Adaptive robust control of flexible systems

In this paper we combine least squares identification with H_∞-control to provide a methodical approach to adaptive robust control. We use periodic resetting of the covariance matrix and update the control design less frequently than the sampling rate for the controller. This approach gives a closed-loop system with bounded l_∞ and l₂ gain when the model mismatch is small in the frequency range where the control gain is large. We apply the method to a model of the Martin Marietta flexible beam. A frequency domain interpretation of the estimator cost function is used to design the prefilter for the identifier. A post-projection scheme using a priori knowledge of the antiresonant damping is used to overcome poor identification of the antiresonances. Excitation ensures that the parameter estimator is stable and an adaptive stopping technique turns the estimator off once the parameter estimates have converged