Multi-speed hybrid powertrain with series and parallel operating modes

A hybrid powertrain comprising:

• an engine having a drive member;
• a multi-speed transmission having an input member and an output member and multiple torque-transmitting mechanisms selectively engageable in different combinations of one or more to provide multiple fixed speed ratios between the input member and the output member;
• a first motor/generator continuously connected for common rotation with the drive member;
• a second motor/generator continuously connected for common rotation with the input member;
• a damper connected with the input member;
• a damper clutch selectively engageable to connect the first motor/generator and the drive member for common rotation with the second motor/generator and the input member through the damper;
• a controller operatively connected to the motor/generators and the damper clutch and configured to establish:
• a hybrid series operating mode when the prime mover is on, the damper clutch is disengaged, the first motor/generator is controlled to function as a generator, and the second motor/generator is controlled to function as a motor;
• a hybrid parallel operating mode when the prime mover is on, the damper clutch is engaged, and the first and second motor/generators are controlled to function as motors;
• and
• wherein the torque-transmitting mechanisms of the multi-speed transmission are controlled to establish the multiple fixed speed ratios during at least one of the hybrid series operating mode and the hybrid parallel operating mode so that a speed of rotation of the second motor/generator decreases when a lower one of the fixed speed ratios between the input member and the output member is established.