Theory of Measurements and Sensors (MEC201) Lecture Notes PDF

Mechanical Engineering Department Theory of Measurements and Sensors (MEC201) Dr. Ashraf Elsayed  Chapter (3) Dynamic Characteristics of Measuring Instruments ‫الخصائص الديناميكية ألجهزة القياس‬ Dr. Ashraf Elsayed...

Mechanical Engineering Department Theory of Measurements and Sensors (MEC201) Dr. Ashraf Elsayed  Chapter (3) Dynamic Characteristics of Measuring Instruments ‫الخصائص الديناميكية ألجهزة القياس‬ Dr. Ashraf Elsayed 2 Chapter (3)- Dynamic Characteristics of Measuring Instruments Performance Characteristics of Instruments 3 Dynamic Characteristics of Measuring Instruments ‫الخصائص الديناميكية ألجهزة القياس‬ 4  Chapter (3)- Dynamic Characteristics of Measuring Instruments Introduction a) Speed Of Response and Measuring Lag ❖ In a measuring instrument: The speed of response (or) responsiveness is defined as the rapidity with which an instrument responds to a change in the value of the quantity being measured (input signal). ‫عرف سرعة االستجابة (أو) االستجابة بأنها السرعة التي تستجيب بها األداة (جهاز القياس) للتغير في قيمة الكمية التي يتم قياسها‬َّ ُ ‫▪ ت‬.)‫(التغير فى قيمة إشارة اإلدخال‬ Lag: It is the retardation or delay in the response of an instrument to changes in the measured variable. The lag is caused by conditions such as inertia, or resistance. ‫ يحدث هذا التأخر بسبب القصور الذاتي أو‬.‫ هو التأخير أو التخلف في استجابة األداة للتغيرات في المتغير المقاس‬:‫▪ الفاصل الزمني‬.‫المقاومة داخل األداة‬ 5  Chapter (3)- Dynamic Characteristics of Measuring Instruments Introduction b) Fidelity (Accuracy) and Dynamic Errors Fidelity (accuracy) of an instrumentation system: It is the degree to which an instrument indicates the changes in the measured variable without dynamic error (faithful reproduction). Or (The term accuracy describes how close the measured value is to the true value). ‫ هي الدرجة التي تشير بها األداة إلى التغييرات في المتغير المقاس بدون خطأ ديناميكي (إستنساخ دقيق) (يصف‬:‫▪ دقة نظام األجهزة‬.)‫مصطلح الدقة مدى قرب القيمة المقاسة من القيمة الحقيقية‬ It refers to the ability of the system to reproduce the output in the same form as the input. If the input is a sine wave, then for 100% fidelity the output should also be a sine wave. Dynamic Error: The difference between the indicated quantity by instrument and the true value of the time quantity (quantity changing with time)..)‫ الفرق بين الكمية المقاسة بواسطة األداة والقيمة الحقيقية للكمية الزمنية (الكمية التى تتغير بمرور الوقت‬:‫الخطأ الديناميكي‬ ▪ 6  Chapter (3)- Dynamic Characteristics of Measuring Instruments Introduction c) Overshoot The Overshoot is defined as the maximum amount by which the pointer moves beyond the steady state..‫❖ يتم تعريف التجاوز على أنه الحد األقصى للمقدار الذي يتحرك به المؤشر خارج الحالة الثابتة‬ ▪ Because of maximum and inertia. A moving part i.e., the pointer of the instrument does not immediately come to reset in the find deflected position. The pointer goes find deflected position. The pointer goes beyond the steady state i.e., it overshoots. 7  Chapter (3)- Dynamic Characteristics of Measuring Instruments Introduction D) Dead Time and Dead Zone Dead time is defined as the time required for an instrument to begin to respond to a change in the measured quantity, it represent the time before the instrument begins to respond after the measured quantity has been altered. ‫▪ يتم تعريف الوقت الميت على أنه الوقت المطلوب لألداة لبدء االستجابة‬ ‫لتغيير في الكمية المقاسة والذى يمثل الوقت قبل أن يبدأ الجهاز في‬.‫االستجابة بعد تغيير الكمية المقاسة‬ Dead zone define the largest change of the measured to which the instrument does not respond. Dead zone is the result as friction backlash in the instrument. ‫ المنطقة الميتة هي ناتجة عن االحتكاك العنيف داخل األداة‬.