Guidance of a moving collocated actuator/sensor for improved control of distributed parameter systems

This paper proposes a scheme for the guidance of a moving collocated sensor/actuator pair for the performance enhancement of a class of spatially distributed processes. It is assumed that a spatially moving source forces the process state to deviate from its equilibrium throughout the spatial domain. Such a configuration minimizes the control effectiveness of a fixed-in-space sensor/actuator pair. To minimize the effects of the moving source on the state regulation, it is assumed that a locally distributed sensor, capable of moving within the spatial domain with a prescribed velocity can also provide locally distributed actuator. Such a pair utilizes locally distributed state information in order to generate the control signal, which takes the form of a locally distributed static output feedback. At a given time interval, the maximum deviation of the spatially localized state from the equilibrium is used to guide the sensor/actuator pair to the next position and at the same time provide a simplified static output feedback controller in order to improve performance. As an extension, a time varying scalar gain is proposed which is updated adaptively, according to the distributed state deviation. Extensive simulation studies applied to a diffusion-advection system are included to verify the effectiveness of a such a moving actuator/sensor pair.