6.1 Smart Base-isolated Building
6.1.2 MR Damper Control Algorithms
6.1.2.2 Fuzzy-logic Control
In addition to the linear-quadratic control algorithm, a fuzzy logic control (FLC) method is also studied in this paper. Fuzzy-logic theory, introduced by Zadeh in 1965, has been extensively applied on complex control problems. FLC is a type of intelligent language control and adopts manual control rules established by engineering intuition and experience. It does not rely on the model of the system and can deal with the nonlinearity of parameters and uncertain problems. It provides a simple and robust nonlinear control strategy. Thus, the FLC can accommodate the uncertainties and un-modeled dynamics of the MR damper.
Fuzzy-logic operations consist of three steps: fuzzification, fuzzy inference and defuzzification. In the fuzzification module, crisp values are converted into fuzzy sets and degrees of membership. A membership function defines how each point in the input space is mapped to a membership value between 0 and 1. The fuzzy inference consists of the linguistic IF–THEN rules, which connect the mapping relationship between the input and output. The defuzzification, opposite to the fuzzification,
scheme of fuzzy inference is shown in Fig.6-4.
The reason for adopting FLC as the control algorithm is that the semi-active control devices have significant inherent nonlinear properties. In current design practice, structures are assumed to behave non-linearly under severe loading conditions. As a result, vibration control using fuzzy logic has attracted the attention of structural control engineers since 1990s (Battaini et al., 1998; Battaini et al., 2004; Samali et al., 2004; Alli and Yakut, 2005; Bhardwaj and Datta, 2006; Shook et al., 2008). Systems with complex mechanisms are difficult to model mathematically, but can be adequately controlled and operated in real world situations. Operator control strategies for such systems, are developed based on intuition and experience, and can be considered as comprised of a set of heuristic decision rules. To sum up, FLC method is flexible and adaptive for additionally control the deformation of the isolated building to prevent the superstructures from damage.
In this study, the control targets using the FLC are: (1) to reduce the displacement of the isolation layer when it is under large deformation; (2) do not apply any force when the isolator deformation is small; (3) to limit the control voltage not to exceed 1.2V;
and (4) to reduce the inter-story drift and absolute acceleration of the superstructure. It is noted that the fuzzy rule base in this study is proposed by engineering experience without optimization. Some optimal approaches for FLC such as genetic algorithm or neural network are not considered.
The displacement and the velocity of the base isolator are used as the control inputs for the FLC. The output of the FLC is the control voltage for the MR damper. In this study, the triangular membership functions are used for all variables as shown in Figs.
6-5a to 6-5c where xb and x& are the displacement and the velocity of the base isolator, b respectively. The membership functions are obtained through trial and error in numerical simulation before the hybrid test. The parameter CV represents the control voltage for the MR damper. The fuzzy rule base is shown in Table 6-2 where NL, NM, NS, ZR, PS, PM, and PL represent negative large, negative medium, negative small, zero, positive small, positive medium, and positive large, respectively.
Mamdani Method is used for fuzzy inference. The advantages of the Mamdani
Method are it is intuitive; it has widespread acceptance; and it is well suited to human input. The Mamdani method has several variations. There are different aggregation operators for the rules, and numerous defuzzification methods that can be used.
Mamdani’s method is used for fuzzy inference as its 'min-max' operation structure is simple. In this study, the union of these two sets in terms of function-theoretic terms is given as follows (the symbol ∪ is the maximum operator and ∩ is the minimum operator): (a) Union: µA(x) ∪ µB(x) = max(µA(x), µB(x)), (b) Intersection: µA(x) ∩ µB(x) = min(µA(x), µB(x)), (c) Implication : A B = min(µA(x), µB(x)), and (d) Aggregation : max(µA(x), µB(x)). For defuzzification, the center of area method is adopted. The surface of the fuzzy rule base is illustrated in Fig. 6-6.
6.1.3 Numerical Simulation
Simulink is used to numerically investigate the feasibility of the two control algorithms. Two limitations of the available MR damper in this study are considered:
(a) the maximum stroke of the MR damper must be smaller than 150mm, and (b) the maximum velocity of the MR damper must be less than 350mm/sec due to the capacity of the actuator. If the peak displacement of any test is larger than 150mm, the servo-hydraulic actuator could damage the MR damper. Therefore, the numerical simulation results are used to decide the PGA level of the earthquake excitation for actual experiments. All the numerical simulations are conducted using a time step size of 0.005 second. The ode5 (Dormand-Prince) solver is adopted in the simulations.
