Nonlinear Control Allocation for Drilling Rigs with an Online Actuator Selection Method

Abstract

Dynamic positioning systems (DPS) on marine vessels exhibit actuator redundancy, with more actuators than degrees of freedom. A control allocation unit is employed to address this redundancy. Practical systems often feature time-varying elements in the effectiveness matrix due to factors such as changing operating conditions, nonlinearity, and disturbances. Additionally, not all thrusters require engagement at each step to counteract disturbances and maintain position. Control efforts can be generated by selecting some thrusters based on their instant effectiveness, while others can remain on standby. Therefore, introducing a control allocation method that calculates the effectiveness matrix online and selects the most efficient thrusters could be effective. This paper introduces a fault-tolerant control allocation strategy for DPS with a varying effectiveness matrix. Specifically, the investigation focuses on a case study featuring eight azimuth thrusters used on a drilling rig. At each time step, the effective matrix is calculated online, followed by the selection of the four most effective thrusters based on the actuator effectiveness index, with the four serving as backups in case of a fault. The proposed strategy has been validated through simulation results, demonstrating advantages such as robustness against changes in the effectiveness matrix and reduced energy usage by the thrusters.

References

[1] Ahani A, Ketabdari MJ. Alternative approach for dynamic-positioning thrust allocation using linear pseudo-inverse model Applied Ocean Research, 2019, 90: 101854.

[2] Bordignon KA Constrained control allocation for systems with redundant control effectors, 1996 Blacksburg Virginia Polytechnic Institute and State University

[3] Biss D, Perkins JD. Application of input-output controllability analysis to chemical processes Proceedings of European control conference, 1993 1056(2)

[4] Brown DT, Ekstrom L. Vessel thruster-thruster interactions during azimuthing operations International Conference on Offshore Mechanics and Arctic Engineering, 2005 991-996(41952)

[5] Buffington JM, Enns DF. Lyapunov stability analysis of daisy chain control allocation Journal of Guidance, Control, and Dynamics, 1996, 19(6): 1226-1230.

[6] Chen M, Ge SS, How BVE, Choo YS. Robust adaptive position mooring control for marine vessels IEEE Transactions on Control Systems Technology, 2012, 21(2): 395-409.

[7] Chen H, Wan L, Wang F, Zhang G. Model predictive controller design for the dynamic positioning system of a semi-submersible platform Journal of Marine Science and Application, 2012, 11: 361-367.

[8] Daoutidis P, Kravaris C. Structural evaluation of control configurations for multivariable nonlinear processes Chemical Engineering Science, 1992, 47(5): 1091-1101.

[9] Enns D. Control allocation approaches Guidance, navigation, and control conference and exhibit, 1998 Reston American Institute of Aeronautics and Astronautics, Inc.(AIAA-98-4109)

[10] Faÿ H Dynamic Positioning Systems: Principles, Design, and Applications, 1990 Paris Ophrys Editions

[11] Fossen TI, Perez T Marine Systems Simulator (MSS), 2004

[12] Fossen TI, Johansen TA. A survey of control allocation methods for ships and underwater vehicles 2006 14th Mediterranean Conference on Control and Automation, 2006 Piscataway IEEE 1-6

[13] Gao D, Wang X, Wang T, Wang Y, Xu X. Optimal thrust allocation strategy of electric propulsion ship based on improved non-dominated sorting genetic algorithm II IEEE Access, 2019, 7: 135247-135255.

[14] Gawronski W, Lim KB. Balanced actuator and sensor placement for flexible structures International Journal of Control, 1996, 65(1): 131-145.

[15] Gopmandal F, Ghosh A, Kumar A. LQ optimal robust multivariable PID control for dynamic positioning of ships with norm-bounded parametric uncertainties Ocean Engineering, 2022, 266: 113054. part 4)

[16] Govin R, Powers GJ. Control system synthesis strategies AIChE Journal, 1982, 28(1): 60-73.

[17] Hać A, Liu L. Sensor and actuator location in motion control of flexible structures Journal of Sound and Vibration, 1993, 167(2): 239-261.

[18] Hovd M, Skogestad S. Procedure for regulatory control structure selection with application to the FCC process AIChE Journal, 1993, 39(12): 1938-1953.

[19] Jafari SR, Khaki-Sedigh A, Birk W. Adaptive multi-objective control allocation with online actuator selection for over-actuated systems International Journal of Dynamics and Control, 2023, 11(3): 1220-1229.

