Optimal transient response shaping for the discrete-time servomechanism problem

The problem of constructing a controller that results in a time response which is smooth, has a desired speed of response, and has little cross-channel interaction, is considered in this paper for the discrete-time servomechanism problem. Subject to fundamental limitations on achievable performance, we satisfy this objective by introducing a new cheap-control quadratic performance index that has the desired transient response characteristics embedded within it. Two examples are used to demonstrate that minimizing the performance index indeed results in a controller which has good transient performance and, in addition, reasonable control effort.