System and method of purifying exhaust gas

A system of purifying exhaust gas, comprising:

• an engine including an injector for dosing fuel thereinto, generating power by burning mixture of air and the fuel, and exhausting the exhaust gas generated during a combustion process to the exterior of the engine through an exhaust pipe;
• a lean NOx trap (LNT) mounted on the exhaust pipe, and configured to absorb nitrogen oxide (NOx) contained in the exhaust gas at a lean air/fuel ratio, to release the absorbed nitrogen oxide at a rich air/fuel ratio, and to reduce the nitrogen oxide contained in the exhaust gas or the released nitrogen oxide;
• a dosing device mounted on the exhaust pipe and configured to dose reducing agent into the exhaust gas;
• a selective catalytic reduction catalyst on a diesel particulate filter (SDPF) mounted on the exhaust pipe downstream of the dosing device, and configured to trap particulate matter contained in the exhaust gas and to reduce the nitrogen oxide contained in the exhaust gas using the reducing agent injected through the dosing device;
• and
• a controller controlling operation of a low pressure-exhaust gas recirculation (LP-EGR) system and dosing of urea solution by predicted probability of ammonia slip to a rear end of the SDPF and an ammonia absorption amount.