Using a while loop in MATLAB, verify your result in (b) by computing the poles of the closed-loop transfer function as k increases from 0.001 in increments of 0.001. When your loop finishes running, display the largest gain k = kmax that guarantees..

I found a stability k factor by hand for a unity feedback control system.

I am geting stuck on this part.

Using a while loop in MATLAB, verify your result in (b) by computing the poles of the closed-loop transfer function as k increases from 0.001 in increments of 0.001. When your loop finishes running, display the largest gain k = kmax that guarantees closed-loop stability. Hint: >> help max, >> help pole, >> help real

this is my code so far.

s = tf('s'); %define transfer function variable
k = 0.001;
SYS = (10*k*(s+1)) / ( s^4 + 4*s^3 + 9*s^2 + (10*k + 10)*s); %define TF
while k < kmax 
    pole(SYS)
    k = k + 0.001; %increment k
end
disp kmax

help would be appreciated

[SL: formatted the code as code]

Answer 1

[Sarvani Panguluri]

Hi,

I assume you are trying to find the maximum k for which the system is stable. As per my knowledge, the system is stable when the poles of closed loop transfer function lie on the left-hand side of the s-plane. So, the real part of the poles have to negative.

try implementing the following code.

s = tf('s'); %define transfer function variable 
k =0.001; 
temp=true; 
  
while temp 
    SYS = (10*k*(s+1)) / ( s^4 + 4*s^3 + 9*s^2 + 10*k*s + 10*k); 
    if(all(real(pole(SYS)) <=0)) 
        k=k+0.001; 
    else 
        temp=false; 
    end 
     
end 
disp(k-0.001) 

Hope it helps!