FUEL TIME OPTIMAL-CONTROL OF THE BENCHMARK PROBLEM/

Design of fuel/time optimal control of the benchmark two mass/spring s ystem is addressed in the frequency domain. The optimal control profil e is represented as the output of a time-delay filter, where the ampli tude of the time delayed signals are constrainted to satisfy the contr ol bounds. The time delays of the filter are determined by solving a p arameter optimization problem that minimizes a weighted fuel/time cost function subject to the constraint that the time-delay filter cancel all the poles of the system and the control profile satisfies the rigi d body boundary conditions. It is shown that three control structures exist: a three switch profile corresponding to the time optimal contro l problem that changes to a six-switch profile corresponding to a cost function that includes a small weight on the fuel. As the weight on t he fuel increases beyond a critical value, the control profile changes to a two-switch profile. The value of the critical weight that repres ents the transition of the control profile from a six-switch to a two- switch control profile is determined.