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: -understands the principles of discrete-time modeling and computer control. -understands the common ideas and differences between analog and digital control. -can design, simulate and implement discrete-time controllers (for example discretized PID or state feedback controllers). -understands the Principle of Optimality. -understands the ideas behind optimal controllers, specifically LQ control. -can design and implement LQ controllers.

Credits: 5

Schedule: 09.09.2022 - 07.12.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Kai Zenger, Ville Kyrki

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


Kai Zenger, Maarintie 8 (TuAs building), room 3574.  Ville Kyrki, TuAs, room 2570


Matti Pekkanen, Karol Arndt, Amin Modabberian, Gökham Alcan

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:

    -Principles of computer control. -Discrete-time modelling, the z-transform, solving difference equations. -Discretization of continuous time dynamical systems. -Basic characteristics of discrete time systems. -Controller design and performance analysis in discrete time. -Discrete-time PID controllers. -Basics in optimal control theory. -Dynamic programming. -Linear quadratic (LQ) control.

  • applies in this implementation

    •Introduction: discrete time vs. continuous time control problem
    •Discretization (state-space, transfer function), ZOH
    •Properties of a discrete-time system (pulse transfer function, pulse response, weighting function, poles, zeros, mapping  of poles from continuous to discrete time systems)
    •Stability (state stability, BIBO-stability, Jury stability test, frequency response, Bode, Nyquist, gain and phase margins)
    •Controllability, reachability, observability
    •Pole placement by state feedback control, regulation and servo problems, static gain
    •State observer, pole placement of the observer, combining of an observer and state feedback controller 
    •Discrete approximations of continuous-time controllers (Euler, Tustin etc.)
    •Discrete PID controller, integrator windup and antiwindup
    •The alias-effect, Nyquist-frequency, choosing the sampling interval, pre-filters
    •Disturbance models (stochastics, expectation, covariance, white noise, AR, MA, ARMA, ARMAX models, spectral  density)
    •Ideas in optimal control:
    •Optimal predictor
    •Minimum variance controller
    •LQ controller.  (Basics of LQG control)

Assessment Methods and Criteria
  • valid for whole curriculum period:

    Teaching methods: Lectures, Exercises, Quizzes, Homework problems, Project assignment.
    Grading: Quizzes, Home assignments, Project assignment, Final exam.

  • applies in this implementation

    12 Quizz problems related to each lecture, 6 homework problems, 2 intermediate exams.  The course is evaluated so that the weights of Quizzes, homework problems and exams are 20%, 40% and 40%, respectively.

    Two intermediate exams, no full exam.  Afterwards, full exams ("Rästitentti") are arranged; their weight is equal to the sum of two intermediate exams.

    Grading:  (Calculated from achievements with weights):

    48%: 1, 60%: 2, 70%: 3, 80%: 4, 90%:5

    Note: In autumn 2022 the course does not have a special project assignment.

  • valid for whole curriculum period:

    Lectures 24 + Self-study after lectures 24 + Exercise sessions 24 + Solving exercise/homework tasks 24 + Project assignment 16 + Exam preparation 20 + Exam 3 = total 135.

    Contact hours: 48 h
    Independent study: 87 h


Study Material
  • applies in this implementation

    Textbook: Åström K. J., Wittenmark B.: Computer Controlled Systems  - Theory and Design (3rd ed.), Prentice-Hall, 1997.

    Lecture notes, 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 (

  • applies in this implementation

    Lectures and exercises are arranged in classroom; no recordings of teaching are available.  Exception: the first lecture is pre-recorded and available only as recording (no classroom lecture).