## 1 Introduction
[17] presented an analytical investigation on actively controlling sound transmission through single rib stiffened double-panel system using the cavity control approach. Results demonstrate that active control can also effectively improve the low frequency sound insulation of such structure. Due to the coupling effects of the ribs, the active control mechanism presents additional prominent differences compared with the traditional results [18; 19], which offer guidance for practical application of this technic. However, for practical applications, it will usually need to add many secondary control forces (control sources) to actively control the structural vibration of the ribbed plate with a large area. For the multi-input error signal multi-output control signal (MIMO) multichannel system (i.e., centralized system), the computational loads of multichannel system will be very large, due to the large number of coupling secondary path between the control sources and the error sensing devices. The results indicate that the control effects and stability cannot be guaranteed, which makes the system infeasible for practical implementations. Compared with the centralized system, the decentralized system--which consists of many decentralized units--is simple and easy to implement. The decentralized unit is the single-input and single-output feedback loop. Normally the decentralized, static gain control of collocated and dual velocity-ideal point force feedback loop is the simplest form of feedback control [20]. Since the sensors and actuators are collocated and dual, then stability is guaranteed [20]. The performance of the decentralized feedback control system has been extensively investigated [21; 22; 23; 24; 25; 26]. [PERSON] et al. [20] compared the performance of the velocity feedback loop of collocated and dual force actuators and velocity sensors, as well as piezoelectric actuators and velocity sensors. Theoretically, the control system uses multiple feedback loops with ideal velocity sensors and point force actuators. However, it needs a real device to produce the force in practice. Multiple electro-dynamic inertial actuators or piezoceramic patches are then used as a means of applying a force. [PERSON] et al. [21; 22; 23] presented a theoretical and experimental investigation to develop a prototype smart panel with 16 decentralized vibration control units for the reduction of sound radiation/transmission of the plate. The feedback loops consist of piezoceramic patches as actuators and accelerometers as sensors. The sensor and actuator are not dual, and the stability of the feedback loop is limited. In order to further set up relevance between the research work and the practical application, [PERSON] et al. [24] designed the decentralized velocity feedback loop with triangularly shaped piezoceramic patch actuators and accelerometer sensors. [PERSON] et al. [25; 26] and [PERSON] et al. [27] used the small-scale proof mass electrodynamic actuator and electrodynamic inertial actuator to construct the feedback loop. The control performance and stability of the system were analyzed. All the results obtained in the above investigations will be helpful for designing and applying this technic. Most of the existing researches used a simple plate as the control object, which allows the attention to be concentrated on exploring the control performance and physical nature of the decentralized control system. As for the more practical structure, such as the ribbed plate widely used in engineering, there is little research on this. Hence, in order to further improve the relevance of the research work with the practical engineering applications, this research uses the rib stiffened plate as the control object, and particularly investigates the control performance of the decentralized velocity feedback controllers with inertial actuators. The mathematical model for predicting the response of the control system with inertial actuators in [25; 26], was a mobility/impedance formulation.