Design of robust controllers for smrt structural systems with structured uncertainties

摘要

Effective integration of sensors, actuators and controllers with the structures is key to the success of smart structures. This concept has been manifested in numerous applications of smart structures in the areas such as civil, aerospace and automotive engineering. Control systems to be integrated with the structure is of paramount importance for ensuring the perormance requirements in the presence of modal parameter variations, modeling errors and control effort constraints. The primary uncertainty associated with smart structural systems us the natural frequency variations. Linear Matrix Inequalities (LMIs) can be utilized to incorporate the real parameter uncertainty due to parameter variations and contol input limits in the controller design. One of the challenges in the design of such controllers is the conservatism due to over bounding effect from the multiple constraints. Additional conservation can also come from the approximation of the real parameteric uncertainty due to modal parameter variations as sector bounded nonlinear, time varying or complex valued uncertainty. Using the traditional modal parameter variations as sector bounded nonlinear, time varying or complex valued uncertainty. Using the traditional robustness analysis methods such as small gain theorem in the controller design will result in conservative designs leading to poor performance. In this paper, we present a controller synthesis procedure based on Popov stability results for reducing the conservatism in the design. Robust controllers are deisned for real-parametric uncertainty arising from natural frequency variations in the presence of control input limits. Maximum possible attenuation in the structural response due to finite energy disturbances is also achieved. Trade-off between the robustness versus the control input limit is discussed. The design produce is applied on a smart structural test article and the results are presented.