Finite settling time control of the double integrator using a virtual trap-door absorber

Finite settling time control of the double integrator is considered. The approach taken is to design a compensator based on a virtual lossless absorber which is tuned so that, at some predetermined time, the virtual subsystem possesses all of the system’s energy. At this time the controller is turned off, and the double integrator remains at rest at the origin. This strategy gives the appearance of instantaneously removing all of the system’s energy as if a trap door had been sprung. A practically useful feature of the virtual trap-door absorber is that only position measurement is required. Parameters for the virtual trap-door absorber controller are chosen, and the resulting controller is compared to the classical minimal-time and minimal-energy controllers, which require measurements of both position and velocity.