Three control algorithms are adopted to determine the control voltage of the MR damper: case (a) a constant voltage of 1.2V, which can be viewed as a passive damper;
case (b) the MR damper is driven by using the LQ control algorithm; and case (c) the MR damper is driven by using the FLC algorithm. Figure 6-7 illustrates the block diagrams of the numerical simulations under different control algorithms for the MR damper. Two earthquake ground acceleration records are used: the 1940 El Centro Earthquake record and the 1999 Chi-chi Earthquake record (TCU068EW). It is worth noting that the TCU068EW record was measured at a near-source location. According to the previous research results, base-isolated buildings are vulnerable to strong near-fault impulsive ground accelerations (Hall et al., 1995). On the other hand,
isolation system for near-source excitations (Ramallo et al., 2002). Thus, the effectiveness of the MR damper in the smart base isolation system is investigated using near-fault ground motions in this study. The duration of the structural responses is 40 seconds including a 30-second earthquake excitation and a 10-second free vibration. Finally, the PGA for the El Centro and the Chi-chi near-fault earthquakes are set at 0.33g and 0.20g, respectively.
Figure 6-8 to 6-10 show the time histories of the displacement of the isolator, the relative displacement of the superstructure, and the absolute acceleration of the superstructure when the building is subjected to the aforementioned two ground motions. Apparently, the displacements of the isolation layer are significantly reduced due to the contribution of the MR damper. The input control voltage for case (a) is always kept 1.2V, which is the maximum input voltage for the MR damper. As a result, the MR damper of case (a) costs the most energy and performs the best among the three cases as shown in Fig. 6-8b. However, the relative displacements and the absolute accelerations of the superstructure of case (a) sometimes become larger than those of the uncontrolled system as shown in Fig. 6-9 and 6-10. Similar observation has been reported by the other researchers (Hall, 1999; Spencer et al., 2000). On the other hand, both the relative displacements and the absolute accelerations of the superstructure are effectively reduced in case (b) and (c). Although the responses of case (c) are sometimes larger than those of case (a), they are still smaller than those of the uncontrolled system. It is noted that the FLC used in case (c) is designed by engineering experiences; however, it still performs fairly-well. In addition, the cost energy in case (c) is less than that in case (a) since the control voltage is mostly smaller than 1.2V during the simulation in case (c). The responses of case (b) perform the best among the three cases due to its process of control force optimization.
Conclusively, numerical simulation results show that the semi-active MR damper can reduce most of the responses of the isolation layer and the superstructure. The MR damper controller by using the LQ algorithm performs the best if a proper set of weightings is selected.
6.1.4 Experimental Validation
The schematic of the 2DOF smart structure is shown in Fig. 6-11a. It is divided into
two parts: (1) the experimental substructure, consisting of the semi-active MR damper, and (2) the numerical model, consisting of the stiffness, damping and mass terms of the superstructure, and the lightly-damped base isolator. The experimental test setup is shown in Fig. 6-11b. The MR damper is pin-connected to a 250kN dynamic servo-hydraulic actuator at one end while the other end is anchored to a reaction frame.
The entire test facility for the smart base-isolation system test is different from that used in the portal frame test in Chapter 5. Instead of using the xPC target and SCRAMNet, the dSPACE system is adopted in the test because it supports a large number of D/A and A/D input/output channels. It provides convenient solutions for automotive and industrial control engineering through integrating the Control Desk and the MATLAB/Simulink programs. The Control Desk program is used to compute and collect the signals from the test system using a friendly graphical-user-interface.
The test facility of this test can be divided into two major components: (a) the dSPACE system, and (2) the MTS GT digital controller. The layout of the test facilities is shown in Fig. 6-12.
The adaptive PLC and control algorithms for the MR damper are implemented into a host computer using the MATLAB/Simulink. With the Real-Time Workshop and C complier, executable codes are created and linked to the dSPACE which runs in real time. Signals generated by the dSPACE are passed to the GT controller (command displacement) and to the MR damper (control voltage) in the analog form through the cables. The measured signals including the displacements and forces of the MR damper are digitized and sent back to the GT controller. After that, the measured signals are sent from the GT controller to the dSPACE to compute the next target displacement and the control voltage. By using these advanced experimental control facilities, complex hybrid simulation tests can be conducted in real time.
