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