Nonlinear Tracking Control of a Cryogenic Separation Process

Abstract

The cryogenic separation process is typically used to extract specific components of the air in high purity gas or liquid forms. This paper proposes a computational approach for synthesizing optimal and suboptimal tracking controllers for a nonlinear model of a cryogenic isotope separation process. The proposed method esssentially formulates a sum of squares (SOS) optimization problem for solving the state-dependent Riccati equation (SDRE) which arises in the considered nonlinear tracking control problem. More specifically, the paper first characterizes an optimal control law which forces the closed loop state trajectories to track a given reference signal and at the same time minimizes a quadratic performance index in an exact manner. Due to a computational issue which arises in synthesizing such an exact control law (i.e. the need to solve the SDRE), the paper then formulates SOS optimization problems for computing sub-optimal tracking control laws. A simulation example describing the design of a tracking controller for the cryogenic isotope separation process plant is then presented to illustrate the effectiveness of the proposed method.