Spatiotemporal disturbance compensation for nonlinear transport processes via moving actuators

Deals with the development of a framework that allows an integrated actuator activation policy and controller synthesis method to be realized through a scheme of moving actuators for the performance enhancement of nonlinear transport processes in the presence of spatiotemporal disturbance variations. The transport processes of interest are modeled by nonlinear parabolic partial differential equations (PDEs) and are frequently encountered in a multitude of industrial applications. Standard state feedback controller synthesis methods based on linear matrix inequality-techniques (LMIs) are employed for a finite-dimensional Galerkin approximation of the original nonlinear distributed parameter system, and the value of an appropriately selected objective function is explicitly calculated by solving a location-parameterized Lyapunov matrix equation. A static optimization algorithm is developed that offers a guidance policy and optimal switching rules between the various actuator positions for process performance enhancement. An example with simulation results of a transport process modeled through Burger's equation is included, in order to evaluate the performance-enhancing capabilities of the proposed scheme.

1 Introduction

In a modern industrial environment, growing demands for manufacturing efficiency, product quality and process safety necessitate the development of reliable process control and monitoring schemes [8]. The above operational requirements are now increasingly imposed on processes that exhibit inherently nonlinear behavior over a wide range of operating conditions [8]. Specifically, key technological needs in traditional, as well as growth areas such as material processing, nanotechnology and biotechnology have underscored the importance of future research activity directed towards the analysis and control of distributed parameter systems [7], [8], [10], [16], 1[7], [24]. In particular, the critical role of actuator placement in the overall process performance characteristics has been widely recognized as an important design component in many control systems [1], [2], [1]8, [2]0, [2], [1], [2]5, [2]6. Specifically, it is broadly acknowledged that an optimal actuator placement according to a set of pre-specified closed-loop performance optimality criteria, results in minimal energy use while key control objectives can be simultaneously attained [8]. However, the traditional approach to the actuator placement problem has been the selection of actuator locations based on open-loop considerations that ensure that necessary controllability criteria are met [20]. This approach relies on a conceptual “decoupling” of the actuator placement problem from the feedback controller synthesis one, which remained largely unaddressed in the above approaches [20]. Quite recently, research efforts focused on the problem of integrating the aforementioned design stages into a coherent scheme [1], [2], [12], [18]. However, in all these approaches the actuating and sensing devices are permanently mounted on a host structure, cavity or chemical reactor [1], [2], [1]–[2]. While optimal versus non-optimal actuator and/or sensor location yielded improved performance, the effect of the spatioternporal variability of the exogenous inputs was nonetheless ignored in all the above approaches. For example, time-varying disturbances might enter at different sections of the spatial domain at different time intervals, and hence, an actuator closer to the disturbance would certainly have more control authority than an actuator far away from the “local” disturbance [13].