Concurrent design of unity-magnitude input shapers and proportional-derivative feedback controllers

Vibration continues to be a problem for many systems, resulting in reductions in safety and efficiency. Residual vibration in flexible structures can be suppressed by generating properly filtered or shaped commands. One type of command generation, called input shaping, is implemented by convolving a sequence of impulses with any desired command. This paper presents a concurrent controller design method that combines PD-feedback control and Unity Magnitude input shaping. Performance limits on allowable overshoot, residual vibration, and peak force from commanded motion are included in the design process. The proposed method also takes into account the effects of disturbances. Example responses are presented and compared to a Linear Quadratic Regulator. The results show that the proposed method leads to a faster response than the LQR method. However, the LQR method outperforms in rejection of disturbances.