Discrete time point-to-point control of flexible structures

The primary objective of this work is to investigate linear time invariant systems undergoing rest to rest maneuvers in a finite time using the discrete time domain approach. Using a given sampling period, the governing equations of linear systems are first discretized into the equivalent discrete time domain representation. To decouple the resulting difference equations, the system equations are converted into the Jordan Canonical Form by using a similarity transformation. The decoupled Jordan Canonical equations are converted to a set of algebraic input/output equations with embedded end-points conditions, by a recursive approach. The optimal or sub-optimal control profiles required to achieve the desired maneuver can be easily calculated through basic manipulation. The sensitivity of the design to the uncertainties in the system parameters is reduced by introducing sensitivity equations, and the design is found to be robust to these uncertainties.