Course detail

Optimalization of Controllers

FEKT-MPC-OPRAcad. year: 2020/2021

The subject is focused especially on:
- How to formulate an optimization problem and how to build a functional evaluating a decision of our interest.
- How to design an algorithm of control, estimation, state filtering and fault detection as a result of solving the optimization problem.
- The implementation of the designed algorithm into the MATLAB and PLC environments.

Learning outcomes of the course unit

Students are able to design a complex control system and transfer it into a real technological process.


The subject knowledge on the Bachelor´s degree level is requested.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Pivoňka, P.: Optimalizace regulátorů. Skriptum, VUT FEKT, Brno, 2005. (CS)
Havlena, V.-Štecha, J.: Moderní teorie řízení, ČVUT Praha, 2000 (CS)
Camacho, E. at all: Advanced control, Springer, 1997 (EN)
Astrom, K.,J.,-WittenmarkB.:Adaptive Control, Addison Wesley, 1995 (EN)

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Materials for lectures and exercises are available for students from web pages of the course. Students have to write a single project/assignment during the course.

Assesment methods and criteria linked to learning outcomes

Project realization: Max. 40 points.
Combined exam includes a written part and an oral examination: Max. 60 points.

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Discrete variants of a PID controller. Some controller modifications designed for implementation in real computers and their tuning will be presented.
2. The basic principles of optimization theory: necessary and sufficient conditions of minima, convex analysis, solving optimization tasks with both equality and inequality constraints (Karush–Kuhn–Tucker conditions), solving a non-linear problems by globally convergent algorithms, introduction into the theory of probability.
3. Formulating the task of optimal control. The implementation of the optimal state-space controller will be discussed.
4. Formulating the task of optimal control. The implementation of the optimal state-space controller will be discussed - continuation.
5. Formulating the task of predictive control. The implementation of the predictive controller will be discussed.
6. Estimation of linear regression model parameters. Some practical aspects such as the model structure selection, numerical filters, estimation in the close-loop feedback system will be discussed.
7. Tracking of time-varying model parameters by adaptive estimation algorithms.
8. Introduction of the Kalman filter and its deployment in the tasks of the state electrical drive estimation.
9. Fault detection and isolation based on the information carried by measured data.
10. Nonlinear parametric estimation and state filtering.
11. Data-driven model merging strategy making the system predictor more refined will be shown. The use of the bank of models for control will be studied.
12. Optimal decision-making in the discrete event systems.
13. Review of the curriculum.


Familiarize students with modern approaches from the field of automatic control, signal processing and decision-making. Students adopt the methodology of the optimal controller design, adaptive controller; build models and perform diagnosis from the experimentally measured data.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Classification of course in study plans

  • Programme MPC-KAM Master's, 1. year of study, winter semester, 6 credits, compulsory-optional

Type of course unit



26 hours, optionally

Teacher / Lecturer

Fundamentals seminar

26 hours, compulsory

Teacher / Lecturer