Fuel/Time Optimal Control
Introduction
There are numerous applications where the a tradeoff between the maneuver time and the fuel consumed is a criterion for the selection of an optimal control profile. Space robots, hard disk drives for laptop computers are some such examples. This work address the design of fuel/time optimal controllers subject to control constraints.
In this article, the fuel/time optimal control of the Floating Oscillator benchmark problem is investigated.
A Java Applet is provided to illustrate the spectrum of optimal control profiles.
An optimal control profile which minimizes the cost function
subject to the state equation and control constraints
and the geometric boundary conditions
.
needs to be designed.
In this section, the control design has been carried out for an undamped Floating Oscillator, as
shown in Figure 1. Some of the results are presented in this section, a more detailed development
and analysis of results can be found in the materials cited in the section on
references shown at the bottom
of this page.
The parameters of the Floating Oscillator, i. e. the masses and the spring stiffness, are all set to unity for the numerical results presented in this section. The maneuver under consideration will result in unit displacement of the Center of Gravity. Figure 2 shows the effect of the penalty W on the control profile.
Below is an Applet which illustrates the different control profiles. The spring stiffness can be chosen by using the rightmost drop-down list. The other drop-down list allows the selection of the control profile. The Start button starts the simulation. The Stop button can be used to stop the simulation at any point in time. Before selecting a new control profile or spring stiffness, the simulation must have stopped.
The work presented in this article has been described in more detail in the following publication:
- Singh, T. 1995. Fuel/Time Optimal Control of the Benchmark Problem. Journal of Guidance, Control and Dynamics, 18(6), 1225-1231.
- Hartmann, R., & Singh, T. 1999. Fuel/Time Optimal Control of Flexible Structures: A Frequency Domain Approach. Journal of Vibration and Control, 5(5), 795-817.
- Liu, S-W., & Singh, T. 1997. Fuel/Time Optimal Spacecraft Maneuvers. Journal of Guidance, Control and Dynamics, 19(2), 394-397.