Instrumentation-Training-Tutorial4

Instrumentation-Training-Tutorial4 - INSTRUMENTATION AND...

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D.J.Dunn 1 INSTRUMENTATION AND CONTROL TUTORIAL 4 – INSTRUMENT SYSTEM MODELS AND CALIBRATION This tutorial is mainly about instrument systems and simple mathematical models. It brings together the various elements covered in tutorials 2 and 3. It leads into more advance work on control system models. It is provided mainly in support of the EC module D227 – Control System Engineering. On completion of this tutorial, you should be able to do the following. Explain the model of a basic instrument system. Calculate the relationship between input and output for complete system. Explain and identify the main errors that occur in instrument systems. Explain the basic principles of calibration. Explain primary and secondary standards. In order to complete the theoretical part of this tutorial, you must be familiar with basic mechanical and electrical science. www.PAControl.com

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D.J.Dunn 2 1. MODELS OF INSTRUMENT SYSTEMS A mathematical model relates the input and output of a system or sub-system. In other words it is a formula relating the input and output. The instrument is usually drawn as a block with the input and output shown. The mathematical model is written inside the block. The general symbol for signals is θ but specific symbols may be used. The suffix i denotes the input and o the output. When the input and output is a simple ratio, the model is just a number representing the ratio of output to input. It is often denoted by G, especially if it is a gain. In such case G = θ o / θ i . If the input and output have different units, then G has units also. WORKED EXAMPLE No.1 Find the output if the input is 10 mW. The gain is a ratio and not in decibels. SOLUTION G = θ o / θ i = 50 θ o = 50 x θ i = 50 x 10 = 500 mW WORKED EXAMPLE No.2 Find the output if the input is 50oC. SOLUTION G = θ o / θ i = 2 μ v/ o C θ i = θ o /2 = 50/2 = 25 μ V SELF ASSESSMENT EXERCISE No.1 1. The input is 2 mm, find the output. (Answer 6 V) 3. The input is 250 rev/min, find the output. (Answer 1.25 V) www.PAControl.com
D.J.Dunn 3 Some sensors have non linear equations and we cannot represent the relationship with a simple ratio so must use the full equation. For example a differential pressure flow meter has an equation Flow rate = C ( p) 1/2 Where C is a constant and p is the differential pressure. WORKED EXAMPLE No.3 The input and output of the D.P. meter is related by the law Q = C ( p) 1/2 Where Q is the input flow rate in m 3 /s, p is the output differential pressure and C is the meter constant. Determine the flow rate when p = 250 Pa and C = 0.0004 m 3 /s per Pa. SOLUTION Q = C ( p) 1/2 = 0.0004 (250) 1/2 = 0.00632 m 3 /s or 6.32 dm 3 /s www.PAControl.com

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D.J.Dunn 4 2. MODELS FOR COMPLETE SYSTEMS A complete instrument system is made up from several sub-systems connected in series. The best way to deduce the input or output of a complete system is a step by step analysis of the information passing
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This note was uploaded on 09/28/2009 for the course X RAY MECH EMP5209 taught by Professor Hui-leo-chen during the Fall '09 term at University of Ottawa.

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Instrumentation-Training-Tutorial4 - INSTRUMENTATION AND...

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