H-Infinity controller design for structural damping

This paper describes a multivariable controller design procedure that uses mixed-sensitivity H-infinity control theory. The design procedure is based on the assumption that structural noise can be modeled as entering a state-space system through a random input matrix. The design process starts with a full-order flexible state-space model that undergoes a frequency-weighted balanced truncation to obtain a reduced-order model with excellent low frequency matching. Weighting functions are then created to specify the desired frequency range for disturbance rejection and controller bandwidth. A structural noise input matrix is also designed to identify system modes where maximal damping is desired. An augmented plant is then assembled using the reduced-order model, weighting functions and structural noise input matrix to create a mixed-sensitivity configuration. A state-space controller is then realized using an H-infinity design algorithm. A two-input, three-output, doubly cantilevered beam system provides a design example. A 174-order, discrete-time, state-space model of the cantilevered beam system was used to generate a reduced 40-order model. A 55-order Hinfinity controller was then designed with a controller bandwidth of approximately 300 Hz. This non-square modern controller uses feedback signals from two piezoelectric sensors, each collocated with one of two piezoelectric actuators, and one highly non-collocated accelerometer. The two piezoelectric actuators provide the control actuation. Frequency analysis and time-domain simulations are utilized to demonstrate the damping performance.