ANALYSIS, DEVELOPMENT AND PERFORMANCE IMPROVEMENT OF DISPLACEMENT TRANSDUCERS

Abstract

Displacement transducers are extensively used for the measurement of physical quantities in Biomedical, Aerospace, Meteorological, Industrial, and Process Instrumentation systems. They act as an essential element between the physical systems and electronic signal processing and conditioning units. Besides responding to desired measurand, the transducer output is also influenced by the changes in excitation parameters and variations in internal and surrounding environmental conditions. In long term use, there are problems of non-linearity in response and instability in operation with these transducers. These problems require smart handling to get reliable and consistent output in response to the desired measurand. There is always a necessity to improve the performance characteristic of each transducer either by developing a new transducer or by improving the design of existing transducer. Analysis, development and 'performance improvement of inductive and capacitive type displacement transducers have been carried out in this work. These transducers are widely used for the measurement of displacement, pressure, force, flow, level, velocity, acceleration, vibration, torque, and several other associated variables. They are used to measure either displacement as a primary variation or displacement as a secondary variation in response to primary variation in some other variable like pressure, force or level. The performance of a displacement transducer can be improved by improving the quality of its materials, by making suitable modification in its assembly or by using an appropriate signal processing circuitry for processing its output. In the present work, latter two aspects have been considered and used for the performance improvement of displacement transducers. The research work reported in this thesis can be broadly divided into four parts. The first part of the work deals with two inductive and one transformative transducers which have been developed and tested for various input conditions. The first transducer is based on inductive ratio technique, the second one

on differential inductive ratio technique and the third one on differential transformative technique. A short circuiting ring (SCR) has been used as a moving element which has the advantage over the conventional cores used as moving element in other types of inductive transducers. There are two coils in inductive transducers. In inductive ratio type, the final output is the ratio of two voltages taken from the two coils of the transducer. It has been found after analysis that the output does not contain terms influenced by variations in excitation parameters and ambient temperature. This transducer has linear response and is free from hysteresis effect besides being rugged in construction, smaller in size, lighter in weight and cheaper in cost. It requires lesser number of turns compared to other uncompensated and compensated types of LVDT transducers. In differential inductive ratio type, the output is the ratio of the difference and the sum of the two voltages taken from the two coils of the transducer. The differential voltage changes with the variation in the measurand. The sum of the two voltages does not change with the variation in the measurand and is taken as a reference signal. The final output does not contain terms influenced by the undesired variations in influencing parameters. This transducer has larger linear range of operation. Differential transformative transducer with SCR has one primary and two secondary coils. This transducer is partially similar in construction to the differential inductive ratio transducer except that its output is obtained by taking the difference and the sum of the two voltages taken from the two secondary coils of the transducer. Due to transformer action, the output is least affected by the noise present on the primary side of the transducer. These transducers have been extensively tested for the changes in excitation conditions and the variations in environmental temperature. The performance has been evaluated and compared with the other types of inductive transducers. The test results show the improvements in the performance of these transducers in comparison with other types of transducers of this family. The second part of the work deals with two types of improved signal processing schemes which have been developed for use with

capacitive displacement transduction techniques which are used for pressure measurement using diaphragm as the primary sensing element. The first method has been developed around a microprocessor based system while the second one around a pseudo-bridge circuit. Besides non-linearity and offset, stray and fringing capacitances are the major problems with the capacitive transducers. Both these techniques take care of different types of problems associated with capacitive transducers and improve their performance. In the microprocessor based method, the errors are eliminated through software processing. The specific problems tackled are the linearization of response and the elimination of constant errors. An efficient fast accessible look-up table method has been developed for linearization. In the second method, a pseudo-bridge circuit has been used in place of ordinary bridge circuit. The ordinary bridge circuit has the requirement to use the transducer at or near balance. But for large deviation from balance or for continuous displacement measurement ordinary bridge is not suitable. Besides this, ordinary bridge circuit offers linearity at the cost of sensitivity, therefore, is not suitable for many practical applications whereas pseudo-bridge circuit offers linearity in wider range without any loss of sensitivity. The output of the bridge is connected to a subtracter and to an adder. The subtractor output represents the variation of the measurand whereas the adder provides the reference signal. The final output is the ratio of these two differential and additive signals and does not contain the terms influenced by variations in the excitation parameters. Also the errors due to offset, stray and fringing capacitances are canceled as the output has been taken in terms of difference of two voltages at the intermediate stage. The schemes have been extensively tested using a capacitor in place of transducer for the changes in excitation voltage and frequency. The test results of these two schemes are consistent and reliable and suit to various applications in practical field. In the third part of the work, two methods have been developed for the linearization of response of various types of displacement transducers, the first one based on first order polynomial method and the second one based on linear

transformation technique. The first order polynomial linearization method has been used in two ways - one through single segment and the other through multi-segment linearization approach using least square method. Single segment linearization provides three times closer response to the actual curve compared to the linearization by joining two extreme points of the actual response curve. Multi-segment technique further improves the linearity. It has been found that there is considerable improvement in the linearity by these techniques in comparison with the usual method of linearization. These methods of linearization are suitable to displacement as well as to other types of transducers. Suggestions have also been made for hardware implementation of these two techniques for dedicated applications. The last part of the work deals with a method developed for taking into account the influence of one or two disturbing variables on the input signal of the transducer. The method is a generalized type and can be used for displacement as well as to other types of transducers. The response characteristic of a transducer is represented by an interpolating polynomial. Their coefficients are considered to be polynomials in terms of the disturbing variables. The coefficients are corrected .to get the effects of disturbing variable incorporated in the final polynomial representing the response characteristic of the transducer. The correction in the coefficients of the polynomial depends upon the order of polynomial. The more is the order of polynomial, the better is the accuracy, but at the cost of complexity in computation. So, one has to compromise between the considerations of the order of polynomial and the complexity in computation. The divided difference technique has been implemented for the optimization of the order of polynomial. In the present case the experimental data of an inductive ratio transducer with SCR has been processed by taking frequency as a disturbing variable in one case and frequency and temperature as two disturbing variables in the other case. The rounding off errors have been minimized by following the set rules. The correction in the input variable by this technique also improves the linearity of the response of the transducer. (iv) With the improved techniques developed in this work, the inductive and capacitive displacement transducers become suitable for all types of indoor and outdoor applications including hostile environments. With enhanced performance, they become modified and improved versions of transducers in their existing family. The analog linearization techniques are tailored solution for a particular transducer whereas digital linearization techniques are versatile types and the same technique can be used for different types of transducers. The divided difference technique is suitable to decide the order of polynomial to be used for processing to incorporate the influence of disturbing variables in the response characteristic of the transducers. The work reported in this thesis provides solution to several existing problems in the area of displacement transducers. Overall, the work makes a positive contribution in the area of performance improvement of displacement transducers.