Vibration suppression in elastic drive systems using the immersion and invariance methodology

This paper presents a new robust control methodology to suppress the torsional vibrations in flexible drive systems. The position control of a nonlinear Two-Mass-Model system (2MM) is designed using the Immersion and Invariance approach. First, appropriate mapping functions are derived to convert the total nonlinear 2MM system into an equivalent reduced order system with rigid dynamics. This reduced order system is used as a target system to design a position controller, which is based on the standard PI type control technique. Next through immersion and invariance, the reduced order controller is applied to the nonlinear 2MM system to suppress the torsional vibrations and yield an over-damped response similar to the target system. The control law derivation and stability analysis of the target system are described and discussed. Simulation and experiments using a 2MM drive system are used to validate the proposed control methodology.