Muntazir Hussain

Room # B–003  Office# 006, Ext: 442

muntazir.hussain@mail.au.edu.pk

https://sites.google.com/u/0/d/1P7qSHVdFmckO2Ocw-B15F0TfIWO_k76L/revisionspreview?revision=1679&pageId=1ZBFXYc9_Uhekl2smqLRmbTY7ENEObHtR&authuser=0

Course Code and Title: EE– 651 Linear Control Systems

Level: Graduate (PhD/MS)

Prerequisite: Knowledge of Control Systems, Laplace Transform, Linear Algebra, and Differential Equations, MATLAB/Simulink.

Course Website: 

Course Material: Click here (Accessible in Air University only, use internet explorer)

1. Understand the Fundamentals of Nonlinear System Behavior: Equip students with the theoretical tools to analyze and characterize the dynamics of nonlinear systems, including stability analysis using Lyapunov theory, phase plane analysis, and describing function methods.

2. Develop Nonlinear Control Design Skills: Teach students to design control strategies for nonlinear systems, such as feedback linearization, sliding mode control, and backstepping, with applications to real-world systems like robotics, aerospace, and autonomous vehicles.

3. Apply Nonlinear Control Methods to Practical Scenarios: Enable students to implement and simulate nonlinear control systems using software tools (e.g., MATLAB, Simulink, ROS) and develop solutions for complex engineering problems, including adaptive and optimal control techniques.

After studying this course, students will be able to:

1. Analyze Nonlinear System Behavior: Students will be able to analyze and characterize the stability and dynamics of nonlinear systems using methods like Lyapunov’s direct method and phase plane analysis.

2. Design Nonlinear Controllers: Students will gain the ability to design and implement nonlinear control strategies, including feedback linearization, sliding mode control, and backstepping, for various engineering applications.

3. Simulate and Apply Control Techniques: Students will be proficient in simulating nonlinear systems and control algorithms using tools such as MATLAB/Simulink and ROS, and applying these techniques to real-world engineering problems.

Nonlinear Systems by Hassan K. Khalil (3rd Edition)

Nonlinear Control Systems by Alberto Isidori

Feedback Control of Dynamic Systems by Gene F. Franklin, J. Da Powell, and Abbas Emami-Naeini

Nonlinear Control Systems and Power System Dynamics by R. C. Dorf and R. H. Bishop

MATLAB/Simulink for Nonlinear Systems - Various resources for practical implementation.

Students will extensively use MATLAB, there will be lab sessions for the analysis and design of nonlinear control problems.

There will be regular assignments during the session. Each of these assignments will be due in the following lecture. Late submissions and copied assignments will not be accepted.

There will be one sessional exam and one terminal exam; the dates will be announced by the course coordinator/examination cell. There will be one presentation or project, and 4–5 quizzes during the lecture hours; some of these quizzes will not be announced in advance.

Sessional Exam 25%

Quizzes 10%

Assignments  10%

Presentation/Project  10%

Terminal Exam 45%

Week 1: Introduction to Nonlinear Systems

• Definition and examples of nonlinear systems

• Differences between linear and nonlinear systems

• Nonlinearity in real-world systems (e.g., robotics, electrical circuits, biological systems)

• Basic concepts in nonlinear system analysis

Week 2: Phase Plane Analysis

• Concept of state-space representation for nonlinear systems

• Trajectories, equilibrium points, and stability

• Methods for analyzing nonlinear systems in phase space

• Example systems and their phase portraits

Week 3: Lyapunov Stability Theory

• Lyapunov’s Direct Method

• Stability of equilibrium points and limit cycles

• Lyapunov functions: Construction and examples

• Global vs. local stability

• Applications of Lyapunov stability in nonlinear control

Week 4: Stability Analysis of Nonlinear Systems

• Input-to-state stability (ISS)

• Popov and Circle Criteria for nonlinear systems

• Comparison of Lyapunov and describing function methods

• Stability analysis using nonlinear system simulations

Week 5: Describing Function Analysis

• Introduction to describing functions for nonlinear systems

• Approximation of nonlinearities using describing functions

• Stability analysis using the describing function method

• Limit cycles and bifurcations in nonlinear systems

Week 6: Control Techniques for Nonlinear Systems

• Linearization around equilibrium points

• Feedback linearization and state feedback

• Passivity-based control

• Sliding mode control: Basic concepts and applications

Week 7: Sliding Mode Control (SMC)

• Sliding mode dynamics and reaching condition

• Design of sliding surfaces

• Chattering phenomenon and its mitigation

• Applications of SMC in robotics, automotive systems, and more

Week 8: Feedback Linearization

• Introduction to feedback linearization

• Exact and approximate linearization techniques

• Control design using feedback linearization

• Examples of feedback linearization in nonlinear systems

Week 9: Backstepping Control

• Introduction to backstepping as a design method

• Backstepping control for nonlinear systems

• Applications of backstepping in robotic and aerospace systems

Week 10: Adaptive Control for Nonlinear Systems

• Overview of adaptive control techniques

• Nonlinear adaptive control design

• Model reference adaptive control (MRAC)

• Applications in systems with unknown parameters

Week 11: Nonlinear System Identification

• Methods for identifying nonlinear systems (e.g., Volterra series, neural networks)

• Least-squares and gradient-based optimization techniques for system identification

• Nonlinear system models and parameter estimation

• Model-based nonlinear control design

Week 12: Optimal Control for Nonlinear Systems

• Pontryagin’s Maximum Principle (PMP)

• Dynamic programming and Hamilton-Jacobi-Bellman (HJB) equation

• Application of optimal control techniques to nonlinear systems

• Example: Optimal trajectory planning for autonomous systems

Week 13: Nonlinear Control Applications

• Application of nonlinear control techniques in robotics (e.g., manipulator control)

• Nonlinear control in autonomous vehicles and drones

• Control of nonlinear electrical circuits and mechanical systems

• Case studies of nonlinear control in real-world systems

Week 14: Review of Course Topics & Advanced Topics

• Recap of key concepts and techniques learned in the course

• Introduction to advanced topics (e.g., stochastic nonlinear systems, nonlinear systems with delays)

• Discussion on emerging trends in nonlinear control systems (e.g., neural networks, deep learning in control)

Week 15: Final Project Presentations / Course Review

• Students present their final projects on nonlinear system analysis and control design

• Review and feedback on final projects

• Open discussion on future research directions in nonlinear systems and cont