Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

48
[email protected] • ENGR-25_Plot_Mode_1.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected] Engr/Math/Physics 25 Chp5 MATLAB Plots & Models 1

description

Engr/Math/Physics 25. Chp5 MATLAB Plots & Models 1. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]. Learning Goals. List the Elements of a COMPLETE Plot e.g.; axis labels, legend, units, etc. Construct Complete Cartesian (XY) plots using MATLAB - PowerPoint PPT Presentation

Transcript of Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

Page 1: Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

[email protected] • ENGR-25_Plot_Mode_1.ppt1

Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Chp5 MATLABPlots &

Models 1

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Learning Goals List the Elements of a COMPLETE Plot

• e.g.; axis labels, legend, units, etc.

Construct Complete Cartesian (XY) plots using MATLAB• Modify or Specify MATLAB Plot Elements:

Line Types, Data Markers, Tic Marks

Distinguish between INTERPolation and EXTRAPolation

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Learning Goals cont

Construct using MATLAB SemiLog and LogLog Cartesian Plots

Use MATLAB’s InterActive Plotting Utility to Fine-Tune Plot Appearance

Create “Linear-Transform” Math Models for measured Physical Data• Linear Function → No Xform• Power Function → LogLog Xform• Exponential Function → SemiLog Xform

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Learning Goals cont

Use Regression Analysis as quantified by the “Least Squares” Method• Calculate

– Sum-of-Squared Errors (SSE or J)The Squared Errors are Called “Residuals”

– “Best Fit” Coefficients– Sum-of-Squares About the Mean (SSM or S)– Coefficient of Determination (r2)

• Scale Data if Needed– Creates more meaningful spacing

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Learning Goals cont

Build Math Models for Physical Data using “nth” Degree Polynomials

Use MATLAB’s “Basic Fitting” Utility to find Math models for Plotted Data

Use MATLAB to Produce 3-Dimensional Plots, including• Surface Plots• Contour Plots

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Why Plot?

Engineering, Math, and Science are QUANTITATIVE Endeavors, we want NUMBERS as Well as Words

Many times we Need to• Understand The (functional) relationship

between two or More Variables• Compare the Values of MANY Data Points

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Why Plot? cont

Plots have TREMENDOUS Utility in Two Major Areas

1. Communication• To Help OTHERS understand the

RESULTS of Your Tests or Experiments or Theories

2. Analysis• To Help You ANALYZE Data or

Theories to Determine the Significance or Meaning of the Data

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Plotting Trivia

Rene Decartes (1596-1650) Developed “Cartesian” (XY) Plots in about 1637

Florence Nightingale Developed the “Polar Area Plot” (Pie Chart) in 1857

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Sys3 2X200 MultiBlok, 997671 250-13.8 PreWeld Pi Tube-1

0

25

50

75

100

125

150

175

200

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Hole Number (1 = closest to Manifold Block)

Ind

ivid

ual

Ho

le

P (

10X

To

rr)

DNS Tube-1 BMayer Tube1

DNS Normalized BMayer Normalized

PARAMETERS• For Single Tube Manifold• Flow = ??/0.24 slpm/hole• Exh to Atm Pressure (~750Torr)• Test Engr = DNStoddard, BMayer• Test Date = 09Mar00/10Mar

file = HbH997671PreW09Mar00.xls

Plot Title

Axis Title

Tic Mark

Tic Mark Label

Lege

nd

Data Symbol

Annot

atio

ns

Axis UNITS Connecting Line

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Gate Voltate to Balance ElectroStatic and Spring Forces vs. d

0

2

4

6

8

10

12

14

16

18

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Cantilever Height, d (µm)

Gat

e P

ote

nti

al

(Vd

c)

file = ElectroStatics_0104.xls

Threshold

Turn-On(Zip-Up)

Turn-Off(Peel-Off)

PARAMETERS• E = 135 Gpa (PolySi)• L = 100 µm• W = 60 µm• t = 3 µm• do = 2 µm• Z = 300 µm • VTh = 17.00396 Vdc• Vr = 7.903 Vdc

