Optimal Locations of Sensors and Actuators for Control of a Pedestrian Bridge

Abstract

Lightweight structures have been increasing in popularity in structural designs. However, they are more prone to disturbances. Therefore, a controller device can be placed on the structure to control the excessive vibrations. Past works have revealed that there exist corresponding optimal locations on the structure for placing the crucial parts of the controller device, the sensor and the actuator, that result in optimal performance of the controller. The physically practical collocated sensor/actuator design controller device can be moved around and deployed to different structures. The ideally more optimal non-collocated sensor/actuator design allows the sensor and the actuator to be placed separately in their corresponding optimal locations, but it may be physically impractical to implement. Hence, this motivates the study of the optimal locations, and to compare the performances of the non-collocated and the collocated sensor/actuator designs for a lightweight aluminum pedestrian bridge subject to pedestrian walking disturbances. The structure is modelled using the Euler-Bernoulli beam theory, and modal and Hermite basis finite element approximations are applied. The linear-quadratic performance objective control (LQ control) is reviewed and applied. Since approximations are applied, a mapping for the state energy weight in the LQ control performance objective functional from the original functional space to a generic approximation functional space is presented in this thesis.

In the preliminary problem in this thesis, influences of the state weights and the disturbances' spatial distributions on the non-collocated and the collocated sensor/actuator designed linear-quadratic Gaussian (LQG) controllers' optimal locations and comparisons of the performances at their optimal locations are studied on a simplified system model with a Gaussian temporally distributed disturbance. Numerical implementation of disturbances is presented, and numerical complications are discussed and provided with solutions.

The comparisons of the non-collocated and collocated sensor/actuator designs for a more realistic bridge model are made using three different state weights. The realistic bridge model is approximated using the Hermite basis finite element approximation. The H2-controller is reviewed and applied. The actuator device dynamics and its noise, a reliable pedestrian loading, and a low pass filter are included in this model to consider more realistic disturbances. The results suggest that the physically more practical collocated sensor/actuator design can achieve similar performances as the ideally more optimal non-collocated sensor/actuator design at their corresponding optimal locations.