This paper deals with a design approach to the synthesis of controllers for nonlinear control systems. The method proposed herein uses the frequency domain circle condition as a sufficiency criterion for insuring absolute stability. While the theory involved is well known, its application as a design tool has not yet been fully appreciated. A major aim of this paper is to indicate means of employing this new theory by use of classical frequency-domain techniques. The circle of nonlinearity from the Nyquist plane is transferred as a region onto the logarithmic gain-phase versus frequency plane using a simple transformation. A system controller or compensator can now be designed, straightforwardly without trial and error, by using the explicit frequency scale. Parameter combinations for system controllers yielding absolute stability can be obtained in a parameter plane or parameter space depending upon compensator configuration. The entire procedure is digital computer oriented but can be accomplished by paper and pencil techniques. Several numerical examples, along with hybrid computer corroboration, illustrate the procedure.
On the Interval Stability of Weak-Nonlinear Control Systems with Aftereffect