DIGITAL CONTROL SYSTEMS
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- SILVIO SIMANI
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- ING-INF/04
Training objectives
- This is the first course of Digital Control Systems and it studies the basic elements of a digital system from the dynamic point of view, by considering the information from its sampled data input to its sampled data output.
The main goal of the course consists of providing the basics to tackle the study of complex digital systems and of their interconnections under proper design constrains imposed by cost, speed, computational cost, robustness, reliability and power consumption.
The main acquired knowledge will be:
- Basic elements of a digital system form a dynamic point of view, considering the information from its sampled data input to its sampled data output;
- Knowledge related to the analysis of discrete-time dynamic systems in steady and transient states and their simulation tools;
- Basic knowledge of a D/A (Digital to Analog) and A/D (Analog to Digital) blocks;
- Basic knowledge to tackle the study of complex digital systems and of their interconnections under the constrains imposed by performances in terms of cost, speed, computational cost, robustness and power consumption.
- Basic knowledge of the mathematical tools for the analysis of the discrete-time and sampled data dynamic systems;
- Basic knowledge of dynamic system software simulation tools.
The basic acquired skills (that are the capacity of applying the acquired knowledge) will be:
- Analysis of the behaviour of discrete time digital systems in steady and dynamic conditions;
- Design of the discrete time dynamic controller for a given system in order to meet proper transient and steady state constraints;
- Identification of the most suitable A/D and D/C elements, as well as the most suitable sampling time for a specific control design and its application;
- Use of simulation numerical programs to analyse digital systems. Prerequisites
- The following concepts and the knowledge provides by the courses of “Fundamentals of Automatic Control” or “Automatic Control” are mandatory:
Basic concepts of mathematics, differential and integral computation;
Knowledge of the basic concepts of Physics;
Knowledge of dynamic systems, their behaviour, and their practical application; methods to analyse dynamic systems in steady and transient states:
Knowledge of the frequency tools for the analysis of dynamic systems;
Ability to analyse and design digital systems. Course programme
- The course consists of 60 hours of teaching activities divided in frontal lectures (40 hours) and guided tutorial in the labs (20 hours).
Digital and analog electronics - Digital systems (2 hours)
Differences between analog and digital systems – Operating levels: systems, functions, behaviour - Basic elements - Digital design evolution – Sampled data Signals - Elements of digital technology.
Static and dynamic control systems (2 hours)
Open loop and feedback basic schemes - Continuous time and discrete time behaviour of a dynamic system - Characteristic parameters of the transient and steady state behaviour - Frequency characteristics and stability margins.
Basic digital system properties (4 hours)
Figure of merits (cost, performance, reliability,....) - I/O characteristics - Dynamic characteristics - Power consumption.
Discrete time modelling tools (8 hours)
Difference and differential equation comparison – Stability and Z-transforms – Comparison between Laplace and Z- transforms.
Sampling and signal conversion (8 hours)
Different problems in digital systems – Steady state and transients in dynamic systems – Discrete time system complexity - Comparison between ideal and real sampling of a signal – Delays – Memory functions - Transmission and conversion of a digital signal.
Discrete time system stability (4 hours)
Input – output stability – Discrete time transfer function – Discrete time zeros and poles – Sampling theory – s and s planes relations – Link between Laplace and Z – transforms – Sampling time selection and related problems.
Discretisation techniques (4 hours)
Forward and backward Euler’s methods – Hold Equivalence method – Tustin’s method – Z – transform method.
A/D e D/A conversion (4 hours)
Conversion and sampling theory – converter general characteristics – Zero order hold and ideal sampler – Anti-aliasing filter basics – Sample & Hold tasks in the frequency domain.
Control Schemes (4 hours)
Control with lead and lag networks – Input – output feedback control – PID standard controller – Controller design with the discretization approach – Equivalence principle design – Root locus design – Bode diagram design.
Dynamic System Simulations (20 hours)
Introduction to Matlab and Simulink – Practical lessons related to the simulations of simple digital systems. Didactic methods
- The course is organised as follows:
40 hours of frontal lectures on all the course’s topics (16 lectures of 2.5 hours each);
20 hours of practical exercises in the Informatics Laboratory concerning the analysis and the simulation of simple dynamic systems (8 lectures of 2.5 hours each). After the guided tutorials the students will have free access to the lab for additional individual tests. Learning assessment procedures
- The aim of the exam is to verify at which level the learning objectives previously described have been acquired.
The examination is divided in 2 sections that will take place in the same day.
A project regarding the simulation and the control design for a simple digital system by using the Matlab and Simulink environments, which aims at understanding if the student has the skills in the analysis and the synthesis of a digital system. To pass this test it is required to get at least 18 points out of 24. The time allowed for this test is 1 hour. It is allowed consulting the Matlab and Simulink programme manual;
One test (multiple choice questions or solutions of numeric exercises) based on all the topics tackled in the class or on the basic concepts of the following courses: “Digital Control System”, with the aim of evaluating how deeply the student has studied the subject and how he is able to understand the basic topics analysed. To pass this test it is required to get at least 1 points out of 7. The time allowed for this test is 1 hour. It is not allowed consulting any textbook or using any PC, smart phone, calculator….;
The final mark is the sum of the 2 marks. To pass the exam it is necessary to get at least 18 point out of 31. If the first test fails or if the final mark is below 18, it is necessary to repeat all the exam’s sections.
Passing the exam is proof of having acquired the ability to apply knowledge and the required skills defined in the course training objectives.
Note finally that the examination can be held in English. Reference texts
- Only the teacher’s handouts, notes and slides are required for the exam and course preparation. They are available from the personal web page of the teacher: www.silviosimani.it/lessons.html
Specific topics can be further developed using the following textbooks, which are not required for attending the lessons and the preparation of the exam:
C. Bonivento, C. Melchiorri R. Zanasi, Sistemi di Controllo Digitale; Esculapio S.R.L. marzo 1995.
R. Isermann, Digital Control Systems, vol. 1; Springer-Verlag 2001.
C. L. Phillips, H. T. Nagle, Digital Control System Analysis and Design; Prentice-Hall 2005.
G. Guardabassi, Elementi di Controllo Digitale; clup - città studi 2004.
Note finally that the course lecture notes and handouts can be provided in English.
