Öz
Anahtar Kelimeler
Structured singular value Uncertainty Robustness Inverted pendulum
Kaynakça
- [1] P. Gaspar, I. Szaszi, and J. Bokor, ”Robust control design for mechanical systems using the mixed μ synthesis,” Periodica Polytechnica Ser. Transp. Eng., v. 30, pp. 37- 52, 2002.
- [2] S. Dussy and L. El-Ghaoui, “Multiobjective bounded control of uncertain nonlinear systems: An inverted pendulum example”, European Control Conference, Brussels, July 1997.
- [3] S. Cheang and W. J. Chen, “Stabilizing control of an inverted pendulum system based on H∞ loop shaping design procedure”, Proceedings of the 3rd World Congress on Intelligent Control and Automation, v. 5, pp. 3385 – 3388, 2000.
- [4] G.A. Medrano-Cerda, “Robust computer control of an inverted pendulum”, IEEE Control Systems Magazine, v.19, pp.58 – 67, 1999.
- [5] K. Ogata, “Modern Control Engineering”, Prentice-Hall Inc. 1990.
- [6] A. Yazıcı, “ Application of sliding mode control on an inverted pendulum system”, Masters thesis, Osmangazi University, December 2000 (in Turkish).
- [7] R. P. Braatz, P. M Young, J. C. Doyle, and M. Morari, “Computational-Complexity Of Mu-Calculation”, IEEE Transactions on Automatic Control, v. 39, pp.1000-1002, 1994.
- [8] A. Nemirovskii, “Several NP-hard problems arising in robust stability analysis”, Mathematics of Control, Signals, and Systems, v. 6, pp. 99–105, 1993.
- [9] M. K. H Fan, A. L Tits, and J. C. Doyle, “Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics”, IEEE Transactions on Automatic Control, v.36, pp. 25-38, 1991.
- [10] P. M. Young, “Structured singular value approach for systems with parametric uncertainty”, Int. Journal of Robust and Nonlinear Control, v.11, pp.653-680, 2001.
- [11] M. Fu and N. E. Barabanov, “Improved Upper Bounds for the Mixed Structured Singular Value”, IEEE Transactions on Automatic Control, v. 42, pp.1447-1452, 1997.
- [12] P. M. Young, M. P. Newlin, and J. C. Doyle, “Computing Bounds For The Mixed- Mu-Problem”, Int. Journal of Robust and Nonlinear Control, v.5, pp. 573-590, 1995.
- [13] K. Zhou and J. C. Doyle, “Essentials of Robust Control", Prentice-Hall, Inc, 1998.
- [14] G. J. Balas, J. C. Doyle, K. Glover, A. Packard, and R. Smith, “ μ -Analysis and Synthesis Toolbox: User’s Guide, MUSYN Inc. and The MathWorks, Inc.”, 2001.
Öz
Robust stability analysis of inverted pendulum system with a fixed linear quadratic feedback is carried out using μ analysis tools. A mathematical model of inverted pendulum system is presented and linearized about the desired equilibrium point. A linear quadratic control feedback matrix is used in the configuration of the nominal inverted pendulum system for its stabilization. After this, uncertainties in the inverted pendulum with a fixed feedback, is modeled in linear fractional transformation form , which is suitable for structured singular value computation. Both parametric and modeling uncertainties are considered in the inverted pendulum system. After deriving out uncertain system model, mixed μ analysis method which is a structured uncertainty analysis method, is used to compute the uncertainty bound that does not cause instability of the inverted pendulum under feedback. A simulation test for validity of the results is provided.
Anahtar Kelimeler
Structured singular value Uncertainty Robustness Inverted pendulum
Kaynakça
- [1] P. Gaspar, I. Szaszi, and J. Bokor, ”Robust control design for mechanical systems using the mixed μ synthesis,” Periodica Polytechnica Ser. Transp. Eng., v. 30, pp. 37- 52, 2002.
- [2] S. Dussy and L. El-Ghaoui, “Multiobjective bounded control of uncertain nonlinear systems: An inverted pendulum example”, European Control Conference, Brussels, July 1997.
- [3] S. Cheang and W. J. Chen, “Stabilizing control of an inverted pendulum system based on H∞ loop shaping design procedure”, Proceedings of the 3rd World Congress on Intelligent Control and Automation, v. 5, pp. 3385 – 3388, 2000.
- [4] G.A. Medrano-Cerda, “Robust computer control of an inverted pendulum”, IEEE Control Systems Magazine, v.19, pp.58 – 67, 1999.
- [5] K. Ogata, “Modern Control Engineering”, Prentice-Hall Inc. 1990.
- [6] A. Yazıcı, “ Application of sliding mode control on an inverted pendulum system”, Masters thesis, Osmangazi University, December 2000 (in Turkish).
- [7] R. P. Braatz, P. M Young, J. C. Doyle, and M. Morari, “Computational-Complexity Of Mu-Calculation”, IEEE Transactions on Automatic Control, v. 39, pp.1000-1002, 1994.
- [8] A. Nemirovskii, “Several NP-hard problems arising in robust stability analysis”, Mathematics of Control, Signals, and Systems, v. 6, pp. 99–105, 1993.
- [9] M. K. H Fan, A. L Tits, and J. C. Doyle, “Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics”, IEEE Transactions on Automatic Control, v.36, pp. 25-38, 1991.
- [10] P. M. Young, “Structured singular value approach for systems with parametric uncertainty”, Int. Journal of Robust and Nonlinear Control, v.11, pp.653-680, 2001.
- [11] M. Fu and N. E. Barabanov, “Improved Upper Bounds for the Mixed Structured Singular Value”, IEEE Transactions on Automatic Control, v. 42, pp.1447-1452, 1997.
- [12] P. M. Young, M. P. Newlin, and J. C. Doyle, “Computing Bounds For The Mixed- Mu-Problem”, Int. Journal of Robust and Nonlinear Control, v.5, pp. 573-590, 1995.
- [13] K. Zhou and J. C. Doyle, “Essentials of Robust Control", Prentice-Hall, Inc, 1998.
- [14] G. J. Balas, J. C. Doyle, K. Glover, A. Packard, and R. Smith, “ μ -Analysis and Synthesis Toolbox: User’s Guide, MUSYN Inc. and The MathWorks, Inc.”, 2001.
Ayrıntılar
| Konular | Elektrik Mühendisliği |
|---|---|
| Bölüm | Araştırma Makaleleri |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2005 |
| Kabul Tarihi | 1 Temmuz 2005 |
| Yayımlandığı Sayı | Yıl 2005 Cilt: 18 Sayı: 2 |
