Relationship between conventional-control-theory figures of merit and quadratic performance index in optimal control theory for a single-input/single-output system

The paper presents a correlation between the figures of merit used in conventional-control-design theory and the elements of the Q matrix in the quadratic performance index that is utilised for an optimal-control-design theory of single-input/single-output systems. This correlation results in a design procedure that utilises a set of curves (Mp, tp, ts and ¿d against qnn) for determining the elements of the Q matrix. In addition to the design procedure, the paper presents an analysis of the steady-state error for ramp inputs; the condition that the dominant roots are the same for any nth-order system, whereas the nondominant root for a specified plant is given by s ¿ ¿K ¿qnn (under the reproducibility condition defined in the paper) and the necessary conditions for an accurate solution of the Riccati equation.