Practical Design and Verification of LQG Controllers as Applied to Active Structures

Abstract

Many mechanical engineers find difficulty in applying LQG controllers to active mechanical structures. Answers to frequently asked questions are provided here, describing in detail the procedure as applied to a ca. 2 m x 0.5 m panel where vibrations are to be actively damped. This application was chosen because of the number of difficulties it can throw light on, while remaining simple enough to be understood with common sense. From another point of view, LQG controllers, as applied to mechanical structures with a theoretical infinity of degrees of freedom, have a bad reputation concerning stability. However, mechanical understanding of the reasons for the behavior helps to find very practical solutions. After reviewing the most important equation sets, a method for designing an LQG-controller is given. It mainly includes the design of the observer filter and the design of a feedback gain matrix considering the ideal knowledge of the system state vector. The test bed and its instrumentation is described. Physical measurements and computations are outlined as well as the integration of both theoretical and practical data into the same procedure aiming to determine system parameters. In the first step, only bending is considered. The experimental behavior shows a spillover due to bending modes not considered. Two methods are proposed in order to suppress this spillover. The first considers the sensor signal given by the uncontrolled dynamics as a noise. The second improves the estimation of the structural state without changing the controller gains. Both have advantages and disadvantages that are outlined. Finally, torsion is included in order to improve the behavior.