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: 06.09.2023 - 12.12.2023

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):

Kai Zenger, TuAs 3574,  kai.zenger(at)

Lectures on Wednesdays at 12.15 – 14.00  hall T3 (C206), Computer building (T-house).

Amin Modabberian, TuAs, 3571, amin.modabberian(at)

Exercises on Thursdays at 14.15 – 16.00  TU4 (1174-1176), TuAs building

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.  The intermediate exams have 3 problems each, max 15+15 = 30 points.  The full exam has five problems, max. 30 points altogether.

    •First intermediate exam on Thursday 19.10.2023, 14:00-16:00.  The second intermediate exam on Thursday 7.12.2023, 14:00-16:00.  Intermediate exams cannot be repeated.  The first full exam is on Tuesday, 12.12.2023, 13:00 – 16:00.  You can participate to all above exams without separate registration (the registration to the course is sufficient).  To all later exams you have to register (next: 8.1.2024).

    •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.  The homework results are scaled to give a maximum of 6 points to be added to the exam result.    The final grade is determined based on the sum of two intermediate exams (or full exam) and the homework points. The grade evaluation is done based on 0-36 points.  18 points is always enough to pass.

  • valid for whole curriculum period:

    Lectures, Exercise hours, Self-study, Homework assignments

    Contact hours: 48h
    Independent study: 85h

  • applies in this implementation

    Contact hours: 12 lectures, 12 exercise hours, 2 hours each: 2x(12+12)=48 hours.

    Self study for lectures and exercises, doing homework and preparing for exams: 85 hours.

    Sum: 48 + 85 hours = 133 hours, which corresponds 5 credits.


Study Material
  • applies in this implementation

    Lecture slides and exercises with solutions.  Homework with solutions.  Exams with solutions.


    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 Language : English

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

    Enrollment :

    Registration takes place in Sisu (

  • applies in this implementation

    Master level course suitable for doctoral studies also.  

    Reasonable background level of basic Control Engineering Theory is needed to be able to follow the course.

Details on the schedule
  • applies in this implementation

    6+6 lecture and exercise weeks, During the examination weeks no other teaching than the exam is arranged in the course.

    6 homework assignments are published on a regular basis, about in 2 weeks intervals.