## 5 Vibration Control of an Isolated Structure
### Comparison of Different Control Schemes  
The developed adaptive seismic isolator can provide stable and reliable magnetic field to enable a controllable structure by energizing field-dependent MRE. The goal for the implementation of control algorithms is to make the isolator dissipate large energy and keep floor displacements stable and within the desired thresholds. Figure 18 shows the displacement of different floors without control. It is observed that in spite of the base floor, the third floor has maximum displacement and the first floor has relatively smaller displacements.  
Figure 19a,b shows the structural displacement of each floor with the implementation of reaching law-based sliding mode control and RBF-based adaptive sliding mode control by incorporating modified M5 which describes the mechanical and magnetic characteristics of MRE nanocomposite. Compared with the displacement amplitude of Figure 19a,b, it can be seen that the displacement of the all floor is controlled due to the installation of RBF adaptive isolator.  
Figure 20 shows the corresponding control forces applied to the structure when implementing these two schemes. Structural nonlinear performance has a strong relationship with the designed MRE-based variable stiffness and damping isolator and the developed control algorithms. The main disadvantage of the sliding mode control includes high frequency oscillation, which is called \"chattering\". For the reaching law-based control method, the chattering phenomenon is obvious, while with the development of adaptive control algorithm based on the RBF model, the chattering effect is dramatically decreased.  
Figure 19: Structural Dynamic Response.  
Figure 18: Structural Dynamic Response without Control.  
Figure 21 shows top floor displacement in different control schemes. Figure 21, No. 0 represents no control effect. No. 1-5 represent Model 1-5 (MRE) applied to reaching law-based sliding mode control scheme, and (MRE) applied to the RBF adaptive sliding mode control method.  
Figure 21 is the application of for MRE with MWCNTs. It can be seen that the maximum floor displacement without control dramatically decreases when implementing the two control schemes. RBF adaptive control shows its superiority over reaching law-based control due to its better controllability. These results also demonstrate the exceptional behavior of novel MRE nanocomposites for energy dissipation and vibration suppression of structural dynamics when applying them on isolation devices. For other Modified Models, similar cases occur but the reduced amplitude is slightly smaller than that of the Modified M5.  
Figure 22 shows the maximum control force applied to the nonlinear structural system when applying different viscoelastic models. The control force is improved by 11.05% when using MRE nanocomposite compared with traditional MRE. Compared with reaching law-based control, RBF adaptive control shows its superior and improved controllability for about 8.63%. This is due to its online adaptability to track the changing trajectory of the system response with high nonlinearity. These phenomena also demonstrate the energy  
Figure 21: Top Floor Displacement for Different Control Schemes.  
Figure 20: Structural Control Force.  
dissipation capability of the \"smart\" laminated MRE nanocomposite in the damping device, which suppresses the structural vibration during operation.