Course code: 242614  Subject title: CONTROL SYSTEMS II  
Credits: 6  Type of subject: Optative  Year: 3  Period: 2º S  
Department: Ingeniería  
Lecturers  
LERA CARRERAS, GABRIEL (Resp)  ELSO TORRALBA, JORGE 
Keywords:Automatic Control, Digital Control, Realtime Control
Field of knowledge: System Engineering ans Automation
CB1: Knowledge in an area of study including aspects implying stateofart 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.
Learning Outcome  Contents  Formative activity  Evaluation method 
Knowing the pros and cons of digital control with respect to analog control.  Part I  A1,A7  Quiz 
Knowing the fundamentals of digital control.  Parts I,II, and III  A1,A2,A5,A6,A7,A8  Quiz, Exam 
Analyzing sampled linear systems, studying their stability and theirtransient and steady state response.  Part II  A1,A2,A5,A6,A7,A8  Quiz, Exam 
Using basic techniques of digital controller design, from both the timedomain and the frequency domain perspective.  Part III  A1,A2,A5,A6,A7,A8  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 selfstudy. There will be two kinds of laboratory sessions: simulation on a software package specialized on dynamical systems and control and realtime 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:
Metodología  Actividad

Horas Presenciales

Horas no presenciales

A1 Clases expositivas/participativas

44


A2 Prácticas

16


A3 Debates, puestas en común, tutoría grupos



A4 Elaboración de trabajo



A5 Lecturas de material


10

A6 Estudio individual


65

A7 Exámenes, pruebas de evaluación

10


A8 Tutorías individuales

5





Total

75


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 CEI6A CEI9A  Exam  20  No  
R1, R2, R3  CG1 CG2 CG3 CG4 CG5 CEI6A CEI9A  Quizzes, Exam  40  Yes  4 
R3, R4  CG1 CG2 CG3 CG4 CG5 CEI6A CEI9A  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.
Part I: Discrete, sampled and hybrid systems
Lecture 1. Computerbased control.
Computerbased control: Basic digital control loop. Pros and Cons ofcomputerbased control. Types of signals. Quantization. Sampling a continuous signal. Reconstruction: the zeroorder 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 splane and the zplane. First and second order systems: step response parameters. Finitetime 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 zeroorder hold.
Lecture 8. Frequency response of discrete and discretized systems.
Frequency transfer function of discrete and discretized systems. Transfer function in the wplane. 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 zplane.
Preliminary considerations. Root locus method and Bode plot method. Analytical synthesis methods. Two degree of freedom systems.
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