System constraints method of controlling operation of an electro-mechanical transmission with an additional constraint

A method for controlling an electro-mechanical transmission operatively coupled to first and second electric machines to transmit power to an output member, the method comprising:

• determining motor torque constraints for the first and second electric machines;
• transforming the motor torque constraints to equations comprising one of horizontal and vertical lines for the first electric machine and transforming the motor torque constraints to equations comprising the other one of horizontal and vertical lines for the second electric machine;
• defining a coordinate space based on the transformed motor torque constraints for the first and second electric machines;
• determining battery power constraints for an electrical energy storage device electrically connected to the first and second electric machines;
• transforming the battery power constraints for the electrical energy storage device to equations of concentric circles having respective radii within the coordinate space, the equations based on the transformed motor torques and a battery parameter defining an absolute minimum possible battery power at given motor speeds of the first and second electric machines;
• determining an additional constraint on the electro-mechanical transmission;
• transforming the additional constraint to an equation comprising a first line within the coordinate space;
• when the battery power constraints are less than sufficient to meet a required battery power for achieving a maximum output torque based upon the motor torque constraints, determining a preferred output torque to the output member of the electro-mechanical transmission that is achievable within the motor torque constraints and is based upon the additional constraint and the battery power constraints;
• transforming the output torque to an equation comprising a second line within the coordinate space;
• controlling operation of the electro-mechanical transmission and the first and second electric machines to achieve the preferred output torque at the output member based upon the motor torque constraints, the additional constraint, and the battery power constraints;
• and
• calculating at least one intersection of the battery power constraints transformed to the equations of concentric circles, the motor torque constraints transformed to the equations comprising one of horizontal and vertical lines for the first electric machine and the motor torque constraints transformed to the equations comprising the other one of horizontal and vertical lines for the second electric machine, the additional constraint transformed to the equation comprising the first line and the output torque transformed to the equation comprising the second line.