‫▪ المنطقة الميتة تحدد أكبر تغيير في عملية القياس والتى ال يستجيب لها الجهاز‬.)‫جهاز القياس‬ 8 (  Chapter (3)- Dynamic Characteristics of Measuring Instruments Introduction E) Frequency Response Frequency response is defined as the ability of a measurement system to accurately reflect dynamic variable changes..‫يعرف االستجابة الترددية بأنها قدرة جهاز القياس على عكس التغيرات فى المتغير الديناميكي بدقة‬ َّ ▪ ▪ For example, the measurement system consists of a pressure sensor and its associated electronics and plumbing. Each component of the system affects the dynamic frequency response. ▪ The frequency response provides complete information about the output of the system for any input. ‫ يؤثر كل مكون من‬.‫ يتكون نظام القياس من مستشعر ضغط وما يرتبط به من أجهزة إلكترونية وأنظمة ضخ‬،‫▪ على سبيل المثال‬.‫مكونات النظام على االستجابة الترددية الديناميكية‬.‫▪ توفر االستجابة الترددية معلومات كاملة حول خرج النظام ألي إدخال‬ 9  Chapter (3)- Dynamic Characteristics of Measuring Instruments Introduction Standard Test Inputs ❖ The dynamic performance of both measuring and control system is determined by applying some known and predetermined input signal to its primary sensing element and then studying the behaviour of the output signals. ‫▪ يتم تحديد األداء الديناميكي لكل من نظام القياس والتحكم من خالل تطبيق بعض إشارات اإلدخال المعروفة والمحددة مسبقًا على عنصر االستشعار‬.‫األساسي الخاص بها ثم دراسة سلوك اإلشارات الخارجه‬ The most common standard inputs used for dynamic analysis a) Step functions. b) Linear (or) ramp functions. c) Sinusoidal (or) sine wave functions. 10 Chapter (3)- Dynamic Characteristics of Measuring Instruments Introduction 11 Ch. (3)- Dynamic Characteristics of Measuring Instruments Measuring System Model 12 Ch. (3)- Dynamic Characteristics of Measuring Instruments Measuring System Model 13 First Order Systems (Step Function Input) 14 Ch. (3)- Dyn. Characteristics of Measuring Instruments First Order Systems (Step Function Input) 15 Ch. (3)- Dyn. Characteristics of Measuring Instruments First Order Systems (Step Function Input) 16 Ch. (3)- Dyn. Characteristics of Measuring Instruments First Order Systems (Step Function Input) 17 Ch. (3)- Dyn. Characteristics of Measuring Instruments First Order Systems (Step Function Input) 63.2% of final value at t = one time constant t = τ −𝒕 Г = 𝒆 = 𝒆−𝟏 = 0.368 τ 18 Ch. (3)- Dyn. Characteristics of Measuring Instruments First Order Systems (Step Function Input) 19 Ch. (3)- Dyn. Characteristics of Measuring Instruments First Order Systems (Step Function Input) 20 Ch. (3)- Dyn. Characteristics of Measuring Instruments Example Example (1). A thermometer acting as a first-order system is initially at a temperature of 35 oC and is suddenly subjected to a temperature of 110 oC. After 8 sec, the thermometer indicates a temperature of 75 oC. Calculate the time constant and the 90 percent rise time for the thermometer. Given Solution 21 Ch. (3)- Dyn. Characteristics of Measuring Instruments Example Example (2). Suppose a bulb thermometer originally indicating 20 oC is suddenly exposed to a fluid temperature of 37 oC. Develop a model that simulates the thermometer output response. If the thermometer has a time constant of 20 ms and subjected to a step change in input, calculate the 90% rise time. Given Solution 22 Ch. (3)- Dyn. Characteristics of Measuring Instruments Example Solution 23 Ch. (3)- Dyn. Characteristics of Measuring Instruments Example Solution 24 Ch. (3)- Dyn. Characteristics of Measuring Instruments Example 25 Ch. (3)- Dyn. Characteristics of Measuring Instruments