In my lab, I am trying to balance an inverted pendulum using simple LQR. To balance the arm I am using a DC motor. Now I have the A, B, C, D matrices. Using those I am able to find the feedback gain 'K' using MATLAB 'lqr' command. There are several parameters needed to find A, B, C, D. Among these are 3 parameters related to electrical characteristics of the DC motor:
- motor torque constant;
- motor back-emf constant;
- motor armature resistance.
There are two DC motors that I am using:
- one is 24 V, 3600 RPM, and;
- the other is rated 12 V but lesser RPM (exact RPM not known).
I have the three electrical characteristics mentioned above for the 12 V rated motor, and using that motor I have successfully balanced the pendulum by a lots of tuning of Q, R matrices.
My problem here is that for the 24 V rated motor I don't have those 3 parameters. And hence my A, B, C, D matrices cannot be found for system using 24 V motor.
My question is will those three parameters really affect the system matrices that much? Or since every other parameter in system remains same except those 3 when I change motor, so even if I use the 12 V motor's electrical characteristics for 24 V motor also, meaning the same A, B, C, D matrices, I should still be able to balance the system?
The reason I am asking this is, because LQR 'K' depends on A, B matrices of system, so if I use the wrong A, B matrices then the resulting 'K' can never actually balance it.
Note: I will use 24 V motor at 12 V supply only since the objective requires to keep 12 V as max control effort.