Fundamental theory of automatic linear feedback control systems

The reasons for using feedback are reviewed. The beneficial aspects of feedback are quantitatively expressed in sensitivity functions and noise transmission functions. The physical constraints on the controlled process (or plant) determine the maximum number of independent functions realizable. Any configuration with the same number of degrees of freedom may be used. With this approach the study of conditional feedback, model feedback, combined positive and negative feedback, etc. is of secondary interest. The benefits of feedback are paid for in gain-bandwidth of active elements over and above what is needed to physically do the job. The minimum price that must be paid is independent of configuration. The system with two degrees of freedom is studied in detail. Two methods are presented for the precise design of a system that will be as insensitive as may be desired to large parameter variations. One method uses root-locus techniques and is suitable for systems with a small number of dominant poles and zeros. The second method is based on frequency response and can be used for systems of any complexity. Numerical examples are given.