6.2 Adaptive Model-based Tracking Control
6.3.3 Tracking Performance Testing
The tracking performance testing is conducted to investigate the stability and performance of the proposed adaptive control scheme prior to the real-time hybrid testing. The boundary conditions for the parameter estimates can be obtained from the system identification test results. The tracking performance of the controller is investigated in time domain. A wide variety of tests are carried out as listed in Table 6-6. The BLWN power remains identical in each excitation. The duration of excitations is 120 seconds. Four control strategies are evaluated with three scenarios of input currents to the MR damper. The results indicate that the RMS errors for the 15Hz BLWN cases are always larger than those for the 5Hz BLWN cases. Moreover, the adaptive control law may not always improve the tracking performance for the two constant input current scenarios because linear models for the passive-off and passive-on cases are good enough within the test frequency range. For the pulse input current case, the adaptive control law improves the tracking performance for both feedforward controller only and feedforward-feedback controllers. This table also demonstrates that the direct adaptive control scheme can effectively parameterize the feedforward controller with respect to the model-based inverse transfer function when the nonlinearity of the MR damper becomes significant. Figure 6-36 shows the time history of the estimated parameters for the case of adaptive feedforward controller and feedback LQG controller under the 15Hz BLWN displacement input and pulse input current for the MR damper. The black dash lines are the upper and lower bounds obtained from the system identification tests. As a result, the estimated parameters vary from time to time because the pulse input current yields the changes of the MR
6.3.4 Real-time Hybrid Testing
A nine-story steel frame benchmark shear building (Ohtori et al., 1994) is selected to further verify the performance of the adaptive model-based control strategy for real-time hybrid testing. This structure has five bays in the NS direction as shown in Fig. 6-37. A linear model of the moment resisting frame is built for the real-time hybrid testing. The first five natural frequencies of the structure are 0.443, 1.18, 2.05, 3.09, and 4.27 Hz, while all modes are assigned with 2% damping ratios. The real-time hybrid tests examine the seismic performance of this building with MR dampers. In this control application, the maximum damper force is determined as 10%
of the building weight, i.e., 4410 kN. Thus, total 18 MR dampers are placed in parallel, and each damper has a force capacity of 200 kN. These dampers are installed at the 1st floor.
For the ground excitation, the far-field 1940 El Centro and near-fault 1995 Kobe earthquake records are selected to evaluate seismic performance of the building, as shown in Fig. 6-38. The intensity of the records is adjusted by a factor of 0.2 and 0.5 in order to investigate the robustness of the proposed adaptive model-based control scheme.
For MR damper control, both passive-mode and semi-active control strategies are evaluated in the real-time hybrid testing. The passive mode only considers the passive-on case with a constant input current of 2.5 Amps. The clipped-optimal control algorithm (Dyke et al., 1996) is used for the semi-active control case. This control approach is a combination of the LQG and clipped-optimal control algorithm.
The LQG design is focused on the minimization of the floor accelerations, while the feedback measurements in the LQG controller are all absolute floor accelerations. To input the appropriate current to the MR damper, the clipped-optimal control algorithm is adopted and given by:
( )
{ }
d max d m m
i =i H f − f f (6-37)
where id is the desired input current, imax is the maximum input current (2.5 Amps in this study); fd is the desired control force that is calculated based on the LQG control
algorithm; fm is the measured force, and H is the Heaviside function.
Both the feedforward and feedback LQG controllers in the real-time hybrid tests and the tracking performance tests are identical. The numerical model, structural control algorithm, and adaptive model-based controller are implemented in dSPACE with a 2000-Hz sampling rate.
The tracking performance of the real-time hybrid testing is first investigated. Table 6-7 demonstrates the RMS errors in the tests subjected to the El Centro earthquake.
