Optimal control using state dependent riccati equation (SDRE) for a flexible cable transporter system with arbitrarily varying lengths

This paper demonstrates a good application of SDRE technology to propose optimal controllers for a flexible transporter system with arbitrarily varying lengths. A model for a flexible cable transporter system with varying cable lengths is developed using Hamilton´s principle. Galerkin´s method is applied to transform the infinite dimensional system into a set of finite dimensional ordinary differential equations (ODEs) with state-dependent coefficients. Based on this approximate finite dimensional model, a stable optimal controller was proposed based on the SDRE techniques. To ensure the stability with unmodeled dynamics due to the neglecting higher modes, H _infin robust method is used with unmodeled dynamics considered as additive uncertainty. The optimal controller guarantees the asymptotic stability of the closed-loop system and effectively suppresses the longitudinal vibration of cables at the same time. The validity of the proposed controller is verified by numerical simulation