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pik1432

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6 years, 122 days
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These are questions asked by pik1432

RE: re-writing a differential equation...

pik1432 245 Maple 2020
October 27 2020
2 2

Hello there, 

Would you please tell me how to re-write the 'PMSM_v_eq' as 'PMSM_flux_eq_desired'? My simple attempt was using the 'solve()' command, but it failed. 

Here is the worksheet:


 

> 

restart;
> 

PMSM_v_eq := V__alphabeta(t) = R__s * i__alphabeta(t) + L__s*diff(i__alphabeta(t), t) + diff(lambda__alphabeta(t), t);

V__alphabeta(t) = R__s*i__alphabeta(t)+L__s*(diff(i__alphabeta(t), t))+diff(lambda__alphabeta(t), t)

 (1)
> 

 

> 

PMSM_flux_eq := solve(PMSM_v_eq, lambda__alphabeta(t));

Error, (in solve) cannot solve expressions with diff(lambda__alphabeta(t), t) for lambda__alphabeta(t)

  
> 

PMSM_flux_eq_desired := lambda__alphabeta(t) =  int(V__alphabeta(t) - R__s * i__alphabeta(t), t) - L__s*i__alphabeta(t);

lambda__alphabeta(t) = int(V__alphabeta(t)-R__s*i__alphabeta(t), t)-L__s*i__alphabeta(t)

 (2)
> 

 


Thank you!

Download PMSM_eq.mw

RE: Substitution...

pik1432 245 Maple
simplification
October 14 2020
1 1

Hello there, 

Would you please tell me how to get the 'Desired' expression from the 'Sec_Z2prim' expression?

My 'Attempt' did not work. 


 

> 

restart;
> 

TR_turns_ratio := N = n2 / n1;

N = n2/n1

 (1)
> 

Sec_Z2prim := Z1 = Z2*n1^2/n2^2;

Z1 = Z2*n1^2/n2^2

 (2)
> 

Attempt := subs(TR_turns_ratio, Sec_Z2prim) assuming (n1 > 0, n2 > 0);

Z1 = Z2*n1^2/n2^2

 (3)
> 

Desired := Z1 = Z2*(1/N)^2;

Z1 = Z2/N^2

 (4)
> 

 

 

Thank you, 
 

Download Q20201014.mw

RE: Trogonomatric identity...

pik1432 245 Maple
simplification trig
October 07 2020
1 1

Hello all, 

Would you allow me to ask this question?

Is there a way to make the expression 'expression1', given below, to expression 'expression3'?


 

> 

restart;
> 

expression1 := -cos(theta)/2 + sin(theta)*sqrt(3)/2;

-(1/2)*cos(theta)+(1/2)*sin(theta)*3^(1/2)

 (1)
> 

expression2 := expand(cos(theta-2/3*Pi));

-(1/2)*cos(theta)+(1/2)*sin(theta)*3^(1/2)

 (2)
> 

is(expression1 = expression2);

true

 (3)
> 

expression3 := cos(theta-2/3*Pi);

-cos(theta+(1/3)*Pi)

 (4)
> 

 


Thank you, 

Download Q20201007.mw

RE: cancelling the same term in numerato...

pik1432 245 Maple
expand
October 05 2020
1 1

Hello there, 

Would you please have a look at this question?

I got the answer in the 'eq_4_35', but what I wanted to see is the 'desired' expression. 

Somehow, the term '3*C' doesn't want to go away from the 'x__0' term, thus I wonder there is a way to cancel the term in the expression. 


 

> 

restart;
> 

eq_4_34 := x__alpha = C*x__a - C/2 * (x__b + x__c);

x__alpha = C*x__a-(1/2)*C*(x__b+x__c)

 (1)
> 

eq_4_33 := x__0 = 1/3*(x__a + x__b + x__c);

x__0 = (1/3)*x__a+(1/3)*x__b+(1/3)*x__c

 (2)
> 

eq_4_33aux := X__sub = (x__b + x__c);

X__sub = x__b+x__c

 (3)
> 

attempt2 := algsubs((x__b + x__c) = X__sub, eq_4_33);

x__0 = (1/3)*x__a+(1/3)*X__sub

 (4)
> 

attempt3 := X__sub = solve(attempt2, X__sub);

X__sub = -x__a+3*x__0

 (5)
> 

eq_4_34x := x__alpha = algsubs((x__b + x__c) = 3*x__0 - x__a, rhs(eq_4_34));

x__alpha = -(1/2)*C*(-x__a+3*x__0)+C*x__a

 (6)
> 

eq_4_35 := x__a = simplify(solve(eq_4_34x, x__a));

x__a = (1/3)*(3*C*x__0+2*x__alpha)/C

 (7)
> 

desired:= x__a = x__0 + (2*x__alpha)/(3*C);

x__a = x__0+(2/3)*x__alpha/C

 (8)
> 

 


 

Download Q20201005_2.mw

RE: Simplifying the result from symbolic...

pik1432 245 Maple
radical simplification
October 01 2020
3 4

Hello there, 

Is there any way to make the equation 'Given_eq_3_37a' in the calculation below to be 'desired'?

Perhaps, the issue of the 'L__1' and '1/L__1' might have been in the way, but perhaps that might be overcome in a different way. 

Thank you, 

In Kwon Park 


 

> 

restart;
> 

Given_eq_3_37 := M = k_ * sqrt(L__1 * L__2);

M = k_*(L__1*L__2)^(1/2)

 (1)
> 

Given_eq_3_30 := k_ = sqrt((L__m)^2 / (L__1 * L__2p));

k_ = (L__m^2/(L__1*L__2p))^(1/2)

 (2)
> 

Given_eq_3_37a := simplify(subs([Given_eq_3_30], Given_eq_3_37));

M = (L__m^2/(L__1*L__2p))^(1/2)*(L__1*L__2)^(1/2)

 (3)
> 

desired := M = sqrt(L__m^2/(L__1*L__2p)*(L__1*L__2));

M = (L__m^2*L__2/L__2p)^(1/2)

 (4)
> 

 


 

Download Q20201001.mw

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