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Academic year
Didactic period
Primo Semestre

Training objectives

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

The main goal of the course consists of providing advanced topics and tools for the study, the observation and the control of complex dynamic systems and of their interconnections under proper design constraints imposed by cost, speed, computational cost, robustness, reliability and power consumption.

The main acquired knowledge will be:

advanced 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 constraints 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 behavior of linear and nonlinear systems in steady and dynamic conditions;
Identification of the most suitable control technique, as well as the most suitable parameters for specific control design and its application;
Use of simulation numerical programs to analyze 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 behavior, and their practical application; methods to analyze dynamic systems in steady and transient states:

- knowledge of the frequency tools for the analysis of dynamic systems;

- ability to analyze and design dynamic systems.

Course programme

The course consists of 60 hours of teaching activities divided into frontal lectures (45 hours) and guided tutorials in the labs (15 hours).

* Introduction to Feedback Control Systems (7.5 hours in classroom).

Basic elements of System Theory - Modelling - Linear Time Invariant Systems - Stability - Controllability and Reachability - Observability and Reconstructability

* Optimal Control for Robotic Systems (10 hours in classroom).

State Feedback and Optimal Control - Euler-Lagrange’s equations - Hamiltonian and Lagrangian functions - Linear quadratic control.

* Optimal State Estimation (7.5 hours in classroom).

Luenberger Observer - Kalman Filter

* Nonlinear Dynamic Systems (12.5 hours in classroom).

Basics of nonlinear control - Stability and Lyapunov’s methods - Feedback Linearization- Sliding Mode Control.

* Mobile Robots and Industrial Manipulators (7.5 hours in classroom).

Motion Planning - Unicycle and Differential Drive - Control of Articulated Robots.

* Simulation and Implementation of Control Systems (15 hours in the laboratory).

Didactic methods

The course is organized as follow:

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

- 15 hours of practical exercises in the Informatics Laboratory concerning the analysis and the simulation of control systems

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 into 2 sections:

- A project regarding the simulation and the control of advanced control scheme 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. It is allowed consulting the Matlab and Simulink programme manual;
One written test based on all the topics tackled in the class, with the aim of evaluating how deeply the student has studied the subject and how he is able to understand the topics analysed. It is not allowed consulting any textbook or using any PC, smartphone, calculator..;

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.

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.

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