A Recusive Algorithm for Synthesizing an Optimal Quadratic Control System

In this paper the feed back matrix K is determined according to the desired polelocation by means of the root-locus method.From K we obtain a row of the matrix P,which makes the nonlinear Riccati equation a linear one.Then the property of the matrix Q is examined with no difficulty.If Q≥0,it means that the control law u(t)=-Kx(t) is an optimal one,which minimizes the value of the quadratic performance index J and so the related closed-loop system is an optimal quadraticone considering Q given above.And it gives a desired pole configuration.A SCR-Dsystem is given as an example,which shows that the calculation of this method is simple.