Optimized trapezoidal acceleration profiles for minimum settling time of the load velocity

This paper deals with a method for generating symmetrical trapezoidal acceleration profiles for the motor of a vibrating system in rest-to-velocity motion. The aim was to significantly reduce the acceleration time and residual load vibration of lightly damped systems. Under undamped conditions, the analytical values of the jerk time are found to be in relation to the estimated natural frequency and the minimum value of the acceleration time is provided, also taking into account a limit value for motor acceleration. The analysis of the sensitive curves allows the designer to understand the magnitude of the residual vibration generated by an incorrect estimate of the natural frequency. Numerical simulations, with a closed-chain controlled motor and a zero or very small structural damping coefficient of the oscillating system, confirm the validity of the proposed method.