With the adaptive law, the RMS errors are effectively reduced. Relatively large RMS errors are also found in all tests under 0.2-intensity seismic excitation because of the signal-to-noise ratio in the load cell. Meanwhile, the RMS errors in the tests under 0.5-intensity excitation are within 1%, indicating that accurate displacements are imposed to the MR damper in the real-time hybrid tests. In the semi-active control cases, the adaptive control scheme performs even better than the passive-on cases in most tests. These tests successfully demonstrate the robustness of the proposed adaptive control scheme. Moreover, Table 6-8 shows the RMS error in the tests subjected to the Kobe earthquake. Due to the near-fault seismic effect, the Kobe earthquake record would result in significant displacements in the building. Even though the impulse-like displacements are observed in these tests, the adaptive control scheme still decreases the RMS errors as compared to the non-adaptive control schemes. Furthermore, the RMS errors are much lower in the tests under 0.5-intesity excitation. In short, the proposed adaptive control scheme further improves displacement tracking in the real-time hybrid testing.
As the proposed adaptive tracking control scheme has demonstrated to be capable of imposing accurate displacements, the following results of the semi-active control implementation are derived based on this tracking control scheme in real-time hybrid testing. Figure 6-39 shows the roof acceleration time histories of the passive-on and the semi-active control strategies subjected to the El Centro earthquake record with an intensity of 0.5. As shown in this figure, the semi-active control strategy can surpass the passive-on case in structural response reductions. The semi-active control strategy meets the design control objective that the roof acceleration is effectively mitigated.
semi-active control strategy is successfully implemented and experimentally verified with the control performance for the seismically excited building.
Table 6-1 Structural properties of the smart base-isolation system
Parameters 4000 3350 1754600
Table 6-2 The fuzzy rule base CV
Table 6-3 Tracking performance for each test in terms of RMS error Earthquake Record (PGA) Controller for the MR damper RMSerror (%)
Passive-on 5.97
Table 6-4 Routh array of the servo-hydraulic system
s3 a3 a1
Table 6-5 Tracking performance in terms of RMS error in the simulations Excitation(Hz) Controller for the MR damper RMSerror (%)
FF 0.788
Table 6-6 Tracking performance for predefined displacement time histories
Current Controller RMS error (%)
5Hz BLWN 15Hz BLWN
Table 6-7 Tracking performance for the tests subjected to El Centro Earthquake
Current Controller RMS error (%)
El Centro x 0.2 El Centro x 0.5
Passive-on
FF 2.131 0.809
FF + Adaptive 1.551 0.792
FF + LQG 1.514 0.590
FF + Adaptive + LQG 1.527 0.578
Semi-active Control
FF 0.909 0.402
FF + Adaptive 0.878 0.387
FF + LQG 0.839 0.304
FF + Adaptive + LQG 0.820 0.292
Table 6-8 Tracking performance for the tests subjected to Kobe Earthquake
Current Controller RMS error (%)
Kobe x 0.2 Kobe x 0.5
Passive-on
FF 1.083 0.828
FF + Adaptive 1.065 0.822
FF + LQG 0.892 0.476
FF + Adaptive + LQG 0.879 0.470
Semi-active Control
FF 0.808 0.887
FF + Adaptive 0.791 0.777
FF + LQG 0.649 0.672
FF + Adaptive + LQG 0.662 0.576
(a)
(b)
Figure 6-1 Force vs. displacement relationships of the MR damper with random displacement and random voltage (a) experimental results, (b) simulation results
(a)
(b)
Figure 6-2 Experimental and analytical MR damper force in (a) test1, (b) test2
mb
Figure 6-3 Two degrees-of-freedom model of a smart structure
Displacement
Figure 6-4 The algorithm of fuzzy control inference
μ
Figure 6-5 Membership functions of (a) the input displacementx , (b) the input b velocity x& , (c) the output control voltage b
-0.2 -0.1 0 0.1 0.2
Figure 6-6 The rule surface of the proposed FLC
Base-isolated
Figure 6-7 Block diagrams of the numerical simulation under different control algorithms for the MR damper: (a) constant voltage, (b) LQ, (c) FLC
(a)
(b)
Figure 6-8 Displacement time histories of the isolation layer (left: 0.33g El Centro;
right: 0.2g TCU068EW): (a) uncontrolled, (b) controlled
(a)
(b)
Figure 6-9 Relative displacement time histories of the superstructure (left: 0.33g El Centro; right: 0.2g TCU068EW): (a) uncontrolled, (b) controlled
(a)
(b)
Figure 6-10 Absolute acceleration time histories of the superstructure (left: 0.33g El Centro; right: 0.2g TCU068EW): (a) uncontrolled, (b) controlled
Figure 6-11 (a) Numerical model and experimental specimen of the smart structure, (b) experimental setup
Figure 6-13 Bode diagram of the second-order digital low-pass filter
Base-isolated PLC Building
FMR Excitation
Force +
-Control Algorithm
xc Servo-Hydraulic
Actuator
xm
MR Damper
Low-pass Filter Delay Estimator
α α α α
state CV
force disp.
