Time-optimal output transitions for minimum phase systems: A frequency domain approach to post-actuation

The fundamental minimum-time optimal output transition (OOT) problem is formulated in the frequency domain for systems with minimum phase stable or asymptotically stable transfer functions. The optimal post-actuated control is first solved for in the time-domain. Determination of the optimal post-actuated control is then shown to be equivalent to canceling both the zeros and poles of the system transfer function. Parameterizations of the control are proposed and solved for in closed-form for both large and small displacements of a system transfer function with a first-order zero and rigid-body dynamics. The proposed approach is then applied to a benchmark output tracking problem and an improvement in transition time is demonstrated when compared to the traditional state-to-state transition (SST) approach to determining the minimum-time control.