Design of an optimal state derivative feedback LQR controller and its application to an offshore steel jacket platform

This paper concerns with the optimal state derivative feedback LQR controllerdesign for vibration control of an offshore steel jacket platform having active tunedmass damper against the wave induced disturbances. Considering that the statederivative signals such as acceleration and velocity are easier to measure ratherthan the state variables such as displacement, state derivative feedback controlstrategy is proposed to obtain practically applicable and easily realizable synthesismethod. On the basis of convex optimization approach, state derivative feedbackLQR controller design is formulated in Linear Matrix Inequalities (LMIs) form toget an optimal feasible solution set. Finally, an offshore steel jacket platformsubject to nonlinear self excited wave force is used to illustrate the effectivenessof the proposed approach through simulations. The results show that proposedstate derivative LQR controller is very effective in reducing vibration amplitudesof each floor of modeled offshore steel jacket platform and achieves compitablecontrol performance to classical LQR controller design.

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Abdel-Rohman, M.(1996). Structural Control of Steel Jacket Platform. Structural Engineering and Mechanics, 4(2), 125-138.
Terro, M.J., Mahmoud, M.S., Abdel-Rohman, M. (1999). Multi-loop Feedback Control of Offshore Steel Jacket Platforms. Computers and Structures, 70(2), 188-202.
Zribi, M., Almutari, N., Abdel-Rohman, M., Terro, M. (2004). Nonlinear and Robust Control Schemes for offshore platforms. Nonlinear Dynamics, 35(1), 61-80.
Wu, H.Z., Bao-lin, Z., Hui, M.A. (2012). Active Non-Fragile Control for Offshore Steel Jacket Platforms. Proceedings of the 31st Chinese Control Conference, 7481-7486, July 25-27, Hefei, China.
Mei , X.Y., Bao-Lin, Z., Jian-Cun, W., Xiefu, J. (2016). Fuzzy H∞ Control for Steel Jacket Platforms with Parameter Uncertainties, Proceedings of the 35st Chinese Control Conference, 3749-3754, July 27-29, Chengdu, China.
Zhang B.L, Ma L., Han Q.L. (2013). Sliding mode H∞ Control for offshore steel jacket platforms subject to nonlinear self excited wave force and external disturbance. Nonlinear Analysis: Real World Applications, 14(1), 163-178.
Li, H.J., Lan S., Hu, J., Jakubiak, C. (2003). H2 active vibration control for offshore platform subject to wave loading. Journal of Sound and Vibration, 263(4), 709-724.
Zhang B.L., Hu Y.H., Tang, G.Y. (2012). Stabilization control for offshore steel jacket platforms with actuator time-delays. Nonlinear Dynamics, 70(2), 1593-1603.
Kwak S.K., Washington G., Yedavalli R.K. (2002). Acceleration-based vibration control of distributed parameter systems using the “reciprocal state-space framework”. Journal of Sound and Vibration, 251(3), 543-557.
Abdelaziz T.H.S. and Valasek M. (2004). Pole placement for SISO linear systems by state derivative feedback. IEE Proceedings-Control Theory and Applications, 151(4), 377-385.
Abdelaziz T.H.S. (2009). Robust pole assignment for linear time-invariant systems using statederivative feedback. Journal of Systems and Control Engineering, 223(2), 187-199.
Abdelaziz T.H.S. (2010). Optimal control using derivative feedback for linear systems. Journal of Systems and Control Engineering 224(2), 187- 202.
Assunçao E, Teixeira MCM, Faria FA et al. (2007). Robust state derivative feedback LMIbased designs for multivariable linear systems. International Journal of Control, 80(8), 1260- 1270.
Faria FA, Assunçao E, Teixeira MCM et al. (2009). Robust state derivative pole placement LMI based designs for linear systems. International Journal of Control, 82(1), 1-12.
Sever M., Yazici H. (2017) Active Control of Vehicle Suspension System Having Driver Model via L2 Gain State Derivative Feedback Controller. 2017 4th International Conference on Electrical and Electronics Engineering (ICEEE 2017), 215- 222, April 8-10,Ankara, Turkey,
Yazici H, Sever M. (2017). L2 gain state derivative feedback control of uncertain vehicle suspension systems. Journal of Vibration and Control,In Press.
Aktas A, Sever M, Yazici H. (2016). Gain scheduling LQR control of linear parameter varying overhead crane. In: IEEE 2016 National Conference on Electrical, Electronics and Biomedical Engineering,232-236, Dec 1–3; Bursa, Turkey.
Sever M, Kaya EE, Arslan MS, Yazici H. (2016). Active trailer braking system design with linear matrix inequalities based multi objective robust LQR controller for vehicle-trailer systems. In: IEEE 2016 Intelligent Vehicles Symposium,726- 731, June 19–22, Gothenburg, Sweeden.
Yazici H, Sever M. (2017). Active control of a non-linear landing gear system having oleo pneumatic shock absorber using robust linear quadratic regulator approach. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering,In Press.
Abdelaziz THS, Valasek M. (2005). State derivative feedback by LQR for linear time invariant systems. IFAC Proceeding Volumes, 38(1), 435-440.
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V. (1994)Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics (SIAM), Philadelphia.
Lin, F. (2007).Robust Control Design an Optimal Control Approach. John Willey&Sons, Hartfordshire.
Bao-Lin, Z., Han, Q.L. (2014). Network-based Modelling and Active Control for Offshore Steel Jacket Platform with TMD Mechanisms. Journal of Sound and Vibrations, 333(25), 6796-6814.
Löfberg, J. (2004) Yalmip: A Toolbox for Modeling and Optimization in MATLAB. Proceedings of the CACSD Conference, Taipei, Taiwan.
Strum, J.F. (1999). Using SeDuMi 1.02 a Matlab for optimization over symmetric cones. Optimization Methods and Software, 11(2), 625- 653.
Zhao, Y., Sun, W., Gao, H. (2010). Robust control synthesis for seat suspension systems with actuator saturation with time varying input delay. Journal of Sound and Vibration, 329(21), 4335- 4353.