[20] Johansen TA, Fossen TI, Berge SP. Constrained nonlinear control allocation with singularity avoidance using sequential quadratic programming IEEE Transactions on Control Systems Technology, 2004, 12(1): 211-216.

[21] Li H, Lin X. Robust finite-time fault-tolerant control for dynamic positioning of ships via nonsingular fast integral terminal sliding mode control Applied Ocean Research, 2022, 122: 103126.

[22] Li J, Xiang X, Yang S. Robust adaptive neural network control for dynamic positioning of marine vessels with prescribed performance under model uncertainties and input saturation Neurocomputing, 2022, 484: 1-12.

[23] Lin Y, Du J, Zhu G, Fang H. Thruster fault-tolerant control for dynamic positioning of vessels Applied Ocean Research, 2018, 80: 118-124.

[24] Liu C, Teng Y, Zhang Y, Zhang L. Model predictive control and thrust allocation for dynamic positioning of vessels International Conference on Guidance, Navigation and Control, 2023 Singapore Springer Nature Singapore 994-1005(845)

[25] Liu X, Chen BM, Lin Z. On the problem of general structural assignments of linear systems through sensor/actuator selection Automatica, 2003, 39(2): 233-241.

[26] Øveraas H, Halvorsen HS, Landstad O, Smines V, Johansen TA. Dynamic positioning using model predictive control with short-term wave prediction IEEE Journal of Oceanic Engineering, 2023, 48(4): 1065-1077.

[27] Naderi M, Khaki Sedigh A. Actuator selection for over-actuated systems using the actuator effectiveness index International Journal of Dynamics and Control, 2020, 8(3): 991-998.

[28] Naderi M, Johansen TA, Sedigh AK. A fault tolerant control scheme using the feasible constrained control allocation strategy International Journal of Automation and Computing, 2019, 16: 628-643.

[29] Perez T, Fossen TI, Sorensen A A discussion about seakeeping and manoeuvring models for surface vessels, 2004 MSS-TR-001

[30] Samar R, Postlethwaite I. Multivariable controller design for a high performance aero-engine In 1994 International Conference on Control-Control’94, 1994 London IET 1312-1317(2)

[31] Septanto H, Adinanta H, Kurniawan E, Mujahid AS, Malakani AI, Afandi MI, Permana C, Nurhadi N. Asymptotic sliding mode control design for ship dynamic positioning system 2023 International Seminar on Intelligent Technology and Its Applications (ISITIA), 2023 Piscataway IEEE 500-504.

[32] Shen H, Wang Y, Wang J, Park JH. A fuzzy-model-based approach to optimal control for nonlinear Markov jump singularly perturbed systems: A novel integral reinforcement learning scheme IEEE Transactions on Fuzzy Systems, 2023, 31(10): 3734-3740.

[33] Sørensen AJ. A survey of dynamic positioning control systems Annual Reviews in Control, 2011, 35(1): 123-136.

[34] Tang L, Wang L, Wang Y, Zhang Y. An enhanced trajectory tracking control of the dynamic positioning ship based on nonlinear model predictive control and disturbance observer Ocean Engineering, 2022, 265: 112482.

[35] Tannuri EA, Agostinho AC, Morishita HM, Moratelli L Jr. Dynamic positioning systems: An experimental analysis of sliding mode control Control Engineering Practice, 2010, 18(10): 1121-1132.

[36] Tohidy S, Sedigh AK. Fault tolerant fuzzy control allocation for overactuated systems 2013 13th Iranian Conference on Fuzzy Systems (IFSC), 2013 Piscataway IEEE 1-5

[37] Tohidi SS, Khaki Sedigh A, Buzorgnia D. Fault tolerant control design using adaptive control allocation based on the pseudo inverse along the null space International Journal of Robust and Nonlinear Control, 2016, 26(16): 3541-3557.

[38] Wang J, Wu J, Shen H, Cao J, Rutkowski L. Fuzzy H ^∞ control of discrete-time nonlinear Markov jump systems via a novel hybrid reinforcement Q-learning method IEEE Transactions on Cybernetics, 2022, 53(11): 7380-7391.

[39] Zhao L, Roh MI. A thrust allocation method for efficient dynamic positioning of a semisubmersible drilling rig based on the hybrid optimization algorithm Mathematical Problems in Engineering, 2015 1-12

[40] Zhang G, Lv S, Huang C, Zhang X. Robust adaptive control for dynamic positioning vehicles in presence of adjustable threshold rule and input constraints Ocean Engineering, 2023, 282: 114950.

RIGHTS & PERMISSIONS

Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature