A robust power absorbing H∞ controller design for flexible structures

An H^∞ mixed sensitivity problem is formulated for the control of uncertain large flexible structures. The plant model is based on the driving point mobility (inverse of the mechanical impedance) for the structure at the junction where the collocated dual actuators and sensors meet the structure. One way to obtain an expression for the point mobility for the structure is by analyzing the wave mode dynamics along its structural members. In the presence of bounded power propagating disturbances we seek a stabilizing controller to minimize their effect in an H^∞ optimal sense. Specifically, we show the minimization of the power of the reflected and transmitted waves at the control junction is equivalent to the minimization of the H^∞-norm of the weighted system sensitivity function together with a weighted output complementary sensitivity function. A weighted constraint on the control input is added in order to yield a robustly stable closed-loop system in the face of additive plant uncertainties. The obtained controller is verified to absorb power from the structure and hence adds overall damping to it.