Robust H2 Control: Linear Matrix Inequality Approach

Multiplier Approach to Robust H2 Control

The subject of this research is the design of Robust Multivariable Controllers based on the Linear Matrix Inequalities (LMI) approach. The specific topics being investigated are Robust H2 methods and their application to practical problems.

Among the advantages of the LMI formulation is the ability to mix robust H2 criteria with other important control system objectives like pole region assignment and H constraints. Furthermore the LMI formulation provides great flexibility in constructing many useful results beyond the standard Algebraic Riccati equation approach.

A major achievement has been the development of a practical, robust multivariable design strategy that has been successfully verified on a number of practical problems. These include the design of controllers for the ACC benchmark problem and a HVDC (High voltage Direct Current) system.

The current focus is on the design of low order and decentralized controllers.

In particular a technique based successive centering algorithms has been successfully developed and applied to the design of controllers for a HVDC system with long cables.

• 2-04.114V
  A. Farag, M. Durrant, H. Werner, K. Abbott : Robust Control of a VSC HVDC Terminal Attached to a Weak AC System, IEEE Conference on Control Applications, 2003.
• 2-04.115V
  A. Farag, H. Werner : K-S-Phi iteration for robust H2 controller synthesis, Proceedings 6th ECC, 2003.
• 2-04.123V
  A. Farag, H. Werner : A design procedure for robust H2 control using a multiplier approach. Proceedings 6th European Control Conference, Cambridge, UK, 2003
• 2-04.125V
  Farag, A.; Werner, H.: Low-Order Robust Decentralized Controller Design For A HVDC Power Link: A Combined Riccati - Genetic Algorithms Approach. In: The 10 IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems. Theory and Applications, Osaka, Japan, 2004 (FaWe04)
• 2-04.127V
  Farag, A.; Werner,H.: Fixed-Structure Controller Synthesis - A Combined Recatti - Genetic Algorithms Approach. In: American Control Conference 2004 ACC, Boston, MA, 2004 (FaWe02)
• 2-04.130V
  Farag, A.; Werner, H.: Low-Order Robust Decentralized Controller Design For A HVDC Power Link Using Successive Centering. In: The 10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, Osaka, Japan, 2004 (FaWe04a)
• 2-04.135V
  Farag, A.; Werner, H.: Constructing Tight LFT Uncertainty Models For Robust Controller Design In: Proceedings IEEE 43rd Conference on Decision and Control, Nassau, Bahamas, 2004 (FaWeAt04a)
• 2-04.136V
  Farag, A.; Werner, H.: Multivariable PID-Controller Design For A Gasifier Plant Using Penalty-Based-Multi-Objective GA In: Proceedings of Control 2004, Bath, UK, 2004 (FaWeAt04)
• 2-04.138D
  Adel Omran Farag: A Practical Approach to Robust Control Using Linear Matix Inequalitites (O.04)
• 2-04.141V
  Farag, A.; Werner, H.; Decentralized Control of Winding Systems for Elastic Webs: a Hybrid Evolutionary-Algebraic Approach in Proceedings 16th IFAC World Congress, Prague (FaWe05a)
• 2-04.142V
  Farag,A.; Werner, H.; Robust decentralized control of a {HVDC} system using an {LMI} approach In Proceedings 16th IFAC World Congress, 2005, Prague (FaWe05b)
• 2-04.143V
  Farag, A.; Werner, H.; Fixed-order control of active suspension : a hybrid evolutionary-algebraic approach in Proc. 16th IFAC World Congress, 2005, Prague (FaWe05)