For a large class of second-order nonlinear systems subjected to broad band random disturbances, average energy and power formulas may be found which permit a strong qualitative and sometimes quantitative understanding of averago system performance to be gained in spite of a lack of precise analytical results. In this paper, these formulas am used to discuss the problem of optimization of servomechanisms in which forces are limited by hard saturation and external disturbances are not negligible. Of particular interest, is the average response of time optimal switched systems when disturbances are present since there is a strong temptation to assume that if a feedback control law can be found which results in a time optimal switched system, the system will automatically use full output efficiency to counteract external disturbances or to follow arbitrary commands. We show that this is not always true. This is important in practice since control systems in general rarely are celled upon to change the state of a system in the presence of no external disturbances. Normally, external disturbances, often random in nature, do exist and the changes in the desired state will not occur in a stepwise fashion. In such a situation, there is no reason why an "optimum" switched system should perform very well.
Average Power Flow to a Class of Second-Order Systems
Consider, the equation m87) + 8(T) = f(T) (1) *This research w&s supported in part by Ihs USAF through the Al?OSkI of ARDC under contruct No. AF 49(638)-1314.