Fuel/Time Optimal Control of the Benchmark Problem


Singh, T.


Journal of Guidance, Control, and Dynamics, 18(6), 1225-1231, 1995.


Design of Fuel/Time optimal control of the benchmark Two-Mass/Spring system is addressed in the frequency domain. The optimal control profile is represented as the output of a time-delay filter, where the amplitude of the time-delayed signals are constrainted to satisfy the control bounds. The time-delays of the filter are determined by solving a parameter optimization problem which 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 rigid body boundary conditions. It is shown that three control structures exist. A three switch profile corresponding to the time-optimal control problem which changes to a six switch profile corresponding to a cost function that includes a small weight on the fuel. As the weight on the fuel increases beyond a critical value, the control profile changes to a two switch profile. The value of the critical weight that represents the transition of the control profile from a 6 switch to a 2 switch control profile is determined.

   Author = {T. Singh},
   Journal = {Journal of Guidance, Control and Dynamics},
   Month = {Nov.},
   Pages = {1225-1231},
   Title = {Fuel/Time Optimal Control of the Benchmark Problem},
   Volume = {18},
   Number = {6},
   Year = {1995}