Robustness analysis applied to substructure controller synthesis

The control design of a six-bay truss structure is a p proached by a Substructure Control Synthesis (SCS) method, and a qualitative measure of robustness for such a controller is offered. The structural model consists of reduced plane frame elements assembled into a six-bay truss. The use of the reduced plane frame elements results in a consistent mass matrix for the truss. The controller is obtained by dividing the truss into two independent substructures sharing interface displacement coordinates. The controller is obtained by designing a controller for each substructure via an LQG method, and subsequently assembling the gains of the substructure controllers with a coupling matrix that enforces the matching of interface displacement coordinates. Robustness of the controller obtained with the SCS method is then evaluated by comparing it to a controller obtained by applying the LQG method directly to the whole truss. This is done by comparing singular-value Bode plots for various transfer functions of the closed-loop system using the two controllers. The controller obtained by the SCS method results in a less robust closed-loop system than the controller obtained directly. This lack of robustness may be acceptable, and the results merely indicate where the lack of robustness is more significant and how it may be related to the substructure controller gains.