Symbolic Toolbox Exponential Equations

Hi Everyone

Getting started with symbolic tool box and live editor.

Trying to enter the below Wiebe Function equation using symbolic toolbox so i can find the derivative and build up the governing equations for the system.

However, getting stuck on simply entering the equation with the syms function, doh, as the e term has (t/td) to the power m+1, can you help with how i actually code this in the live editor so i can use and later solve for dx

Thanks everyone.;-)

My attempt at creating x

syms x exp t t_d m
t_d = sym('t_d')

x = 1 - exp(-6.908*(t/t_d))^(m+1)

Answer 1

[Ameer Hamza]

exp is a built-in function. Don't define it as a variable.

syms x t t_d m
x = 1 - exp(-6.908*(t/t_d)^(m+1));
dxdt = diff(x,t)

Result

dxdt =
 
(1727*exp(-(1727*(t/t_d)^(m + 1))/250)*(t/t_d)^m*(m + 1))/(250*t_d)

If you use live script, it will also render the equation to be displayed properly

[PB75]

Thanks Ameer,

Great response.

When i enter the value of C which is -6.908 it does not fully simplify the equation in live editor, hence you have to divide through by 250 on num and dem, is this due to the decimal places on that constant? can this be simplified within syms?

Thanks again

Patrick

t_d =

x =

dxdt =

[Ameer Hamza]

Is there a specific reason for simplifying it to that value?

[PB75]

Just trying to follow the derivation in the journal paper without questioning the code or equation in matlab

[Ameer Hamza]

Try this to get fractional values

syms x t t_d m
x = 1 - exp(-6.908*(t/t_d)^(m+1));
dxdt = vpa(diff(x,t))

[PB75]

Thanks

[Ameer Hamza]

Glad to be of help.