Optimum stability in control system design

Abstract

This thesis develops for the first time a general approach to the design of control systems that emphasizes optimum system stability as the primary design criterion. The design method is to select controller parameters that place the system's rightmost eigen value as far to the left as possible in the s-plane. When the system is operating at this point it is said to be in a state of optimum stability. This method is applied to the design of PI and PID controllers as more than 95% of controllers used in industrial applications are either PI or PID type (see references in section 6.1.1). The optimum stability design method is developed in the context of the root locus diagram, performance integrals, the Lyapunov matrix equation, and the Routh array and the equivalences between these characterizations are explored.