## 4 Modeling and Control of MR Dampers for Structural Buildings
### Semi-Active Controllers for MR Dampers
(2021) conducted a study in which the instantaneous variable was constructed via the Hilbert transform to represent the instantaneous characteristics of the excitation to further improve the accuracy of the MR damper model. The study suggested that, in the case of MR dampers, there is a correlation between the momentary variable and its nonlinear behavior. Therefore, studies related to this subject were investigated. In their study, [PERSON] et al. repaired the MR damper neural network model for the first time using the instantaneous characteristics of the excitation. The results indicated that instantaneous characteristics play an important role in the model's accuracy. The study also found that the accuracy increased by more than 50% in comparison with the general model. Additionally, the target force could be tracked using the model's precise control strategy [184]. Fuzzy controllers are the most common type of controller used in MR damper applications for both structures and vehicles as the performance of traditional controllers, such as LQG and H2/LQG controllers, usually depends entirely on the accuracy of the system's dynamic modeling, while complex structural systems have nonlinearity and uncertainty in both the loading and magnitude of the structural properties. This makes it difficult to identify an accurate dynamic model for a traditional control design. As such, new control algorithms can solve these problems with very few optimizations. Several studies found that fuzzy controllers can solve this problem as well. Fuzzy logic control is based on set theory and consists of four components that simulate human reasoning: a fuzzy interface, a rule base, a decision-making interface, and defuzzification. [PERSON] and [PERSON] implemented a MR device with fuzzy control in seismic cases to investigate the nonstationary random responses of two adjacent tall buildings. Fuzzy control rules were used to model failure data by calculating the desired stress to produce reasonable control in each mode. As such, the process controls were optimized in conjunction with the first observation for the first vibration mode. This control strategy successfully increased the dynamic performance of the control devices, which could adjust the damping force by increasing the building's response without increasing the mechanical energy. [PERSON] and [PERSON] concluded that control algorithms are very important when optimizing the response of building structures to seismic loads [185]. Although this was corroborated by [PERSON] et al., unlike [PERSON] and [PERSON], who applied MR dampers with fuzzy control in buildings, [PERSON] et al. used MR dampers as the base isolation of a building structure. The fuzzy control presented was also an intelligent multi-objective fuzzy-genetic controller. The controllers of their study aimed to improve the upper insulation characteristics and reduce the large bottom displacements under seismic loads. Unlike other controllers, the core of the fuzzy controller was conceptually constructed using factory-related control expertise. Moreover, a multi-genetic algorithm was applied to the fuzzy controller to optimize the controller's performance. This resulted in similar findings to those of [PERSON] and [PERSON], where fuzzy controllers performed better than other controllers [186]. In addition, studies on control were also performed by [PERSON] et al., who argued about developing the law of autonomous semi-active control as a simplified semi-active control algorithm for seismic response reduction. The strategy of this method is to generate the desired hysteretic loop to absorb as much energy as possible with a semi-active device. The energy absorption capacity, which was similar to that of the friction damper in the study, is given by the hysteretic loop generated by the semi-active control. This minimizes the disadvantages of the friction damper, such as a large residual displacement and the generation of high frequencies in the damping force [187]. Several years earlier, [PERSON] et al.