Synthesis of locally lumped controls for membrane stabilization with optimization of sensor and vibration suppressor locations

An approach for synthesizing a control function for lumped sources in distributed feedback systems is proposed. The problem of membrane vibration suppression by point stabilizers is considered as an example. The parameters to be optimized in the problem are (1) the locations of the stabilizers, (2) the locations of the points of membrane state measurements, and (3) linear feedback parameters determining the dependence between the membrane state measurements and the stabilizer operation modes. Formulas for computing the gradient of the cost functional with respect to the optimization parameters are derived. Computer experiments are performed using first-order numerical optimization methods, and the influence exerted by measurement errors on the process of membrane stabilization is analyzed.