Frequency domain analysis and robust control design for an ideal flexible beam

We study the problem of designing a feedback controller for a highly flexible Euler-Bernoulli beam using a distributed-parameter H^∞-method. Employing skew Toeplitz theory, we derive the H^∞-optimal controller for a weighted mixed sensitivity design for the beam. Based on the structure of the optimal controller we obtain suboptimal, finite-dimensional, linear, time-invariant controllers. With this approach we are able to include the added difficulties of a pure time delay and a noncollocated actuator/sensor pair directly into the design process.