Reduced order robust controllers for an experimental flexible grid

A procedure for the design and implementation of reduced-order robust controllers for active vibration control on an experimental flexible grid structure is presented. The experimental structure consists of a 5-ft × 5-ft grid made of 2-in-wide, 1/8-in-thick aluminum strips. The grid hangs vertically, being cantilevered at the top to a large T-beam anchored to a cinder block wall. The grid structure is represented by a 75-degree-of-freedom finite-element model, and the controller uses three piezoelectric accelerometer sensors to command three noncollocated DC motor torquers. The modified balance-truncation model-reduction method is used to derive a control synthesis model. These reduced-order models preserve stabiilty, controllability, and observability, and have a good frequency response match at low frequencies. A 10-mode mathematical representation of the experimental grid structure has non-minimum-phase zeros. The effects of non-minimum-phase zeros on the performance of a closed-loop LQG/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 variations.