Transient Control In Multivariable Systems: A Study Motivated By Fuel Cells

Controlling the transient response of variables for which sensing or accurate estimation is not feasible, and a detailed plant model is also largely unavailable, poses significant challenges. It is a situation that is true in solid oxide fuel cells. In SOFCs, transient control is essential for fuel utilization, especially if the fuel cell is to be operated in a dynamic load-following mode at high fuel utilization. The objective is to design the control input(s) such that it isolates the output (fuel utilization in this case) from measurable disturbances, while the plant itself maybe largely unknown. The features assumed known are the output's functional dependence on states which is essentially the output definition, and the steady-state equation relating the multiple inputs and the output of interest. Simulations have shown good disturbance rejection in fuel utilization through input shaping. This idea is abstracted to linear multi-variable systems to provide conditions when this approach is applicable. The analysis is carried out in time-domain as well as in frequency domain (through singular value analysis). The type of output variables that are amenable to transient control using this approach is derived through analysis. It is shown that the fuel utilization, although inherently nonlinear within the nonlinear dynamics of the fuel cell, has some similarities with the linear abstraction that leads to the observed transient control.