Preshaping command inputs for explicit fractional derivative systems: Application to CRONE control

Shaping command input or preshaping is used for reducing system vibration in motion control. Desired systems inputs are altered so that the system finishes the requested move without residual vibration. This technique, developed by N.C. Singer and W.P. Seering, is used for example in the aerospace field, in particular in flexible structure control. This paper presents the extension of this method for explicit fractional derivative systems (generalized derivative systems). A robustness study is then presented, and preshaping is applied to improve second generation CRONE control (explicit fractional derivative transfer function) response time. Shaper coefficients are calculated in real time using properties of explicit fractional derivative systems and results in simulation are given.

1 Introduction

Developing the control of a process that carries out a task results from two stages of design: control synthesis and path planning. Path planning is divided into two parts: path generation and motion control. By means of command inputs, path planning determines how to follow the path depending on the desired performances and physical constraints of the actuators. It is then necessary to determine an algorithm able to calculate command inputs for feedback control systems, while minimising the response time as well as the residual oscillations.