How to implement an LQR controller when the system's state variables and control inputs have different units?

Hello,

I am wondering how to implement an LQR controller when the state variables and control inputs have different units.

For example, if the state vector is x=[β p r φ ψ F_T]^T and the control input vector is u=[δa δr δT]^T, with the units of the state variables and control inputs being (rad, rad/s, rad/s, rad, rad, lbf) and (rad, rad, lbf) respectively, how should I account for these unit differences when designing the LQR controller? I am particularly curious about how these units should be handled during both the controller design and when plotting the results of the state variables and control inputs, etc.

Answer 1

[Sam Chak]

Hi @준호

Could you provide a simple code example involving lqr() to illustrate your concern? There should not be any issues with the control input if you ensure that both the left-hand and right-hand sides of the equation have the same dimensions. If you still have concerns, one approach is to non-dimensionalize the entire system before performing the LQR computation.