Input Shapers against System Parametric Uncertainty

In the genre of residual vibration reduction, Input Shaping is a relatively new feed-forward control strategy. It is accomplished by convolving a sequence of impulses with a desired system command to produce a shaped input which is used to drive the system. In this research, methodologies for designing the impulse sequence for five different schools of input shapers including negative shaper, for a standard second order system are presented. Simulations evaluate their performance both in absence and presence of parametric uncertainties in the system. A conglomerate of three performance measures has been used for analysis of each shaper, namely, peak value, rise time and percentage peak overshoot (PPO). The robustness of each of them is also studied for different level of uncertainty in system dynamics e.g. natural frequency and damping ratio of the system. Semi analytical results show an increase in shaper robustness with increase in impulse length, albeit, with a delayed system response. Observations suggest the shapers to be more robust to variation in plant damping ratio as compared to a similar variation system natural frequency.