Numerical investigation on optimal actuator/sensor location of parabolic PDEs

The objective of this investigation is to provide a methodology for obtaining the optimal location of actuators and sensors in systems (thermal/fluids/material processing) whose dynamics are described by parabolic partial differential equations. The method to be employed for this optimal actuator/sensor location is based on optimal/robust control. First, an optimal state feedback gain, parametrized by the unknown actuator locations, is found by minimizing an appropriately chosen (control) performance index. Minimization of the optimal value of the quadratic cost is then performed with respect to (spatial) locations in order to attain the minimum of this location-parametrization performance index. Its minimum then yields the optimal actuator location. The incorporation of partial measurements, which introduces the sensor location(s) into the control problem, is achieved by forcing the resulting system to be a dissipative one, i.e. have a strictly positive real transfer function. This is done so that when either a simple static output feedback, even with a non-optimal static gain, or a sector-bounded nonlinear output feedback, would guarantee closed loop stability. Numerical examples with simulation results are presented to support this investigation