Exhaust purification system and control method of the same

An exhaust purification system comprising:

• an NOx reduction catalyst, which is provided in an exhaust system of an internal combustion engine and reduces and purifies NOx in an exhaust gas;
• and
• a regeneration treatment controller, which recovers an NOx purification capacity of the NOx reduction catalyst by lowering an excess-air-ratio of the exhaust gas to a predetermined target excess-air-ratio,
• wherein the regeneration treatment controller:
• sets a target injection amount of at least one of a post injection and an exhaust pipe injection that is required for setting an excess-air-ratio of the exhaust gas to the target excess-air-ratio, based on a suction air amount of the internal combustion engine, the target excess-air-ratio, and a fuel injection amount of the internal combustion engine;
• and
• controls an injection amount of at least one of the post injection and the exhaust pipe injection, based on the target injection amount,
• wherein the regeneration treatment controller sets a value, which is obtained by subtracting the fuel injection amount of the internal combustion engine from a value obtained by dividing the suction air amount of the internal combustion engine by a product of the target excess-air-ratio a fuel specific gravity, and a theoretical air-fuel ratio, as the target injection amount.