Volume 3 Issue 4 - February 15, 2008
Modeling and Robust Active Control of a Pneumatic Vibration Isolator
Ping-Chang Chen1 Ming-Chang Shih2*

1Ph.D. student 2Professor Department of Mechanical Engineering
Email: mcshih@mail.ncku.edu.tw

Paper published in Journal of vibration and control, Vol.13 No. 11, pp. 1553-1571(2007)

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Due to rapid development of micro processing, precise measurement, and high-accuracy manufacturing, vibration disturbance becomes non-negligible because its amplitude is close to the cared dimension of operation. Most advanced instruments or high-precision machines including atomic force microscopes, laser interferometers, and semiconductor exposure apparatus are vibration-sensitive and must to be operated in a stable environment. Vibration disturbance can be induced by various sources, such as human walking, rotation of running machines, motion of outdoor vehicles, and earthquakes, and is exhibited in a specific frequency range depending on the source. The passive pneumatic vibration isolators are frequently used because of its simple structure and low cost, however, for this isolator, vibration disturbance is amplified at the resonant frequency, which is normally less than 3Hz. Hence, several active isolation approaches by using piezoelectric and magnetostrictive actuators have been presented to improve the isolation performance. However, the stroke of the piezoelectric and magnetostrictive actuators is only several dozens of micrometers, thus restricting the performance of the low-frequency isolation. The active pneumatic control scheme has recently been developed to suppress the vibration disturbance. Those results also demonstrated its feasibility. The pneumatic drive can provide larger actuating stroke and lower magnetic field than piezoelectric and electromagnet actuators can.
Figure 1 Schematic diagram of the pneumatic servo controlled isolator

To evaluate the performance of the active pneumatic vibration isolation, an active vibration isolator is designed and fabricated, and is also fixed on the specific vibration test equipment. Figure 1 schematically depicts the designed servo controlled pneumatic vibration isolator. The piston can support the payload when the isolator is pressurized by the compressed air through the bottom port and reaches the set pressure. The pneumatic servo valve is connected to the top port, and the air flow through the top port, including the direction and the flow rate, can be controlled by the electronic signal. For the convenience of the research, the simulated adjustable restrictor is located outside the isolator and built between the top and bottom ports.
Figure 3 Photograph of the experimental setup
Figure 2 Schematic diagram of the vibration test rig


Figure 2 illustrates the vibration test rig and the schematic diagram employed in this study. The simulated vibration from the floor is generated by the servo controlled hydraulic cylinder. The pneumatic servo valve, shut-off valve, and the top port of the isolator are connected together in sequence. The vibration is measured by accelerometers, and is integrated to the voltage signal of velocity using the integrator circuit. The signal acquisition and voltage output are obtained by the interface card. Figure 3 shows a photograph of the experimental setup.

Some basic assumptions are applied in this study before deriving the equations of the isolator, then, a useful linear mathematical model based on the air dynamic behavior was derived. The equivalent spring constant, damping coefficient of the rubber, and the flow gain of the servo valve were obtained using experimental identification. The block diagram of the linearized pneumatic servo controlled vibration isolator is shown in the figure 4.
Figure 4 Open loop block diagram of the linearized pneumatic servo controlled vibration isolator

In the study, the main objective of applying the active control scheme is to reduce the vibration from the floor, particularly in the low-frequency range. The robust H controller is suitable for the active control system in these considerations. The H control theory uses the weighting functions to determine the bounds of the nominal plants in the presence of uncertainties and disturbances. Figure 5 shows simplified block diagram of the nominal plant, the controller, and the weighting functions. The weighting functions in the block diagram reflect various objectives. The weight Wp(s) represents the requirement of active control performance. The term Wr(s) provides the restriction of the control signal magnitude without saturation.
Figure 6 Block diagram of the augmented system
Figure 5 Block diagram of the simplified robust controlled vibration isolator with weighting functions


To obtain the robust controller K(s), the feedback control system in Figure 5 must be converted into the augmented plant P(s) using linear fractional transformations (LFT). Figure 6 shows the block diagram of the augmented plant associated with the robust controller.

The controller is designed by applying robust control theory according to the nominal plant and selected weighting functions. The transmissibility curves of passive and active isolators were measured in the frequency range of 0.5–80Hz, and are illustrated in Figure 7. The experimental results demonstrate that the active isolator performed better than the passive isolator, the designed active controller lower the transmissibility curve to less than 0dB in low frequency range(<10Hz), and also reduced the resonant peak effectively. Compared to the recent pneumatic isolation techniques, the result is the optimal one.
Figure 7 Experimental results of transmissibility vs. frequency of passive and active vibration isolators
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