Patent ID: 8745967

Claim:
A method for controlling regeneration in an after-treatment component of an exhaust system, the component comprising a catalyst, the method comprising: determining a first value of a controlled parameter at a first time; determining a second value of the controlled parameter at a second time occurring a time increment after the first time; determining a rate of change of the value of the controlled parameter by dividing a difference between the first value of the controlled parameter and the second value of the controlled parameter by the time increment; determining a value of an error term by subtracting a value of a target parameter from a current value of the controlled parameter; determining a value of a gain exponent by dividing a thermal inertia of an exhaust stream flowing through the exhaust system by a thermal inertia of the catalyst; determining a value of a tuned gain exponent by multiplying the value of the gain exponent by a tuning factor; determining a value of a proportional gain factor as e x , wherein e is a mathematical constant “e”, and wherein x is (−1) multiplied by the value of the tuned gain exponent; determining a value of a derivative gain factor by multiplying the value of the proportional gain factor by the tuning factor; determining a value of a derivative control parameter by multiplying the rate of change of the controlled parameter by the value of the derivative gain factor; determining a value of a proportional control parameter by multiplying the value of the error term by the value of the proportional gain factor; determining a value of a raw control increment by adding the value of the derivative control parameter to the value of the proportional control parameter; determining a value of a rational control increment by multiplying the raw control increment by the thermal inertia of the exhaust stream; and adjusting the controlled parameter based on the value of the rational control increment.