Model identification of a kulite pressure transducer

A simple model of a Kulite pressure transducer is identified. A parametric linear time invariant system whose response matches the experimental data is constructed. Our results show that the transducer may be modeled as a third order system with one real pole, a pair of complex conjugate poles with small damping, and a real zero. The transfer function of the identified model may be used to compute the frequency response (magnitude and phase) of the transducer for frequencies up to about 300 kHz. The identified model may also be used to reconstruct the input to the transducer given a record of its output. The accuracy of the identified model is limited by the fact that the experimental inputs used for identification are step inputs (shock waves). KULITE RESPONSE TO WEAK SHOCKS The four-inch shock tube, in the Aerospace Sciences Laboratory at Purdue University, was used to provide a known input for a hemisphere-cylinder model with a Kulite pressure transducer mounted in the nose. [1] Weak shocks were produced which were impinged upon this system to excite the Kulite resonance frequency. 'Supported in part by the National Science foundation under VIA award no. ECS-93-58288. f Associate Professor ' Research Assistant 1 Copyright ©1996 by the American Institute of Aeronautics and Astronautics, Inc. AE Rights Reserved. Apparatus fc Procedure The tip of the hemisphere-cylinder model (2.5 inches in length) was placed at the end of the driven section of the shock tube as shown in Figure 1. A Kulite Pressure transducer, model XCQ-062-25A, was mounted inside the model and flush with the nose. This Kulite was constructed without screens so that the diaphragm was as nearly flush with the front face as possible. The remaining space was factory filled with RTV. The silicon-based strain-gauge transducers were supplied with 5.00 V from a REF02 integrated circuit. [2] The Kulite output was amplified by Burr-Brown INA103 instrumentation amplifiers; the DC-output voltage was multiplied by 100, and then AC-coupled and further amplified by 100 using a second INA103. The AC-coupled signal was high-pass filtered at 840 Hz. The amplifiers have a small-signal bandwidth of 800 kHz at a gain of 100. The distance between the tip of the model and Kulite system and the second Kistler pressure transducer (K -2) was 6.2 inches. K -2 was then 24.1 inches away from the first Kistler transducer (K-l) (i.e. 30.3 inches from the Kulite system). The model 603A Kistler pressure transducers were connected to a model 504A amplifier. The Kistler amplifier was set so that the pressure-gauge conversion factor was 28.4 psi/V [3]. The Validyne pressure transducer, model DP15-22, with a 20 psi gauge diaphragm was hooked up to the driver section of the tube and connected to a Validyne carrier demodulator, model CD223. The zero and the span on the Validyne amplifier were adjusted to provide maximum resolution. A Seegers pressure gauge (model no. SS-2170-30), with 0.05 psi gauge subdivisions and a 0 to 30 psig range, was also connected to the driver section and provided a means of calibrating the Validyne and Kulite pressure transducers. Diaphragms, made out of aluminum foil, wax paper, and 0.001 inch mylar, were used to obtain a driving pressure range between 1.0 psig and 12.0 psig. The driven section was operated at atmospheric pressure. A LeCroy 9304AM digital oscilloscope was used to record the data, which was sampled at 50 MHz with 250,000 pts/channel. The LeCroy oscilloscope has four channels, and resolves eight bits to a bandwidth of 100 MHz and includes analog amplifiers that resolve to 2 mV/division for a maximum of ten divisions. The LeCroy oscilloscope was set up to acquire data on four channels which were hooked up to the Kulite, Validyne, and the Kistler's, Kl and K-2, respectively. After each run, the output from the Validyne was recorded and the other channels were saved to disk. The trigger was set in order to capture the driving pressure, measured using the Validyne, before the diaphragm broke and the run began. The shock tube was operated by placing a diaphragm between the driven and driver sections. For each run, the pressure of the flow ahead of the shock wave (pj) was at atmospheric in the driven section. The pressure in the driver section (p4) was then increased until the diaphragm broke. This caused a shock wave to travel downstream towards the end of the driven section. The Kistler pressure transducers (K-l and K -2) and the Kulite were used to detect the shock wave as it passed by. The static pressure behind the shock was measured by the Kistlers and the total pressure by the Kulite. The pressure behind the shock wave (pg) was also computed in two different ways. One way involved the measured time and distance between the Kistlers and the Kulite pressure transducers, from which the shock speed was computed. The speed of sound (a) in the driven section was determined from the initial temperature (T), the ratio of specific heats (7) assumed constant at 1.4, and the gas constant (R) at 286.8 J/kg-K where a = T/*/RT. The shock Mach number was then known, along with the initial conditions pi and P4. Using standard compressible flow relations [4], pressure behind the shock was calculated from the initial conditions alone and then from the shock Mach number (Ms), and plotted in Figure 5. The equations used to compute the flow properties in the shock tube are El Pi (7i -1) 71