Simple method for the design of single-input optimum regulators and servomechanisms

The quadratic-cost infinite-time optimal-regulator problem is considered. A simple procedure is described for the calculation of the optimal feedback coefficients for a linear time-invariant system having one control input. The method is based on a pole-placement procedure due to Flower and a relationship between the closed-loop characteristic frequencies and the system transfer-function matrix. The method is more direct than by the algebraic Riccati equation and enables solutions to quite complex problems to be found by mostly hand calculations. A computer program for finding the roots of a polynomial is all that is required.