Adaptive H∞ control with application to systems with structural flexibility

• Published in: IEEE transactions on automatic control Vol. 42; no. 10; pp. 1358 - 1369
• Main Authors: KELLY, J. H, YDSTIE, B. E
• Format: Journal Article
• Language: English
• Published: New York, NY Institute of Electrical and Electronics Engineers 01.10.1997
• Subjects: Adaptative systems; Applied sciences; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Robotics; Robust control; Stability; Least squares method; Flexible structure; H infinite control; Frequency domain method; SISO system; System identification; Adaptive control; Beam(mechanics); Robotics; Manipulator
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/9.633825

We develop a robust adaptive control algorithm using a combination of H(infinity) design and system identification. We derive frequency-dependent bounds for the tolerated unmodeled dynamics and show that the approach gives a closed-loop system with bounded l(infinity) and l2 gain when the model mismatch is small in the frequency range where the control gain is large. Our application focus is systems with structural flexibility. We present a parameter estimation algorithm that uses constrained least squares with prefiltering to overcome the problem of identifying lightly damped antiresonances. The estimation and control design are executed at a low frequency and only when parameter updating is needed. This allows us to apply computationally expensive control design and signal processing algorithms. It also eliminates many of the problems of earlier adaptive controllers by turning off the estimator. We show results from the application of adaptive H(infinity) control to a high-fidelity model of the Martin Marietta flexible beam testbed. (Author)