Incorporating spatial frequency weighting and frequency domain methods in integrated actuator and controller design for a class of parabolic partial differential equations

The present work re-examines the problem of actuator selection for a class of distributed parameter systems within the context of spatial frequencies. The proposed location optimization is viewed within the prism of spatial frequency weighting of a closed loop performance measure. By the proper weights in the Linear Quadratic Regulator parameters, that incorporate the spatial regions where the state is more important, and hence to be regulated to zero faster than at other regions of the spatial domain, an integrated actuator location and controller design is proposed. The resulting optimization measure is taken as the location-parameterized LQR optimal cost. Additional robustness with respect to the spatial distribution of disturbances is subsequently attained via the use of the H₂ norm of the closed loop transfer function and the location optimization measure. The applicability of the proposed scheme is demonstrated by extensive simulation studies.