This study proposes an approach to synthesize a three-impulse sequence input shaper with a negative impulse, known as Unity Magnitude (UM) shaper. The corresponding analytic model has been already achieved for undamped and low-damped systems. In this paper, the analytic design of UM shaper is demonstrated for the generalized case of damped systems for both types: integer and fractional orders. Hence, the UM shaper model has been designed for second-order systems with damped dynamics, associating a graphical fitting and an analytical procedure; then, it has been extended to explicit fractional derivative systems. Moreover, the feasibility and the effectiveness of the proposed on-off profile prefilter applied on a second-generation controller have been substantiated by experimental results on an instrumented DC motor bench.
The efficiency of polycentric development strategies in the context of economic crisis. Case study - the development of Southwest Oltenia region - Romania