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gkokovidis

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20 years, 291 days
Draeger Medical Systems, Inc.
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Regards,
Georgios Kokovidis
Dräger Medical

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These are answers submitted by gkokovidis

Not yet...

gkokovidis 2370
January 16 2011
1 1

This might be a bug.  Maple does not like improper transfer-functions, where degree(num) > degree(den), or the numerator in "s" being an order higher than the denominator, regardless of denominator value.  For example,

restart:
with(DynamicSystems):
sys1 := TransferFunction(s):PrintSystem(sys1);

gives, Warning, improper transfer-function, degree(num) > degree(den)

Even if you were to convert (k*s^2/(s+20))  to  (k*s-20*k+400*k/(s+20)), you would get the same error in your example. 

Try using block diagram reduction equations in Maple directly and then plugging the output into your system.

 

> 

restart:
> 

a:=(10/(s*(s+10)));

(1)
> 

b:=(k*s^2/(s+20));

(2)
> 

tfsyspos:=a/(1+a*b);

(3)
> 

simplify(%);

(4)
> 

tfsysneg:=a/(1-a*b);

(5)
> 

simplify(%);

(6)
> 

 

Download tfsys.mw

 

 

Regards,

Georgios Kokovidis

Dräger Medical

evalb...

gkokovidis 2370
January 15 2011
0 0

Another way to test equivalence using evalb.

> 

restart:
> 

a:=(x+3)^2*(x-4);

           (1)
> 

b:=x^3+2*x^2-15*x-36;

 (2)
> 

expand(a)-b;

                                                         (3)
> 

evalb(expand(a)-b=0);

                                                   (4)
> 

 

 

Download evalbpoly.mw

 

Regards,

Georgios Kokovidis

Dräger Medical

?isolate...

gkokovidis 2370
January 14 2011
0 0

Look at the help page for the ?isolate command.

 

Using one of your equations from above:

isolate(v=L*(iM-im)/Ton,im);

          im = -v*Ton/L+iM

 

Regards,

Georgios Kokovidis

Dräger Medical

maximize piecewise error...

gkokovidis 2370
January 14 2011
1 0

The minimize and maximize commands do not work over the whole range for your piecewise defined function (0..1).  Try the Minimize and Maximize commands, which are part of the Optimization package.  Unlike the minimize and maximize commands, the computation is performed in floating-point for Minimize and Maximize.

 

> 

restart:
> 

g:=x->(piecewise(0 <= x, 7.5, 0))-(piecewise(0.5 < x,9, 0))-(piecewise(0.4 < x and x <= 0.6, 30*x-12, 0.6 < x,6, 0));

(1)
> 

plot(g,0..1);

 
> 

maximize(g(x),x=0.45..0.55,location);

(2)
> 

maximize(g(x),x=0..0.55,location);

(3)
> 

with(Optimization):Digits:=20:
> 

Minimize(g(x),x=0..1);

(4)
> 

Maximize(g(x),x=0..1);

(5)
> 

Maximize(g(x),x=0.45..0.55);

(6)
> 

Maximize(g(x),x=0..0.55);

(7)
> 

 

 

Download minmaxpiecewise.mw

 

Regards,

Georgios Kokovidis

Dräger Medical

?odeplot...

gkokovidis 2370
January 08 2011
0 1

See examples at the end of the help file for ?odeplot command.

 

Regards,

Georgios Kokovidis

Dräger Medical

Direction field...

gkokovidis 2370
January 07 2011
0 0

Hard to say without looking @ your code:



 

> 

restart:
> 

with(DEtools):
> 

eq:=diff(y(t),t)=.2*t*y(t);

(1)
> 

DEplot(eq,y(t),t=-1..1,y=-1..1);

 
> 

eq2:=diff(y(x),x) =.2*x*y(x);

(2)
> 

DEplot(eq2,y(x),x=-1..1,y=-1..1);

 
> 

 

 



Download dirfield.mw

 

 

 

Regards,

Georgios Kokovidis

Dräger Medical

dualaxisplot...

gkokovidis 2370
January 05 2011
1 1

dualaxisplot should work for this.  See example below.

with(plots):
listplot([seq([i,i],i=1..10)]);
listplot([seq([i,1/i],i=1..10)]);

a1:=listplot([seq([i,i],i=1..10)],color=red):
a2:=listplot([seq([i,1/i],i=1..10)],color=blue):
dualaxisplot(a1,a2);

Regards,

Georgios Kokovidis

Dräger Medical

# - comment...

gkokovidis 2370
January 02 2011
0 1

One way to preclude your code from executing would be to make it a comment.  Put a number sign '#' in front of each line that you wish to remain inactive.

