How can I use the function coeffs() as the input to the function tf()?

This code works to give me the root locus of my system, but I have to manually enter the coefficients

num = [1, 117/10, 24477/400, 5584/125, -2315137/40000, 36905889/40000, -66965649/160000, -921912043/80000, 34652192177/640000, -4796713113/25600, 62141795103/160000, -223688325847/320000, 32896376299/40000, -7904756769/10000, 708588777/2000, -52514891/800];
den = [1, -4/5, -5929/400, -14969/2000, 56007543/160000, -550116261/400000, 187999365153/64000000, -1333141873017/320000000, 1759926060179/400000000, -120268082137481/32000000000, 819503408996093/320000000000, -4388359670461129/3200000000000, 338687548373223/640000000000, -1907357941873611/12800000000000, 306186935180877/10240000000000, -4892378756049/1024000000000]

sys = tf(num,den);

rlocus(sys);

However, the following code is not working. I imagine that the output of coeffs() &/or fliplr() is not technically an array despite appearing so when I print the output.

syms s
n = (s^2+10*s+50)*(s^2+8.6*s+21.73)*(s^2-0.7*s+0.1625)*(s^2-2*s+3.25)^2*(s^2+4)^2*(s-2.2);
x = expand(n);
d = (s^2+8.6*s+26.33)*(s^2+0.3*s+0.6625)*(s^2+0.09)*(s^2-0.8*s+0.25)*(s^2-0.9*s+0.5625)*(s^2-2*s+2.69)*(s^2-4*s+4.0225)*(s-2);
y = expand(d);

num = coeffs(x);
num = fliplr(num)
den = coeffs(y);
den = fliplr(den)

sys = tf(num,den); %error line

figure(1)
rlocus(sys)

If someone could help me figure out how to modify the second chunk of code so that the transfer function is created that would be much appreaciated.

Answer 1

[Sam Chak]

Use double().

syms s
n = (s^2+10*s+50)*(s^2+8.6*s+21.73)*(s^2-0.7*s+0.1625)*(s^2-2*s+3.25)^2*(s^2+4)^2*(s-2.2);
x = expand(n)

x = 

d = (s^2+8.6*s+26.33)*(s^2+0.3*s+0.6625)*(s^2+0.09)*(s^2-0.8*s+0.25)*(s^2-0.9*s+0.5625)*(s^2-2*s+2.69)*(s^2-4*s+4.0225)*(s-2);
y = expand(d)

y = 

num = coeffs(x);
num = double(fliplr(num))

num = 1×16

1.0e+05 * 0.0000 0.0001 0.0006 0.0004 -0.0006 0.0092 -0.0042 -0.1152 0.5414 -1.8737 3.8839 -6.9903 8.2241 -7.9048 3.5429 -0.6564

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

den = coeffs(y);
den = double(fliplr(den))

den = 1×16

1.0e+03 * 0.0010 -0.0008 -0.0148 -0.0075 0.3500 -1.3753 2.9375 -4.1661 4.3998 -3.7584 2.5609 -1.3714 0.5292 -0.1490 0.0299 -0.0048

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

●

sys = tf(num,den); %error line

figure(1)
rlocus(sys)

Answer 2

[Voss]

The error message states:

"The values of the "Numerator" and "Denominator" properties must be row vectors or cell arrays of row vectors, where each vector is nonempty and containing numeric data."

In the first code snippet you posted num and den are numeric, so tf works; in the second num and den are symbolic, so tf throws the error. See: Choose Numeric Or Symbolic Arithmetic

You can convert the symbolic num and den to numeric (specifically, double-precision floating point) values using the double function:

syms s
n = (s^2+10*s+50)*(s^2+8.6*s+21.73)*(s^2-0.7*s+0.1625)*(s^2-2*s+3.25)^2*(s^2+4)^2*(s-2.2);
x = expand(n);
d = (s^2+8.6*s+26.33)*(s^2+0.3*s+0.6625)*(s^2+0.09)*(s^2-0.8*s+0.25)*(s^2-0.9*s+0.5625)*(s^2-2*s+2.69)*(s^2-4*s+4.0225)*(s-2);
y = expand(d);

num = coeffs(x);
num = fliplr(num)

num = 

den = coeffs(y);
den = fliplr(den)

den = 

% sys = tf(num,den); %error line

sys = tf(double(num),double(den));

figure(1)
rlocus(sys)

Answer 3

[Paul]

Unless there are reasons to use syms other then to compute the polynomials, it's probably better and easier to avoid syms altogether.

Instead

s = tf('s');
n = (s^2+10*s+50)*(s^2+8.6*s+21.73)*(s^2-0.7*s+0.1625)*(s^2-2*s+3.25)^2*(s^2+4)^2*(s-2.2);
d = (s^2+8.6*s+26.33)*(s^2+0.3*s+0.6625)*(s^2+0.09)*(s^2-0.8*s+0.25)*(s^2-0.9*s+0.5625)*(s^2-2*s+2.69)*(s^2-4*s+4.0225)*(s-2);
h = n/d;
rlocus(h)

●

Or find the roots of each term in n and d and go to zpk form.

If really need or want to use syms with coeffs, you're already aware of the fliplr issue. But, using coeffs that way will ignore zero coefficients, which will lead to an error in the Control System Toolbox.

For example

syms s
n = 3*s^3 + 1;
num = double(fliplr(coeffs(n))) % should be [3 0 0 1]

num = 1×2

3 1

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

To get all of the coefficients, use the 'All' option. But with 'All' the coefficients come out from highest to lowest degree, so don't flip

num = double(coeffs(n,'All'))

num = 1×4

3 0 0 1

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>