Finite Frequency Static Output Feedback $H_{\infty}$ Control Design of a Urea-Selective Catalytic Reduction Aftertreatment system

This work concerns the finite frequency static out-put feedback (FFSOF)
$H_{\infty}$
controller design for the urea-based selective catalytic reduction (SCR) system in Diesel engines based descriptor approach to reduce nitrogen oxides (
$NO_{x}$
) emissions. The state space model of the urea-SCR system in Diesel engines is firstly, linearized around an average operating point of the urea-based SCR systems. Then, the objective is to regulate the concentration of
$NO_{x, out}$
at outlet of a catalyst in the SCR model to desired reference concentration by controlling the concentration of
$NH_{3,in}$
at inlet of a catalyst. By applying the generalized Kalman Yakubovich Popov (gKYP) lemma and Lyapunov functions, sufficient conditions are established to ensure both the good reference trajectory tracking and the prescribed
$H_{\infty}$
performance of the concentration of
$NO_{x, in}$
at inlet of a catalyst variation. Simulation results using nonlinear urea-SCR system of Diesel engines is provided to illustrate the performance of the developed method.