If a control system is to be synthesized, it is inferred that a plant or process is present which must be controlled, and the problem of how to design the control system then arises. The first step is to decide on performance specifications to which the complete system must conform. These specifications may involve such things as the system steady state response, transient response, or frequency response. Any of several synthesis methods may then be applied to complete the system design.
In this study a synthesis method is developed for single-loop linear feedback systems. First, the number of compensating poles and zeros and the approximate location of each is determined by conventional methods. A set of functions, one for each specification and one involving each plant pole, is written in terms of the system singularities with the compensation singularity positions as variables and each such function is equated to zero. linear approximations of each of these generally non-linear functions are obtained by expanding each function with a multivariable Taylor series and retaining only linear terms. Expansion is about a point described by the approximate singularity values. This linear set of equations is solved by the Gauss-Jordan elimination method. Due to truncation of the Taylor series, this does not give an exact solution to the original specification equations but will serve as a second approximation which is used as a new point of Taylor series expansion. This iterative process is repeated until a satisfactory solution is found.
This entire iterative technique is adapted for digital computer programming and flow charts for such a program are drawn --Abstract, page ii
