Robust Control of Elastic Drive Systems Using The Immersion and Invariance Methodology

Abstract

This thesis is divided into three main parts. The first part 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. The second part of the thesis presents the design of a nonlinear reduced order observer to estimate the load side position and load side speed of an elastic drive system. A reduced order observer is designed using the notion of invariant manifold. First, a manifold is defined in terms of the error dynamics, and then mapping functions are chosen in such a way that the error dynamics become asymptotically stable at the origin. Asymptotic stability of the error dynamics at the origin is proved. Simulation and experimental results are shown to validate the proposed methodology. Then the observer is combined with an I&I position controller and the results are validated through simulations and real time experiments. In the third part of this thesis, the input/output feedback linearization technique is explained and implemented on the same system. External and internal dynamics are derived for the 2MM. Feedback linearization gains are designed for external linear dynamics. The stability of the zero dynamics is also derived. Then, the I&I methodology, input/output feedback linearization, and PID position controllers are compared on the basis of their transient step response and robustness to external disturbance and parameter variations.