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.