Nonlinear optimal control for interconnected PMSM electrically-driven gas-compressors

Abstract

The interconnection of gas compressors in series or parallel mode is needed in natural gas processing stations to achieve more efficient pressure management and to perform mixing of gas flows coming from different pipelines. In this article a nonlinear optimal control approach is developed for multiple interconnected gas compressors where each compressor is actuated by a PMSM (permanent magnet synchronous motor). Actually, the considered interconnection scheme consists of two parallel compressors with their outputs to be serially connected to a third compressor. Each gas compressor is actuated by a permanent magnet synchronous motor. First, the aggregate state-space model of the interconnected compressors is developed and its differential flatness properties are demonstrated. This is an implicit proof of the system’s controllability. Next, the state-space model of the interconnected compressors system undergoes linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a temporary operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the interconnected gas compressors a stabilizing H-infinity (optimal) feedback controller is defined. To compute the stabilizing gains of this controller an algebraic Riccatic equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis.