experiment manual anemometer

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ManualAnemometer (Hot wire)Manual remote experimentProject e-Xperimenteren+

W.Wijngaard

2 februari 2006


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Manual Anemometer (Hot wire)

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Colofon


Manual remote experiment

Project e-Xperimenteren+

Stichting Digitale Universiteit

Oudenoord 340, 3513 EX Utrecht

Postbus 182, 3500 AD Utrecht

Phone 030 - 238 8671

Fax 030 - 238 8673E-mail [email protected]

Author(s)W.Wijngaard

Copyright

Stichting Digitale Universiteit

De Creative Commons Naamsvermelding-GeenAfgeleideWerken-NietCommercieel-licentie is vantoepassing op dit werk. Ga naar http://creativecommons.org/licenses/by-nd-nc/2.0/nl/ om deze

licentie te bekijken.

Date

2 februari 2006


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Table of contents

1 Introduction 4 2 Theory 5

2.1 Dynamic theory of the anemometer. 5 3 Setup 6 4 Remote interface 8

4.1 Tab 1 (Process Test) 9 4.1.1 Experiment 1 : 9 4.2 Tab 2 (Controlled System) 10 4.2.1 Experiment 2 : 10 4.2.2 Experiment 3 : 12 4.2.3 Experiment 4 : 13 4.2.4 Experiment 5 : 14 4.3 Tab 3 (Autocovariance of Error) 15

5 Constants and parameters 16


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1 Introduction

An anemometer is an instrument for measurement of the velocity of a fluid or gas. Herethe gas is common air. The instrument is fast and sensitive when used in the rightway. (John P. Bentley : Principles of measurement systems. Longman, London and NewYork (1983) pp. 307-323)

Principle of operation : A thin tungsten wire heated by an electrical current is cooled byair. The temperature of the wire may be calculated from the resistance. Therefore thevelocity of the air may be calculated from the resistance R of the wire and the electricalcurrent I through the wire.

Measure R and IMeasure R and IMeasure R and IMeasure R and I ------------------------> Calculate air velocity V> Calculate air velocity V> Calculate air velocity V> Calculate air velocity V

In practice the resistance R is made constant by using a Wheatsone bridge in which theerror voltage E is automatically controlled to zero (see the following figure). Thecontrolsystem is changing the supply voltage Y of the bridge until E is zero. In this way Yis proportional to the current I through the wire.


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2 Theory

2.1 Dynamic theory of the anemometer.

T h e w i r e i s a p p r o x i m a t e l y a f i r s t o r d e r s y s t e m . A s m a l l c h a n g e i n i n p u t p o w e r w i l l r e s u l t i n

a c h a n g e i n t h e t e m p e r a t u r e o f t h e w i r e w i t h o n e t i m e c o n s t a n t s u g g e s t i n g a f i r s t o r d e r

s y s t e m . I n e x p e r i m e n t 1 i n c r e a s i n g t h e s u p p l y v o l t a g e Y o f t h e b r i d g e w i l l i n c r e a s e t h e

r e s i s t a n c e a n d t h e r e f o r e d e c r e a s e E . T h e o u t p u t o f t h e s y s t e m i s c h o s e n t o b e - E m a k i n g

t h e p r o c e s s g a i n K p

p o s i t i v e . F r o m t h i s e x p e r i m e n t K p

a n d t h e t i m e c o n s t a n t m a y b e

d e t e r m i n e d . A s a n a l t e r n a t i v e t h e n o n l i n e a r s y s t e m m a y b e l i n e a r i z e d t o c a l c u l a t e K p

a n d

t h e t i m e c o n s t a n t .For the nonlinear theory see the companion website.

Control by Y=K r*E+Y0 will deliver a system with a timeconstant

Increasing K p*Kr will deliver a faster system. However the computer introduces a delay by

sampling at the moments n*T (n integer). Due to this delay the limiting value for K p*Kr is

When K r*Kp is increasing above this value the system will start to oscillate. Optimization of

the system is possible by increasing this limiting value. This may be effected by a largersamplerate (decreasing the sampletime T). The limiting formula for K r*Kp given abovemay be derived with the assumption that the program, after reading the inputvoltage,calculates the ouputvoltage without any delay. This is certainly not true. The delay will bea value between zero and one sampletime. With the maximum delay of one sampletimethe limiting value of K r*Kp is according to the complete theory approximately two timessmaller.


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3 SetupThe wire is placed in a windtunnel for exclusion of external draughts and may be movedto and fro by a motor for calibration of the system. A fan may be used to deliver areproducible airflow.

Mechanical Setup


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Motor and wire outside windtunnel


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4 Remote interfaceBelow is a description of the software interface of the experiment. In the companion website 5

experiments have been described. The panel is organized in a common panel and three tabs.

The common panel includes the measurement range, the samplerate and the measurement time.The number of samples is calculated and given as an indicator. Pressing the Start Test button is

starting the measurement. The common panel includes a graph of the Error voltage E versus the

measurement time.

