Synthesis of Controllers for the Active Mass Driver System in the Presence of Uncertainty

The structured singular value ( ) synthesis technique is used to design controllers for the Active Mass Damper (AMD) Benchmark problem. In addition to stated performance objectives, robustness of the controllers to high frequency unmodeled dynamics (the neglected high frequency modes of the evaluation model), modeling error in the actuator dynamics and variations in the rst structural natural frequency and damping value are considered in the design. The resulting controller achieves similar performance levels on the nominal evaluation model and the evaluation model with signi cant changes in its rst natural frequency and damping value. Benchmark Problem: Active Mass Driver The structured singular value ( ) framework is applied to the Active Mass Driver (AMD) benchmark problem describe in references [1, 2]. The objective is to actively control this three-story, single-bay, scale model of a building. A single active mass driver (AMD) actuator, located on the third oor of the structure, is used for control. The base of the structure is mounted to a shake table to simulate earthquake loadings. Six measurements are available for feedback: accelerometers at the base of the structure, on each story, and on the actuator mass and an LVDT displacement sensor attached to the actuator. The objective is to design a discrete-time feedback compensator that minimizes ten performance objectives. Five of the performance objectives correspond to minimizing rms errors and the other ve objectives correspond to minimizing maximum displacements, accelerations and voltages. Two linear time-invariant