Performance limitations imposed by actuator constraints

Presented in this paper are the effects of actuator rate and output saturation on the regulating capability of an uncertain, unstable system subjected to an external step disturbance, w(t). The maximum control effort delivered from the actuator is bounded as |u(t)| ≤ u, (1 - e^-rt) when subjected to a saturating step input. The effects are represented as bounds on the allowable disturbance step size which is an explicit function of the actuator limitations, the degree of instability, and initial condition(s). The class of systems addressed are single-input-output (SIO) regulating systems whose unstable parts are i) real and unique, and/or ii) real and repeated. A stabilizability condition derived from a simple Lyapunov type constraint is used to determined the allowable disturbance tolerance.