Performance Enhancement of Controlled Diffusion Processes by Moving Actuators

The present research work deals with the systematic development and implementation of a practical algorithm for an actuator activation and control policy through a scheme of moving actuators for systems governed by parabolic partial differential equations (PDEs). Systems of parabolic PDEs typically describe diffusion and other transport processes often encountered in a multitude of industrial applications. Under the proposed algorithmic scheme, one way to view the system under consideration is to assume that it has multiple actuators and it is desired to activate only one such actuator during a given time interval while the remaining actuators remain dormant. The same algorithm can also be applied to a system with a single actuator capable of moving at a priori selected positions within the spatial domain. Standard state feedback controller synthesis methods based on linear matrix inequality-techniques (LMIs) are employed for a finite-dimensional Galerkin approximation of the original distributed parameter system, and the value of an appropriately selected objective function (performance index/functional) is explicitly calculated by solving a location-parameterized Lyapunov matrix equation. On the basis of the aforementioned explicit characterization of the objective function values, a systematic optimization algorithm can be developed that offers a transparent guidance policy and optimal switching rules between the various actuator positions for performance enhancement purposes. An illustrative example with simulation results of an 1-D diffusion process is included to support the paper’s theoretical findings and evaluate the performance-enhancing capabilities of the proposed scheme in a typical industrial process such as the one considered in the present study.

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