An Analysis of Quadratic Linearization of Three Phase Horizontal Gravity Separator

Control by linearization of nonlinear system has been in focus and widely accepted by the control system experts. Dynamic model of Three Phase Horizontal Gravity Separator (TPHGS) has nonlinear characteristics. Various control techniques have been proposed to control TPHGS. In this paper approximate linearization technique due to Kang and Krener is applied to linearize the nonlinear system. TPHGS is described by nonlinear differential equations. A transformation of variables leads to state equations describing TPHGS. Considering deviation about set points of variables, a control affine system is derived. Approximate linearization in the form of quadratic linearization is applied to the control affine system describing the TPHGS. The linear equations involving the coordinate and input transformation coefficients are solved. Application of input and coordinate transformation leads to a linear system with third and higher order nonlinearities. A realistic numeric example together with a simulation illustrates the application of quadratic linearization. Approximate linearization avoids the zero dynamics which may arise in exact feedback linearization.

[1]  Stig Strand,et al.  Model Predictive Control (MPC) of a Gas-Oil-Water Separator Train , 1995 .

[2]  J.H. Taylor,et al.  Modeling and Control of Three-Phase Gravilty Separators in Oil Production Facilities , 2007, 2007 American Control Conference.

[3]  P. A. Krishnamoorthy,et al.  Generalized quadratic linearization of machine models , 2011 .

[4]  Sigurd Skogestad,et al.  A simple dynamic gravity separator model for separation efficiency evaluation incorporating level and pressure control , 2017, 2017 American Control Conference (ACC).

[5]  Gordon H. Huang,et al.  Fuzzy logic control for a petroleum separation process , 2008, Eng. Appl. Artif. Intell..

[6]  R. Devanathan.  Necessary and sufficient conditions for quadratic linearization of a linearly controllable system , 2004 .

[7]  Julio E. Normey-Rico,et al.  Disturbance Estimator based NonLinear MPC of a Three Phase Separator , 2012 .

[8]  John Baillieul,et al.  Mathematical control theory , 1998 .

[9]  Zhenyu Yang,et al.  On the innovation of level control of an offshore three-phase separator , 2010, 2010 IEEE International Conference on Mechatronics and Automation.

[10]  Arthur J. Krener,et al.  Extended normal forms of quadratic systems , 1990, 29th IEEE Conference on Decision and Control.

[11]  Mohammad Reza Saeb,et al.  Application of evolutionary computational approach in design of horizontal three-phase gravity separators , 2014 .

[12]  V. Kamaraj,et al.  Application of quadratic linearization to control of Permanent Magnet synchronous motor , 2011, 2011 1st International Conference on Electrical Energy Systems.

[13]  Sigurd Skogestad,et al.  Virtual inflow monitoring for a three phase gravity separator , 2017, 2017 IEEE Conference on Control Technology and Applications (CCTA).