# NONLINEAR CONTROL SYSTEMS cod. 15651

1° year of course - First semester
Professor
Automatica (ING-INF/04)
Field
Ingegneria informatica
Type of training activity
Characterising
42 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in - - -

## Learning objectives

The aims of the course in relation to knowledge and understanding are:
- Understanding of the phenomena of nonlinear dynamical systems: multiple equilibria, stability/instability, limit cycles.
- Knowledge of the stability theory and its extensions.
- Knowledge of the main methods of feedback nonlinear control. Notes on feedforward/feedback methods.
In relation to the capability of applying knowledge and understanding, the aims are:
- Skill to analyze nonlinear systems.
- Skill to build mathematical models of the kinematics of wheeled vehicles and of simple mechatronics systems.
- Skill to design and simulate nonlinear control systems with the aid of a computer.

- - -

## Course unit content

Introduction: Mathematical models and nonlinear phenomena. Examples. Existence and uniqueness of the solutions of state-space nonlinear models. The comparison lemma.
Second-order systems: Qualitative behavior of linear systems. Phase diagrams. Multiple equilibria. Limit cycles. Poincaré-Bendixson criterion.
Lyapunov stability theory: Autonomous systems. Lyapunov’s theorem. La Salle’s invariance principle. Linear systems and linearization. Regions of attraction. Nonautonomous systems and Lyapunov’s theorems. Linear time-varying systems and linearization. Converse theorems. Boundedness of state motions.
Frequency domain analysis of feedback systems: The describing function method. Common nonlinearities. The extended Nyquist criterion and the orbital stability of limit cycles.
Nonlinear control: Stabilization methods with state feedback: feedback linearization, control Lyapunov functions, integrator backstepping. Regulation methods: integral regulators, dynamic inversion, feedforward/feedback schemes.

- - -

## Bibliography

- Pdf slides of the lessons on the web site of the course.
1) H.J. Marquez – Nonlinear control systems: analysis and design, Wiley, 2003.
2) H.K. Khalil – Nonlinear Systems. Third edition. Prentice-Hall, 2002.
3) J.-J. E. Slotine, W. Li – Applied Nonlinear Control. Prentice-Hall, 1991.

## Teaching methods

Classroom sessions with alternate use of slides and explanations at the blackboard. Exercises in the classroom of modeling nonlinear systems (mechatronics systems,magnetic levitation, kinematic models of wheeled vehicles). Exercises in the laboratory of analysis and synthesis with the aid of MATLAB software.

## Assessment methods and criteria

Written examination and subsequent oral examination.

- - -