Optimal Location of Sensors and Actuators on the Circular Membrane

The paper considers the problem of sensor and actuator placement for plates with circular geometry, which is described by the circular membrane distributed parameter system. The criterion for computing the optimal location is based on the system energy distribution, presented by system Gramians. The main effort to obtain this location relies on the Gramians computation. Explicit formulas for deriving the Gramians are presented by using the principle of time space separation in obtaining the solution of the wave equation. Criterion based on system energy for optimal placement is also developed.