Optimal actuator placement for controlling concentration profiles via process tomography

Abstract

In this article, the optimal control of a chemical plant driven by an inverse problem is considered. More specifically, the problem of optimal actuator placement when controlling the concentration of a target substance in rapidly moving fluid is investigated. In this example, the actuators are injectors through which strong concentrate is injected into the fluid in order to obtain a desired concentration profile. The target substance is assumed to obey the stochastic convection-diffusion model and the process is monitored with electrical impedance tomography, the inverse problem of which is notoriously ill-posed even under stationary conditions. The associated reconstruction problem is formulated as a state estimation problem and is intertwined with the determination of the optimal time-varying controls. The model-based linear quadratic Gaussian control strategy is used in the determination of the control inputs. The controller settings affect both the overall controller capabilities per se and the performance of the controller via the embedded state estimation procedure. Although it is obvious that proper actuator setting can have a major impact on the control performance of the system, the optimisation has seldom been carried out over the entire controller chain which includes also the state estimation procedure. When the observation modality exhibits ill-posed characteristics, the state estimates may be rendered useless and the controls far from optimal. The studied case shows that the actuator setting affects the state estimation accuracy and the controller quality significantly.