Example Given Solution 26 Ch. (3)- Dyn. Characteristics of Measuring Instruments Example Given Solution 27  First Order Systems (Periodic Function Input) 28  Chapter (3)- Dynamic Characteristics of Measuring Instruments First Order Systems (Periodic Function Input) The frequency response of a first order system is obtained by applying sine waves of known amplitude at the input and examining the output response. Here the input has a cycle variation, the input The frequency or harmonic response is a varies sinusoidal with a constant amplitude measure of the capability of the system to mathematically it may be represented as respond to inputs of cyclic nature. ‫التردد أو االستجابة التوافقية هو مقياس لقدرة النظام على االستجابة للمدخالت ذات‬ ‫الطبيعة الدورية‬ 29  Chapter (3)- Dynamic Characteristics of Measuring Instruments First Order Systems (Periodic Function Input) Lag 30  Chapter (3)- Dynamic Characteristics of Measuring Instruments First Order Systems (Periodic Function Input) M≤1 31  Chapter (3)- Dynamic Characteristics of Measuring Instruments First Order Systems (Periodic Function Input) 32  Chapter (3)- Dynamic Characteristics of Measuring Instruments First Order Systems (Periodic Function Input) A B 33  Chapter (3)- Dynamic Characteristics of Measuring Instruments First Order Systems (Periodic Function Input) 34  Chapter (3)- Dynamic Characteristics of Measuring Instruments Example (1) A certain thermometer has a time constant of 10 s and is subjected to a very slow harmonic temperature variation of amplitude of 20 oC and a frequency of 0.01 Hz. What is the phase lag of the thermometer and the amplitude attenuation? Given Solution 35  Chapter (3)- Dynamic Characteristics of Measuring Instruments Example (2) Given Solution 36  Chapter (3)- Dynamic Characteristics of Measuring Instruments Solution 37 Dynamic Characteristics of Measuring Instruments ‫الخصائص الديناميكية ألجهزة القياس‬ Second Order Systems 38  Chapter (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems 39 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems 𝑲 𝝎𝒏 = 𝒎 40 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems 41 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems 𝝎𝒅 𝒇𝒓𝒆𝒒𝒖𝒂𝒏𝒄𝒚 𝒓𝒂𝒕𝒊𝒐,𝒓 = = 𝟏 −𝟐 𝝎𝒏 𝝎𝒅 = Damped Natural Frequency 𝑲 𝒒 𝝎𝒏 = = 𝒎 𝑱 = 𝟐 𝐤𝐦 𝑫𝒂𝒎𝒑𝒊𝒏𝒉 𝒓𝒂𝒕𝒊𝒐 = 42 = γ Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems −𝝅 Overshoot = exp 𝟏−𝟐 43 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems 44 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems The settling time is defined as the time required for the output to settle within a definite range ±2% of the final value. ± 2 ٪ ‫يتم تعريف وقت االستقرار على أنه الوقت المطلوب الستقرار اإلخراج ضمن نطاق محدد‬.‫من القيمة النهائية‬ 𝝅 𝟏 Rise Time (𝒕𝒓 )= Time Constant,𝝉 = 𝝎𝒅 𝝎𝒏 45 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems Example (2) 46 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems 47 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems 48 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems The expression describing the motion of linear displacement of the second order systems. 49 Ch. (3)- Dynamic Characteristics of Measuring Instruments Example 50 Ch. (3)- Dynamic Characteristics of Measuring Instruments Example 51 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems The expression describing the motion of rotational displacement of the second order systems. 52 Ch. (3)- Dynamic Characteristics of Measuring Instruments Example 53 Ch. (3)- Dynamic Characteristics of Measuring Instruments Example 54 Ch. (3)- Dynamic Characteristics of Measuring Instruments Second Order Systems Report 55 Thank you for your attention 56