Public University of Navarre

Castellano | Academic year: 2018/2019 | Previous academic years:  2017/2018  |  2016/2017 
Bachelor's degree in Industrial Engineering
Course code: 242614 Subject title: CONTROL SYSTEMS II
Credits: 6 Type of subject: Optative Year: 3 Period: 2º S
Department: Ingeniería

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Keywords:Automatic Control, Digital Control, Real-time Control


Field of knowledge: System Engineering ans Automation


  • Introduction to computer-based control.
  • Stability and time response (transiend and steady state) of computer controlled systems.
  • Design of digital controllers in the time domain and in the frequency domain.
  • Implementation of controllers in a real control system.


General proficiencies

CB1: Knowledge in an area of study including aspects implying state-of-art knowledge.
CB5: Learning skills required to undertake further studies with a high degree of autonomy.
GG1: Ability to write, sign and develop problems.
GG2: Ability to manage activities involved in projects.
GG3: Knowledge on basic and technological subjects.
GG4: Ability to solve problems.
CG5: Knowledge to carry out measurements, calculations, etc.


Specific proficiencies

CEI6-A: Knowledge of automatic regulation and control techniques and their application to industrial automation.
CEI9-A: Ability to design industrial control and automation systems.


Learning outcomes

  • R1: Knowing the pros and cons of digital control with respect to analog control.
  • R2: Knowing the fundamentals of digital control.
  • R3: Analyzing sampled linear systems, studying their stability and their transient and steady state response.
  • R4: Using basic techniques of digital controller design, from both the time-domain and the frequency domain perspective.
Learning Outcome Contents Formative activity Evaluation method
Knowing the pros and cons of digital control with respect to analog control. Part I A-1,A-7 Quiz
Knowing the fundamentals of digital control. Parts I,II, and III A-1,A-2,A-5,A-6,A-7,A-8 Quiz, Exam
Analyzing sampled linear systems, studying their stability and theirtransient and steady state response. Part II A-1,A-2,A-5,A-6,A-7,A-8 Quiz, Exam
 Using basic techniques of digital controller design, from both the time-domain and the frequency domain perspective. Part III A-1,A-2,A-5,A-6,A-7,A-8 Quiz, Exam



The subject has a theoretical/practical orientation, combining classroom lectures, laboratory sessions and autonomous learning on the part of the student.

Classroom lectures will consist of theoretical explanations of the fundamental aspects of each lesson, as well as solutions to questions raised by the students based on their own self-study. There will be two kinds of laboratory sessions: simulation on a software package specialized on dynamical systems and control and real-time control of industrial devices, where the students will test the validity of the theoretical apparatus of the course.

To understand the subject and secure an adequate performance, the student must comply with the following requirements:

  • Regular class attendance.
  • Careful reading and thorough study of all materials provided for each lesson.
  • Solving the exercises, case-studies and homework assignments suggested along the course.
  • Active participation in all discussions held in the classroom.
  • Adequate preparation of the laboratory sessions, according to the lecture guides.
  • Use of office hours to solve any doubts that may arise during the course.
Complementing the teaching, the tool "MiAulario" will be used tofacilitate the communication between the students and the teacher. It will also make available the schedule of the differenct activities and the teaching material, and it will be used to receive the assingned works.
Metodología - Actividad
Horas Presenciales
Horas no presenciales
A-1 Clases expositivas/participativas
A-2 Prácticas
A-3 Debates, puestas en común, tutoría grupos
A-4 Elaboración de trabajo
A-5 Lecturas de material
A-6 Estudio individual
A-7 Exámenes, pruebas de evaluación
A-8 Tutorías individuales


Relationship between formative activities and proficiencies

Actividad formativa



Spanish and English



Quizzes will be held throughout the course, in which the students must prove having aquired the required knowledge. They will take place at the end of each part, whose approximate duration is one month, although it may change according to the academic schedule. Quizzes of parts I and II weight 15% each, and that of part III weights 10% in the final grade. There is a retake for all of them.

Regarding the laboratory sessions, an exam will be held at the end of the course in which the student must show the practical skills gained during the course. There is no retake for this axam, and its weight in the final grade is 20%.

A final exam is held at the end of the semester. Its purpose is to assess the student's ability to undertake the design of a digital control system. Theoretical contents are not evaluated. Rather, the idea is to apply the aquired knowledge in the analysis of a simplified control problem, and in the design of digital controllers for it. Simultaneously, the student will have the chance to pass the quizzes that he or she has not passed yet.

Students who do not take this final exam will be evaluated as "absent", even if they have taken some of the quizzes.

