Bang-Bang Control of a Floating Oscillator

The objective of this paper is to use a simple bang-bang control law to create rest-to-rest command inputs for a floating oscillator. This work is motivated by previous work on bang-bang control for systems with two integrators. The advantage of the proposed bang-bang controller is its simplicity and robustness. The bangbang control signal switches between a maximum and minimum value once over the duration of the control signal. The amplitude and duration are computed from the desired move distance and the system parameters. The robustness of the proposed controller to model uncertainty is measured by the percent overshoot in the response once the system has reached the desired move distance. For the proposed controller, numerical simulations of the floating oscillator demonstrate that the robustness improves as the duration of the bang-bang command signal increases and that, given a fixed duration, a further improvement in robustness is obtained over a limited but significant range of uncertainty by using multiple switches within the duration of the bang-bang signal.