Solve is not providing correct solution

I am trying to solve the below equation which is a part of a transfer function calculation.

clear
syms a b c d k

Hhf=6;
Q=3;

Coeff2=0;
Coeff3=0;

assume(a,["positive","real"]);
assume(b,["positive","real"]);
assume(c,["positive","real"]);
assume(d,["positive","real"]);
assume(k,["positive","real"]);
eq1=vpa(a==10^(Hhf/20))
eq2=vpa(a-b*(k*Q)==Coeff2)
eq3=vpa(a-(c-d)*k==Coeff3)
eq4=vpa(1+a+b+c==7.5)
[a,b,c,d,k]=solve([eq1,eq2,eq3,eq4], [a,b,c,d,k]);
a=double(subs(a));
b=double(subs(b));
c=double(subs(c));
d=double(subs(d));
k=double(subs(k));

a, b, c, d, k, a-b*(k*Q), a-(c-d)*k, 1+a+b+c

The output is below:

a = 1.9953

b = 0.6651

c = 3.8397

d = 1.8444

k = 1

a-b*(k*Q) = 2.2204e-16

a-(c-d)*k = -2.2204e-16

The "a-b*(k*Q)" and "a-(c-d)*k" are very smal numbers but are not zero as requested. These values when multiplied with others are changing the transfer function. Any idea how can be resolved.

Giannis

[VBBV]

use round function to make it zero and then use in the transfer function

double(round((a-b*(k*Q)),1));
double(round((a-(c-d)*k),1));
double(round((1+a+b+c),1));

[NGiannis]

@VBBV

Thanks for your reply.

The solution you provided make the "a-b*(k*Q)" and "a-(c-d)*k" zero. I need to use the "a-b*(k*Q)" and "a-(c-d)*k" also the individual numbers a, b, c, d, k on equations.

[VBBV]

Ok, check whether the following

a-b*(k*Q), a-(c-d)*k,

operations on a, b,c,d k, & Q are correct. Can you tell how they change the transfer function ? Is code called inside a loop with inputs to transfer function?

Answer 1

[Dyuman Joshi]

When you use vpa on symbolic numbers, you lose precision.

When you convert the symbolic numbers to double precision values using double, you lose precision.

And that's why the values are not exactly 0.

If you remove those conversions, the values will, in fact, be 0.

syms a b c d k

Hhf=6;
Q=3;

Coeff2=0;
Coeff3=0;

assume(a,["positive","real"]);
assume(b,["positive","real"]);
assume(c,["positive","real"]);
assume(d,["positive","real"]);
assume(k,["positive","real"]);

eq1=(a==10^(Hhf/20));
eq2=(a-b*(k*Q)==Coeff2);
eq3=(a-(c-d)*k==Coeff3);
eq4=(1+a+b+c==7.5);
[a,b,c,d,k]=solve([eq1,eq2,eq3,eq4], [a,b,c,d,k]);


a, b, c, d, k, a-b*(k*Q), a-(c-d)*k, 1+a+b+c

a = 

b = 

c = 

d = 

k = 

1

ans = 

0

ans = 

0

ans = 

[NGiannis]

@Dyuman Joshi

Thanks you for your reply.

The solution you provided make the "a-b*(k*Q)" and "a-(c-d)*k" zero. I was using the double(subs(number)) in order to be able to use the values on s-domain. When appling the values on transfer funciton I am getting "Unable to convert tf to sym".

[Dyuman Joshi]

Yes, Control system functionalities in MATLAB, like tf, do not accept symbolic numbers as input (this issue has been raised quite a few times by others as well).

I understand your situation, but unfortunately, you will have to work with the limited precision of double precision numbers, where the values are not exactly zero.