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: 15.09.2021 - 22.12.2021

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), room 3574.  kai.zenger(at)

Assistant: Nguyen Khac Hoang, Maarintie 8 (TuAs), room 3571,

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 give max 15+15 points.  Full exam gives max 30 points.  The student can participate to any or all exams, if she/he wishes.  The better result from two intermediate exams or one full exam counts.  Six homework problems (Assignments) are given, from which at least three have to be done.  The maximum points from all six problems are scaled to give max 6 points to be added to the exam results.  The full maximum is then 30+6=36 points.  The grade limits are decided at the end of the course, but 18 points are always enough to pass the course.  A typical (example) grading would be:

    Points:        Grade

    18-19            1

    20-22            2

    23-25            3

    26-28            4

    29-                5

  • valid for whole curriculum period:

    Lectures, Exercise hours, Self-study, Homework assignments

    Contact hours: 48h
    Independent study: 85h

  • applies in this implementation

    Lectures 2h/week, Exercises 2h/week, Assignments 3h/week, Self study 2h/week, Preparation to exam(s) 25h.

    12 study weeks.

    All together 133 h = 5 points.


Study Material
  • valid for whole curriculum period:

    Glad, Ljung: Control Theory, Multivariable and Nonlinear Methods (Taylor and Francis 2000). Lecture slides, Exercises with solutions.

  • applies in this implementation

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

    2. Skogestad, Postlethwaite: Multivariable Feedback Control, (Analysis and Design), Wiley, 2005.

    3. Kirk: Optimal Control Theory, An Introduction, Dover, 2004.

    4. Wang: Model Predictive Control System Design and Implementation Using MATLAB.

Substitutes for Courses


Further Information
  • valid for whole curriculum period:

    Teaching Period:

    2020-2021 Autumn I-II

    2021-2022 Autumn I-II

    Course Homepage:

    Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu ( instead of WebOodi.

    Registration in WebOodi is mandatory