Plotting multiple outputs with varying inputs in same graph

I am trying to plot for multiple values of b on the same graph without for loop, any way to do this?

Code:

m1 = 10; m2 = 350; kw = 5e5; ks = 1e4; b = 2000; s = tf('s');
transfer = (((kw*b)/(m1*m2))*(s+ks/b))/(s^4 + (b/m1 + b/m2)*s^3 + (ks/m1 + ks/m2 + kw/m1)*s^2 + (kw*b/(m1*m2))*s+ (kw*ks)/(m1*m2));
step(transfer); 

Answer 1

[Walter Roberson]

It is tricky to do without a loop at some level.

One approach is to use a symbolic approach. The symbolic approach can deal with the fact that you are dividing by vector of transfer functions: tf() objects do not support the ./ operation, but symbolic objects can. But after you have the symbolic expressions you need to convert them back to tf() objects, and the easiest way to do that is to arrayfun(), since the functions that extract coefficients from polynomials do not accept vectors of expressions.

b = 1500:500:2500;
m1 = 10; m2 = 350; kw = 5e5; ks = 1e4;
syms s
transfer = (((kw*b)./(m1*m2)).*(s+ks./b))./(s^4 + (b/m1 + b/m2).*s^3 + (ks/m1 + ks/m2 + kw/m1).*s^2 + (kw*b./(m1*m2))*s + (kw*ks)./(m1*m2))

transfer = 

transfer = simplify(transfer)

transfer = 

transfer = arrayfun(@sym2tf, transfer)

transfer =
 
  From input 1 to output:
                        6.185e17 s + 4.123e18
  ------------------------------------------------------------------
  2.886e12 s^4 + 4.453e14 s^3 + 1.473e17 s^2 + 6.185e17 s + 4.123e18
 
  From input 2 to output:
                        2.749e17 s + 1.374e18
  ------------------------------------------------------------------
  9.621e11 s^4 + 1.979e14 s^3 + 4.909e16 s^2 + 2.749e17 s + 1.374e18
 
  From input 3 to output:
                        3.436e17 s + 1.374e18
  ------------------------------------------------------------------
  9.621e11 s^4 + 2.474e14 s^3 + 4.909e16 s^2 + 3.436e17 s + 1.374e18
 
Continuous-time transfer function.

step(transfer.')

function as_tf = sym2tf(tf_as_sym)
   [n, d] = numden(tf_as_sym);
   np = sym2poly(n);
   dp = sym2poly(d);
   as_tf = tf(np, dp);
end

[Walter Roberson]

Using tf() with arrayfun turned out to be easier than I expected.

b = 1500:500:2500;
m1 = 10; m2 = 350; kw = 5e5; ks = 1e4;
s = tf('s');
transfer = arrayfun(@(b) (((kw*b)/(m1*m2))*(s+ks/b))/(s^4 + (b/m1 + b/m2)*s^3 + (ks/m1 + ks/m2 + kw/m1)*s^2 + (kw*b/(m1*m2))*s + (kw*ks)/(m1*m2)), b)

transfer =
 
  From input 1 to output:
                  2.143e05 s + 1.429e06
  ------------------------------------------------------
  s^4 + 154.3 s^3 + 5.103e04 s^2 + 2.143e05 s + 1.429e06
 
  From input 2 to output:
                  2.857e05 s + 1.429e06
  ------------------------------------------------------
  s^4 + 205.7 s^3 + 5.103e04 s^2 + 2.857e05 s + 1.429e06
 
  From input 3 to output:
                  3.571e05 s + 1.429e06
  ------------------------------------------------------
  s^4 + 257.1 s^3 + 5.103e04 s^2 + 3.571e05 s + 1.429e06
 
Continuous-time transfer function.

step(transfer.')