Learning outcome
Criteria Evaluation  activity
Weight(%) Retake Minimum grade
 R3, R4 CG1 CG2 CG3 CG4 CEI6-A CEI9-A  Exam  20  No  
 R1, R2, R3 CG1 CG2 CG3 CG4 CG5 CEI6-A CEI9-A  Quizzes, Exam  40  Yes 4
 R3, R4 CG1 CG2 CG3 CG4 CG5 CEI6-A CEI9-A  Quizzes, Exam  40  Yes 4

The final grade will be calculated according to the aforenetioned weights for those students whose marks in the quizzes and exam are no lower than the minimum required. To pass the subject, the global grade must not be lower than 5.

At the end of the course, a retake exam will be held, according to the regulation of the evaluation processes of the Public University of Navarra. All students can take this exam, either those who have not passed some of the tests, or those who want to improve their grades.

After that, the final grade is calculated for all the students. If it is not lower than 5, but the mark in any of the tests is lower than the minimum one, the final grade will be 4.9.




Module I: Discrete, sampled and hybrid systems
In this module, the simple digital control loop is presented and the effect of the introduction of the computer in such loop is studied. A/D and D/A converters are introduced and the main advantages and disadvantages of digital control systems are analyzed in comparison to the analog control ones. The different types of systems appearing in the digital control loop are presented and the necessary tools are introduced for their study (Z transform, Modified Z Transform, ...)

Module II: Analysis
The techniques needed to study the stability and behavior of discrete systems in the temporal and frequency domains are introduced. The behavior of discrete and sampled systems is characterized, and it is shown how to obtain a discrete model that verifies a set of specifications. The effect of sampling from the frequency point of view is analyzed, as well as the effect of the sampling and retention process on a signal by means of a Zero Order Hold.

Module III. Design and synthesis of controllers
Digital controller design techniques are introduced, both by emulation of analog controllers and by direct digital design. Various techniques for controller synthesis are presented, such as the Truxal method and pole placement. They are generalized for the case of two-degree-of-freedom control systems, so that systems can be obtained that meet both reference tracking and disturbance rejection specifications.



Part I: Discrete, sampled and hybrid systems


Lecture 1. Computer-based control.

Computer-based control: Basic digital control loop. Pros and Cons ofcomputer-based control. Types of signals. Quantization. Sampling a continuous signal. Reconstruction: the zero-order hold.

Lecture 2.  Z Transform.

Sequences and Z transform. Properties. Inverse Z transform. Discrete transfer function.

Lecture 3.  Discrete and sampled systems.

Discrete and sampled systems. Holds.

Lecture 4. Hybrid systems and their representation.

Hybrid systems. Discrete and analog representation. Block diagrams. Behaviour between samples.


Part II: Analysis.


Lecture 5. Stability and steady state

Definition. Stability ans poles of the discrete transfer function. Stability criteria: bilinear transform and Routh criterion, Jury criterion. Stability of a continuous system and its discretized model. Error sequences. Precision of discrete feedback systems: standard errors and steady state error coefficients.

Lecture 6. Time response: transient response.

Relation between the poles of the discrete transfer function and the transient response. Relationbetween the s-plane and the z-plane. First and second order systems: step response parameters. Finite-time response. Cancelations. Interpolation models.

Lecture 7. Sampling and reconstruction: frequency analysis.

Fourier spectrum of a sampled signal.Sampling theorem. Aliasing and inluence of noise. Ideal reconstruction filter. Frequency transfer function of the zero-order hold.

Lecture 8. Frequency response of discrete and discretized systems.

Frequency transfer function of discrete and discretized systems. Transfer function in the w-plane. Bode diagram.


Part III: Controller design and synthesis


Lecture 9. Digital controller design through continuous design.

Introduction: realizability of a digital controller. Performance specifications and choice of the samplig time. Design of digital controllers via continuous design: presentation of the method and feasibility conditions. Discretization of a continuous controller.

Lecture 10. Design of digital controllers in the z-plane.

Preliminary considerations. Root locus method and Bode plot method. Analytical synthesis methods. Two degree of freedom systems.



Acceda a la bibliografía que su profesor ha solicitado a la Biblioteca.


  • K. J. Aström, B. Wittenmark, ¿Computer controlled Systems¿, 3rd edition, Prentice Hall, 1997
  • G.F. Franklin, J.D. Powell, M.L. Workman, "Digital Control of Dynamic Systems", 2nd edition, Addison Wesley, California, 1998.
  • N. S. Nise, "Control Systems Engineering", 6th edition, John Wiley & Sons


  • Raymond G. Jackot, "Modern Digital Control Systems", 2nd edition, Marcel Dekker, inc. New York, 1995.
  • J. Ackermann, ¿Sampled-Data Control Systems¿, Springer-Verlag, 1985
  • K. Ogata, "Discrete Time Control Systems", 2nd edition, Prentice-Hall International, 1996.
  • F. Golnaraghi and B. C. Kuo. Automatic Control Systems, Wiley