Numerical study of the efficiency of modal filter method and observer method for implementation of modal control of vibrations of elastic systems

The article compares the efficiency of two methods for implementing modal control for active vibration suppression of distributed elastic systems. The former is the modal filter method, which implies a linear transformation of measured and control signals; the latter is the method of modal observers, which uses the object model to reconstruct the state vector from the measurement signals. For this purpose, the problem of suppression of forced bending vibrations of a thin metal beam at several lower resonance frequencies has been solved numerically for two different objects. The simulation results showed an undeniable advantage of the observer method over the modal filter one. The inherent effects of signal transmission in the control loop, occurring in real systems but usually neglected in numerical studies were analyzed. It was established that these phenomena had a significant impact on the efficiency of the synthesized control systems. Therefore, they must be taken into account in numerical simulations.