Robust PID Decentralized Controller Design Using LMI
AbstractThe new LMI based method for robust stability analysis for linear uncertain system with PID controller is proposed. The general constrained structure of controller matrix is considered appropriate for both output feedback and decentralized control and the respective guaranteed cost control design scheme is presented. The sufficient robust stability condition is developed for extended quadratic performance index including first derivative of the state vector to damp oscillations. The obtained stability condition is formulated for parameter-dependent Lyapunov function.
 Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan (1994). Linear matrix inequalities in system and control theory. SIAM Studies in Applied mathematics, Philadelphia.
 Han, J. and R.E. Skelton (2003). An LMI optimization approach for structured linear controllers. In: Proc. 42nd IEEE CDC, Hawaii, USA, pp. 5143-5148.
 Henrion, D., D. Arzelier and D. Peaucelle (2002). Positive polynomial matrices and improved LMI robustness conditions. In: 15th IFAC World Congress, Barcelona, Spain.
 deOliveira, M.C., J. Bernussou and J.C. Geromel (1999). A new discrete-time robust stability condition. Systems and Control Letters, 37, pp. 261-265.
 deOliveira, M.C., J.F. Camino and R.E. Skelton (2000). A convexifying algorithm for the design of structured linear controllers. In: Proc. 39nd IEEE CDC, Sydney, Australia, pp. 2781-2786.
 Ge, Ming, Min-Sen Chiu, Qing-GuoWang (2002). Robust PID controller design via LMI approach. Journal of Process Control, 12, pp.3-13.
 Gyurkovics, E., Takacs, T. (2000): Stabilisation of discrete-time interconnected systems under control constraints. IEE Proceedings - Control Theory and Applications, 147, No. 2, 137-144
 Peaucelle, D., D. Arzelier, O. Bachelier and J. Bernussou (2000). A new robustD-stability condition for real convex polytopic uncertainty. Systems and Control Letters, 40, pp. 21-30.
 Rosinová, D., V. Veselý and V. Kuˇcera (2003). A necessary and sufficient condition for static output feedback stabilizability of linear discrete-time systems. Kybernetika, 39, pp. 447-459.
 Rosinová, D. and V. Veselý (2003). Robust output feedback design of discrete-time systems – linear matrix inequality methods. In: 2th IFAC Conf. CSD'03 (CD-ROM), Bratislava, Slovakia.
 Skelton, R.E., T. Iwasaki and K. Grigoriadis (1998). A Unified Algebraic Approach to Linear Control Design, Taylor and Francis.
 Veselý, V. (2003). Robust output feedback synthesis: LMI Approach. In: 2th IFAC Conference CSD'03 (CD-ROM), Bratislava, Slovakia.
 Zheng Feng, Qing-Guo Wang, Tong Heng Lee (2002). On the design of multivariable PID controllers via LMI approach. Automatica, 38, pp.517-526.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.