Selecting the level of actuator saturation for small performance degradation of linear designs

This paper addresses the problem of selecting an actuator so that the performance degradation due to its saturation is sufficiently small. The following scenario is considered. The plant is assumed to be linear and the problem of colored noise disturbance rejection is addressed. The controller is designed using a linear technique (for instance, PID, LQG, etc). This controller is to be implemented with a saturating actuator. How large should the level of saturation be so that the performance will not degrade too much? We provide an answer to this question (in terms of the Nyquist plot of the loop gain) for any desired level of degradation. In addition, the following rule-of-thumb is established: To guarantee less than 10% of performance degradation, the level of actuator saturation should be at least twice larger than the standard deviation of the signal at the controller output in linear design.