Multivariable vibration control of a coupled flexible structure using QFT

Quantitative feedback theory (QFT) is a valuable control strategy for multivariable systems that contain parametric uncertainty. This paper uses multivariable quantitative feedback theory (QFT) to design an internal model reference loop (IMRL) controller. The QFT IMRL method allows a single controller to be designed for large time-invariant parameter variations by forcing the system transfer function matrix to be diagonally dominant. The controller architecture causes the coupled system to behave like the uncoupled system with proper choice of reference model. The design method is extended to discrete time by using a pseudo-continuous time (PCT) approach. The control application is extended to robust disturbance rejection rather than robust tracking by designing an outer-loop controller to reduce the sensitivity of each diagonal element. The structure to be controlled is a two degree of freedom flexible beam with variable coupling. The result of the control method is one single discrete decentralized controller able to robustly reject disturbances with nearly identical performance for a large variation in coupling and inertia.