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Fei Liu | Applied Mathematics, University of Waterloo
Optimal Locations of Sensors and Actuators for Control of a Pedestrian Bridge
This thesis studies the optimal locations and compares the performances of the non-collocated and the collocated sensor/actuator designed controllers 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 collocated sensor/actuator designed controllers’ optimal locations and comparisons of the performances at their optimal locations are studied on a simplified system model. The simplified system model with a Gaussian temporally distributed disturbance is approximated using the Modal approximation. The linear-quadratic Gaussian (LQG) controller design that achieves the LQ performance objective for controlling initial conditions response and Gaussian disturbance response is applied to this preliminary problem. Numerical implementation of stochastic 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 from using 3 different state weights. The realistic bridge model is approximated using the Hermite basis finite element approximation. The -controller is reviewed and applied. The actuator device dynamics and its high frequency noise, a reliable pedestrian loading, and a low pass filter are included in this model to consider more realistic disturbances. Results show that the differences in the performances of the non-collocated and collocated sensor/actuator controllers at their optimal locations are non-significant. Moreover, as the state weight increases, the difference in the two designs’ optimal performance index values vanishes, and thus the differences in their performances vanish.