Direct connection between time-domain performance and frequency-domain characteristics

Presented are the relationships between the transient response characteristics of a closed-loop system due to a step input and the frequency response characteristics which influence this response. The class of transfer functions addressed include those which are RH₂. The relationships developed are for the problem: Given: Y(s) = H(s)R(s) where H(s) ε RH₂ and R(s) is ys. Find: The relationship ∥y(t)∥_∞ ≤ Λy ∥H (jω)∥_∞ where the scaling factor Λ is a function of the frequency-domain characteristics of H(s). These relationships are useful for feedback control in that hard time-domain constraints can be enforced as amplitude and phase conditions on the open-loop transfer function. Two applications using these relationships are developed. The first application demonstrates controller design for an actuator saturation constraint. The second application is the development of a performance prediction technique for minimum phase, stable regulating systems.