Synthesis of Feedback Control Systems by Means of Pole and Zero Location of the Closed Loop Function

In the past, feedback control systems have been designed by methods employing educated guesses, guided conception or dynamic synthesis.¹ Under the restrictive assumption that the fixed part of the system¿the summing point, final control element and essential auxiliaries peculiar to the particular system¿can be described by a linear differential equation with constant coefficients, a method is suggested herein whereby feedback control systems can be synthesized to prescribed performance requirements by a more direct procedure. A mathematical description of the desired frequency response, based on the location of the poles and zeros of the closed loop function, is made which insures that the specifications of velocity or acceleration error constant, bandwidth, and relative stability will be met and provides for acceptable system transient response. Algebraic manipulation yields the transfer function of main loop and subsidiary feedback loop corrective networks required to meet the specifications.