TYPICAL SECTION PROBLEMS FOR STRUCTURAL CONTROL APPLICATIONS

Two low order problems are studied which capture some of the important fundamental physics associated with the control of structures. The or der of the problems is kept low to allow the derivation of a closed-fo rm solution. This identifies the dependency of the solution on the bas ic parameters of the problem. These two problems derive the optimal H- 2 and H-infinity control for a spring/mass system described by a secon d order, ordinary differential equation. The H-2 solution is compared with the closed-form H-2 solution to the optimal regulator for an infi nite rod and beam whose behaviors are described by second order, parti al differential equations. This comparison identifies the analogies be tween the typical section problem and a simple structural control prob lem. The optimal control solutions for the H-2 and H-infinity problems are expanded upon by optimizing passive parameters. This reduces tota l closed-loop cost and is analogous to a control/structure optimizatio n problem. It is found that certain levels of finite passive damping a nd stiffness are desirable even if they are available at no cost in th e H-2 problem, and that additional stiffness (any amount) and damping (up to zeta = 1/root 2) enhances performance in the H-infinity problem . It is shown that while the structure and control must be designed si multaneously to optimize an H-2 performance metric, sequential design will work in some cases which use an H-infinity performance metric. Th ese simple problems reveal important properties of more complex struct ural control problems.