Robust sensor location optimization in distributed parameter systems using functional observers

The focus of this work is to provide an insight into the judicious positioning of either a sensor device or a collocated actuator/sensor pair in SISO transport systems represented by parabolic differential equations. The optimal, with respect to a given measure, placement of a sensor device has a significant effect on the overall performance of a controller with a considerable contribution in energy reduction. This is more evident in the case of a functional observer, i.e. an observer that estimates not the entire state, but a weighted product of the state. When a functional observer is used to estimate the (inner) product of the state with a feedback gain, the computational demand is significantly reduced since now only a scalar quantity is estimated as opposed to a high-dimensional observer required in an observer-based controller. The efficiency and performance of the functional observer is additionally enhanced when the sensor location is embedded into the control design. By incorporating the effects of exogenous inputs that enter the system via a given distribution vector, a sensor location-parameterized measure is considered and static optimization allows one to optimize both the sensor location and the performance of the resulting functional observer-based controller. A case study of a diffusion process is presented where the performance-enhancing capabilities of the proposed location optimization and control scheme is evaluated through detailed simulation studies.