Method and system of controlling exhaust after-treatment apparatus for vehicle

A system for operating an exhaust after-treatment apparatus, comprising:

• a memory configured to store program instructions;
• and
• a controller configured to execute the program instructions, wherein the program instructions when executed configured to:
• detect signals from a front lambda sensor and a rear lambda sensor of a Lean NOx Trap (LNT), when an engine is driven in a rich mode;
• acquire a temperature of exhaust gas detected by a temperature sensor, when the engine is driven in a rich mode;
• compare the signals from the front lambda sensor and the rear lambda sensor to detect a breakthrough time when a breakthrough occurs between the signals from the front lambda sensor and the rear lambda sensor;
• determine an additional rich time period based on the breakthrough time and the temperature of exhaust gas;
• and
• transmit a signal to drive the engine in the rich mode for the additional rich time period after the breakthrough time.

A non-transitory computer readable medium containing program instructions executed by a processor or controller, the non-transitory computer readable medium comprising:

• program instructions that detect signals from a front lambda sensor and a rear lambda sensor of a Lean NOx Trap (LNT), when an engine is driven in a rich mode;
• program instructions that acquire a temperature of exhaust gas detected by a temperature sensor, when the engine is driven in a rich mode;
• program instructions that compare the signals from the front lambda sensor and the rear lambda sensor to detect a breakthrough time when a breakthrough occurs between the signals from the front lambda sensor and the rear lambda sensor;
• program instructions that determine an additional rich time period based on the breakthrough time and the temperature of exhaust gas;
• and
• program instructions that transmit a signal to drive the engine in the rich mode for the additional rich time period after the breakthrough time.

The non-transitory computer readable medium of claim A, further comprising:

• program instructions that determine the additional rich time period to be a, when the temperature of exhaust gas is less than T1 and the breakthrough time is less than t1;
• program instructions that determine the additional rich time period to be a+β, when the temperature of exhaust gas is less than T1 and the breakthrough time is greater than or equal to t1 and less than t2;
• and
• program instructions that determine the additional rich time period to be a+γ, when the temperature of exhaust gas is less than T1 and the breakthrough time is greater than or equal to t2,
• wherein β<γ and t1<t2.