The stability of decentralized multichannel velocity feedback controllers using inertial actuators

The application of direct velocity feedback control on vibrating structures is well known to provide additional damping and reduce vibration levels. A number of previously studied control systems use multiple feedback loops with ideal velocity sensors and force actuators. While accelerometer signals may be utilized to accurately estimate velocity, there is rarely a structure off which one may react an ideal force. This paper concentrates on the use of multiple electrodynamic inertial actuators as a means of applying a force. A time domain model of a plate structure with multiple velocity sensors and collocated inertial actuators is derived. This model is then used to optimize the decentralized controller in order to minimize the total kinetic energy of the plate. These results are compared with those obtained with a decentralized controller in which each local loop has the same gain. It is demonstrated that for low control efforts, and hence control gains, both controllers perform almost identically, however at large gains the equal gain controller becomes unstable. The cause of this instability is attributed to the resonance of the inertial actuator. The implications of using multiple inertial actuators is discussed and some experimental results are presented and compared with simulations.