Experiment Setup

The structural system introduced in this study is modeled by a 3-story steel frame with a piece of equipment located in the second floor. This steel frame is designed to be an almost full-scale prototype building with 2 meters by 3 meters floor area and 3 meters story height. The mass of the second and third floors was 6 tons, and the mass of the first floor and the equipment was 3 tons. To mitigate the vibration transmitted to the equipment, which was mimic by the mass blocks, one CSS system and one MR damper were installed between the equipment and the top of the first floor. This CSS system was designed with a natural period of 2 seconds and the friction was ignored because the curvature was quite small (with a radius of 0.994 meters) and the surface was lubricated. The MR damper had a compatible stroke with this CSS system. The structural system as well as the control system was constructed and tested on the shaking table system at NCREE, as shown in Figure 6.1.

Furthermore, the front view of the structural system and the close snapshot of the control system are shown in Figure 6.2. The detailed design of the equipment isolation system integrated with the CSS system, the MR damper, and the stopper (for safety concerns) is shown in Figure 6.3.

Structural System and Equipment Isolation System

A pretest was done using white-noise excitations before the formal tests so that the modal frequencies of the structural system can be first identified from the measured responses using well-known system identification methods, such as stochastic subspace identification (SSI). Figure 6.4 shows one set of time history collected in the pretest and Figure 6.5 displays its Fourier spectrum.

Note that the first three modes of the structural system were distributed from 1 Hz to 5 Hz and the cutoff frequency of the white-noise excitations was around 50 Hz. Based on the SSI analysis, the identified modal frequencies were 1.02 Hz, 3.16 Hz, and 5.01 Hz; the corresponding damping ratios were 4.73%, 2.35%, and 0.43%, respectively.

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The natural period of the CSS system was 2 seconds. Thus, the stiffness and damping coefficients in Equation (5.64) can be determined using the recursive least square (RLS) technique, and these parameters were 𝑚₂ = 𝑚₃ = 6 tons and 𝑚₁ = 𝑚₄ = 3 tons, 𝑘₁ = 1378.33 kN/m, 𝑘₂ = 1420.76 kN/m, 𝑘₃ = 1420.96 kN/m, 𝑘₄ = 29.61 kN/m, and 𝐂̅ = 0.588081𝐌̅ 𝐪̈(𝑡) + 0.006129𝐊̅𝐪(𝑡) under the assumption of Rayleigh damping. By using these vectors and matrices, the four modal frequencies were identified as 0.49 Hz, 1.09 Hz, 3.37 Hz, and 5.22 Hz and the corresponding four mode shapes are showed in Figure 6.6. Before the formal tests, this numerical model was used for the simulation and optimization.

Semi-active Control Device

A MR damper with 6 kN maximum force and ±150 millimeters (mm) maximum stroke was employed in the experimental study as a semi-active control device. Figure 6.7 shows the schematic and the photo of the MR damper. This MR damper was designed, manufactured, and assembled in the laboratory at NCREE. To generate an electromagnetic field for the transition of MR fluid, a voltage controlled current source (VCCS) was used to feed current to the self-made MR damper with a 24 volts power supply. The VCCS is Model No. 4122Z manufactured by Copley Controls Corporation and the supplied current is proportional to the applied voltage (command voltage), i.e., the command voltage of 1.0 volt corresponds to a supplied current of 2.0 ampere.

Before the formal tests, a performance test was conducted to determine the voltage-dependent characteristics, as shown in Figure 6.8. The hysteresis loops of the MR damper with various voltage levels (from 0.0 volt to 0.3 volts with an increment of 0.05 volts) are shown in Figure 6.9. The force-displacement and force-velocity relationships under different voltage levels are clearly shown in this figure. Several important properties addressed in Section 5.3.3 can be also observed in this MR damper; increasing energy dissipation, initial stiffness, and Coulomb friction. Again, the voltage‐

dependent parameters, 𝐶_𝑑(𝑣), 𝛼_𝑑(𝑣), 𝛽_𝑑(𝑣), and 𝛾_𝑑(𝑣), in Equation (5.65) and Equation (5.67) can be identified using the RLS technique and Table 6.1 presents these parameters. Thus, the Bouc-Wen model was used herein to represent the behavior of the MR damper, and the command voltage can be inversely obtained by linearly interpolating each voltage level with this numerical model.

