Why would you want to set the input-weighted matrix R to zero?
If you set R to zero in the LQR control gain design, it means that you are assigning zero importance to the control effort in the cost function. In this case, the LQR control algorithm will mainly focus on minimizing the state error (based on the weight matrix Q) while disregarding the control effort.
Practically, setting R = 0 implies that the control gain matrix K will not have any contribution from the control input term. Consequently, the gain matrix K may become infinitely large to drive the state error to zero in a split second. This makes the tuning process becomes impractical.
