Optimal control of a nonlinear cryogenic separation process via SDRE method

The cryogenic separation process is an air separation technology which is used to produce specific components of the air in gases or liquid form with high purity. This technology is frequently used in liquified natural gas (LNG) industries, nuclear isotopes separation and cryogenic fuels production for space shuttle. This paper proposes an optimal control design method for a nonlinear model of a cryogenic separation process. The method combines the state-dependent Riccati equation (SDRE) method and the sum of squares (SOS) optimization technique. The paper first characterizes a stabilizing control law which minimizes a quadratic performance index of the process in an exact manner. Due to the difficulties in synthesizing such an exact optimal control (i.e. due to the need to solve the SDRE), the use SOS optimization techniques for computing sub-optimal control laws is then introduced. The proposed method is illustrated through the design of a controller which maximizes the fraction of a particular isotope production in a cryogenic separation process plant.