The given paper investigates the model problem of mitigating random vibrations of a hinged beam using evenly distributed actuators on it. It has been proposed to synthesize the regulators based on the modal decomposition of a controlled object using the linear-quadratic criterion of quality. We have also proposed a quasioptimal method with the minimisation of multiplicity linear-quadratic criteria successively starting with the first eigenform. The mathematical modeling of forced random vibrations and various algorithms of mitigation has been conducted. The robustness of modal regulators has been investigated by varying their parameters. The results have demonstrated a very good degree of mitigation forced random vibrations of a modeling object, especially in the modal control case in comparison with other strategies to solve control problems.