Question

Design a digital PID controller based on the Ziegler_Nichols method for for the following system:

G(s)=s/((s+1)^4 )

use the sampling time of T=0.1 seconds and simulate the resulting controlled system by applying a unit

step and then changing the value of input to another value after some appropriate time

Discus the effect of set point change.

Answer 1

Solution:

MATLAB Code:

num=[1 0]

den=[1 4 6 4 1];

sys=tf(num,den)

step(sys)

Output:

Digital PID controller:

MATLAB Code:

num=[1.05 4.2 4.2]

den=[1 0]

Ts=0.1

sys=tf(num,den,Ts)

Output:

For closed loop system:

MATLAB Code:

num=[1.05 4.2 4.2]

den=[1 4 6 4 1]

sys=tf(num,den)

step(sys)

T=feedback(sys,1)

step(T)

Output:

For open loop system with time t = 0.1s,

MATLAB Code:

num=[1.05 4.2 4.2];

den=[1 4 6 4 1];

sys=tf(num,den)

t=0:0.01:0.1

step(sys,t)

Output:

For open loop system with time t>0.1s( input magnitude value changes)

MATLAB Code:

num=[1.05 4.2 4.2];

den=[1 4 6 4 1];

sys=tf(num,den)

t=0.1:0.01:15;

opt=stepDataOptions('InputOffset',0,'StepAmplitude',2);

step(sys,opt,t)

Output: