Chapter 1 Introduction to Measurement Systems
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4/3/2019 Advanced Measurement Systems and Sensors Dr. Ibrahim Al-Naimi Chapter one Introduction to Measurement Systems 1 4/3/2019 Outlines • Control and measurement systems • Transducer/sensor definition and classifications • Signal conditioning definition and classifications • Units of measurements • Types of errors • Transducer/sensor transfer function • Transducer characteristics • Statistical analysis Closed-loop Control System 2 4/3/2019 Measurement System Transducer and Signal Conditioning 3 4/3/2019 Transducer Element • The Transducer is defined as a device, which when actuated by one form of energy, is capable of converting it to another form of energy. The transduction may be from mechanical, electrical, or optical to any other related form. • The term transducer is used to describe any item which changes information from one form to another. Transducer and Sensor • Transducers are elements that respond to changes in the physical condition of a system and deliver output signals related to the measured, but of a different form and nature. • Sensor is the initial stage in any transducer. • The property of transducer element is affected by the variation of the external physical variable according to unique relationship. 4 4/3/2019 Transducers classification • Based on power type classification - Active transducer (Diaphragms, Bourdon Tubes, tachometers, piezoelectric, etc…) - Passive transducer (Capacitive, inductive, photo, LVDT, etc…) Transducers classification • Based on the type of output signal - Analogue Transducers (stain gauges, LVDT, etc…) - Digital Transducers (Absolute and incremental encoders) 5 4/3/2019 Transducers classification • Based on the electrical phenomenon or parameter that may be changed due to the whole process. - Resistive transducer - Capacitive transducer - Inductive transducer - Photoelectric transducer Transducers and Sensors According to the physical variable to be measured, the transducers can be classified to: • Mechanical Transducers • Thermal Transducers • Optical Transducers 6 4/3/2019 Transducer Element • Single stage (direct) • Double stage (indirect) Single Stage Transducer 7 4/3/2019 Double Stage Transducer Typical Examples of Transducer Elements 8 4/3/2019 Typical Examples of Transducer Elements Typical Examples of Transducer Elements 9 4/3/2019 Signal Conditioning Signal conditioning refers to operations performed on signals to convert them to a form suitable for interfacing with other elements in control system • Analog signal conditioning. • Digital signal conditioning. Analog Signal Conditioning • Analog signal conditioning provides the operations necessary to transform a transducer output into a form necessary to interface with other elements in control system. 10 4/3/2019 Analog Signal Conditioning • It is possible to categorize signal conditioning into several general types: - Signal level and bias changes - Linearization - Conversion - Filtering Unites of Measurements • The base units, which have been established in The 14th General Conference on Weights and Measures (1971), will be used in this course. • The base measurement system is known as SI which stands for French “Le Syste´me International d’Unite´s”. 11 4/3/2019 Unites of Measurements Block Diagram Symbols • A block diagram approach is very useful in discussing the properties of elements and systems. 12 4/3/2019 Type of Errors • Systematic errors: Errors that tend to have the same magnitude and sign for the given set of conditions, such as instrument, environmental, and loading errors. This type of error can be eliminated by applying the proper calibration. • Random (or Accidental) errors: These errors are of variable magnitude and sign and do not obey any known law. Theses errors caused due to random variation in the parameter or the system of measurement, such as the accuracy of measuring small quantities. This type of error can be calculated by using statistical analysis. Type of Errors • Gross errors: These are generally the fault of the person using the instruments, and are due to: – Incorrect reading of instruments . – Incorrect recording of experiment data.. – Incorrect use of instruments. These errors may be of any magnitude and cannot be subjected to mathematical treatment. 13 4/3/2019 Statistical Analysis of Error in Measurement • Mean Value x x ........ x x x 1 2 n n n n • Standard Deviation d 2 d 2 ........... d 2 1 2 n Where: n d1 x1 x d2 x2 x Note: if the number of samples is less than 20, (n) in the standard deviation law will be replaced by (n-1) Statistical Analysis of Error in Measurement Interpretation of Standard deviation • If the error is truly random and we have large sample of readings, the data and the standard deviation is related to the normal probability curve. • The normal probability curve has the following characteristics: – 68% of readings lie within ±1σ of the mean – 95.5% of readings lie within ±2σ of the mean – 99.7% of readings lie within ±3σ of the mean 14 4/3/2019 Transfer Function/Mathematical Model • An ideal or theoretical input–output (stimulus– response) relationship exists for every sensor. • This input–output relationship may be expressed in the form of a table of values, graph, mathematical formula, or as a solution of a mathematical equation. • If the input–output function is time invariant (does not change with time) it is commonly called a static transfer function or simply transfer function. Transfer Function/Mathematical Model • A static transfer function represents a relation between the input stimulus s and the electrical signal E produced by the sensor at its output. This relation can be written as E=f(s). • Normally, stimulus s is unknown while the output signal E is measured and thus becomes known. The value of E that becomes known during measurement is a number (voltage, current, etc.) that represents stimulus s. • A job of the designer is to make that representation as close as possible to the true value of stimulus s. 15 4/3/2019 Transfer Function/Mathematical Model • In reality, any sensor is attached to a measuring system. One of the functions of the system is to “break the code E” and infer the unknown value of s from the measured value of E. Thus, the measurement system shall employ an inverse transfer function s=f -1(E)=F(E), to obtain (compute) value of the stimulus s. • It is usually desirable to determine a transfer function not just of a sensor alone, but rather of a system comprising the sensor and its interface circuit. Transfer Function/Mathematical Model • Preferably, a physical or chemical law that forms a basis for the sensor’s operation should be known. • If such a law can be expressed in form of a mathematical formula, often it can be used for calculating the sensor’s inverse transfer function by inverting the formula and computing the unknown value of s from the measured output E. • In practice, readily solvable formulas for many transfer functions, especially for complex sensors, does not exist and one has to resort to various approximations of the direct and inverse transfer functions. 16 4/3/2019 Function Approximations • Approximation is a selection of a suitable mathematical expression that can fit the experimental data as close as possible. • The act of approximation can be seen as a curve fitting of the experimentally observed values into the approximating function. • The approximating function should be simple enough for ease of computation and inversion and other mathematical treatments, for example, for computing a derivative to find the sensor’s sensitivity. Function Approximations • Initially, one should check if one of the basic functions can fit the data and if not, then resort to a more general curve-fitting technique, such as a polynomial approximation. • The simplest model of a transfer function is linear. It is described by the following equation: • As shown in the following figure, it is represented by a straight line with the intercept A, which is the output signal E at zero input signal (s=0). The slope of the line is B (sensitivity). 17 4/3/2019 Function Approximations Function Approximations • Initially, one should check if one of the basic functions can fit the data and if not, then resort to a more general curve-fitting technique, such as a polynomial approximation. • The simplest model of a transfer function is linear. It is described by the following equation: • As shown in the following figure, it is represented by a straight line with the intercept A, which is the output signal E at zero input signal (s=0). The slope of the line is B (sensitivity). 18 4/3/2019 Function Approximations • Note that the previous equation assumes that the transfer function passes, at least theoretically, through zero value of the input stimulus s. • In many practical cases it is just difficult or impossible to test a sensor at a zero input. Thus, in many linear or quasilinear sensors it may be desirable to reference the sensor not to the zero input but rather to some more practical input reference value s0. If the sensor response is E0 for some known input stimulus s0, the previous equation can be rewritten in a more practical form: Function Approximations • The reference point has coordinates s0 and E0. For a particular case where s0=0, Eq. (2) becomes Eq. (1) and E0=A. • The inverse linear transfer function for computing the input stimulus from the output E is given by: • Note that three constants shall be known for computing the stimulus s, sensitivity B, s0 and E0 of the reference point. 19 4/3/2019 Function Approximations • Very few sensors are truly linear. • In the real world, at least a small nonlinearity is almost always present, especially for a broad input range of the stimuli. Thus, the previous equations represent just a linear approximation of a nonlinear sensor’s response, where a nonlinearity can be ignored for the practical purposes. • In many cases, when nonlinearity cannot be ignored, the transfer function still may be approximated by a group of linear functions (linear piecewise approximation).