Tab 1 (Process Test) : By choosing this Tab the control-loop is in manual. In this way the

properties of the so called Process may be investigated. This Tab should be used for

Experiment 1.

Experiment 1 : Measurement of the error voltage E as a function of the supply voltage Y . Tab2 (Controlled System) : This is the central part of the user Interface.

Experiment 2 : Measurement of the gain K p of the process and the time constant of the process(with K r=0).

Experiment 3 : Optimization of the Control parameters in still air.

Experiment 4 : Calibration of the system with reciprocating movement of the wire in still air.

Experiment 5 : Measurement of the air velocity generated by a fan.

Tab 3 (Autocovariance of Error) : Delivers only a graphical representation of the characteristics of

the signal in terms of the autocovariance function.


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4.1 Tab 1 (Process Test)

4.1.1 Experiment 1 :

Measurement of the error voltage E as a function of the supply voltage . Using this Tab the supply

voltage Y is changed linearly from 0 to the chosen value of Ymax in the Total Time chosen in thecommon background panel.

Common Panel Controls loop rate (scan rate) : The samplefrequency in samples per second (upper limit 200000). Total Measuring Time per Test


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4.2 Tab 2 (Controlled System)

In Tab 2 (Controlled System) the control parameters may be chosen. The supply voltage Y is

calculated using the formula Y=Kr*E+Y0+Ystoor.

E is the error voltage of the bridge.

Kr is the gain of this P-control algorithm.Y0 is the offsetvoltage . Y0 should be chosen approximately equal to the value of the supply

voltage for which the bridge is in balance (E=0).

Ystoor is an extra testsignal. Here Ystoor is a square wave . The number of periods and the

amplitude may be chosen here.

In Tab 2 the motor and the fan can be activated.


Measurement of the gain K p of the process and the timeconstant of the process.

Parameters : Kr=0 (control not in effect), Motor and Fan off. At first the operating point should

be chosen by changing Y0 (with Ystoor=0) until the bridge is balanced (error E is nearly zero). A

result is given here.

Common Panel extra Control : Number of samples to neglect : The samples at the beginning of the Test are sometimes

not representative, being too large or too small. Neglecting these samples will deliver moreuseful Graphs.

Tab 2 (Controlled System) Controls : Y0 : The constant offset of the supply voltage of the bridge. Kr : The gain of the controller. Amplitude Ystoor : Ystoor is a square wave here with the chosen amplitude. Number of Periods : The number of periods (per test) of the square wave Ystoor.

Motor-Fan : A switch between Motor and Fan. Motor : The signal to the motor (with Motor-Fan at Motor). Fan : The signal delivered to the Fan (with Motor-Fan at Fan).


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Tab 2 (Controlled System) Indicators : Control Signal Y versus Time : A Graph of the supply voltage Y versus Time.

The gain K p and the timeconstant of the process may be evaluated from the stepresponsegenerated with Ystoor with Kr=0, as given in the following picture.


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Optimization of the Control parameters in still air. The controlloop may be optimized by using Ystoor

as a testsignal. A result is given here.


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The system is calibrated by moving the wire through still air. The movement is generated by a

motor. The motor delivers a reciprocating movement of the wire with an amplitude of 1.00 cm. In

this case Ystoor is chosen to be zero.


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Measurement of the air velocity generated by a fan.

When the Motor-Fan switch is pointing to Fan, the Fan will be powered when the measurement is in

progress. So the fan will start at time 0 of each measurement.


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4.3 Tab 3 (Autocovariance of Error)

Delivers only a graphical representation of the characteristics of the errorsignal in terms of the

autocovariance function. The autocovariance may be used as a test for nearly oscillating behavior

or for the characterization of the flow from the fan.

Tab 3 (Autocovariance of Error) Controls :

Width Autocovar from center : The width of the autocovariance function to be displayed.

Tab 3 (Autocovariance of Error) Indicators :

Autocovariantie_Errror : The Graph of the autocovariance of the errorsignal of the bridge.


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5 Constants and parametersIn the table below some relevant parameters of the experiment are summarized.

Name Description Value / range, error, unitLoop rate (scan rate) The sample rate of the Analog Input

channels

10 20000 Hz

Total measuring time Measuring time per test 0,01 10 seconds

Number of samples to

neglect

0 - total number of

samples

Ymax In experiment 1 the supply voltage Y is

changed form 0 to Ymax

0 10 Volt

Y0 Offset in Y=Kr*E+Y0 0 10 Volt

Kr Gain of the controller 0 - 1000

Motor Supplyvoltage for the motor 0 3 Volt

Fan Supplyvoltage for the Fan 0 - 6 Volt

Amplitude Ystoor Amplitude of the extra voltage supplied to

the bridge

0 1 Volt

Number of Periods Number of periods of the extra voltage in the

measuring time

0,5 20

Width autocovariance

from center

Width of the autocovariance graph 5 total number of

samples


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experiment manual anemometer

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