Vr Arrow CallOut

Theoretical Plot → NO Data Markers

Important Output Value

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

MATLAB Plot Example

Consider a Rocket Launch

A Math Model for the Height, y, vs. the Distance, x:

xy 73.143.0• Where both x & y

are in units of miles

Use MATLAB to Plot y vs x for a 51 mi DownRange Dist

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The Results

0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Distance (mi)

Hei

ght (

mi)

Rocket Height as a Function of Downrange Distance

>> x = [0:0.1:51];>> y = 0.43*sqrt(1.73*x);>> plot(x,y)>> xlabel('Distance (mi)')>> ylabel('Height (mi)')>> title('Rocket Height as a Function of Downrange Distance')

The Command Session

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Plot OutPut

The plot appears in the Figure window Output from One of

1. Use the menu system. Select Print on the File menu in the Figure window. Answer OK when you are prompted to continue the printing process.

2. Type print at the command line. This command sends the current plot directly to the printer.

3. Save the plot to a file to be printed later or imported into another application such as PowerPoint. You need to know something about graphics file formats to use this file properly. See the subsection Exporting Figures.

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Elements of a Useful Plot

The essential features of a Maximally Understandable Plot1. Each axis must be labeled with the name

of the quantity being plotted and its units. – If two or more quantities having different

units are plotted (such as when plotting both speed and distance versus time), then indicate the units in the axis label if there is room, or in the legend or labels for each curve

2. Each axis should have regularly spaced tick marks at convenient intervals - not too sparse, but not too dense - with a spacing that is easy to interpret and interpolate. – e.g.; use 0.1, 0.2, and so on, rather than 0.13,

0.26

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Elements of a Useful Plot cont

3. If you plot more than one curve or data set, label each Curve/DataSet on its plot or use a legend to distinguish them.

4. If you are preparing multiple plots of a similar type or if the axes’ labels cannot convey enough information, use a title. When in Doubt, TITLE

5. If you plot measured data, plot each data point with a symbol such as a circle, square, or cross – use the same symbol for every point in the

same data set. – If there are many data points (within a single

Data-Set), then plot them using the dot symbol.

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Elements of a Useful Plot cont

6. Sometimes data symbols are connected by lines to help the viewer visualize the data, especially if there are few data points. However, connecting the data points, especially

with a solid line, might be interpreted to imply knowledge of what occurs between the data points. Take appropriate care to prevent such MisInterpretation.

7. If you are plotting points generated by evaluating a function (as opposed to measured data), do not use a symbol to plot the points. Instead, be sure to generate many points, and connect the points with solid lines. The Curve should be SMOOTH

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

grid Command

The grid command displays gridlines at the tick marks corresponding to the tick labels. • Type grid on to add gridlines; • Type grid off to stop plotting gridlines. • When used by itself, grid toggles this

feature on or off, but you might want to use grid on and grid off to be sure.

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

axis Command The axis command overrides the

MATLAB Default selections for the axis limits.

The basic syntax: axis([xmin xmax ymin ymax]).

This command sets the scaling for the x- and y-axes to the minimum and maximum values indicated. Note that, unlike an array, this command does not use commas to separate the values.

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

LineWidth Command

MATLAB’s Default width and color for a plotted line are• Thin• Blue

This “thin blue line” is often hard to SEE and to PHOTOCOPY

Use 'LineWidth',n, to increase WIDTH

Use color-spec to make BLACK

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Affect of grid, axis, LineWidth

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

2

2.5

3

3.5

4

Distance (mi)

Hei

ght

(mi)

Rocket Height as a Function of Downrange Distance

plot(x,y, 'k', 'LineWidth', 3), xlabel('Distance (mi)'),... ylabel('Height (mi)'),grid on, axis([0 51 0 4.1]),... title('Rocket Height as a Function of Downrange Distance')

Command Session

Compare to the Previous Version

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Plotting Vectors A single Row or

Column Vector, v, can be plotted as plot(v)• The X-Axis value

= Vector Index; 1, 2, 3,...n

• The Y-Axis value = Vector-Value

Example: Plot TOP DataSet from sld-9 using Row Vector

The 39 Data Points for Vector, p

The Plot Statement

>> p = [143, 151, 164, 149, 154, 169, 164, 172, 181, 183, 167, 177, 163, 199, 164, 168, 162, 155, 191, 153, 151, 150, 143, 177, 142, 145, 138, 136, 147, 143, 161, 137, 138, 138, 136, 140, 147, 148, 151]