Figure 6-14 Block diagram of the compensation strategy and control algorithm in the experiments
(a) (b)
Figure 6-15 (a)Time history of delay estimate, (b) time history of generated command, and measurement
(a)
(b)
Figure 6-16 Displacement time histories of the base isolator (0.33g El Centro):
(a) controlled, (b) uncontrolled
(a)
(b)
Figure 6-17 Time histories of the superstructure’s (0.33g El Centro): (a) story drift, (b) absolute acceleration
Connection broken
Figure 6-18 Displacement time histories of the isolation layer in each case (0.2g TCU068EW)
Figure 6-19 The broken pin connector due to too large displacement
(a)
(b)
Figure 6-20 Displacement time histories of the base isolator (0.15g near-fault Chi-chi):
(a) controlled, (b) uncontrolled
(a)
(b)
Figure 6-21 Time histories of the superstructure’s (0.15g near-fault Chi-chi):
(a) story drift, (b) absolute acceleration
Figure 6-22 Error displacement time histories in each case (0.33g El Centro)
Figure 6-23 Error displacement time histories in each case (0.15g TCU068EW)
Figure 6-24 Relationship between the command and measured displacements
xc[n]
xc[n-1]
Command
Measured Disp.
xm[n]
xm[n-1]
TA[n]
A[n]
Figure 6-25 Illustration of the tracking indicator
(a) (b)
Figure 6-26 Displacement tracking indicator for the two cases:
(a) 0.33g El Centro, (b) 0.15g near-fault Chi-chi
(a)
(b)
Figure 6-27 Time histories of the calculated and measured velocities for LQ-controlled case: (a) 0.33g El Centro, (b) 0.15g TCU068EW
Figure 6-28 Time histories of the desired and measured control forces for LQ controlled case (0.33g El Centro)
y uFB
uFF
+ +
u GFF(s)
LQG Gyu(s)
+ _
r e
Figure 6-29 Model-based feedforward and feedback control scheme
θ
( ) 0 g θ = ( )
∇ g θ
( )
−∇ J θ
Pr( ) θ
S
Figure 6-30 Illustration of parameter projection
y uFB
uFF
+ +
u GFF(s)
LQG Gyu(s)
+ _
r e
SPM Adaptive
Law
Figure 6-31 Adaptive model-based feedforward and feedback control scheme
(a) (b)
(c) (d)
Figure 6-32 Estimated parameter a3 with different values of adaptive gain:(a) γ3=0.5, (b) γ3=1, (c) γ3=2, (d) γ3=5
Figure 6-33 Time history of parameter estimates in the simulation
MR damper Servo-hydraulic actuator
Figure 6-34 Test setup for experimental validation at SSTL
(a) (b) (c)
Figure 6-35 Transfer functions of the servo-hydraulic system and the identified model:
(a) 0 Amp (b) 2.5 Amps, (c) pulse
Figure 6-36 Time histories of the estimated parameters
Figure 6-37 The nine-story structure used in the test (Ohtori et al., 1994)
(a)
(b)
Figure 6-38 Ground acceleration time histories: (a) 1940 EI-Centro, (b)1995 Kobe
Figure 6-39 Time histories of the roof acceleration under the El Centro earthquake