H∞ Optimal Control of Smart Structures


The design and implementation of control strategies for large, flexible smart structures presents challenging problems. One of these problem areas is the uncertainty of the natural frequencies of the structure. These uncertainties stem from control structure interaction, modelling errors, and parameter variations (such as fuel consumption). They are important because the natural frequencies of flexible structures tend to be lightly damped and closely spaced. Presently, neither the LQG/LTR controller algorithms nor the H∞ controller algorithms can account directly for natural frequency uncertainties and both algorithms suffer drastic performance degradation in the face of these uncertainties. In order to overcome this problem, we developed a new algorithm called H∞ robust control for natural frequency variations (H∞/NF) that includes the knowledge of the natural frequency uncertainty bounds. In addition, we were successful in implementing this algorithm on a flexible smart structure in our laboratory. This smart structure was a cantilever beam that used NiTiNOL shape memory alloy (SMA) actuators. The performance of H∞NF algorithm was compared with the modified LQG/LTR algorithm using a settling time specification. The H∞/NF controller exhibited dramatically reduced sensitivity to natural frequency uncertainty as compared to the modified LQG/LTR controller. An additional problem area when dealing with smart structures is the limited control effort available from actuators. The standard LQG/LTR control algorithm produced controllers that saturated the NiTiNOL actuators used on the test article. To overcome this saturation problem, we used a modified LQG/LTR design algorithm. Because the initial H∞/NF algorithm did not allow the designer to specify available controller effort, we extended the results by including a control effort cost penalty in the H∞/NF algorithm. This algorithm couples a control effort penalty with the H∞/NF algorithm allowing the designer a trade-off between natural frequency sensitivity and maximum controller effort. We successfully implemented the proposed algorithm on a simple cantilever beam test article.


Electrical and Computer Engineering


U.S. Air Force Academy, Grant DAAH 04-93-G-0214

International Standard Serial Number (ISSN)

1996-756X; 0277-786X

Document Type

Article - Conference proceedings

Document Version

Final Version

File Type





© 2024 Society of Photo-optical Instrumentation Engineers, All rights reserved.

Publication Date

01 May 1994