BSc:NonLinearControlTheory

Nonlinear Control Theory

• Course name: Nonlinear Control Theory
• Course number: XYZ
• Knowledge area: Control Engineering

Administrative details

• Faculty: Computer Science and Engineering
• Year of instruction: 4th year of BS
• Semester of instruction: 2nd semester
• No. of Credits: 4 ECTS
• Total workload on average: 144 hours overall
• Frontal lecture hours: 2 per week
• Frontal tutorial hours: 2 per week
• Lab hours: 2 per week
• Individual lab hours: 0
• Frequency: weekly throughout the semester
• Grading mode: letters: A, B, C, D

Prerequisites

• Physics I
• Physics II
• Mathematical Analysis I
• Mathematical Analysis II
• Analytic Geometry and Linear Algebra I
• Analytic Geometry and Linear Algebra II
• Control Theory

Course outline

This introductory course considers the fundamental principles and techniques of nonlinear control systems, providing basic information on mathematical modeling, vector spaces and norms, Phase plane portraits, Lyapunov stability, Jacobian-based linearization and MIMO-based state-space representation. It covers stability analysis of nonlinear and time-varying systems, and Internal stability of feedback systems. During the course students will become familiar with control pronciples for nonlinear control systems. This course includes practical simulation exercises and a control design project.

Expected learning outcomes

• Understanding nonlinear and time-varying systems
• Realizing the limits of nonlinear systems
• Amplitude, phase and frequency analysis of nonlinear control systems
• Techniques for the stability analysis of nonlinear and time-varying systems
• Jacobian linearization and gain scheduling
• State-Space Modelling

Expected acquired core competences

• Time and Frequency analysis
• Building controllers
• Tools: MATLAB / Simulink
• Nonlinear control system analysis
• Control design for nonlinear systems

Detailed topics covered in the course

The topics below are presented with the granularity of at most the academic hour of instruction. For each topic it is specified if it an Introduction to the topic, a Deep explanation, or a Review of a subject already covered in another course.

• Introduction to nonlinear and time-varying systems
• Mathematical background, including vector spaces and norms
• Local Decompositions of Control Systems
• Global Decompositions of Control Systems
• Techniques for the stability analysis of nonlinear and time-varying systems
• Internal stability of feedback systems. Phase plane portraits
• Lyapunov stability theorems. Popov and circle criteria for nonlinear feedback systems
• Passivity and small gain for nonlinear operators
• Overview of design for nonlinear systems
• Jacobian linearization and gain scheduling
• Input-Output Maps and Realization Theory
• Theory of Nonlinear Feedback for Single-Input Single-Output Systems
• Theory of Nonlinear Feedback for Multi-Input Multi-Output Systems
• Geometric Theory of State Feedback
• Tracking and regulation
• Global feedback design for SISO Systems

Expected learning outcomes

• Understanding in Nonlinear Control System characteristics: controllability, stability and regulation quality
• Realizing the limits of the Nonlinear Systems
• Amplitude, phase and frequency analysis of control systems
• Time analysis of control systems
• Building PID controllers and compensators
• State-Space Modelling
• State observer applying

Expected acquired core competences

• Time and Frequency analysis for nonlinear control system
• Control system analysis
• Building controllers
• Tools: MATLAB / Simulink
• Nonlinear control system analysis

Reference material

• Slides will be provided during the course

Required computer resources

Students are required to have laptops.

Evaluation

• Quizzes (20%)
• In-class activity (10%)
• Mid-term exam (5%)
• Final exam (10%)
• Home Assignments (30%)
• Project (25%)