Step-response behaviour of a speed-control system with a back-e.m.f. nonlinearity

It is shown that, under certain conditions, a speed-control system with a back-e.m.f. nonlinearity fails to reach the demanded speed in response to a step-function input. This is equivalent to a restriction on the region of asymptotic stability of the steady state of the system. The restriction is investigated by means of the Lyapunov method, and an analytical expression is obtained for it. The nonlinearity is a function of two variables, and the functions V and V used are not sign-definite in the entire phase plane. A technique is used for deriving analytical results in this situation, and the resulting sufficient conditions are compared with exact results.