Data Acquisition (DAQ) System and Control System

To extract the dynamic characteristics and collect the feedback signals, accelerometers, velocity meters, and linear variable displacement transformers (LVDTs) were installed on each floor, the equipment, and the ground. The accelerometers used in this shaking table test were Model 141B, Setra System; the velocity meters were VSE-15A, Tokyo Sokushin; the LVDTs are Temposonics II

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and G Series, MTS. In addition to the response measurements, one load cell, TCLK-50KNA, manufactured by Tokyo Sokki Kenkyujo was also installed on the MR damper to measure the damper forces. To synchronize these signals, all the 5 accelerometers, 5 velocity meters, 5 LVDTs, and 1 load cell implemented in the experimental study were simultaneously sampled by one data acquisition (DAQ) system, made by Pacific Instruments Inc., with a sampling rate of 200 Hz. The DAQ system then fed the response measurements into the controller, dSPACE system, but the damper forces were not included because they were estimated by this dSPACE system according to the numerical model developed for the MR damper. The dSPACE system is an embedded system with a flexibility that used in the shaking table test to perform the control algorithms and generate command voltages to the VCCS, as shown in Figure 6.10.

The tight integration of dSPACE system with MATLAB and Simulink, developed by MathWorks, provides a powerful tool for hardware-in-the-loop (HIL) simulation, which is the major task in this chapter. MATLAB (matrix laboratory) is a numerical computing environment and proprietary programming language; Simulink is a graphical programming environment for modeling, simulating, and analyzing dynamic systems. The response measurements were fed into the dSPACE system and hence the analog-to-digital converters (ADCs) or digital-to-analog converters (DACs) converted and processed the signals according to the Simulink model, as shown in Figure 6.11 and Figure 6.12. To achieve the HIL simulation, the LQR, the DSMC, the WDSMC, and the inverse (MR damper) model were then programmed as different Simulink models, as shown in Figure 6.13. All these models had some initial signal processing blocks, as shown in Figure 6.14, before actually feeding into the control algorithms.

Earthquake Excitation

Three earthquakes in Table 5.1 were selected in the experimental study, including the El Centro earthquake, the Kobe earthquake, and the Chi-chi earthquake (TCU129). All these three earthquakes were in NS direction and the PGA was scaled up/down to the target PGA as an input excitation in each test. The acceleration response spectrum of these earthquakes is shown in Figure 6.15. It can be clearly observed that the Kobe earthquake has a relatively large response between 0.3 seconds and 1 second while the Chi-chi earthquake (TCU129) is between 0.1 seconds and 0.3 seconds. Besides, the El Centro earthquake excites all the range between 0.1 seconds and 1 second.

Control Scenarios and Strategies

To demonstrate the advantage of the WDSMC, several control scenarios and strategies were conducted in the shaking table test, as listed in Table 6.2. First, the equipment was fixed on the floor

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to represent a normal scenario. Then, the equipment was installed on the CSS and this equipment isolation system was located on the same position to represent an isolated scenario. Finally, the self-made MR damper was involved to dissipate the vibration energy. In the scenario of passive control, the MR damper was fed with a set of constant command voltages and, by applying a constant command voltage throughout the earthquake duration, the MR damper worked as a passive control device. In the scenario of semi-active control, the command voltages changed according to the control algorithms, and different control strategies were optimized based on the performance indices and the objective functions listed in Section 5.3.1. The schedule of the formal tests is shown in Figure 6.16.

The results from different control scenarios and strategies were compared to discuss the control performance of different control algorithms.