Control and stabilization of a linearized system of conservation laws

Abstract

It is considered the combined heat electricity generation system where the steam extraction of the turbine is connected to the heat consumer by a steam pipe described by a system of conservation laws. There exist two ways of linearizing these conservation laws. In this paper the two resulting linearized conservation laws are unified in a single model with non-standard boundary conditions arising from the controlled bilinear model of the steam turbine with a single steam extraction. Using the standard models of the fluid dynamics, including sub-critical and critical flow equations, the boundary conditions are also nonlinear. The basic model considered throughout the paper contains the linearized conservation laws and the nonlinear boundary conditions. The model thus obtained is submitted to the augmented validation procedure that includes: well posedness in the sense of Hadamard (existence, uniqueness and continuity with respect to data and initial conditions), possible invariant sets and inherent stability of the uncontrolled model. If the boundary conditions are also linearized, a bilinear control system is obtained and a quadratic Liapunov functional allows feedback control synthesis for system stabilization, the resulting feedback control structure being linear with saturation.