Degree in Telecommunications Systems Engineering

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Control Systems

This course aims to introduce the student to the basic control theory for dynamic systems. In the first part of the course the basic principles of automatic control and the different representation of dynamic systems will be studied. In the second part, stability of dynamic systems will be studied. The third part of the course will consist on the design of controllers based on the transfer function of the system. In the last part of the course, a brief introduction to state-space control will be given.
Type Subject
Previous Knowledge

Circuit Theory and Feedback


Learning Outcomes of this subject are:
1 Basic knowledge in control and modelling of dynamic systems by means of differential equations.
2 Transformation of linear differential equations to block diagrams, to transfer function and state-space models.
3 Time response analysis of dynamic systems and system identification based on time response.
4 Stability study of dynamic systems.
5 Design of controllers in the frequency domain based on specifications.
6 Evaluation of the performance of the designed controller based on the time response.


Part I. Basic control concepts and representation of dynamic systems
1. Introduction to control systems
1.1 Definitions: Plant, controller, output variable, control variable, disturbances
1.2 Open-loop and closed-loop systems

2. Dynamic systems
2.1 Types of dynamic systems
2.1.1 Time-variant and time-invariant systems
2.1.2 Linear and non-linear systems
2.1.3 Linearization of non-linear systems
2.2 Mathematical model of electrical and mechanical systems
2.3 Representation in the frequency domain
2.3.1 Transfer functions
2.3.2 Poles and zeros of a system
2.3.3 Canonic form and canonic gain
2.4 Block diagram representation
2.5 Systems with multiple inputs and outputs
2.6 Representation in state-space

Part II. Time response and stability study
3. Time response characterization of a dynamic system
3.1 Introduction
3.2 Elementary input signals
3.3 First order systems
3.4 Second order systems
3.5 Higher order systems

4. Stability analysis
4.1 Introduction
4.2 Stability by means of pole localization in the complex plane
4.3 Routh-Hurwitz criterion
4.4 Steady-state error and system type

Part III. Controller design in the frequency domain
5. Analysis and design of control systems
5. Analysis and design of control systems
5.1 Proportional, Integral and Derivative control actions
5.1.1 Proportional controller
5.1.2 Proportional-Integral controller
5.1.3 Proportional-Integral-Derivative (PID)
5.2 Analysis and design of controllers based on root locus
5.2.1 Root locus
5.2.2 Controller design based on root locus
5.3 PID tuning by means of Ziegler-Nichols method

Part IV. Introduction to state-space
6. State-space
6.1 Definitions and state representation
6.2 Transfer functions to state-space
6.3 State-space to transfer functions
6.4 Poles, zeros and system order in state-space


The course will be based on theoretical classes that will be accompanied by examples and exercises. Moreover, practical lessons will be held using Matlab.


A. Exams
D. Problems done at home

The course is distributed in three partials, each one with its corresponding exam. To pass a partial it is necessary to have a mark equal or superior to four.

The subject´s mark is calculated from the arithmetical mean of the three partials mark, whenever it is equal or superior to four. In order to pass the subject the partials mean must be equal or superior to five.

In the June exam students must do those partials which haven´t been done or passed during the course.

In the case of failing a partial in the June exam (mark lower than five), in the September exam students can redo the failed partials.

Evaluation Criteria

To pass the course, a minimum grade of five (5) is required. The final grade will be computed as follows:

Course_grade =
20% · AC_Grade +
20% · Practices_Grade +
60% ·Exams_Grade

AC_Grade will represent the continuous evaluation along the semester. It will evaluate the student participation through weekly exercises proposed and done in class.

Practices_Grade will evaluate two practice report. Matlab software will be used to simulate dynamical systems and to design controller.

Exams_Grade is the grade of the two examen done during the semester: the checkpoint exam and the final exam. Since the learning is incremental, some knowledge of the checkpoint exam will be required for the final exam. An equation sheet will be allowed at the exam. To pass the course, minimum grade of 4.0 is required in Exams_Grade. It will be computed as follows:

• If Checkpoint_Grade > 4.0 and FinalExam_Grade > 4.0:

Exams_Grade =
Max ( 50% · Checkpoint_Grade +
50% · FinalExam_Grade,

• If Checkpoint_Grade < 4.0 i FinalExam_Grade > 4.0

Exams_Grade =
100% · FinalExam_Grade

• If FinalExam_Grade < 4.0:
extraordinary evaluation.

Those students who do not pass the ordinary evaluation will have to attend the extraordinary evaluation to do a second-chance exam. The practice part can also be recovered once the task has been agreed with the professor. The continuous evaluation will not recoverable. The final grade will be computed as follows:

Course_Grade =
20% · AC_Grade +
20% · Practices_Grade +
60% · Second-chance_exam

Basic Bibliography

Ogata, Katsuhiko, Control Modern engineering
B.C. Kuo, Digital Control Systems, Holt, Rinehard and Winston

Additional Material

D'Azzo-Houpis, Control Linear systems
Ogata, Katsuhiko, Discrete-Time Control Systems, Prentice-Hall
P. De Larminat, Automatique des sistemes lineaires, Flammarion Sciencies
G. Rao, Complex digital control systems, Van Nostrand-Reinhold
J. Corominas, Introduction to the computer process control, Marcombo
J.M. Angulo, Course of robotics, Paraninfo
R. Dorf, Automatic control systems. Theory and practice, Fondo Educativo Interamericano
L. Pontryaguine, Theorie mathematique des processus optimaux, Mir
M. El-Hawary, Control System Engineering, Reston
Olle I. Elgerd, Control Systems Theory, Mc. Graw-Hill
Y. Faes, Commande des Processus Industriels par calculateur, Masson
V. Hernando Gutierrez, PLCs and his application to the industrial computer science, Comisión Cursos AEIT/COIT
S.M. Shinners, Modern Control Systems. Theory and Application, Addisson-Wesley Charles L. Phillips / H. Troy Nagle, Sistemas de Control Digital. Análisis y Diseño, Gustavo Gili