Synthesis of feedback systems with specified open-loop and closed-loop poles and zeros

This paper describes a graphical method for synthesizing a compensation network where the fixed poles and zeros of the open-loop system are given and the closed-loop poles and zeros are independently specified. The resulting network is general in that it may have both real and complex poles and zeros. The method does not rely on cancellation techniques to determine the compensation network which is often simpler than one which would have resulted from the use of such techniques. In contrast to the Bode and Nyquist methods, wherein phase and gain requirements over a frequency band are used to generate compensation networks, this approach uses requirements at points in the s-plane, such as those imposed by desired transient response, to construct a solution of the problem. The graphical procedure is iterative. In many cases, convergence is rapid, and several techniques are suggested throughout the paper to further increase the speed of solution.