I'm currently doing a controls project involving a self-balancing robot(or two wheeled inverted pendulum). I have been able to stabilize the system with the use of PID and optimal state feedback.
Now I'm wanting to adjust the LQR matrices so as to improve the battery runtime of the robot by a certain percentage(20%). I'm sure whether that is possible, but the problem I'm facing is how to show mathematically the relation with the Q and R matrices to the voltage being applied.
It would be very helpful if any one had any suggestions, or have come across a similar problem.
Apologies for a poor wording/ description of the problem, I'm still a student.