Question:

Take a second order system and apply various configurations of continuous time and discrete

time PID controller.

Solution:

We will take the same second order system which we took in Assignment # 02 i.e simple mass

spring damper system.

m= 1kg , b=10 N.s/m , k=20 N/m , f=1N

G(s)=1/s2+10s+20 [Ref: Feedback Control Systems, 4

th Edition C.L Phillips and R.D

Harbor]

Configuration # 01

Kp=350, Ki=300, Kd=50

Simulation

Output

Configuration # 02

K=350, A1 = 1, A2=0.2

Simulation

Output

Configuration # 03

Simulation

K=400 , A=0.07 , a = 3

Output

Configuration # 04

Simulation

Output

Discrete PID

Positional Form

Sampled at T= 1 sec

Kp=2.5 , Ki= 4.8 , Kd=0.2

Output

Velocity Form

Sampled at T= 1 sec

Kp=2.5 , Ki= 4.8 , Kd=0.2

Output