Master's defence | Arman Tavakoli, H2-Optimal Sensor Location | Applied Mathematics

M3-2134

Candidate

Arman Tavakoli, Applied Math, University of Waterloo

Title

H₂-Optimal Sensor Location

Abstract

Optimal sensor placement is an important problem with many applications such as placing thermostats in rooms, installing pressure sensors in chemical columns or attaching vibration detection devices to structures. Frequently, this problem is encountered while noise is present; therefore, one approach to the problem is to combine it with a control strategy designed for systems that have exogenous disturbing inputs, called H₂-optimal control. In this work, the optimal sensor location and the H₂-optimal control problems are explained independently and then combined into one problem called the H₂-optimal sensor location.

The problem is examined for the Euler-Bernoulli equation on a one-dimensional beam and the heat equation in a two-dimensional room. Optimal sensor location is calculated numerically for both models, and multiple scenarios are considered where the location of the disturbance and the actuator are varied. The effects of different model parameters such as the weight of the state and the disturbance are investigated.

For a system that is heavily weighted by the disturbance, it is found that the optimal sensor location tends to collocate with the disturbance. A larger weight for the state variable tends to move the optimal sensor location towards the actuator.