Point-to-Point Positioning of Flexible Structures using a Time Domain LQ Smoothness Constraint

An analytical procedure to implement optimal smoothing of the finite-time control waveform for point-to-point control problem is presented, which minimizes an Optimality constraint consisting of a linear combination of the quadratic norms of its time derivatives. It is shown that the resulting control input is essentially the minimum norm solution augmented to satisfy some additional continuity requirements in the time domain. Application of the proposed technique to finite-time maneuvering of flexible structure is experimentally demonstrated and performances are compared using control torques evaluated based on different orders of the smoothness constraint and those of the truncated plant model.