The damping ratio of an optimal control system

Optimal control theory is used to design a second-order linear control system with step response that is, in a certain sense, the best possible. The damping ratio of this optimal system is compared with the value
(1/\sqrt{2})
of damping ratio that is conventionally assumed to give good performance. For a special class of second-order controlled objects, the optimal system has damping ratio
1/\sqrt{2}
.