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– 756 Robust Control Systems

Level: Graduate

Prerequisite: Knowledge of Control Systems, Linear Systems, Linear Algebra, Understanding of MATLAB, and Differential Equations.

Course Website: 

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

1.— Analyze the behavior of uncertain dynamic systems with exogenous disturbances

2.— Analyze the multi-input multi-output systems in the frequency domain

3.— Describe the desired behavior of the uncertain dynamic systems using principal gains and operators norms

4.— Design the controllers using the recently developed approaches, that is, the LQG approach, H- infinity approach, mu-synthesis, LMI approach, etc.

5.— Reduce the order of the higher order systems/compensator to decrease implementation cost.

Robust Control Systems is an advanced course for the analysis and design of linear time-invariant control systems.  This course will enable the students to synthesize controllers for uncertain systems with external disturbances. Upon completing this course, students will:

1. Gain a solid understanding of robust control principles, including H-infinity and μ-synthesis.

2. Be able to design and analyze robust controllers for systems with uncertainties, disturbances, and noise.

3. Be proficient in using modern tools (e.g., LMIs, MATLAB) for robust control design and analysis.

4. Apply robust control methods to real-world systems and assess the trade-offs between robustness and performance.

Text Book

1. Maciejowski, J. J., Multivariable feedback design, 1991, Addison-Wesley.

2. Skogestad, S., Multivariable Feedback Control, 2nd edition, 2005, Wiley-Interscience.

3. Zhou K., Essentials of Robust Control, 1997, Prentice Hall.

Students will extensively use MATLAB Robust Control Toolbox. There will be lab sessions for the analysis and design of robust control problems.

There will be regular assignments during the session; most of them will be computer–based. 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 Robust Control

• Overview of robust control and its importance in practical systems

• Challenges in system modeling and uncertainties

• Basic concepts in robust control (stability, performance, uncertainty modeling)

• Applications of robust control in real-world systems (e.g., robotics, aerospace, automotive)

Week 2: Uncertainty in Control Systems

• Types of uncertainties: parametric uncertainty, unmodeled dynamics, external disturbances

• Modeling uncertainties using perturbation theory and uncertainty sets

• Representation of uncertainty in system models (e.g., structured vs. unstructured uncertainty)

• Performance degradation due to uncertainty

Week 3: H-infinity Control - Fundamentals

• Introduction to H-infinity control theory

• H-infinity norm and its significance in robust performance

• Synthesis of H-infinity controllers for SISO and MIMO systems

• Properties of H-infinity controllers (robustness, performance, stability)

Week 4: H-infinity Control - Design Methodology

• Control design using the H-infinity criterion

• Controller synthesis using the Riccati equation and convex optimization

• Frequency domain methods for H-infinity control design

• Practical implementation and challenges

Week 5: Frequency Domain Techniques for Robust Control

• Bode plots and Nyquist diagrams for robustness analysis

• Sensitivity and complementary sensitivity functions

• Robustness margins and their interpretation in frequency domain

• Stability and performance trade-offs in robust control design

Week 6: μ-Synthesis (Mu-Synthesis)

• Introduction to structured singular value (μ) and μ-synthesis

• Problem formulation and interpretation of μ-analysis

• Synthesis techniques for designing robust controllers using μ-synthesis

• Applications and examples of μ-synthesis in control design

Week 7: Robust Stability Analysis

• Lyapunov’s direct method in the context of robust control

• Stability under uncertainty: small gain theorem and passivity

• Robust stability analysis using the Kharitonov theorem and circle criterion

• Numerical methods for robust stability analysis

Week 8: Robust Control Design Using Linear Matrix Inequalities (LMIs)

• Introduction to Linear Matrix Inequalities in robust control

• Convex optimization and LMI-based controller design

• Solving LMIs for H-infinity and μ-synthesis problems

• Practical examples of LMI-based robust controller design

Week 9: Time-Domain Methods for Robust Control

• Time-domain performance criteria (overshoot, settling time, etc.)

• Robust control design using Lyapunov methods and state feedback

• Application of robust control to time-varying and nonlinear systems

• Simulations and analysis in time domain

Week 10: Multi-Objective Robust Control

• Multi-objective control design and optimization

• Balancing robustness, performance, and energy consumption

• Trade-offs in multi-objective robust control design

• Practical applications (e.g., drone control, robotic arms)

Week 11: Robust Control for Uncertain Nonlinear Systems

• Extending robust control to nonlinear systems

• Methods for robust control of nonlinear systems (e.g., sliding mode control, backstepping)

• Robust stability and performance in nonlinear systems

• Simulation examples with nonlinear dynamics and uncertainties

Week 12: Real-Time Implementation of Robust Controllers

• Challenges in real-time implementation of robust controllers

• Computational complexity and hardware limitations

• Implementation of H-infinity and μ-synthesis controllers in hardware

• Case study: Robust control for unmanned aerial vehicles (UAVs) or industrial robots

Week 13: Applications of Robust Control in Engineering

• Robust control in aerospace (e.g., aircraft flight control systems)

• Robust control in automotive systems (e.g., adaptive cruise control, autonomous vehicles)

• Robust control in robotics (e.g., robot arm motion control, multi-agent systems)

• Robust control for power systems, electrical grids, and renewable energy integration

Week 14: Review of Advanced Topics in Robust Control

• Recent advancements in robust control (e.g., robust adaptive control, learning-based control)

• Control of hybrid systems and systems with time delays

• Discussion on open problems and future directions in robust control

• Case studies of modern robust control applications

Week 15: Final Project Presentations / Course Review

• Student presentations on final projects: Robust control applications in real systems

• Review and discussion of course material

• Feedback and conclusions