Method for exhaust gas after-treatment of an internal combustion engine having at least one SCR catalyst

A method for exhaust aftertreatment of an internal combustion engine having at least one selective catalytic reduction (“SCR”) catalyst supplied with exhaust gas of the internal combustion engine through an exhaust path, the method comprising:

• virtually dividing the at least one SCR catalyst into n-bricks (nb) in a direction of flow of the exhaust gas;
• determining desired NH3 target fill levels (NH3Soll,i) for the at least one SCR catalyst as a function of a desired target NOx conversion efficiency (ηNOx);
• assuming a steady state condition for the determination of the desired NH3 target fill levels (NH3soll,i);
• determining the desired NH3 target fill levels (NH3soll,i) for the at least one SCR catalyst by means of an inverse SCR model (F−1) by means of a current NOx concentration (NOxUs) upstream of the SCR catalyst, an SCR catalyst temperatures of the bricks (TSCR,i), an exhaust mass flow (dmEG), an oxygen concentration (O2), an exhaust pressure (p) upstream of the SCR catalyst and a desired target NOx conversion efficiency (ηNOx);
• and
• performing a regulation of the SCR catalyst as a function of the determined NH3 target fill level (NH3soll).