The GT controller is a well-tuned proportional-integral controller and able to form a closed-loop servo-hydraulic system. All the tests are conducted using a time step size of 0.005 second. The response of the MR damper is velocity-dependent; therefore, the achieved velocity for the MR damper is crucial to the test accuracy. The achieved
the test. As a result, a second-order digital low-pass filter is used to cut off the measurement noises over 30Hz. The magnitudes of the signals passed by the filter are 30% reduced at the frequency of 30Hz as shown in Fig. 6-13. The block diagram of the real-time hybrid testing is illustrated in Fig. 6-14 where xc and xm are the command and measured displacements, respectively.
Before performing the real-time hybrid tests, a sinusoidal loading test is conducted to online identify the initial delay constant α for the PLC. However, the measured displacements are filtered by a low-pass filter, which induces additional magnitude reduction and time delay as shown in Fig. 6-13. Therefore, PLC is expected to compensate the combined effects of the low-pass filter and the dynamics of the servo-hydraulic system. A 50mm, 0.4Hz sinusoidal displacement excitations are used to identify the delay constant. The adaptive gain is tuned as 1500 in the identification test. The delay estimate converges within 2 seconds as shown in Fig. 6-15a.
Meanwhile, the command and measured displacements agree with each other fairly well after 2 seconds as shown in Fig. 6-15b. This demonstrates that the PLC successfully compensates the time delay and the magnitude reduction caused by the servo-hydraulic actuator and the low-pass filter. The converged number of the delay estimate 8, i.e., 8 time steps, is adopted as the initial delay constant for the PLC during the real-time hybrid testing. The adaptive gain for the delay estimator is set at 100 to prevent it from oscillating.
Again, three control algorithms are adopted to determine the control voltage of the MR damper: case (a) a constant voltage of 1.2V; case (b) the MR damper is controlled by using the LQ control algorithm; and case (c) the MR damper is controlled by using the FLC algorithm. Fig. 6-16a shows the isolator displacement time histories using the 0.33g 1940 El Centro Earthquake and the aforementioned three different control algorithms for the MR damper. It appears that case (a) performs the best, in terms of reducing the isolator displacements, among the three cases because the control voltage is kept at the maximum control voltage for the MR damper 1.2V. Using the MR damper, the displacements of the isolator in all the three cases are significantly reduced compared with the uncontrolled building as shown in Fig. 6-16b. Figures 6-17a and 6-17b show the relative displacement and the absolute acceleration time histories of the superstructure in each case. Compared with case (a), both cases (b)
and (c) have smaller relative displacements and absolute accelerations in the superstructure. This clearly demonstrates that the semi-active controlled damper can effectively reduce the isolator displacement, the relative displacements and absolute accelerations of the superstructure as well.
When the smart base isolation system is subjected to the 0.20g near-fault Chi-chi Earthquake, the state feedback control gains and the fuzzy rule base remain unchanged. However, as mentioned in the system identification, the forces measured from the MR damper specimen are smaller than those obtained from the numerical simulation. As a result, the isolator displacements in the validation test are larger than those computed in the analytical simulation. If the peak displacement of any test is greater than 150mm, the servo-hydraulic actuator could damage the MR damper. The peak displacement in case (c) is greater than 140mm which is the safety limit of the MR damper. In fact, when the 0.2g Chi-Chi Earthquake record was applied in NCREE laboratory, the peak actuator displacement exceeded 150mm and fractured the MR damper-to-actuator connection. Figure 6-18 shows the displacement time histories of the isolation layer measured from the tests in each case. Unfortunately, the peak displacement in case (c) is larger than 150mm. The connection between the servo-hydraulic actuator and the MR damper is broken (Fig. 6-19) and the test is stopped. After replacing the connector and checking the serviceability of the MR damper, the PGA of the near-fault Chi-chi Earthquake is reduced to 0.15g for the subsequent tests. The isolator displacement time histories in each case and the uncontrolled building are shown in Figs. 6-20a and 6-20b, respectively. Again, case (a) performs the best among the three cases. The relative displacement and the absolute acceleration time histories of the superstructure in each case are shown in Figs. 6-21a and 6-21b. Compared with case (a), both cases (b) and (c) have smaller relative displacements and absolute accelerations in the superstructure. From these real-time hybrid tests, the advantages of using a smart base isolation system in reducing the isolator displacements without increasing the accompanying accelerations have been observed.
