Abstract. A solution to the problem of robust control over gas-lifted oil wells operation is proposed. The described solution is suitable for parametric uncertainty, unknown initial conditions, and necessity of output signal (volume flow at the well outlet) measurement. The model of the process is represented by ordinary differential equations derived from the Navier-Stokes equations using the straight lines approximation. The control signal is variation of flow rate of the gas supplied to the well. A modified back-stepping algorithm is used for control algorithm synthesis. Implementation of a single filter for the system condition by the control signal and straightforward control laws obtained using real differentiating element, allow to simplify the calculations and implementation of the control system. The trajectory which is a solution to linear-quadratic model problem is taken as a standard action Simulation results are presented to demonstrate the effectiveness of the proposed scheme which is robust to parametric perturbations caused by variations of physical and chemical parameters of the process.

Keywords: robust control, back-stepping method, gas lift process

References:

1. Shurov V.I. Tekhnologiya i tekhnika dobychi nefti (Technology and Technology of Oil Production), Moscow, 1983. (in Russ.)
2. Aliev F.A., Mutallimov M.M., Ismailov N.A., Radzhabov M.F. Automation and Remote Control, 2012, no. 8, pp. 3–15. (in Russ.)
3. Eikrem G.O., Aamo O.M., Foss B.A. SPE Production & Operations, 2008, no. 23, pp. 2–21.
4. Eikrem G.O., Imsland L.S., Foss B.A. Proc. of the 2003 International Symposium on Advanced Control of Chemical Processes, Oulu, Finland, 2003, pp. 21–28.
5. Aamo O.M., Eikrem G.O., Siahaan H.B., Foss B.A. Journal of Process Control, 2004, no. 3(15), pp. 247–257.
6. Imsland L.S., Eikrem G.O., Foss B.A. Control Engineering Practice, 2004, no. 3(7), pp. 24–29.
7. Eikrem G.O., Aamo O.M., Foss B.A. SPE Production & Operations, 2006, no. 2(21), pp. 112–119.
8. Imsland L.S., Foss B.A., Eikrem G.O. Proc. of the European Control Conference, 2003, pp. 2499–2504.
9. Furtat I.B., Tupichin E.A. Proc. of the 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014, Międzyzdroje, Poland, September 2–5, 2014, pp. 183–188.
10. Furtat I.B., Tupichin E.A. Proc. of the 2014 IEEE International Conference on Control Applications (CCA), Part of the 2014 IEEE Multi-conference on Systems and Control, Antibes, France, October 8–10, 2014, pp. 941–946.
11. Charnyy I.A. Neustanovivsheesya dvizhenie real'noy zhidkosti v trubakh (Unsteady Movement of Real Liquid in Pipes), Moscow, 1951.
12. Furtat I.B., Tupichin E.A. Proc. of the 6th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), St. Petersburg, Russia, October 6–8, 2014. pp. 541–545.
13. Aliev F.A., Mutallimov M.M. Math. Probl. Engin., 2010, ID 191053.
14. Furtat I.B., Furtat E. Tupichin E.A. 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems (MICNON 2015), Abstracts of Papers, St. Petersburg, Russia, June 24–26, 2015. Р. 1056—1061.
15. Furtat I.B., Tupichin E.A. Izv. vuzov. Priborostroenie, 2015, no. 3(58), pp. 173–178. (in Russ.)