OVERVIEW

The aim of the course is to present the basic concepts and methods for the analysis and design of controllers for multivariable linear time invariant systems (MIMO LTI systems) of interest within robotics applications. The models used in the course are mainly those based on state-space equations. Basic robot control allocation problems will be illustrated as well as motion control ones.

AIMS AND CONTENT

LEARNING OUTCOMES

The objective of the module is that of presenting the basic methodologies for the analysis and control of multivariable systems with particular emphasis on linear time invariant ones. The module will start with a review of the basic concepts relevant to (linear) systems in state space form. Stability and structural properties of state space multivariable dynamic systems will be addressed with particular emphasis on the linear time invariant case. Matrix pseudo inversion methods will be discussed with reference to robot inverse kinematics and control allocation problems. The module will end with the treatment of some specific topics concerning multivariable control methods as applied in robotics scenarios (eg. linear state space observers used for robot navigation or control allocation used for robot control).

AIMS AND LEARNING OUTCOMES

Attendance of the lectures, active participation during the lab exercise hours (Matlab coding), and individual study will enable the student to:

a) Build and analyze linear time-invariant multivariable system models.

b) Linearize nonlinear multivariable dynamical system models.

c) Solve basic control allocation problems building on matrix pseudo inverse methods.

d) Design regulators for Multi Input Multi output Linear Time Invariant (MIMO LTI) systems in state space form capable of ensuring a certain closed-loop dynamics, even in the case in which the state of the system is not fully accessible.

PREREQUISITES

Fundamentals of Linear System Theory and Classical Control Theory.

TEACHING METHODS

The teaching consists of lectures, totaling about 30 hours, and a Matlab based  laboratory of about 10 hours for coding and simulating practical examples. The laboratory will be taught by the lecturer in charge of teaching, assisted by laboratory tutors. All laboratory activities will refer to topics and methods previously introduced during the lectures. In the practical part, students, divided into groups of two or three and with the support of lecturers and tutors, will have to code and simulate the systems on which the example focuses. At the end of each activity (preferably) or before the exam, students will have to submit a short report with the results obtained from the lab activity. These reports and the developed codes will be discussed during the exam. The organization and dates of the laboratory activities will be communicated directly by the lecturers at the beginning of class.

SYLLABUS/CONTENT

1) Basics on modeling and analysis of linear multivariable systems (continuous time).

2) Stability and structural properties of linear multivariable dynamic systems.

3) Matrix pseudo inversion methods for control allocation, inverse kinematics and motion control within robotics applications.

4) Pole assignment and state observers for linear multivariable time invariant dynamic systems.

5) Brief introduction to nonlinear dynamical systems and their properties.

6) Linearization of continuous time nonlinear multivariable systems along a nominal trajectory.

 Details of the syllabus might be subject to minor changes depending on students background and on the needed time to cover specific topics.

RECOMMENDED READING/BIBLIOGRAPHY

Papers and notes distributed by the lecturer;
H. Kwakernaak, R. Sivan - Linear Optimal Control Systems - Wiley 1972

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

Please refer to the official calendar of lessons of the Robotics Engineering Masters portal.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral exam: students will be asked describe, explain and provide examples of multivariable systems properties illustrated during the course. Simple exercises will be discussed to highlight multivariable systems properties and to assess the students ability to analyses and solve practical cases. The lab exercises reports and codes developed by the students during the course will also be discussed during the exam. 
Students with learning disorders ("disturbi specifici di apprendimento", DSA) will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the delegate of the Engineering courses in the Committee for the Inclusion of Students with Disabilities. In particular, students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the professor of the course  and with Professor Federico Scarpa (federico.scarpa@unige.it ), the Polytechnic School - Engineering's disability liaison.

ASSESSMENT METHODS

The oral exam will test the effective acquisition of basic knowledge of the multivariable systems properties addressed during the course. Open questions will allow the assessment of the ability to apply the knowledge on practical robotic examples using a clear and correct terminology. The student should be able to link and integrate knowledge learned during laboratory activities with that provided during the face-to-face lectures. Overall, the oral examination will aim to assess not only whether the student has achieved an adequate level of knowledge, but whether he or she has acquired the ability to critically analyze multivariable systems problems in robotics that will be posed during the exam.