We study the interaction of chirped electromagnetic pulses with intersubband transitions of a double semiconductor quantum well. We consider the ground and first excited subbands and give emphasis to controlled intersubband population transfer. The system dynamics is described by the nonlinear density matrix equations that include the effects of electron-electron interactions. These equations are solved numerically for various values of the electron sheet density for a realistic double GaAs/AlGaAs quantum well, and the efficiency of population transfer is discussed.