>> plot(p), xlabel('Hole No'), ylabel('DelP (10x Torr)'),...title('Distribution Tube Uniformity Test'), grid

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Vector Plot

0 5 10 15 20 25 30 35 40130

140

150

160

170

180

190

200

Hole No

Del

P (

10x

Tor

r)

Distribution Tube Uniformity Test

Sys3 2X200 MultiBlok, 997671 250-13.8 PreWeld Pi Tube-1

0

25

50

75

100

125

150

175

200

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Hole Number (1 = closest to Manifold Block)

Ind

ivid

ua

l H

ole

P

(1

0X

To

rr)

DNS Tube-1 BMayer Tube1

DNS Normalized BMayer Normalized

PARAMETERS• For Single Tube Manifold• Flow = ??/0.24 slpm/hole• Exh to Atm Pressure (~750Torr)• Test Engr = DNStoddard, BMayer• Test Date = 09Mar00/10Mar

file = HbH997671PreW09Mar00.xls

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Complex Number Plots

MATLAB can Not Plot x vs z if z is Complex

For Complex z, the statement plot(z) is effectively the Same as plot(real(z), imag(z))

Example Plot for

Command Session

100for

7.03.0cos

n

jz n

>> w = 0.3-.7j>> n = [0:0.1:10];>> z = cos(w.^n);>> plot(z), xlabel('Re'), ylabel('Im')>> u = cos(w^4.7)u = 1.0011 - 0.0386i>> u = cos(w^.6)u = 0.9182 + 0.3476i

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Complex Plot

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Re

Im

100for

7.03.0cos

n

jz n

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

fplot → “Smart” Plotting

To make a quick Function-Plot, use MATLAB’s fplot

Need Only• The FUNCTION• Independent

Variable RANGE

The fplot Syntax:fplot(‘string’, [xmin, xmax])

• Where

– String Text String that describes the function

– xmin & xmax are the plotting Range:

Example the transient Response for an RLC Circuit (c.f. ENGR43):

ttetu t 13sin1113cos73.0

• Apply fplot over the range of 0-9 sec

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The fplot

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-10

-5

0

5

10

15

ttetu t 13sin1113cos73.0

fplot('(exp(-0.3*t))*(7*cos(13*t) - 11*sin(13*t))', [0 9])

Command Session

>> u = '(exp(-0.3*t))*(7*cos(13*t) - 11*sin(13*t))';>> fplot(u, [0 9])

EQUIVALENT Session

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Anonymous Function & fplot

0 5 10 15 20 25 30 35-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

uofx = @(x) cos(x)/log(x+3)

fplot(uofx, [0 37]),grid

Command Session

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Beware fplot Syntax

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-10

-5

0

5

10

15

uoft = @(t) (exp(-0.3*t)).*(7*cos(13*t) - 11*sin(13*t))

fplot('uoft', [0 9]),grid

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1

2

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5

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7

8

9

fplot(uoft, [0 9]),grid

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Plot Polynomials w/ polyval

Recall the Polynomial fcn; e.g.

• Where– p is a Vector

containing of the (constant) coefficients of the polynomial

y = polyval(p,x)

Find y using MATLAB’s polyval function

1953117 23 xxxy

– x is the Value of the independent variable

Evaluate the example polynomial at x = 73

>> P = [17 -31 5 19];>> Y_73 = polyval(P,73)Y_73 = 6448474

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Plotting w/ polyval

Let’s Plot this Polynomial over −1.8 x 4.2

Note the Zero Coeff. For the 3rd Degree Term

94.111.673.4031.2 2345 xxxxxy

>> p5 = [1,-2.31,0,-4.73,6.11,1.94];>> x = [-1.8:.01:4.2];>> plot(x, polyval(p5,x)), xlabel('x'), ylabel('y = f(x)')

The Command Window Session

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

The polyval Plot (also fminbnd)

