Schematic diagrams of (a) the active vibration isolation and (b) the electrical damping. The system consists of a primary feedback loop for active vibration cancellation, a displacement channel for suppressing drift, and a velocity feedback loop used to damp the mechanical resonances. For reference, the name of each functional block is given and the corresponding transfer function is labeled. τ and τ1 are the time constants of the corresponding integrators.
The aluminum mounting structure for the PZT actuator and the accelerometer. A cantilever is formed by cutting a groove into the aluminum block. The actuator is installed vertically with its moving end pushing from the bottom against the cantilever to preload the PZT. The accelerometer (CA-YD-109A) is rigidly mounted on the top of the cantilever and is coaxial with the actuator.
Joint responses of the PZT-accelerometer and PZT–strain-gauge modules. (a) Amplitude response. (b) Phase response. The accelerometer (CA-YD-109A) is of a piezoelectric type with a sensitivity of 10 858.4 pC/g from 0.2 to 500 Hz. Symbols are the experimental data obtained by driving the PZT with a sinusoidal signal. The response of the PZT–strain-gauge module is measured together with a preamplifer. The strain gauge is located on the side surface of the PZT that is encapsulated in a stainless-steel tube.
(a) Amplitude and (b) phase responses of a tubular PZT with and without electrical damping. The accelerometer (62 g, 7703A-100) is directly attached to the PZT and an extra load of 420 g is added to the top of the accelerometer. Symbols are measured with a lock-in amplifier (SR830) that works as double integrators. Strong resonances at 1.8 kHz and 6.3 kHz are suppressed by electrical damping. Resonances close to 10 kHz and beyond are not damped due to the accumulated 180° phase lag above 8 kHz.
(a) and (b) The frequency responses of the acceleration (A a A offset ) and displacement (A x A id ) channels before adder 1. (c) and (d) The frequency response of the subsystem (A a A offset + A x A id )A la , the open-loop response of the entire system, and the vibration rejection ratio.
Vibration noise and contributions from the electronic noise. All noises are referred to the output of the charge amplifier. The ground vibration and the residual vibration noises are measured by a FFT analyzer (SR760) at the output of charge amplifier without and with active vibration isolation, respectively. Close-loop contributions from the charge amplifier and the servo are calculated and converted to vibration noise. The electronic noise of the charge amplifier ultimately sets the lowest limit of the residual vibration.
Simplified noise model. e c and e s represent the noises of charge amplifier and servo, respectively. e vib is the ground vibration and υ f is the actuating signal applied on the PZT. The servo encompasses all circuits except the charge amplifier.
Extending the vibration isolation to 0.1 Hz by moving the crossover between the displacement and acceleration channels from 0.6 Hz to 0.06 Hz. The strain coefficient of the PZT actuator is increased by a factor of 10, shifting the gain profile of the acceleration channel upward by 20 dB. For displacement channel, the break point of the lead compensator is moved one decade towards lower frequency range and thus the gain profile below the breakpoint is shifted downward by 40 dB.
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