3.3 Vibration Control Using Piezostack Mount
4.1.4 Control Results
Figure 4.15 shows an experimental setup for the evaluation of vibration control per- formance of the hybrid active mount. A 100 kg mass is loaded on the top plate of the mount, while the base plate is excited by an electromagnetic shaker. The base is excited with vibration levels according to the specifi cation shown in Figure 4.8. An accelerometer is installed on the mass to measure its acceleration for feedback, which is integrated to obtain the velocity signal by using an integrator circuit. The controller is implemented by using dSPACE DSP board DS1104, in which high-speed A/D and
D/A converters are integrated. The sampling rate of the control system is chosen to be 10 kHz. As the vibration from the base is transmitted to the mount, the SMC is acti- vated to attenuate the vibration at the supported mass. The dynamic response signals are acquired from the accelerometer installed at the supported mass via dSPACE DSP board DS1104. It is also noted that a low-pass fi lter is used at the control input signal (before the high-voltage amplifi er in Figure 4.15) to prevent high-frequency switching in the control signal as chattering occurs. The cutoff frequency is set at 1200 Hz. The fi lter bandwidth covers the whole frequency range of interest.
The hybrid active mount system is controlled by the SMC. The sliding surface gradient matrix, S, is chosen as [153 0.996 −60.15 −0.266] by using the robust eigenstructure assignment method [19]. This method renders the assigned poles as
s(t) =Sxˆ (t)
fp(t) = –(SB)–1[SAxˆ (t)+k. sat(s(t))]
V y=y2
ˆx Hybrid active mount system
Luenberger observer 1/α
fp Sliding mode controller
d
·
x.(t) = Ax(t) + Bfp(t) + L(y(t) – Cx(t))
FIGURE 4.14 Block diagram of the control system.
Control voltage
Mass acceleration Signal conditioning amplifier
High-voltage amplifier Shaker
A/D converter dSPACE DS1104
(controller) D/A converter Hybrid
mount Mass
FIGURE 4.15 Experimental apparatus for vibration control.
insensitive to the parameter uncertainties as possible in sliding phase. The observer gain matrix, L, is designed as [−37.5 −566490 −2.53 9884]T by using the con- ventional pole placement technique. The upper bounds of uncertainties for the rubber element stiffness (δkr) and damping coeffi cient (δbr) are experimentally identifi ed by 32,089 and 107. The upper bound of disturbance δd and the constant η are chosen to be 80 and 10, respectively. Figure 4.16 shows the vibration control performance at 100 Hz sinusoidal excitation with the acceleration amplitude of 2.37 m/s2. When the controller is not activated, the acceleration of the supported mass is suppressed to 0.074 m/s2 due to the passive element, or −30.1 dB in terms of the transmissibility ratio defi ned in Equation 4.1. When the controller is turned on, it can be seen that the acceleration at the mass is effectively reduced to 0.025 m/s2, or −39.5 dB in total (compared with the excitation). In other words, the isolation performance in the con- trolled case has been improved −9.4 dB more compared with that in the uncontrolled case. Figure 4.17 presents the control performance at 400 Hz. From the experimental results, it can be seen that when the controller is turned on, the vibration of the mass is attenuated from 0.114 to 0.014 m/s2, or equivalently, −18.4 dB more than in the uncontrolled case. Another experiment was performed at 1000 Hz excitation, and the control result is shown in Figure 4.18. It is also seen that by activating the controller, the vibration at the mass has been attenuated −15.1 dB more than in the uncontrolled case. It is noted that the stiffness of the piezostack is much higher than that of the rubber element. Therefore, the performance of the mount in the passive case (uncon- trolled) is nearly the same as that of the rubber mount.
–300 –200 –100 0 100 200 300
Control voltage (V)
Time (s)
1.5 2.0 2.5 3.0
1.5 2.0 2.5 3.0
–0.10 –0.05 0.00 0.05 0.10
Acceleration (m/s)
FIGURE 4.16 Control performance at 100 Hz excitation. (From Nguyen, V.Q. et al., Proc.
Inst. Mech. Eng.: Part C, J. Mech. Eng. Sci., 223, 1327, 2009. With permission.)
1.5 2.0 2.5 3.0 –400
–200 0 200 400
Control voltage (V)
Time (s)
1.5 2.0 2.5 3.0
–0.14 –0.07 0.00 0.07 0.14
Acceleration (m/s)
FIGURE 4.17 Control performance at 400 Hz excitation. (From Nguyen, V.Q. et al., Proc.
Inst. Mech. Eng.: Part C, J. Mech. Eng. Sci., 223, 1327, 2009. With permission.)
1.5 2.0 2.5 3.0
–400 –200 0 200 400
Control voltage (V)
Time (s)
1.5 2.0 2.5 3.0
–0.30 –0.15 0.00 0.15 0.30
Acceleration (m/s)
FIGURE 4.18 Control performance at 1000 Hz excitation. (From Nguyen, V.Q. et al., Proc.
Inst. Mech. Eng.: Part C, J. Mech. Eng. Sci., 223, 1327, 2009. With permission.)
Other experiments are carried out to evaluate the control performance at many exci- tation frequencies within the range of 20–1000 Hz. The control results are summarized in Table 4.1, where Ab is amplitude of the base acceleration; Amu and Amc are ampli- tudes of the mass accelerations in uncontrolled and controlled cases, respectively; Tu and Tc are the acceleration transmissibilities from base acceleration to supported mass acceleration in the uncontrolled and controlled cases, respectively. These acceleration transmissibilities with respect to the excitation frequency are plotted in Figure 4.19
1000 100
20 –80 –60 –40 –20 0
Frequency (Hz)
Controlled Uncontrolled
Magnitude (dB)
FIGURE 4.19 Acceleration transmissibility of the hybrid active mount system. (From Nguyen, V.Q. et al., Proc. Inst. Mech. Eng.: Part C, J. Mech. Eng. Sci., 223, 1327, 2009. With permission.)
TABLE 4.1
Experimental Results at Several Exciting Frequencies
Freq (Hz)
Uncontrolled Controlled
Ab (m/s2) Amu (m/s2) Tu (dB) Amc (m/s2) Tc (dB) Tc − Tu (dB)
20 0.471 0.1013 −13.4 0.1001 −13.5 −0.1
50 1.183 0.0663 −25.0 0.0511 −27.3 −2.3
70 1.664 0.0605 −28.8 0.0442 −31.5 −2.7
100 2.369 0.0742 −30.1 0.0250 −39.5 −9.4
200 4.737 0.1281 −31.4 0.0180 −48.4 −17.0
300 7.106 0.1137 −35.9 0.0173 −52.3 −16.3
400 9.474 0.1136 −38.4 0.0137 −56.8 −18.4
500 11.843 0.1640 −37.4 0.0143 −58.6 −21.2
600 14.209 0.1972 −37.2 0.0164 −58.7 −21.5
700 16.578 0.1973 −38.5 0.0224 −57.4 −18.9
800 18.951 0.1802 −40.4 0.0224 −58.5 −18.1
900 21.323 0.1756 −41.7 0.0301 −57.0 −15.3
1000 23.687 0.1836 −42.2 0.0322 −57.3 −15.1
for comparison. From these results, it can be assured that the vibration control perfor- mance can be signifi cantly improved by activating the piezostack actuators. However, in the low frequency, the vibration attenuation is not so good as the results at high fre- quencies. This is because the actuating force is relatively small at low frequency. In the hybrid active mount, the actuating force is mainly generated by the inertial force.