Designing unity magnitude input shaping by using PWM technique

Abstract

This paper proposes a method for reducing vibrations in flexible systems by using the input shaping. A new input shaper technique based on Pulse Width Modulation (PWM) is used to shape the input. Since unity magnitude (UM) input shaping is easy to implement and provides less control duration, it has been preferred for many application areas. An analytical solution to time locations of the UM shaper requires very complex mathematical expressions due to involving in dependent constraint equations. This paper presents a simple PWM based input shaping method. The proposed technique allows designing UM shapers without analytical solution especially for the shapers having higher order impulse sequence. The method requires only the estimated value of system natural frequency and damping ratio. Desired numbers of impulses can be obtained by comparing reference signal amplitude and carrier wave frequency of a PWM. Analysis and experimental results demonstrate the effectiveness of the proposed method.