Actuator Selection Based on a Reduced-Order Model Using Balanced Proper Orthogonal Decomposition with Input-Output Projection

Actuator placement optimization based on a reduced-order model is essential for controlling a high-dimensional system in real time. This paper discusses actuator placement in an unstable high-dimensional system based on a reduced-order model obtained by BPOD with input–output projection. Actuator locations in a linearized Ginzburg–Landau model are optimized with three objective functions based on a Riccati equation, a controllability Gramian, and an impulse response matrix. Further, the computation time for actuator selection and the resulting LQR performance are evaluated. The LQR performance is basically high when actuators are placed based on the Riccati equation or the impulse response matrix. The computation time of the method based on the impulse response matrix is much smaller than that of the other two methods. Thus, the method based on the impulse response matrix seems to have more advantages than the other two methods in terms of optimizing the actuator locations of the analyzed model. Moreover, it seems to be beneficial to place actuators with a low-dimensional model using this method.