## 4 Modeling and Control of MR Dampers for Structural Buildings
### Semi-Active Controllers for MR Dampers  
One of the advantages of MR dampers with semi-active systems is that they can be used in either passive or semi-active mode to control a building structure. When the device is not controlled, it becomes a passive system (Figure 12), where electrical current is constantly supplied to the MR damper. In this scenario, no feedback data are required. In this system, passive-on and passive-off controls correspond to when the maximum current and the minimum current, respectively, are applied to the damper ([PERSON] and [PERSON], 1994). Figure 11: Comparison between predicted (black) and experimentally obtained (red) responses for the Gamota and Filisko model ([PERSON] and [PERSON], 1994). A semi-active control system is shown in Figure 13. As there is feedback, it requires controllers and sensors to provide feedback data according to their needs. In general, a semi-active control system can be defined as a device that does not require energy to be inputted into the controlled system. The current entering the MR damper is instead allocated to control the damping force by changing the magnetic flux intensity of the coil. However, under certain conditions, the current cannot change the direction of the damping force as this is performed by an active system damper. As such, a MR damper with a semi-active system requires several sensors, such as an accelerometer and load cell displacement transducers, to provide feedback so that it can optimally control the damping force. Therefore, several MR damper controllers, such as controllers based on a LQR, controllers based on a LQG, neural network controllers, and fuzzy controllers, have been developed. A LQR is a control system that is often used to control structures via a feedback controller that aims to provide stable movement. [PERSON] et al. developed a similar type of control system--a H2/LQG-based clipped optimal control system--to counteract earthquake vibrations in three-story structures. [PERSON] and [PERSON] (2000) investigated the seismic responses of a six-story building that had been retrofitted with MR dampers on the first and second floors by using a variety of semi-active control algorithms, such as a truncated optimal controller, to control the building structure's response to ground motion. The study found that the algorithm that used the LQG method (the optimal truncated controller) was suitable for MR dampers in a manner similar to the Lyapunov control algorithm and the modulated homogeneous friction algorithm. The optimal truncated algorithm achieved a significant reduction in the seismic response (21.4% to 29.6%). These findings were corroborated by [PERSON] et al. (2001), who also conducted a similar case study by applying a LQG controller to a small-scale six-story sliding building and compared the experimental responses obtained using a Lyapunov controller. The tests carried out in these two studies at various levels of excitation proved that MR dampers performed better than passive dampers in various situations. Additionally, semi-active systems were found to require only a small amount of power to outperform passive systems [182; 183]. Neural network controllers are another type of controller investigated in the development of MR dampers. The use of these controllers is quite popular with researchers in the mechanical, electrical, and structural engineering fields. Unlike clipped optimal controllers, when modeling MR dampers, neural network controllers take into account the current input applied to the device and the piston velocity/displacement, which are often  
Figure 12: Block diagram of a passive system for a MR damper [181]. Figure 13: Block diagram of a semi-active controlled system for a MR damper [181]. inaccurate. Therefore, the historical value of the input is used to improve the estimate. [PERSON] et al.