Regards,

Georgios Kokovidis

Dräger Medical

functional notation...

gkokovidis 2370
December 26 2010
1 0

One way to do this is with functional notation.

 

> 

g := x -> x^2;

(1)
> 

L:=[1,2,3,4,5];

(2)
> 

g~(L);

(3)
> 

 

 

Without functional notation, you could do it like this, using L from above.

seq(x^2 , x = L);

Using eval.

f:=x^2;

seq(eval(f,x=L[i]),i=1..nops(L));

Download func_notation.mw

 

 

Regards,

Georgios Kokovidis

Dräger Medical

another answer...

gkokovidis 2370
December 03 2010
2 1

If you plot your function, and then zoom in using range values for x and y, you will see that it has 2 roots.  fsolve will find both of them, depending on where your guess value for x happens to be.  You can then use fsolve with the avoid option.  Another way is to use the Roots command from the Student[Calculus1]) package.  This will find both roots over the given range.  Either way, starting with a plot is a good idea to get an overview of what your function looks like.



 

> 

restart:
> 

equ1:=(500*.87)*(1-(1/x)^.2385)-(288*(x^.3174-1))/(.85);

(1)
> 

plot(equ1, x=0..2,y=-0.5..0.5);

 
> 

with(Student[Calculus1]):
> 

Roots(equ1, 0.5 .. 1.5);

(2)
> 

fsolve(equ1,x=1.2);

(3)
> 

fsolve(equ1,x,avoid={x=1});

(4)
> 

 

 



Download solve_eq.mw

 

Regards,

Georgios Kokovidis

Dräger Medical

?remove...

gkokovidis 2370
December 01 2010
1 0

remove is the command you are looking for.

?remove will take you to the help page with examples.

 

Regards,

Georgios Kokovidis

Dräger Medical

?assign...

gkokovidis 2370
November 28 2010
1 1

Without making changes to your code, you can add the following line right after fsolve...

assign(%);

Then, if you enter a[5], you will get 7.837455611.

 

Regards,

Georgios Kokovidis

Dräger Medical

1 way...

gkokovidis 2370
November 28 2010
0 0

Here is one way.  There might be a command, but it is not obvious to me right now.



> 

restart:
> 

R[1]:=-20;

(1)
> 

R[7]:=4;

(2)
> 

R[2]:=-10;

(3)
> 

R[3]:=0;

(4)
> 

R[4]:=3.1;

(5)
> 

R[5]:=7;

(6)
> 

R[6]:=24;

(7)
> 

a1:=seq(R[i],i=1..7);

(8)
> 

a2:=sort([a1],`<`);

(9)
> 

for i from 1 by 1  while type(a2[i],posint) = false do od; print(a2[i]);

(10)
> 

 



Download smallest_int_find.mw

Regards,

Georgios Kokovidis

Dräger Medical

?pointplot3d...

gkokovidis 2370
November 28 2010
0 0

The command for plotting points in 3d is ?pointplot3d.  You can create your own points in the worksheet, or import them from a file.  An example below, taken from the help pages, with a few tweaks.

 



 

> 

?pointplot3d
> 

> 

 
> 

 

 



Download pplot3d.mw

 

 

Regards,

Georgios Kokovidis

Dräger Medical

?dfieldplot...

gkokovidis 2370
November 26 2010
1 3

Look at the code below, and compare it to what you did to see where the problems occur.  First is the use of * as a multiplication between x and y.  Second, you have y as a function of x, so you must use it this way when you describe the differential equation.  The help file for the dfieldplot command shows this as well.  Start there, and use the examples provided as a "template" for the rest of your problems.



 

> 

restart:
> 

with(DEtools):
> 

dfieldplot(diff(y(x), x) = sin(x*y(x))+3*x^2+x^(1/3)+4*y(x)^2+5*y(x), y(x), x = -5 .. 5, y = -5 .. 5, title = `tangent field`, color = black);

 
> 

 

 



Download dfieldplot_exampl.mw

 

 

Regards,

Georgios Kokovidis

Dräger Medical

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