Parameter Sensitivity of Closed Loop System Response

The transient response of a linear feedback control system is characterised by the s plane pole positions of the closed-loop system transfer function, particularly by those of the dominant poles. During a design procedure these pole positions are changed by varying the parameters which are under the control of the designer until the transient performance specification of the system is satisfied. These pole positions can also change as a result of variations in system parameters not under the control of the designer, for example, due to component tolerances or environmental changes. A necessary part of the design procedure is therefore the determination of the sensitivities of the pole positions to system parameter variations. Insofar as the design procedure seeks to predict closed-loop system behaviour from open-loop system information it is desirable that these sensitivities are determined from the same information in order that sensitivity considerations may be introduced at an early stage. This may be accomplished by an extension of the complex frequency response method for feedback control system design.