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## CONTROL OF LINEAR MULTI-VARIABLE SYS.

CODE 80181 2022/2023 5 cfu during the 1st year of 10635 ROBOTICS ENGINEERING (LM-32) - GENOVA ING-INF/04 English GENOVA 1° Semester AULAWEB

## 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 obejctive of the course is that of presenting the basic methodologies for the analysis and control of linear (time-invariant) multivariable systems. The course will start with a review of the basic concepts relevant to linear stystems, in continuous and discrete time. Stability and structural properties of linear multivariable dynamic systems will be addressed. Matrix pseudo inversion methods will be discussed with reference to robot inverse kinematics and control allocation problems. The course will end with the treatment of some specific topics concerning linear multivariable control, as closed-loop pole assignment and feedback control based on state observers.`

### AIMS AND LEARNING OUTCOMES

At the end of the course, the students will be able to:

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

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

c) Design regulators capable of ensuring a certain closed-loop dynamics, even in the case in wich the state of the system is not fully accessible.

### PREREQUISITES

Fundamentals of Linear System Theory and Classical Control Theory.

### TEACHING METHODS

Lessons and computer exercises.

### SYLLABUS/CONTENT

1) Basics on modeling and analysis of linear multivariable systems (continuous and discrete);

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.

### RECOMMENDED READING/BIBLIOGRAPHY

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

## TEACHERS AND EXAM BOARD

### Exam Board

GIOVANNI INDIVERI (President)

MICHELE AICARDI

GIORGIO CANNATA

ENRICO SIMETTI (President Substitute)

## LESSONS

### LESSONS START

https://corsi.unige.it/10635/p/studenti-orario

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

Oral 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.

### ASSESSMENT METHODS

The students will be evaluated on the basis of their capability to solve simple analysis and control problems.

### Exam schedule

Date Time Location Type Notes
18/01/2023 10:00 GENOVA Orale
06/02/2023 10:00 GENOVA Orale
05/06/2023 10:00 GENOVA Orale
27/06/2023 10:00 GENOVA Orale
14/07/2023 10:00 GENOVA Orale
27/07/2023 10:00 GENOVA Orale
14/09/2023 10:00 GENOVA Orale