Quadratic linearization of three phase horizontal gravity separator

The linearization of nonlinear control system has gained importance in the control arena. There are several works done by mathematicians and control engineers to linearize nonlinear systems so that the control can be effectively applied. Here we apply approximate linearization method by Kang and Krener to linearize the state space model of the three phase horizontal gravity separator and suppress the nonlinearities. The separator dynamic equations are transformed to avoid singularities. Using Binomial series expansion, a state space model of the separator is derived. The model is further transformed in terms of deviation about a steady state operating point which results in a control affine system. The linearization of the model is then performed by eliminating the quadratic terms in the derived state space equations. The elimination of second order terms is done by satisfying the necessary and sufficient conditions for quadratic linearization. The approximate quadratic linearization is effective as it eliminates the dominant quadratic terms while avoiding the zero dynamics issues which could arise in feedback linearization.