Robust Control of Elastic Drives Through Immersion and Invariance

This paper presents a new robust control method 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 (I&I) approach. First, appropriate mapping functions are derived to convert the actual nonlinear 2MM system into an equivalent reduced order system with rigid dynamics. This reduced order model is used as a target system to design a position controller, which is based on the standard proportional-integral-type control technique. Next, through I&I, the reduced order controller is applied to the nonlinear 2MM system to suppress the torsional vibrations and yield an overdamped response similar to the target system. The control law derivation and stability analysis of the target system are described and discussed. Simulations and experiments using a 2MM drive system are used to validate the proposed control methodology. The performance of the proposed I&I control scheme is also compared with the standard input/output feedback linearization technique.