A method to control an internal combustion engine provided with a mass flow sensor (9; 39) and with an exhaust system for the exhaust gases of a motor vehicle having an exhaust duct and an exhaust gas after-treatment system comprising at least one catalytic converter arranged along the exhaust duct ; a burner , which is suited to introduce exhaust gases into the exhaust duct so as to speed up the heating of said at least one catalytic converter , wherein inside the burner there is defined a combustion chamber , which receives fuel from an injector , which is designed to inject fuel into the combustion chamber , and fresh air through an air feeding device , which is provided with a pumping device feeding air, and with a shut-off valve arranged upstream of the burner ; the method comprises the following steps: calculating the thermal power (P OBJ ) needed to reach the nominal operating temperature of said at least one catalytic converter ; determining the objective air flow rate (ṁ A_OBJ ) to be fed to the burner in order to obtain said thermal power (P OBJ ) needed to reach the nominal operating temperature of said at least one catalytic converter ; determining the nominal number (N NOM ) of revolutions with which to operate the pumping device by means of a map depending on the objective air flow rate (ṁ A_OBJ ), on the ambient pressure (P ATM ), on the ambient temperature (T ATM ) and on the pressure (P A ) of the air flowing into the burner ; determining a closed-loop contribution (N CL ) of the number of revolutions with which to operate the pumping device by means of a PID controller, which tries to zero a difference between the objective air flow rate (ṁ A_OBJ ) and the air flow rate (ṁ A ) determined through the mass flow sensor (9; 39); determining a further contribution (N ADAT ) of the number of revolutions with which to operate the pumping device depending on the integral action of the PID controller under stationary conditions; and determining the actual number (N) of revolutions with which to operate the pumping device by means of the sum of the nominal number (N NOM ) of revolutions, of the closed-loop contribution (N CL ) of the number of revolutions with which to operate the pumping device and of the further contribution (N ADAT ) of the number of revolutions with which to operate the pumping device . calculating the thermal power (P OBJ ) needed to reach the nominal operating temperature of said at least one catalytic converter ; determining the objective air flow rate (ṁ A_OBJ ) to be fed to the burner in order to obtain said thermal power (P OBJ ) needed to reach the nominal operating temperature of said at least one catalytic converter ; determining the nominal number (N NOM ) of revolutions with which to operate the pumping device by means of a map depending on the objective air flow rate (ṁ A_OBJ ), on the ambient pressure (P ATM ), on the ambient temperature (T ATM ) and on the pressure (P A ) of the air flowing into the burner ; determining a closed-loop contribution (N CL ) of the number of revolutions with which to operate the pumping device by means of a PID controller, which tries to zero a difference between the objective air flow rate (ṁ A_OBJ ) and the air flow rate (ṁ A ) determined through the mass flow sensor (9; 39); determining a further contribution (N ADAT ) of the number of revolutions with which to operate the pumping device depending on the integral action of the PID controller under stationary conditions; and determining the actual number (N) of revolutions with which to operate the pumping device by means of the sum of the nominal number (N NOM ) of revolutions, of the closed-loop contribution (N CL ) of the number of revolutions with which to operate the pumping device and of the further contribution (N ADAT ) of the number of revolutions with which to operate the pumping device . <EOS>