Sensitivity functions of self-oscillations in bang-bang systems with nonlinear plant

Abstract

Bang-bang systems with a bistable relay element and smooth nonlinear plant are discussed. Methods for evaluating the sensitivity functions of self-oscillations to variations of the plant parameters are proposed; these are the sensitivity of periodic trajectories, self-oscillation period, and stability criterion. Exact methods for investigating bang-bang systems are used to ensure validity of sensitivity functions. Variational equations are used to derive sensitivity functions. An example is given to illustrate the derivation of sensitivity functions.