Air-fuel ratio control apparatus for an internal combustion engine

An air-fuel ratio control apparatus for an internal combustion engine, said air-fuel control apparatus comprising:

• a catalyst disposed in an exhaust passage of said internal combustion engine;
• a downstream-side air-fuel ratio sensor disposed in said exhaust passage and downstream of said catalyst, said downstream-side air-fuel ratio sensor including an element outputting an output value varying in response to an oxygen partial pressure;
• and
• a controller configured to:
• perform a feedback control to:
• (i) increase an air-fuel ratio of said engine, said air-fuel ratio of said engine being a mixture supplied to said engine in a period in which a lean request is occurring to require said air-fuel ratio of said engine to be increased so that an output value of said downstream-side air-fuel ratio sensor changes to be closer to a predetermined target value, and (ii) decrease said air-fuel ratio of said engine in a period in which a rich request is occurring to require said air-fuel ratio of said engine to be decreased so that said output value of said downstream-side air-fuel ratio sensor changes to be closer to said target value;
• obtain, as a first extreme value, said output value of said downstream-side air-fuel ratio sensor when a state in which said output value deviates a greatest amount from a predetermined reference value changes to a state in which said output value changes to be closer to said predetermined reference value;
• obtain, as a second extreme value, said output value of said downstream-side air-fuel ratio sensor when a state in which said output value changes to be closer to said predetermined reference value changes to a state in which said output value deviates a greatest amount from said predetermined reference value;
• set a first value as said target value when said first extreme value is obtained, said first value being a value between said obtained first extreme value and said reference value, and thereafter, determine and set, as a function of the first extreme value and the second extreme value, a second value as said target value when said second extreme value is obtained, said second value being a value between said obtained second extreme value and said obtained first extreme value;
• and
• change said target value to gradually change to be closer to said predetermined reference value over a time period, from a certain value within either one of:
• (i) a range at a larger side of said reference value, and (ii) a range at a smaller side of said reference value, and in which said output value of the downstream-side air-fuel ratio sensor is present, said predetermined reference value being a value within a certain range including a value which is equal to said output value of said downstream-side air-fuel ratio sensor when an oxygen partial pressure of a gas reaching an element of said downstream-side air-fuel ratio sensor is equal to an oxygen partial pressure obtained when an air-fuel ratio of said gas is equal to a stoichiometric air-fuel ratio.