Plot symbolic expresion dependent on one parameter on complex plane, making the parameter take a range of values.

Greetings,

I have the following expresion:

syms N A a dw;
N=subs(4/A^2/pi*(sqrt(A^2-a^2)-1i*a),a,1)

N = 

I'd like to make the parameter A variate from 1 to positive inf and plot the resulting complex number on the nyquist plot:

nyquist(tf(pi,[1 2 0]));

My first tought was to use subs in order to get a vector but I was wondering if the symbolic toolbox has something in order to get the result to inf.

Thanks!

Answer 1

[Gayatri Rathod]

Hi naga,

Here are a few approaches to make the parameter A vary from 1 to positive inf:

1. MATLAB has a function called limit that can be used to find the limit of a symbolic expression as a variable approaches a specific value or infinity.

• In your case, you can use the limit function to find the limit of N as A approaches infinity. Here's an example code snippet that should work:

N = 4/A^2/pi*(sqrt(A^2-a^2)-1i*a); 
N_inf = limit(N, A, inf); 
nyquist(tf(pi, [1, 2, 0])); % plot the Nyquist diagram for the transfer function 
hold on; 
plot(real(N_inf), imag(N_inf), 'ro');  % add a red dot to indicate the limit point  

• Here, N is your symbolic expression and N_inf is the limit of N as A approaches infinity. The nyquist function is used to plot the Nyquist diagram for the transfer function tf(pi, [1, 2, 0]). plot is used to add a red dot at the limit point. The hold on command is used to prevent the Nyquist diagram from being cleared before the dot is added.
• Note that the limit of N as A approaches infinity depends only on the highest order term in the expression.
• 2.Symbolic Math Toolbox in MATLAB has a function called "symfun" that allows you to create symbolic functions with variables that can vary over a range. You can use this function to create a symbolic function for your expression and then plot it using the "nyquist" function.
• Here's an example code snippet that shows how to use "symfun" to create a function for your expression and then plot it over a range of values for A:

N = 4/A^2/pi*(sqrt(A^2-a^2)-1i*a); 
N_fun = symfun(N, A); 
nyquist(N_fun(A), [1, inf]); 

• Here, "N_fun" is a symbolic function for your expression with "A" as the input variable. The nyquist function is then called with "N_fun(A)" as the first argument. The second argument to nyquist is a range of values for "A" that you want to plot over, which in this case is from 1 to positive infinity.

You can read more about the limit, plot, symfun functions and hold on from the following documentations: limit function, plot function, symfun function, hold on function.

Hope it helps!  

Regards,

Gayatri Rathod