Performance cost functions for a reaction-jet-controlled system during an on-off limit cycle

In this paper, analytical expressions are obtained for performance cost functions which describe the behavior of a second-order nonlinear control system during an on-off limit cycle. The cost functions are 1) fuel consumption per second (and the associated percent on-time and control pulse width); 2) average error; 3) peak-to-peak, limit-cycle amplitude; and 4) limit-cycle period. Each of these functions is expressed in terms of the amplitudes of the limit-cycle switch states and The results, which are given for a stable and an unstable plant, do not depend upon a specified control law.