The performance of the real-time hybrid test depends on the difference between the computed command and the measured displacements. For simplicity, the error can be
e[n]=xc[n]−xm[n] (6−17)
The errors of the tests subjected to 0.33g El Centro and 0.15g TCU068EW ground motions are shown in Fig.6-22 and Fig.6-23, respectively. It is observed that most the error displacements are within 2mm during the tests. An example case, case(b) subjected to 0.33g El Centro ground motion, is used to illustrate the relationship between the command and the achieved displacements as shown in Fig. 6-24. It is observed that the PLC performs well even when a low-pass filter is adopted for the measured signals.
The tracking performance of a real-time hybrid test concerns the difference between the computed command and the measured displacements. The root mean square (RMS) error is widely used as an index of the tracking performance for its simplicity.
The RMS error is defined as: respectively. Good tracking performance is indicated by a low RMS error. Table 6-3 shows the RMS errors of the six tests described above. It can be found that all the RMS errors are within 6% indicating that the adaptive PLC compensates the servo-hydraulic system fairly well. It is noted that the passive-on case has a larger RMS error than the other two semi-active controlled test cases. This is because in the passive-on case, minor oscillations can be observed when the structural responses are small, as shown in the beginning of the ground motion as shown in Fig. 6-21.
Immediately after the constant input voltage 1.2V was applied in the case (a) test, there existed a small but significant enough restoring force (about 0.5kN) measurable from the MR damper. This small measurable MR damper force might have been larger than the actual restoring force due to the stiffness of the structure. As a result, the computed target displacements could have been significantly affected for any time steps when the actual structural restoring forces are relative small. Even so, the RMS
errors for the case (a) test are still acceptable. When the control voltage varied from time to time, the oscillation is no longer visible in the two semi-active test cases (b) and (c).
The tracking performance can also be evaluated by introducing the so-called tracking indicator (TI) proposed by Mercan and Ricles in 2007. The TI for a real-time hybrid test can be calculated as:
( )
values for the enclosed and complementary enclosed areas are set as zero. A positive slope of the TI corresponds to a lagged actuator response, meaning that negative damping is introduced into the real-time hybrid testing. On the other hand, a negative slope of the TI represents a leading actuator response, indicating that artificial damping is added into the test. In addition, a zero slope of the TI demonstrates a perfect tracking, i.e., the measured and command displacements are identical. Figure 6-26 shows the displacement TI time histories for all tests. It shows that the actuator responses of the constant voltage test case are mostly lagged, while the actuator performs much better in the other two test cases. This is because the MR damper was oscillating when the displacements were small in the constant voltage test case. As a result, these high-frequency oscillations have led to the significant tracking errors resulted in the worst TIs. Even so, all the TIs are considered acceptable as they are all close to zero. A good tracking performance of the proposed PLC has been confirmed in these tests.The responses of the MR damper highly depend on its velocity and the control voltage.
However, the servo-hydraulic actuator is displacement-controlled instead of velocity- controlled during the test. In this study, the desired velocity is computed from the state space equation introduced earlier, while the achieved velocity is acquired by directly differentiating the measured displacements. If the differences between the
desired and the achieved velocities are significant, the responses of the MR damper might not be accurate enough and could even lead to a meaningless test result.
Although the imposed displacements are shown very close to the desired displacements, it has not been shown that the achieved velocities are also close to the desired ones. Figure 6-27 illustrates the desired and the achieved velocity time histories for the test case (b) using the LQ-controlled MR damper. It appears that the achieved velocity becomes less agreeable with the desired values. This could be due to the measurement noises when the velocities are small even though the signals have
Although the imposed displacements are shown very close to the desired displacements, it has not been shown that the achieved velocities are also close to the desired ones. Figure 6-27 illustrates the desired and the achieved velocity time histories for the test case (b) using the LQ-controlled MR damper. It appears that the achieved velocity becomes less agreeable with the desired values. This could be due to the measurement noises when the velocities are small even though the signals have