Robust Control Using an Extended H-Infinity Approach: Concepts and Application

Ismaila Tijani, Agus Budiyono

Abstract


The need to robustify a control system against uncertainty in the plant parameters has been one of the fundamental design objective in the robust control field. One of the elegant approach of achieving this objective involves incorporating the v-gap metric into the well-known H-infinity Loop Shaping Design Procedures (H∞ LSDP). This integrated approach, known as an Extended H-Infinity approach provides an intuitive description of plant parametric uncertainty and as rightly called, extends the conventional H∞ LSDP to effectively handle such problem. Meanwhile, the conceptual formulation of this approach has received less attention in the literature which in turns limits its applications. In this paper, the concepts of the extended H-infinity in terms of mathematical description, problem formulation, design challenges and proposed procedures for practical applications are presented. A practical application to a small scale unmanned helicopter control is provided to demonstrative the effectiveness of the approach in robust control of dynamic system especially to parametric uncertainty.

Keywords


V-gap; Robust Control; Extended H-Infinity; Parametric Uncertainty

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References


Zames, G., & Francis, B.A., (1983). Feedback, minimax sensitivity and optimal robustness. IEEE Transaction on Automatic Control, 28, 585–600.

Stoorvogel, A. A., (1992). The H∞ control problem: a state space approach. Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor U.S.A.

La Civita, M., Papageorgiou, G., Messner, W.C. & Kanade, T., (2006). Design and Flight Testing of an H∞ Controller for a Robotic Helicopter. Journal of Guidance, Control, and Dynamics, 29(2), 485–494.

Yue, A., Postlethwaite I. & Padfield G., (1989). H∞ design and the improvement of helicopter handling qualities. Vertica, 13(2), 119-132.

Luo, C. C., Liu, R. F., Yang, C. D. & Chang, Y. H., (2003). Helicopter H-infinity control design with robust flying quality. Aerospace Science and Technology, 7(2), 159-169.

Hong-qiang, W., Ashfaq A. M., Dao-bo W. & Hai-bin D., (2009). Robust multi-mode flight control design for an unmanned helicopter based on multi-loop structure. International Journal of Control, Automation, and Systems 7(5):723-730

Feng Lin and Olbrot A. W., (1996). “ An LQR Approach to Robust Control of Linear Systems with Uncertain Parameters”, Decision and Control, Proceedings of the 35th IEEE Conference, vol. 4.

S. B. Chen (1993). "The robust optimal control of uncertain systems - state space method", IEEE Trans. Automat. Contr. , vol. 38 , no. 6 , pp.951 -957 , 1993

John, C. M., Michiel N. & Pascale B. (1994). Identification and control of a model helicopter in hover. Proceeding of the American Control Conference Baltimore, Marvland, June,1994.

Castillo-Effen, M., Castillo C., Moreno W., & Valavanis K. P. (2007). Control Fundamentals of Small Miniature Helicopters - A Survey. Kimon P. Valavanis (ed.) Advances in Unmanned Aerial Vehicles, 73-118. Springer.

P. P. Khargonekar , I. R. Petersen and K. Zhou (1990). "Robust stabilization of uncertain linear systems: quadratic stabilization and H-infinity control theory" , IEEE Trans. Automat. Contr. , vol. 35 , no. 3 , pp.356 -361 , 1990

Grimble, M. J., Johnson, M. A. (1991). H-infinity robust control design-a tutorial review, Computing & Control Engineering Journal, 2(6), 275-282.

Gu, D., Petko, H. P. & Mihail, M. K. (2005). Robust control design with MATLAB. Springer-Verlag London Limited.

Keith, G. & Duncan, M., (1989). Robust Stabilization of Normalized Coprime Factor Plant Descriptions with and Bounded uncertainty. IEEE Transactions on automatic control, 34(8), 82-1

McFarlane, D. & Glover, K., (1990). Robust controller design using normalized coprime factor plant descriptions. Springer Verlag Lecture notes in control and information science series.

Petersen I.R., Ugrinovskii V. A & Savkin, A.V., (2000). Robust control design using H∞ method. Springer-Verlag, London. pp.151-155

McFarlane, D. & Glover K., (1992). A loop shaping design procedure using H-infinity synthesis. IEEE Transactions on Automatic Control, 37(6),759-769.

D.Y. Jong, T.S. Kang, H. R. Dharmayanda and Agus Budiyono, H‐Infinity Attitude Control System Design for a Small Scale Autonomous Helicopter with Nonlinear Dynamics and Uncertainties, J of Aerospace Engineering, October, 2012

H. R. Dharmayanda, T. Kang, Agus Budiyono, Byeongha Kim, W Adiprawita, Parameter Identification and Design of a Robust Attitude Controller Using H∞ Methodology for the Raptor E620 Small Scale Helicopter, International Journal of Control, Automation, and Systems, 10(1):88-101, 2012

Wisnu Adi Pradana, Endra Joelianto, Agus Budiyono and Widyawardana Adiprawita, Robust MIMO H∞ Integral-Backstepping PID Controller for Hovering Control of Unmanned Model Helicopter, J of Aerospace Engineering, 24(4):454-462, 2011

Tijani I.B, Rini Akmeliawati, Ari Legowo, Agus Budiyono, and A. G. Abdul Muthalif, Robust Controller for Autonomous Helicopter Hovering Control, J of Aircraft Engineering and Aerospace Technology., 83(6), 2011

Vinnicombe, G., (1999). Uncertainty and Feedback: loop-shaping and the v-gap metric. Imperial College Press, London.

Tijani I.B.. Flight control system with MODE based H-infinity for small scale autonomous helicopter. PhD thesis submitted to Mechatronics engineering department, IIUM, Malaysia, October 2012b.

Ismaila B. Tijani , Rini Akmeliawati , Ari Legowo , Agus Budiyono , Asan G. Abdul Muthalif , (2014) "Hybrid DE-PEM algorithm for identification of UAV helicopter", Aircraft Engineering and Aerospace Technology: An International Journal, Vol. 86 Iss: 5, pp.385 – 405

Ismaila B. Tijani, Rini Akmeliawati, Ari Legowo, Agus Budiyono, Nonlinear Identification of a Small Scale Unmanned Helicopter using Optimized NARX Network with Multiobjective Differential Evolution, Engineering Applications of Artificial Intelligence, 33(2014):99-115, August, 2014




DOI: http://dx.doi.org/10.21535%2Fjmsa.v1i1.896

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