How to properly set up my Transfer function

syms s
J1 = 0.0024;
C1 = 0.007;
K12 = 2.8;
a = 0;
z = 1;
b = 1;
p = 1;
Kc = .1;
Kh = ((16000)*(1/(2*pi))*(32));
Ka = (10/32768)*2*0.1*3;


Gn = (Kh*Ka)/J1
Gd = s^2 + (C1/J1)*s + K12/J1


Cn = Kc*(a*s+z)
Cd = (b*s+p);
% Cs = Cn/Cd;



num = [Cn * Gn]
dem1 = Cd*Gd 
dem2 = Cn * Gn
dem = (dem1 + dem2)
% Tf = num/(dem1 + dem2)

sys = tf(num,dem)

step(10000*sys)

Answer 1

[Reshma Nerella]

Hi,

The numerator and denominator coefficients of transfer function should be a row vector or a cell array of row vectors. In the above of code

num = [Cn * Gn]
>> 6835652755764317/10995116277760

class(num)
>> 'sym'

You need to convert 'num' to a vector.

dem = (dem1 + dem2)
>> (s + 1)*(s^2 + (35*s)/12 + 3500/3) + 6835652755764317/10995116277760

class(dem)
>> 'sym'

Convert 'dem' to a vector of polynomial coefficients.

For example,

sys(s)=1/(2s2+3s+4);

Specify the numerator and denominator coefficients ordered in descending powers of s, and create the transfer function model.

numerator = 1;
denominator = [2,3,4];
sys = tf(numerator,denominator)

sys =
 
         1
  ---------------
  2 s^2 + 3 s + 4
 
%Continuous-time transfer function.

For more information on tf function, refer to the documentation page

[Jorje German]

Is that what class(num) and class(dem) do? So I also need to add the "sys" after each of them?

[Jorje German]

So I was able to refine my code with your help and ended up with something that looks and provides the correct transfer functions. However I know what when p = -.5 or -.1 my sys should explode and become unstable. However, right now when I plot it, it doesnt really grow exponentially. I cant figure out why.

syms s
J1 = 0.0024;
C1 = 0.007;
K12 = 2.8;
a = 0;
z = 1;
b = 1;
p = -.1;
Kc = .1;
Kh = ((16000)*(1/(2*pi))*(32));
Ka = (10/32768)*2*0.1*3;

%plant Transfer Function
numg = [(Kh*Ka)/J1];
demg = [1 (C1/J1) (K12/J1)];

%Controller Transfer Function.
numc = [Kc*a z*Kc];
demc = [b p];

%verying that they are correct.
sysg = tf(numg,demg)
sysc = tf(numc,demc)

%Combining them
Tfnum = conv(numc,numg);
% Tfd= conv(demc,demg) + Tfnum
Tfdem = [1 (2.916+p) (2.916*p+1166.67) (1166.67*p+627.7)];

TF = tf(Tfnum,Tfdem);

step(10000*TF)

[Paul]

Why do you think that p = -0.1 and p = -0.5 should make the system unstable, when using all of your other parameters?

I don't think the equation for Tfdem is quite correct. Instead of trying to do it by hand, you can get the closed loop transfer function directly:

TF = feedback(sysc*sysg,1)

[Jorje German]

really? I didn't know I was able to do this. Let me give it a shot.

[Jorje German]

Thank you for the advise. I do have one more question. How do I go about finding the zeros, poles, and gains. Ive tried doing

rlocus(TF) 

and just clicking on the information. Ive also tried

[z,p,k] = zpkdata(TF) 

but I cannot access the data.

[Paul]

zpkdata returns z and p in cell arrays; they need to be accessed as such:

>> TF=feedback(sysc*sysg,1)

TF =
 
              621.7
  ------------------------------
  s^3 + 2.817 s^2 + 1166 s + 505

>> [z,p,k]=zpkdata(TF);
>> z{:}

ans =

  0×1 empty double column vector

>> p{:}

ans =

  -1.1916 +34.1163i
  -1.1916 -34.1163i
  -0.4334 + 0.0000i

>> k

k =

  621.6990

[Jorje German]

Thank you very much. You were very hepful