Reduced Order Robust Controllers for an Experimental Flexible Grid

The design and implementation of control strategies for large, flexible structures presents challenging problems. One of the difficulties in controller design arises from the incorrect knowledge of the structural parameters. This paper describes a procedure for designing and actual implementation of reduced order robust controllers for active vibration control on an experimental flexible grid structure. The experimental structure consists of a 5¿ × 5¿ grid made up of 2" wide, 1/8" thick aluminum strips. The grid hangs vertically down, being cantilevered at the top to a large I-beam anchored to a cinder block wall. The grid structure is represented by 75 degrees of freedom, finite element model and the controller uses three piezoelectric accelerometer sensors to command three non-collocated DC motor torquers. The modified balance-truncation model reduction method is used to derve a control synthesis model. These reduced order models preserve stability, controllability, observability and have a good frequency response match at low frequences. A 10-mode mathematical representation of the experimental grid structure has non-minimal phase zeros. The effects of non-minimum phase zeros on the performance of a closed loop LOG/LTR controller are investigated. The reduced order controllers are implemented on the structure using an ISI Max 100 computer. Experimental closed loop performance of the grid is obtained for various parameter variatons.