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.


  • \$\begingroup\$ If you learn how to "research" about 100k other students did this before you for the last 50 yrs. I think now it's called "re-surf" Academic and scholar sites. \$\endgroup\$ – Sunnyskyguy EE75 Mar 14 at 23:21
  • \$\begingroup\$ Hint surf for "unique minimum that can be obtained by solving the Algebraic Riccati Equation" or LQR Control Energy savings like cars comes from limiting the acceleration. \$\endgroup\$ – Sunnyskyguy EE75 Mar 14 at 23:26

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