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Academic year
Didactic period
Primo Semestre

Training objectives

This is the advanced course of Automatic and Digital Nonlinear Control techniques for complex systems, and it studies advanced elements of a control system from the dynamic point of view, by considering nonlinear dynamic processes from their input-output pint of view.

The main goal of the course consists of providing advanced topics and tools for the study and the control of complex dynamic 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 nonlinear control techniques for a complex process form a dynamic point of view, considering the information from its input to its output variables;
Knowledge related to the analysis of nonlinear dynamic systems in steady and transient states and their advanced simulation tools;
Basic knowledge of nonlinear blocks and control techniques;
Basic knowledge of the tools to tackle the study of complex 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 nonlinear mathematical tools for the analysis of nonlinear dynamic systems;
Basic knowledge of nonlinear 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 nonlinear systems in steady and dynamic conditions;
Design of nonlinear dynamic controller for a given system in order to meet proper transient and steady state constraints;
Identification of the most suitable nonlinear elements, as well as the most suitable parameters for a specific control design and its application;
Use of simulation numerical programs to analyse nonlinear systems.


The following concepts and the knowledge provided by the course 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 (48 hours) and guided tutorial in the labs (12 hours).

* Introduction to Feedback Control Systems (8 hours in classroom).

Linear and nonlinear control – Basic elements of a nonlinear control scheme (at a basic level: single blocks; at a control scheme level: functional blocks) – Problems of the design of control schemes with different levels of abstraction – Basics on the evolution of the nonlinear control designs – Differences between real and ideal cases.

* Linear and Nonlinear Optimal Control (8 hours in classroom).

The fundamental problem of optimisation – Eurler-Lagrange’s equations – Hamiltonian and Lagrangian functions – lagrange multipliers principle – Linear quadratic control.

* Neural Networks (8 hours in classroom).

The linear perceptron – Feed-forward multilayer neural networks – The training algorithm – Design of an multilayer neural network – Neural controller synthesis with the controller model reference method.

* Principles of Fault Diagnosis (8 hours in classroom).

Fault models – Residual generation – Residual evaluation – Parity equation method – Output observer design – Parametric estimation schemes – Kalman filter for fault diagnosis.

* Nonlinear Dynamic Systems (10 hours in classroom).

Basics of nonlinear control – Stability and Lyapunov’s methods – Fedback linearisation approach – Sliding Mode Control.

* Fundamentals of fuzzy logic and fuzzy control (8 hours in classroom).

Fuzzy numbers and fuzzy sets – Basics of fuzzy logic – The fuzzy inference system – Mamdami and Sugeno models – Rules and inference tables – Design of a fuzzy PID controller. Fuzzy modelling and identification for the design of a fuzzy controller – Adaptive Neuro-Fuzzy Inference Systems.

Didactic methods

The course is organised as follow:

- 48 hours of frontal lectures on all the course’s topics;

- 12 hours of practical exercises in the Informatics Laboratory concerning the analysis and the simulation of nonlinear dynamic systems. 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 nonlinear 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 complex process. 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 course: “Control Techniques and Diagnosis”, with the aim of evaluating how deeply the student has studied the subject and how he is able to understand the 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

Teacher’s handouts and slides are only required for the exam and the course preparation. They are available from the personal web page of the teacher:

Specific topics can be further developed in the following textbooks, which are not fundamental for the exam nor the course preparation:

- "Progetto di sistemi di controllo", M. Tibaldi. - 2. ed. - Pitagora, 1995.

- "Applied nonlinear control", J.J. Slotine, W. Li. - Prentice Hall, 1991.

- "A course in fuzzy systems and control", L.-X. Wang - Prentice Hall, 1997.

- "Neural Networks for Identification, Prediction, and Control", D.T. Pham and X. Liu - Springer Verlag, 1995.

- "Model-based Fault Diagnosis in Dynamic Systems Using Identification Techniques", S. Simani, C. Fantuzzi, R. J. Patton - Springer, 2003.

Note finally that the course lecture notes and handouts can be provided in English.