94.111.673.4031.2 2345 xxxxxyThe

FigureWindow

>> pofx = @(x) x.^5 - 2.31*x.^4 - 4.73*x.^2 + 6.11*x + 1.94pofx = @(x)x.^5-2.31*x.^4-4.73*x.^2+6.11*x+1.94

>> [xmin, minval] = fminbnd(pofx, 0,3)

xmin = 2.1371e+000

minval = -1.0212e+001

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Find Local Minimum

Find The MIN between 1-3 using polyval and min commands

-2 -1 0 1 2 3 4 5-100

0

100

200

300

400

500

600

x

y

>> x1 = [1:.001:3];>> y1 = polyval(p5,x1);>> [yMin, kMin] = min(y1)

yMin = -10.2117

kMin = 1138

>> xMin = x1(kMin)

xMin = 2.1370

94.111.673.4031.2 2345 xxxxxy

2117.10,1370.2

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Saving Figures

To save a figure that can be opened in subsequent MATLAB sessions, save it in a figure file with the .fig file name extension

To do this, select Save from the Figure window File menu or click the Save button (the disk icon) on the toolbar.

If this is the first time you are saving the file, the Save As dialog box appears. Make sure that the type is MATLAB Figure (*.fig). Specify the name you want assigned to the figure file. Click OK.

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Why .fig File?

The MATLAB FIG-file is a binary format to which you can save figures so that they can be opened in subsequent MATLAB sessions.

What is Saved whole figure, including • Graph(s), • Graph data• Annotations

Edit later withOUT ReDoing DATA

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Saving to .fig – Step-1

1. In Figure 1 Window Click File→Save As...

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Saving to .fig – Step-2

2. To Open Using MATLAB Select the .fig file-format

3. Type in a descriptive FileName and hit Save

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Exporting Figures

To save the figure in a format that can be used by another application, such as the standard graphics file formats; e.g., TIFF or JPG, perform these steps1. Select Export Setup from the File menu.

This dialog lets you specify options for the output file, such as the figure size, fonts, line size and style, and output format

2. Select Export from the Export Setup dialog. A standard Save As dialog appears.

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Exporting Figures cont

3. Select the format from the list of formats in the Save As type menu. – This selects the format of the exported file and

adds the standard file name extension given to files of that type The Instructor likes the .jpg (Joint Picture experts

Group) format; a good compromise of: compatibility, file-size, and resolution

4. Enter the name you want to give the file, less the extension. Then click Save.

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Exporting to file Step-1

1. In Figure 1 Window Click File→Export Setup...

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Saving to file Step-2

2. In the Export Setup Dialog Box Click Export

3. In the Save As Dialog Box Type in a descriptive FileName and hit Save

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The .jpg export

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Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Windows ClipBoard Copy

MATLAB provides a Very Nice Utility in which a Plot is sent to the MSWindows ClipBoard for Subsequent Pasting into Other Applications

To Save to the ClipBoard1. Select Copy Options from the Edit menu.

The Copying Options page of the Preferences dialog box appears.

2. Complete the fields on the Copying Options page and click OK.

3. Select Copy Figure from the Edit menu.

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Copy to Clipboard Step-1

1. In Figure 1 Window Click Edit→Copy Options...

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Copy to Clipboard Steps 2&3

2. In the Preferences Dialog Box check the Copy-Options Boxes as you see Fit

3. Close the Dialog Box

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Copy to Clipboard – Steps 4&5

4. In the Figure Window use File → Copy Figure to send the plot to the clipboard

5. Paste the plot image into PowerPoint, Word, etc.

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The Copy Figure export

-2 -1 0 1 2 3 4 5-100

0

100

200

300

400

500

600

x

y =

f(x

)

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All Done for Today

The Best Plot EVERDone

The French engineer, Charles Minard (1781-1870), illustrated the disastrous result of Napoleon's failed Russian campaign of 1812. The graph shows the size of the army by the width of the band across the map of the campaign on its outward and return legs, with temperature on the retreat shown on the line graph at the bottom. Many consider Minard's original the BEST statistical graphic ever drawn.

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Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Appendix 6972 23 xxxxf