Solve using MATLAB design a proportional P proportionalinteg

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.

Solution

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