Solve using MATLAB: design a proportional (P), proportional-integral (PI), and p
ID: 1841474 • Letter: S
Question
Solve using MATLAB:
design a proportional (P), proportional-integral (PI), and proportional-integral-derivative (PID) controller for a plant based on the Ziegler-Nichols tuning rules. The plant transfer function is given by
The PID controller we will consider has the transfer function
where U(s) is the controller output, E(s) is the error signal between the reference input and the actual plant output, Kc is the proportional gain, Ti is the integral time (in seconds), and Td is the derivative time (in seconds). The Ziegler-Nichols step-response method is based on the following steps 1. Excite the open-loop plant with a unit step that starts at time t = 0 seconds. 2. From the plant response plot, register the values of the parameters a and L (see Figure 1). 3. Using Table 1, identify the appropriate PID parameters, Kc, Ti , and Td for a P, PI, and a PID controller.
G(s) = (s+1 )T.Explanation / Answer
using matlab:
1.plant function:
function[wp]=createplant(num,den)
syms s;
wp=tf(num,den);
end
2.function wc=zieglernicholasPID(kc,ti,td)
s=tf('s');
wc=kc*(1+(1/(ti*s))+td*s);
end
3.plant and controller:
function sys=CLS(wp,wc)
CLS=feedback(series(wp,wc),1);
end
from graph obtained
a=8
l=3.627
k ti td
p 0.125
pi 0.1125 10.881
pid 0.15 7.254 1.8135