A Practical Approach to Reducing LMI-Based Stability Tests for Large-Scale Nonlinear Motion Control Systems

This paper addresses stability analysis of industrial high-precision nonlinear motion control systems using linear matrix inequalities (LMIs). Large-order state-space models required for accurate system representation can lead to computational challenges when solving the LMIs numerically. Using established tools from robust control theory, we present an approach that overcomes these limitations by using a low-order system approximation and treating the discrepancy between the approximation and the true system as an uncertainty. This uncertainty will be modeled in the frequency-domain. Stability for the low-order model is ensured through solving LMI conditions. Stability for the true system is guaranteed with an additional small-gain argument. The approach is demonstrated through a numerical example and an industrial case study on a lithography machine.