 07.09.2022 - 13.12.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Kai Zenger, Arto Visala

Contact information for the course (applies in this implementation):

Lecturer: Kai Zenger, Maarintie 8 (TuAs house), room 3574.  

Assistant: Hoang Nguyen Khac, room 3571.

The lecturer and assistant are available after teaching sessions and also whenever they are present.  Email contact is always possible.  Meeting can be agreed by email as well.  Remote meetings can also be arranged, if necessary.

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English


  • valid for whole curriculum period:

    Basic model types of multivariable linear systems. Structural properties of multivariable systems. Canonical control configurations. Analysis of the closed-loop system by sensitivity functions. Fundamental restrictions in control. Relative gain array analysis and decoupling compensators.  Dynamic programming and linear quadratic control.  Loop shaping techniques. Introduction to model predictive control

  • applies in this implementation

    •Classical control theory: SISO-systems, linear or linearized system models
    •Extension to multivariable (MIMO) systems
    •Performance and limitations of control
    •Uncertainty and robustness,
    •LQ and LQG control
    •Optimal control
    •Introduction to Model Predictive Control

Assessment Methods and Criteria
  • valid for whole curriculum period:

    Two intermediate exams or full exam, homework assignments, which are assessed

  • applies in this implementation

    Two intermediate exams or one full exam are needed to pass the course.   Six homework problems are given during the course. You must do and leave for evaluation at least three homework problems.  However, to get more homework points it is reasonable to do as many homework exercises as possible, preferably them all. 

  • valid for whole curriculum period:

    Lectures, Exercise hours, Self-study, Homework assignments

    Contact hours: 48h
    Independent study: 85h


Study Material
  • applies in this implementation

    Textbook:  Glad, Ljung:  Control Theory, (multivariable and nonlinear methods), Taylor and Francis, 2000.

    Lecture slides, exercises with solutions, homework with solutions. 

Substitutes for Courses


Further Information
  • valid for whole curriculum period:

    Teaching Language : English

    Teaching Period : 2022-2023 Autumn I - II
    2023-2024 Autumn I - II

    Enrollment :

    Registration takes place in Sisu (

Details on the schedule
  • applies in this implementation

    Both lectures and exercise sessions are in classroom.  No recordings are arranged.  Exception: The first lecture (Wednesday 7.9 ) is pre-recorded, because the lecturer is absent.