Decentralized Vibration and Shape Control of Structures with Colocated Sensors and Actuators

This paper introduces a decentralized shape and vibration controller for structures with large and potentially unknown system order, model-parameter uncertainty, and unknown disturbances. Controller implementation utilizes distributed, colocated, and independent actuator-sensor pairs. Controller design requires knowledge of the relative degrees of the actuator and sensor dynamics and upper bounds on the diagonal elements of system's high-frequency gain matrix. Closed-loop performance is determined by a parameter gain, which can be viewed as the cutoff frequency of a low-pass filter. For sufficiently large parameter gain, the closed-loop performance is arbitrarily small. Numerical examples are used to demonstrate the application and effectiveness of the decentralized controller, and we present experimental results for a setup consisting of a cantilever beam with piezoelectric actuators and strain-gauge sensors.